MACHINES, TECHNOLOGIES, MATERIALS · 2018. 10. 10. · Prof. Anatoliy Kostin RU ... Doctor of Sciences, Professor of Machine Tools and Systems Department of the National Technical

INTERNATIONAL SCIENTIFIC CONFERENCE MACHINES, TECHNOLOGIES, MATERIALS

15-18.03.2017, BOROVETS, BULGARIA

PROCEEDINGS

YEAR I, ISSUE 1 (1), SOFIA, BULGARIA 2017

VOLUME I “MACHINES”

ISSN 2535-0021 (PRINT) ISSN 2535-003X (ONLINE)

PUBLISHER:

SCIENTIFIC TECHNICAL UNION OF MECHANICAL ENGINEERING INDUSTRY-4.0

108, Rakovski Str., 1000 Sofia, Bulgaria tel. (+359 2) 987 72 90,

tel./fax (+359 2) 986 22 40, [email protected] www.mtmcongress.com

INTERNATIONAL EDITORIAL BOARD

Chairman: Prof. DHC Georgi Popov Vice Chairman: Prof. Dr. Eng. Tsanka Dikova Members: Acad. Ivan Vedyakov RU Acad. Yurij Kuznetsov UA Prof. Aleksander Mihaylov UA Prof. Anatoliy Kostin RU Prof. Adel Mahmud IQ Prof. Ahmet Ertas TR Prof. Andrzej Golabczak PL Prof. Boncho Bonev BG Prof. Gennady Bagluk UA Prof. Detlef Redlich DE Prof. Dipten Misra IN Prof. Dmitry Kaputkin RU Prof. Eugene Eremin RU Prof. Ernest Nazarian AM Prof. Juan Alberto Montano MX Prof. Esam Husein KW Prof. Ivo Malakov BG Prof. Krasimir Marchev USA Prof. Leon Kukielka PL Prof. Lyudmila Ryabicheva UA Prof. Milan Vukcevic ME

Prof. Mladen Velev BG Prof. Mohamed El Mansori FR Prof. Movlazade Vagif Zahid AZ Prof. Nikolay Dyulgerov BG Prof. Oana Dodun RO Prof. Olga Krivtsova KZ Prof. Peter Kostal SK Prof. Raul Turmanidze GE Prof. Renato Goulart BR Prof. Roumen Petrov BE Prof. Sasho Guergov BG Prof. Seiji Katayama JP Prof. Sergej Dobatkin RU Prof. Sergej Nikulin RU Prof. Stefan Dimov UK Prof. Svetan Ratchev UK Prof. Svetlana Gubenko UA Prof. Tale Geramitchioski MK Prof. Vadim Kovtun BY Prof. Viktor Vaganov RU Prof. William Singhose USA Prof. Yasar Pancar TR

C O N T E N T S

FUTURE OF MACHINE-TOOL BUILDING — CORE OF ENGINEERING TECHNOLOGY Yu.N. Kuznetsov .................................................................................................................................................................................................. 4 ADAPTIVE CONTROL OF NONLINEAR TWO DIMENSIONAL AIRFOIL MODEL Boğaç Bilgiç ....................................................................................................................................................................................................... 11 BALANCE CONTROL OF SEGWAY ROBOTS USING ADAPTIVE-ROBUST CONTROLLER Prof. M.Sc. Burkan R. PhD., M.Sc. Özgüney Ö.C. ............................................................................................................................................ 14 EULER BERNOULLI THEORY FOR A 3-DIMENSIONAL,VARIABLE-CURVETURE BEAM L.Emir Sakman, Aşkın Mutlu ............................................................................................................................................................................. 18 VIRTUAL MODELING AND SIMULATION OF A CYLINDER BUNDLE VERTICAL AND ROTATIONAL DROP Ass. Prof. Aleksandar Kostikj PhD, Prof. Milan Kjosevski PhD. ...................................................................................................................... 20 РЕЛАТИВНО ИЗНОСВАНЕ НА ЛИФТЕРИ Стоименов Н. .................................................................................................................................................................................................... 25 COMPARISON OF NUMERICAL AND EXPERIMENTAL RESULTS OF STRESSDEFORMATION STATE IN A PIPELINE BRANCH Prof. dr Bajić D. PhD, M.Sc. Ćulafić S. ............................................................................................................................................................. 29 INFLUENCE OF TEMPERATURE ON DIELECTRIC BREAKDOWN OF WORKING FLUID VAPOR IN HEAT PIPE M.Sc. Nemec P. PhD., Prof. RNDr. Malcho M. PhD., M. Sc. Palacka M. ........................................................................................................ 33 INFLUENCE OF THE SOIL PARTICLES ON THE WEAR OF PLOUGHSHARES DURING PLOUGHING Opačak I., mag.ing.mech., Putnik I., mag.ing.mech., Samardžić M. ................................................................................................................. 36 ЗЪБНА ПРЕДАВКА С ПРОМЕНЛИВО ПРЕДАВАТЕЛНО ОТНОШЕНИЕ ас. инж. Георгиев И. ......................................................................................................................................................................................... 40 КОНСТРУКТИВНИ И КИНЕМАТИЧНИ ОСОБЕНОСТИ НА ПЛАНЕТНАТА ПЛАВНОРЕГУЛИРУЕМА ЗЪБНА ПРЕДАВКА ас. инж. Георгиев И. ......................................................................................................................................................................................... 43 MINIATURE DEVICE FOR ENERGY CONVERSION – BASIC BUILDING ELEMENTS IN MECHATRONICS Assoc. Prof. Abadjieva E. PhD., Prof. Naganawa A. PhD., Prof. Abadjiev V. PhD., D.Sc. ............................................................................. 46 МОДЕРНИЗАЦИЯ РАЗГРУЗОЧНОГО УСТРОЙСТВА БЕГУНОВ МОКРОГО ПОМОЛА С ЦЕЛЬЮ ПОВЫШЕНИЯ ЭФФЕКТИВНОСТИ РАБОТЫ Казак Ирина Александровна, к.п.н. ................................................................................................................................................................ 50 ESTIMATION OF ULTIMATE LOADS FOR CLIP CONNECTION WITH PARTIAL SWEEP OF SHAFT Ass. Prof. PhD Ropyak L., Prof. DSc Shatskyi I., Ass. Prof. PhD Velychkovych A. ....................................................................................... 53 INVESTIGATION OF HEAT PIPE'S PERFORMANCE PARAMETERS DEPENDING ON DIFFERENT CONDITIONS Radovan Nosek1, Jan Siazik, Michal Holubcik, Jozef Jandacka ....................................................................................................................... 57 ОТНОСНО БЕЗОПАСНАТА ЕКСПЛОАТАЦИЯ НА АСАНСЬОРИ Assoc.Prof. Dr. Krasimir Krastanov ................................................................................................................................................................... 60 VIBRATION CHARACTERISTICS OF QUARTER CAR SEMI-ACTIVE SUSPENSION MODEL - NUMERICAL SIMULATIONS AND INDOOR TESTING Assist. Prof. Eng. Pavlov N. PhD., Eng. Sokolov E. PhD .................................................................................................................................. 63 EXPERIMENTAL STUDY TO THE MACHINE FOR DRESSING OF WATER HOLDING MATERIALS INTO THE SOIL Mitev. G.V., Kr. Bratoev .................................................................................................................................................................................... 69 FUZZY PROPORTIONAL DERIVATIVE APPROACH FOR VIBRATION CONTROL OF VEHICLES Asst. Prof. Taskin Y. PhD................................................................................................................................................................................... 73

FUTURE OF MACHINE-TOOL BUILDING — CORE OF ENGINEERING TECHNOLOGY

Yu.N. Kuznetsov Doctor of Sciences, Professor of Machine Tools and Systems Department of the National Technical University of Ukraine “Igor Sikorsky

Kyiv Polytechnic Institute”

Abstract: This article presents the results of scientific research performed by scientists at NTUU Igor Sikorsky Kyiv Polytechnic Institute in the creation and genetic forecasting of the development of a new generation of machine tools and associated mechanisms using the latest advances incorporated into an interdisciplinary intellectual field and based on a unified structured and systematic approach. It is suggested that the revival of the domestic machine-tool building can be done by virtue of an innovation breakthrough and implementation of the "Overdo without catching up!" strategic goal.

KEYWORDS: MACHINE-TOOL BUILDING, ANTHROPOGENIC SYSTEMS, GENETIC FORECASTING, MASS POINT, ARTIFICIAL INTELLIGENCE

Introduction The major tendency of the modern age is the market-orientated

production, which is not possible without the integration of science, education, manufacturing and service industry, as well as the achievement of such goals: [2, 8, 21]: 1. Productivity increase. 2. Product quality improvement. 3. Reduction of production costs due to energy and resource savings. 4. Improvement of labour conditions and reduction of physical labour percentage. 5. Facilitation and reduction of monotonous intellectual (mental) labour. 6. Expansion of technological and functional capabilities of the equipment. These goals have defined the world trends of engineering technology development [2, 13, 19, 21]. In a modern independent state these goals cannot be achieved without a highly developed domestic machine-tool building industry — the core of engineering technology, where main products, being machine tools, are regarded as machines creating other machines [2, 5]. Machine tools are the foundation for the production of any process equipment, as well as other engineering systems (ES) of various purpose that compose anthropogenic systems (AS) [1], which change over time in a result of the purposeful human activity.

The goal — proceeding from the analysis of past and present state of the machine-tool building, to propose ways to overcome the crisis and predict the development with consideration of latest achievements in modern science, giving examples of interdisciplinary structured and systematic approach.

Problem state From the first years of the Soviet regime, the machine-tool

building has a strategically disastrous slogan — "Catch up and outdo!" (first lathe machines of Moscow-based "Red Proletarian" factory were called DIP-200 — DIP being an abbreviation of "Catch up and outdo!" in Russian, with a height of centres being

200 mm, and even with CNC integration, like in 16K20F3S1 model, have never surpassed similar machines of leading foreign producers). We have always been convinced that we should stay in the wake of the leading companies and states, closely following their steps and taking any advances, seen at international exhibitions, as the basis for development. In the late 80's of the previous century some attempts have been made to go the other way (for example, Ivanovo Machine-Tool Building Plant, which began manufacturing modern multi-purpose machine tools such as IR-500 using modular approach, Kiev Plant Of Computer-Controlled Machines named after Gorky, which pioneered with CNC integrated multi-spindle automatic lathe machines). However, the unexpected happened and Ukraine, which ranked second in the USSR after the Russian Federation, has lost the lead — many machine-tool building plants have lost momentum and even stopped their activity. For example, "Vercon" public company, which was previously widely know by the production of multispindle automatic and semi-automatic lathe machines in a full range of sizes — from the lightest to super heavy [19, 24].

Today there is still an opportunity (if the government changes its approach) to revive the domestic machine-tool building industry and other machine building industries (aircraft industry, shipbuilding, agricultural machinery building, instrument making industry). To accomplish this, the correct strategic motto "Outdo without catching up!" should be adopted and innovative breakthrough (Fig. 1) should be done in science, education and industry using the latest advances in various sciences (genetics, cybernetics, informatics, synergetics, socionics and etc.) incorporated in the interdisciplinary intellectual field and based on a unified structured and systematic approach (NBIC, as example, — NANO, BIO, INFO, COGNO technologies) [3, 4, 7, 10, 11, 22].

Fig. 1. Visual comparison of the improper (left) and proper (right) machine-tool building development ways and mottos (centre)

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The proposed scientific approach, which ensures the innovative breakthrough

The postulate of the new scientific approach — transcending from living Nature to the creation of anthropogenic systems, which include static and dynamic machine, electrical, construction ES by virtue of Human intelligence, that is declared in philosophical ideas and prophecy of academic V.I. Vernadsky [5]: "With the emergence of the intellectually gifted living creature, our planet enters a new stage of its history. The biosphere becomes noosphere (sphere of mind)... We are just beginning to create an overwhelming power of scientific thought, the greatest creative power of Homo Sapiens, human's free personality, the greatest known manifestation of its cosmic force, which rule is yet to come..." ("noosphere " term was coined by the French scientists: mathematician and philosopher Edward Peru, a geologist and paleontologist Teilhard de Chardin). Creation of new evolving ES is impossible without analysis and consideration of the accumulated human experience, which is how the genetic information on a variety of media is transferred from generation to generation. The history of human society development and technology evolution has always been connected with mechanics [9]. However, after the discovery of electricity, any human activity and ES development without it seem unthinkable now [1]. Electricity has become the main source of energy for ES, as well as the primary transducer of alternative sources (water, wind

and solar), competing with gasoline and gas. This trend identified a special role of electromechanical science associated with the study and creation of electromechanical energy converters, which are directly used in manufacturing processes, transportation, distribution and consumption of electrical energy. By analogy with the periodic system of electromagnetic elements (primary electromagnetic field sources), called electromagnetic genome [18], which was proposed by Professor V.F Shinkarenko, and relying on principles of self-organization and the genetic principle "from simple to complex", the new perspective on the mass point is proposed, being carrier of genetic information to create "object" and "process" type ES [13, 17]. This mass point at the genetic level is conditionally named "mechanical gene" and carries information about translational and rotational movements, loads and their directions (Fig. 2).

Fig. 2. Mass point (point O) is a mechanical gene carrying information about

translational ( ; ) and rotational ( ; ) movements and loads with indicated direction

Символ «принципа всеобщего различия» по Лейбницу

Leibnitz "universal diversity principle" symbol

The mass point can be fixed, being the information about static "object" type AS

(tools, structures that house processing equipment systems) and variable, such as the information about dynamic "process" type AS [1, 13, 18].

Fixed mass point together with building up the genetic information and increasing structure complexity is used in geometry of static AS (Fig. 3). For the first time, the author declared about the mass point in fixing mechanisms' flux forces with of alphanumeric encoding in the report [15].

Fig. 3. Examples of mass point transfer (a) and object complexity increase with accumulation of genetic information in the context of

image, figure and body creation in one-dimensional (b), two-dimensional (c) and three-dimensional (d) space The variable mass point with genetic information accumulation

and structure complexity increase is used to transfer information from one point to another, and for point to point interaction.

By analogy with Flynn classification, which first appeared in cybernetics as applied to computers [3] and later in ES theory [16], all kinds of information transfer by mass points and their interactions can be represented by four classes (Fig. 4). Similarly to the electromagnetic field, in mechanics, we can talk about the field of forces, which can serve as the initial structure comprising an ordered set of mechanical genes with a given spatial sequence of their placement (distribution) within the boundaries of geometrized topological space (surface).

Thanks to fruitful cooperation of technicians and electricians using genetic approaches in electrical engineering and universal genetic synthesis operators (replication, inversion, crossing, crossover, mutation) [18,22,25,26] fundamentally new mechanisms, assemblies and machine tools were created, which have any mechanical transmissions replaced with electromagnetic ones: motor-driven multispindle heads (Ukrainian Patent No. 110074); motor-driven revolving heads (Ukrainian Patent No. 109191); machine tool spindle assembly (Ukrainian Patent No. 112234); device for oscillating drilling of composite materials (Ukrainian Patent No. 113101); motor-driven spindle carrier [24], multi-axis pyramidal arrangement mobile drilling and milling machine (Ukrainian Patent No. 101447).

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Fig. 4. Ways of information transfer and mass point interaction according to Flynn classification: a – single input, single output; b – single input, multiple outputs; c – multiple inputs, single output; d – multiple inputs, multiple outputs

Instead of the conventional multispindle head with gears (present time) (Fig. 5), motor-driven spindle heads (future) (Fig. 6) are proposed.

Fig. 5. Conventional multispindle head (present time): 1 – casing; 2

– bolts; 3 – spindle-bearing sleeve; 4 – spindle axis; 5 – tool spindles; 6, 7 – front and rear tool spindle bearing sections; 8, 9 – gears; 10 – drive shaft with bearings 11, 12

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0.2у х 4 0.2у

Instead of the conventional revolving head with gears connecting to machine spindle (present time) (Fig. 7, a), the motor-driven revolving head (future) (Fig. 7, b) is suggested, in which the gear rotation mechanism with a separate motor can be replaced by a hybrid electromechanical system with a conical stator and cylindrical rotors (genetic formula 0.2у х 0.2у [22].

a) b)

Fig. 7. Revolving head (present time) (a) and motor-driven revolving head (future) under the Ukrainian Patent No. 109191 with the genetic

formula 0.2у х 0.2у (b): 1 – casing; 2 – bolts; 3 – turning spindle unit; 4 – spindle axis; 5 – casing 1 lower edge; 6 – revolving faceplate; 7 – tool spindles; 8, 9 – front and rear tool spindle bearing sections; 10 – bevel gears on spindle 7 ends; 11, 18 – central bevel gears on the drive shaft; 12,13 – drive shaft bearings; 14 – central shaft on bearings 15 and 16; 17, 18 – bevel gears pair; 19 – faceplate rotation motor; 20, 21 – cylindrical gear pair; 22 – cone-shaped stator; 23 – rotary motion armature with windings 24; 25 – faceplate 6 on bearings 26, 27

The use of high-speed motor-driven spindles (M-S) in

multispindle automatic and semi-automatic lathe machines allows to discard gears from the main drive motor (past) (Fig. 8,

a), as well as individual motors with couplings (present) (Fig. 8, b) and significantly shorten kinematic chains and spindle carrier (SC) weight (future) (Fig. 8, c, d) [24].

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FUTURE

Fig. 8. The evolution of the main drive motor (of spindle rotation) in multispindle automatic lathe machine with a revolving spindle carrier

(SC): a – past; b – present; c, d – future (M — main drive motors; М …М – spindle drive motors … ; М … М – motor-driven spindles; … – motor-driven spindle stators; … – motor-driven spindle rotors;

C – common stator for all M-S

When speaking about the future of global and domestic

machine-tool building industry development [13,19,21], we should resort to the scientific approach, as well as known and new methods of forecasting and prediction for periods of 50-100 years or more ahead. The following types of forecasting can be

distinguished in engineering: science (engineering) forecasting [16, 20]; scientific forecasting [3]; genetic forecasting [22, 23]. In case of scientific forecasting for 20-30 years, the systematic and morphological approach proves to be effective [14, 20], which is illustrated by the example of a future machine tool (Fig. 9).

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Fig. 9. Mobile multi-axis drilling and the milling machine of the future without mechanical transmission according to the patent for an invention No. 101447 with genetic formulas of assemblies (mechanisms)

Genetic prediction based long-term forecast with 100% accomplishment probability can be represented as a prediction pyramid (Fig. 10). As the size (weight) of a part Gp or machine tool Gm increases, their relationship and machine tool shape changes: I. Quick-assembly and ultra-precision mini machine tools

consisting of modules in a case with an integrated computer control system.

II. Bench-top machines or 3D-printers with artificial intelligence, controlled from a computer (smartphone) or a chip integrated into a human head.

III. Floor-standing (ground) mobile multi-axis robot car machine tools with frame-shell undercarriage system, which can freely move through the workshop and machine the workpieces.

IV. A building (workshop) with a workpiece placed on the floor (perhaps, grown with a 3D-printer) and intelligent robotic machine tools moving across the walls and ceiling.

V. The outdoor area under a canopy with a workpiece placed on the floor (perhaps, grown with 3D-printers) and intelligent robotic machines with tools of various purpose and design moving across and around it.

For all future machine tools when approaching the workpiece shape to the shape of the finished part, i.e. filmed while substantially reducing allowances, and cutting forces at high processing speeds, and with the transition to the frame and enveloped carrier system (frame, columns, pillars, etc.) unnecessary in the bases, from the mini-machine and up to the unique.

CL (2.0 × 0.2y)

FL 2.2 (x × y)

TF 0.2 y FL 2.2 (x × y)

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Fig. 10. Geometrical model of evolution prediction for machine tools of different sizes

Conclusion 1. It becomes evident that Human is not the sole creator of

technological progress, as previously thought, but remains only Nature's apprentice. All that many generations of professionals have invented, was long before designed by Nature in its genetic flows. Nature sets the structural organisation laws, creates genetic flows of development of complex systems and dictates strict rules of their composition.

2. The era of the transition from the virtual to the real is coming, as the manufacturing technologies and means (material and energy flows) were and always remained the basis for the material production progress ("more-better-cheaper"), rather than computers, accustoming to virtual activities that relate to information flows, which are always only secondary and auxiliary.

3. New ideas are always faced with an army of routinists, but only such bold ideas, thanks to the knowledge and respect for the laws of Nature, lead to the creation of sustainable and competitive real production objects. It can be expressed in words by Professor of Bauman MSTU L.I. Volchkevich [3]: "Confrontation of the new and nominally-promising, which is not yet practised and risky in comparison with well-known and thoroughly familiar, cannot proceed without a conflict, without breaking the psychological stereotypes, without understanding and compromise...".

4. Also, it is good to keep in mind the words of academician Konstantin Skryabin: "Who possesses the genetic information, will own the world!".

Literature 1. E.P. Balashov. Evolutionary Synthesis /E.P. Balashov –

Moscow: Radio and Communications, 1985. – 328 p. 2. B.N. Biryukov. Machines creating machines /B.N.

Biryukov. – Kyiv: Technics, 1987. – 141 p. 3. Ye.I. Bruhovich. On the issue of society computerization.

- //Mathematical Machines and Systems. – 1997, No. 2. – p-p. 122-132.

4. N.I. Vavilov. Homologous series law in hereditary variation/N.I. Vavilov. – St. Petersburg: Science, 1987. – 267 p.

5. V.I. Vernadsky. Biosphere and noosphere /V.I. Vernadsky. – Moscow: Iris-press, 2007. – 576 p.

6. L.I. Volchkevich. Automation of industrial processes: Textbook /L.I. Volchkevich. – Moscow: Mechanical Engineering, 2005. – 380 p.

7. F.G. Hegel Science of Logic. – St. Petersburg: 1997. – 191 p.

8. V.A. Dobrovolsky. General principles of modern machine design /V.A. Dobrovolsky, L.B. Ehrlich. – Kyiv. – Moscow: Mashgiz, 1956. – 110 p.

9. A.Yu. Ishlinskii. Mechanics: concepts and objectives, applications /A.Yu Ishlinskii. – Moscow: Science, 1985. – 624 p.

10. E.N. Knyazeva. Synergetics. Non-linearity of time and coevolution landscapes / E.N. Knyazeva, S.P. Kurdyumov. Moscow: "Komkniga" publishing, 2014 – 272 p.

11. G.P. Korotkova. Integrity principles (on the question of the relationship between living and non-living systems) / G.P. Korotkova – St. Petersburg: published by Leningrad University, 1968. — 160 p.

12. Yu.N. Kuznetsov. Genetic and morphological approach to the creation of anthropogenic systems on the example of machine tools. IIX International Scientific Conference "Modern Problems of

Mechanical Engineering" (Mechanical Engineering – 2014 ", Gomel, 23-24.10.2014. – p.

13. Yu.N. Kuznetsov. Evolutionary and genetic synthesis of modern technological equipment // Cutting and tools in technological systems: International scientific - techn. coll. - Kharkiv: NTU "KPI", 2008. – Issue 85. - p-p. 149-162.

14. Yu.N. Kuznetsov, Zh.A. Hamuyela Gerra, Poparov A. Genetic-morphological approach to the creation and development of forecasting of clamping mechanisms for rotating parts // Journal of the Technical University – Sofia. – Plovdiv branch, Bulgaria Fundamental Sciences and Applications. – Bulgaria, vol. 19, Book 2, 2013 – p.p. II 7 – II 13.

15. Yu.N. Kuznetsov. Theoretical foundations for optimal design of clamping mechanisms. Book of reports of Anniversary conference with international participation, dedicated to the 1300th anniversary of Bulgaria and the 90th anniversary of the BCB, Gabrovo (PRB), 1982. 2. p-p. 3-58.

16. Yu.N. Kuznetsov. Theory of technical systems: Textbook / Yu.N. Kuznetsov Yu. K. Novoselov, I. V. Lutsiv. – Sevastopol: SevNTU publishing, 2010. – 252 p.; 2011. – 254 p. (Ukrainian); 2012. – 256 p. (English).

17. Yu.N. Kuznetsov. A new point of view at the mass point as the carrier of genetic information at creation of technical systems // Proceedings of the International scientific and practical conference "Fundamental Principles of Mechanics", Novokuznetsk: SIC MS, 2016. – No. 1. – p-p. 26-40.

18. Yu.N. Kuznetsov. Creation of new generation of machine tools using genetic and morphological approach (Parts 1, 2) // International Scientific Conference "UNITECH 10" - Gabrovo, Volume 2; 2010. – p-p. II-79 – II-91.

19. Yu.M. Kuznetsov Current state, prospects of development and production of machine tools in Ukraine // Journal of the Academy of Engineering Sciences of Ukraine, No. 1 (41), 2011. – p-p. 2-10.

20. Yu.M. Kuznetsov Prediction of technical system development: Educational aid / Yu.M. Kuznetsov, R.A. Sklyarov; editor – Yu.N. Kuznetsov – Kyiv: "AMOK" LLC - "GNOSIS" PE, 2004. – 323 p.

21. Yu.N. Kuznetsov Arrangement of machines with parallel structure mechanisms: Monograph / Yu.N. Kuznetsov, D.O. Dmitrіiev, G.Yu. Dіnievich. – Kherson: PE Vishemirsky V.S., 2009. – 456 p.

22. Shinkarenko V.F. Electromechanical systems evolution theory basics. – Kyiv: Naukova Dumka, 2002. – 288 p.

23. Shinkarenko V.F. Genetic prediction as a systematic basis in the management strategy of innovative development of technical systems // Contributions of Tavria State Agrotechnological University - Issue 11. – Vol. 4. – 2011. – p-p. 3-19.

24. Ibrahem Farhan Salman Alrefo, Yu. N. Kuznetsov. Evolution and genetic forecasting of multispindle automatic lathe development // Вісник ХНТУ №2(57), 2016. – p-p. 17-22.

25. Shynkarenko Vasyl, Kuznetsov Yuriy. Interdisciplinary approach to modeling and synthesis of difficult technical systems // Journal of the Technical Universitу Gabrovo, Vol. 52, 2016. – p-p. 24-28.

26. Yuriy Kuznetsov, Vasyl Shynkarenko. The genetic approach is the key to innovate synthesis of complicated technical systems // Journal of the Technical University – Sofia, Plovdiv branch, Bulgaria. Fundamental sciences and application, Vol. 16, book 2, 2011. – p-p. 15-34.

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ADAPTIVE CONTROL OF NONLINEAR TWO DIMENSIONAL AIRFOIL MODEL Boğaç Bilgiç

Department of Mechanical Engineering, Engineering Faculty – Istanbul University, Turkey

[email protected]

Abstract: In this paper, an adaptive control method is improved for airfoil model. By using energy method, the governing equations of the nonlinear 2-D airfoil model are obtained. As known, the system exhibits different behaviors at different speeds. For this purpose, flutter speeds are investigated and phase portraits of pitching are shown at critical speeds. Flutter for airfoils is such an enormous problem which have been considered. An adaptive control method is improved for minimizing the vibration at pre-flutter speed, flutter speed and post-flutter speed regimes. To show that the controller system works, controlled and uncontrolled airfoil model are simulated simultaneously. Results of these simulations are demonstrated graphically at the conclusion part.

Keywords: AIRFOIL, ADAPTIVE CONTROL, FLUTTER.

1. Introduction Nonlinear two-dimensional airfoil model has been used in much

recent research because it is more simple and useful than others [1-4]. Through this model, three dimensional airfoils can be modelled as two dimensional and investigated non-linear phenomenon. Flutter is a dynamic instability phenomena resulting from the interaction between an elastic structure and the flow around the structure, for which the prevention technology is very important in the design of aircraft. In 2008, Zheng and Yang analyze the flutter speed using Hopf bifurcation theory [5]. And then, many active controllers have designed to prevent the flutter [6-8].

In this paper, firstly airfoil is modelled, and investigated the flutter speed. Then, new adaptive controller was represented and its achievements are shown graphically.

2. Modelling of Airfoil

Fig. 1 Sketch of two-degree-of-freedom airfoil.

The sketch of a 2D lifting surface featuring plunging and pitching degrees of freedom, elastically constrained by a linear translational spring and nonlinear torsional spring respectively is shown in Fig.1. Based on the energy method, the governing equations of the lifting surface with differential cubic nonlinear stiffness in pitching direction can be expressed as [5]

𝑚𝑚ℎ + 𝑆𝑆∝��𝛼 + 𝑐𝑐ℎ ℎ + 𝐾𝐾ℎℎ = 𝐿𝐿 (1)

𝑆𝑆∝ℎ + 𝐼𝐼∝��𝛼 + 𝑐𝑐𝛼𝛼 ��𝛼 + 𝐾𝐾𝛼𝛼𝛼𝛼 + 𝑒𝑒𝐾𝐾𝛼𝛼𝛼𝛼3 = 𝑀𝑀 (2)

𝐿𝐿 = − 𝜌𝜌∞𝑈𝑈∞𝑏𝑏3𝑀𝑀∞

�12ℎ + 12(1− 𝑎𝑎)𝑏𝑏 ∝+ 12𝑈𝑈∞ ∝ ⋯… + 𝑀𝑀∞

2 𝑈𝑈∞(1 + 𝑘𝑘) ∝3 � (3)

𝑀𝑀 = 𝜌𝜌∞𝑈𝑈∞𝑏𝑏2

3𝑀𝑀∞�

12(1 − 𝑎𝑎)𝑈𝑈∞ ∝ +12(1− 𝑎𝑎)ℎ + ⋯… (16 − 24𝑎𝑎 + 12𝑎𝑎2)𝑏𝑏 ∝+ ⋯

…𝑀𝑀∞2 𝑈𝑈∞(1 + 𝑘𝑘)(1 − 𝑎𝑎) ∝3

� (4)

Where; 𝑚𝑚 is mass of the wing, 𝑆𝑆∝ = 𝑚𝑚𝑥𝑥∝𝑏𝑏 is the wing mass static moment about the elastic axis, 𝐼𝐼∝ = 𝑚𝑚(𝑟𝑟∝𝑏𝑏)2 is the inertial moment of the wing about the elastic axis, 𝑐𝑐ℎand 𝑐𝑐𝛼𝛼 are the linear plunging and pitching damping coefficients, 𝐾𝐾ℎ and 𝐾𝐾∝ are the plunging and pitching stiness coefficients, 𝑒𝑒 is the non-dimensional

nonlinear stiness coefficient, 𝑏𝑏 is the wing’s semi-chord length, ℎ is the plunging displacement, ∝ is the pitching angle, 𝐿𝐿 and 𝑀𝑀 are the aerodynamic force and moment, 𝑀𝑀∞ is the flight Mach number, 𝜌𝜌∞ is the density of the air, 𝑈𝑈∞ is the air speed, 𝑘𝑘 is the isentropic gas coefficient and 𝑎𝑎 is dimensionless elastic axis position measured from the leading edge.

Equations (3) and (4) are written in equations (1) and (2), and then should be taken the parameters as below,

𝜉𝜉 = ℎ 𝑏𝑏⁄ (5)

𝜏𝜏 = 𝑈𝑈∞𝑡𝑡 𝑏𝑏⁄ (6)

𝜔𝜔ℎ = �𝐾𝐾ℎ 𝑚𝑚⁄ (7)

𝜔𝜔𝛼𝛼 = �𝐾𝐾𝛼𝛼 𝐼𝐼𝛼𝛼⁄ (8)

𝜔𝜔� = 𝜔𝜔ℎ 𝜔𝜔𝛼𝛼⁄ (9)

𝜇𝜇 = 𝑚𝑚 (4𝜌𝜌∞𝑏𝑏2)⁄ (10)

𝑉𝑉 = 𝑈𝑈∞ (𝑏𝑏𝜔𝜔𝛼𝛼 )⁄ (11)

the dimensionless equations of motion of the airfoil corresponding to Equations (12) and (13).

𝜉𝜉 + 𝑥𝑥𝛼𝛼��𝛼 + 2𝜍𝜍ℎ𝜔𝜔�𝑉𝑉 𝜉𝜉

+ �𝜔𝜔�𝑉𝑉�

2𝜉𝜉 = ⋯

…− 1𝜇𝜇𝑀𝑀∞

�𝜉𝜉 + (1 − 𝑎𝑎)��𝛼 + 𝛼𝛼 + 𝑀𝑀∞2

12(1 + 𝑘𝑘)𝛼𝛼3� (12)

𝑥𝑥𝛼𝛼𝑟𝑟𝛼𝛼2𝜉𝜉 + ��𝛼 + 2𝜍𝜍𝛼𝛼

1𝑉𝑉 ��𝛼 +

1𝑉𝑉2 𝛼𝛼 +

𝑒𝑒𝑉𝑉2 𝛼𝛼

3 = ⋯

…− 1𝜇𝜇𝑀𝑀∞𝑟𝑟𝛼𝛼2

⎣⎢⎢⎢⎡ (1 − 𝑎𝑎)𝛼𝛼 + (1 − 𝑎𝑎)𝜉𝜉…

… + �43− 2𝑎𝑎 + 𝑎𝑎2� ��𝛼…

… + 𝑀𝑀∞2

12(1 + 𝑘𝑘)(1 − 𝑎𝑎)𝛼𝛼3⎦

⎥⎥⎥⎤ (13)

Where 𝜍𝜍ℎ = 𝑐𝑐ℎ 2�𝐾𝐾ℎ𝑚𝑚⁄ and 𝜍𝜍𝛼𝛼 = 𝑐𝑐𝛼𝛼 2�𝐾𝐾𝛼𝛼𝐼𝐼𝛼𝛼⁄ . If equations (12) and (13) are arranged,

𝜉𝜉 = −𝑥𝑥𝛼𝛼��𝛼 − �2𝜍𝜍ℎ𝜔𝜔�𝑉𝑉 +

1𝜇𝜇𝑀𝑀∞

� 𝜉𝜉 − �𝜔𝜔�𝑉𝑉�

2𝜉𝜉 …

…− (1−𝛼𝛼)𝜇𝜇𝑀𝑀∞

��𝛼 − 1𝜇𝜇𝑀𝑀∞

𝛼𝛼 − 𝑀𝑀∞ (1+𝑘𝑘)12𝜇𝜇

𝛼𝛼3 (14)

��𝛼 = −𝑥𝑥𝛼𝛼𝑟𝑟𝛼𝛼2𝜉𝜉 + �

43 − 2𝑎𝑎 + 𝑎𝑎2

𝜇𝜇𝑀𝑀∞𝑟𝑟𝛼𝛼2−

2𝜍𝜍𝛼𝛼𝑉𝑉 �𝛼𝛼 + �

1 − 𝑎𝑎𝜇𝜇𝑀𝑀∞𝑟𝑟𝛼𝛼2

−1𝑉𝑉2�𝛼𝛼

…

… + �𝑀𝑀∞ (1+𝑘𝑘)(1−𝑎𝑎)12𝜇𝜇𝑟𝑟𝛼𝛼2

− 𝑒𝑒𝑉𝑉2�𝛼𝛼3 + 1−𝑎𝑎

𝜇𝜇𝑀𝑀∞𝑟𝑟𝛼𝛼2𝜉𝜉 (15)

are obtained.

If equation (15) is written in equation (14) and then equation (14) is written equation (15) and they are arranged,

11

𝜉𝜉 = −

⎝

⎛ 1

�1 − 𝑥𝑥𝛼𝛼2𝑟𝑟𝛼𝛼2�⎠

⎞ ∗ …

…

⎩⎪⎪⎪⎨

⎪⎪⎪⎧ �2𝜍𝜍ℎ

𝜔𝜔�𝑉𝑉

+ 1𝜇𝜇𝑀𝑀∞

+ (1−𝑎𝑎)𝑥𝑥∝𝜇𝜇𝑀𝑀∞𝑟𝑟𝛼𝛼2

� 𝜉𝜉 + ⋯

… ��𝜔𝜔�𝑉𝑉�

2� 𝜉𝜉 + ⋯

… �(1−𝑎𝑎)𝜇𝜇𝑀𝑀∞

+�4

3−2𝑎𝑎+𝑎𝑎2�𝑥𝑥∝𝜇𝜇𝑀𝑀∞𝑟𝑟𝛼𝛼2

− 2𝜍𝜍𝛼𝛼𝑥𝑥∝𝑉𝑉

� ��𝛼 + ⋯

… � 1𝜇𝜇𝑀𝑀∞


− 𝑥𝑥∝𝑉𝑉2� 𝛼𝛼 + ⋯

… �𝑀𝑀∞ (1+𝑘𝑘)12𝜇𝜇

+ 𝑀𝑀∞ (1+𝑘𝑘)(1−𝑎𝑎)𝑥𝑥∝12𝜇𝜇𝑟𝑟𝛼𝛼2

− 𝑒𝑒𝑥𝑥∝𝑉𝑉2 � 𝛼𝛼3

⎭⎪⎪⎪⎬

⎪⎪⎪⎫

(16)

��𝛼 =

⎝

⎛ 1

�1 − 𝑥𝑥𝛼𝛼2𝑟𝑟𝛼𝛼2�⎠

⎞ ∗ …

…

⎩⎪⎪⎪⎨

⎪⎪⎪⎧ �1−𝑎𝑎+𝑥𝑥∝

𝜇𝜇𝑀𝑀∞𝑟𝑟𝛼𝛼2+ 2𝜍𝜍ℎ𝜔𝜔�𝑥𝑥∝

𝑟𝑟𝛼𝛼2𝑉𝑉� 𝜉𝜉 + ⋯

… �𝜔𝜔�2𝑥𝑥∝

𝑟𝑟𝛼𝛼2𝑉𝑉2 � 𝜉𝜉 + ⋯

… �43−2𝑎𝑎+𝑎𝑎2+(1−𝑎𝑎)𝑥𝑥∝

𝜇𝜇𝑀𝑀∞𝑟𝑟𝛼𝛼2− 2𝜍𝜍𝛼𝛼

𝑉𝑉� ��𝛼 + ⋯

… �1−𝑎𝑎+𝑥𝑥∝𝜇𝜇𝑀𝑀∞𝑟𝑟𝛼𝛼2

− 1𝑉𝑉2� 𝛼𝛼 + ⋯

… �𝑀𝑀∞ (1+𝑘𝑘)(1−𝑎𝑎+𝑥𝑥∝)12𝜇𝜇 𝑟𝑟𝛼𝛼2

− 𝑒𝑒𝑉𝑉2� 𝛼𝛼3

⎭⎪⎪⎪⎬

⎪⎪⎪⎫

(17)

are acquired.

Let 𝑥𝑥1 = 𝜉𝜉 , 𝑥𝑥2 = 𝛼𝛼 , 𝑥𝑥3 = 𝜉𝜉 and 𝑥𝑥4 = ��𝛼, equations (16) and (17) can be written as the lower order differential form

��𝑥1 = 𝑥𝑥3 (18)

��𝑥2 = 𝑥𝑥4 (19)

��𝑥3 = −� 1

�1−𝑥𝑥𝛼𝛼2

𝑟𝑟𝛼𝛼2�� ∗ …

…

⎩⎪⎪⎪⎨

⎪⎪⎪⎧ �2𝜍𝜍ℎ

𝜔𝜔�𝑉𝑉

+ 1𝜇𝜇𝑀𝑀∞


� 𝑥𝑥3 + ⋯

… ��𝜔𝜔�𝑉𝑉�

2� 𝑥𝑥1 + ⋯

… �(1−𝑎𝑎)𝜇𝜇𝑀𝑀∞

+�4

3−2𝑎𝑎+𝑎𝑎2�𝑥𝑥∝𝜇𝜇𝑀𝑀∞𝑟𝑟𝛼𝛼2

− 2𝜍𝜍𝛼𝛼𝑥𝑥∝𝑉𝑉

� 𝑥𝑥4 + ⋯

… � 1𝜇𝜇𝑀𝑀∞


− 𝑥𝑥∝𝑉𝑉2� 𝑥𝑥2 + ⋯

… �𝑀𝑀∞ (1+𝑘𝑘)12𝜇𝜇

+ 𝑀𝑀∞ (1+𝑘𝑘)(1−𝑎𝑎)𝑥𝑥∝12𝜇𝜇𝑟𝑟𝛼𝛼2

− 𝑒𝑒𝑥𝑥∝𝑉𝑉2 � 𝑥𝑥2

3⎭⎪⎪⎪⎬

⎪⎪⎪⎫

(20)

��𝑥4 = � 1

�1−𝑥𝑥𝛼𝛼2

𝑟𝑟𝛼𝛼2�� ∗ …

…

⎩⎪⎪⎪⎨

⎪⎪⎪⎧ �1−𝑎𝑎+𝑥𝑥∝

𝜇𝜇𝑀𝑀∞𝑟𝑟𝛼𝛼2+ 2𝜍𝜍ℎ𝜔𝜔�𝑥𝑥∝

𝑟𝑟𝛼𝛼2𝑉𝑉� 𝑥𝑥3 + ⋯

… �𝜔𝜔�2𝑥𝑥∝

𝑟𝑟𝛼𝛼2𝑉𝑉2 � 𝑥𝑥1 + ⋯

… �43−2𝑎𝑎+𝑎𝑎2+(1−𝑎𝑎)𝑥𝑥∝

𝜇𝜇𝑀𝑀∞𝑟𝑟𝛼𝛼2− 2𝜍𝜍𝛼𝛼

𝑉𝑉� 𝑥𝑥4 + ⋯

… �1−𝑎𝑎+𝑥𝑥∝𝜇𝜇𝑀𝑀∞𝑟𝑟𝛼𝛼2

− 1𝑉𝑉2� 𝑥𝑥2 + ⋯

… �𝑀𝑀∞ (1+𝑘𝑘)(1−𝑎𝑎+𝑥𝑥∝)12𝜇𝜇𝑟𝑟𝛼𝛼2

− 𝑒𝑒𝑉𝑉2� 𝑥𝑥2

3⎭⎪⎪⎪⎬

⎪⎪⎪⎫

(21)

The parameters used in this work are chosen as 𝜇𝜇 = 50 , 𝜔𝜔� = 1, 𝑥𝑥∝ = 0.25, 𝑟𝑟𝛼𝛼2 = 0.5, 𝛼𝛼 = 0.5, 𝜍𝜍ℎ = 𝜍𝜍𝛼𝛼 = 0.1, 𝑒𝑒 = 20, 𝑀𝑀∞ = 6,

𝑎𝑎 = 0.5 and 𝑘𝑘 = 1.4 . Initial conditions are 𝑋𝑋(0) = [0 0.001 0 0].

From figure 2, we can see that there are complicated responses of the airfoil model, such as convergence (see Figure 2(a)), limit cycle oscillation (Figure 2(b)), divergence (Figure 2(c)) and even chaos (Figure 2(d)). In particular, divergent and chaotic motions of the airfoil will give the aircraft a serious flight safety problem. To prevent the flutter, next, the adaptive control algorithm method will be applied to design an active controller.

Fig. 2 Response plots at different V. (a) V=8.132; (b) V=10.388; (c) V=10.572; (d) V=17.934 [6]

12

3. Design of Adaptive Controller System can be described

��𝒙 = 𝒇𝒇(𝒙𝒙) + 𝒈𝒈(𝒙𝒙)𝑢𝑢 (22)

where

𝒈𝒈(𝒙𝒙) = [0 0 1 0]𝑇𝑇 (23)

Adaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain.

The behavior of the airfoil varies greatly according to the speed. Because of this, adapting control rule is created. PID controller and only P controller in different conditions can be used. Errors 𝑒𝑒𝜉𝜉 = 𝑒𝑒1 = 𝑥𝑥1𝑟𝑟𝑒𝑒𝑟𝑟 − 𝑥𝑥1 = 𝜉𝜉𝑟𝑟𝑒𝑒𝑟𝑟 − 𝜉𝜉 and 𝑒𝑒��𝜉 = 𝑒𝑒3 = 𝑥𝑥3𝑟𝑟𝑒𝑒𝑟𝑟 − 𝑥𝑥3 =𝜉𝜉��𝑟𝑒𝑒𝑟𝑟 − 𝜉𝜉 determine which controller can be used.

𝑢𝑢 = � 𝑢𝑢𝑝𝑝 𝑖𝑖𝑟𝑟 |𝑒𝑒1| < 𝑒𝑒1𝑐𝑐 𝑎𝑎𝑎𝑎𝑎𝑎 |𝑒𝑒3| > 𝑒𝑒3𝑐𝑐𝑢𝑢𝑝𝑝𝑖𝑖𝑎𝑎 𝑜𝑜𝑡𝑡ℎ𝑒𝑒𝑟𝑟𝑒𝑒𝑖𝑖𝑒𝑒𝑒𝑒

� (24)

Where, 𝑒𝑒1𝑐𝑐 and 𝑒𝑒3𝑐𝑐 are critical error values.

𝑢𝑢𝑝𝑝𝑖𝑖𝑎𝑎 (𝜏𝜏) = 𝐾𝐾𝑝𝑝𝑒𝑒1(𝜏𝜏) + 𝐾𝐾𝑖𝑖 ∫ 𝑒𝑒1(𝑒𝑒)𝑎𝑎𝑒𝑒 + 𝐾𝐾𝑎𝑎��𝑒1(𝜏𝜏)𝜏𝜏0 (25)

𝑢𝑢𝑝𝑝(𝜏𝜏) = 𝐾𝐾𝑝𝑝𝑒𝑒1(𝜏𝜏) (26)

where 𝐾𝐾𝑝𝑝 , 𝐾𝐾𝑖𝑖 , and 𝐾𝐾𝑎𝑎 all non-negative, denote the coefficients for the proportional, integral, and derivative terms, respectively.

Uncontrolled Controlled

Fig. 3 Achievement of controller at V=10.388





4. Conclusion In this work, an adaptive controller for non-linear two

dimensional airfoil model is proposed. Nonlinear characteristics of flutter with different flow speed are analyzed. The simulated results show that the design controller can effectively suppress airfoil flutter, which provides a valuable reference to solve the active control problem of airfoil flutter.

References 1) Ashley H. and Zartarian G., Piston theory – a new aero-

dynamic tool for aeroelastician, Journal of the Aeronautical Science, 1956, 23(12), 1109-1118.

2) Lee B.H.K., A study of transonic flutter of a two-dimensional airfoil using U-g and p-k methods, National Aeronautical Establishment Scientific and Technical Publications, 1984.

3) Feixin C., Jike L., and Yanmao C., Flutter analysis on an airfoil with nonlinear damping using equivalent linearization, Chinese Journal of Aeronautics, 2014, 27(1), 59-64.

4) Zheng G., Nonlinear aeroelastic analysis of a two-dimensional wing with control surface in supersonic flow, Acta Mech Sin, 2010, 26, 401-407.

5) Zheng G. and Yang Y., Chaotic motions and limit cycle flutter of two-dimensional wing in supersonic flow, Acta Mechanica Solida Sinica, 2008, 21(5), 441-448.

6) Wang Y., Zhang Q., and Zhu L., Active control of hypersonic airfoil flutter via adaptive fuzzy sliding mode method, Journal of Vibration and Control, 2013, 21(1), 134-142.

7) Bueno D. D., Góes L. C. S. and Gonçalves P. J. P., Control of limit cycle oscillation in a three degrees of freedom airfoil section using fuzzy Takagi-Sugeno modeling, Hindawi Publishing Corporation Shock and Vibration, 2014, Article ID 597827.

8) Qian D.,and Dong-li W., Flutter control of a two dimensional airfoil using wash-out filter technique, Chinese Journal of Aeronautics, 2005, Vol. 18, No. 2.

9) Yağız N., Non-linear Control Theory, Unprinted lecture notes, 2005.

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13

BALANCE CONTROL OF SEGWAY ROBOTS USING ADAPTIVE-ROBUST CONTROLLER

Prof. M.Sc. Burkan R. PhD.1, M.Sc. Özgüney Ö.C. 2.

Faculty of Mechanical Engineering – Istanbul University, Turkey1

Faculty of Mechanical Engineering – Istanbul University, Turkey2

[email protected], [email protected]

Abstract: Due to its compatibility and functionality, segways have been widely used in many countries. It was first introduced in December 2001.Yet, segway robots are faced with problems such as friction and external disturbances. Therefore, some controllers are designed to overcome with these problems. In previous studies, traditional controllers are used to balance a two-wheeled segway robot. The aim of this study is to minimize the trajectory tracking error. Due to external disturbances, such as wind, force and torque, robot parameters cannot be calculated exactly. Hence, the parameters of the robot are assumed to be unknown. In such situations, adaptive and robust controllers give better results. Adaptive and robust control laws were examined and adaptive-robust system was designed for the segway robot. Then Lyapunov function was defined and this adaptive-robust controller was derived from the Lyapunov function. And this control system applied to a two-wheeled segway robot model.

Keywords: LYAPUNOV THEORY, ADAPTIVE CONTROL, ROBUST CONTROL

1. Introduction In this study adaptive-robust and fuzzy logic controllers are

developed for balancing Segway robot. There are lots of studies about balancing Segway robots.

Grepl [1], deals with the modelling and control of balanced wheeled autonomous mobile robot. In his study SimMechanics is used for modelling mobile robot. LQR and feedback linearization controllers are compared. Kim and Jung [2], used fuzzy logic control system for two-wheeled mobile robot. PID and fuzzy logic controllers are used to control both position and balance of two-wheel mobile robot. Performance of the PID and fuzzy logic controllers are compared through extensive experimental studies. Sangfeel, Eunji, KyungSik and ByungSeop [3], presented the fuzzy logic controller for inverted pendulum type mobile robot. They designed conventional fuzy logic controller. Chiu and Peng [4], designed fuzzy logic control system for two-wheel transporter control system. In their study, experimental results show that the fuzzy logic controller can control the whole system very well. Xu, Guo, and Lee [5], presented a Takagi–Sugeno-type fuzzy logic controller on a two-wheeled mobile robot. Their model consists of two wheels in parallel and an inverse pendulum. Finally, the results shows that fuzzy logic controller shows superior performance.

It is not easy to control inverted pendulum type systems because this type of system is a typical complex nonlinear systems. Kwak and Choi [6], designed two fuzzy logic control systems for the control of a Segway mobile robot. First they introduce the Segway robot and then analyze the system. Then they propose the design of two fuzzy logic control system for the position and balance control of the Segway mobile robot. A software fuzzy logic controller was implemented using a PIC microcontroller in Reid’s [7] project. Hadiya, Rai, Sharma, More [8], describes the design and construct a fully functional two wheeled balancing vehicle. In this paper, the vehicle is designed for a single person. And the vehicle is driven by forward and backwards movements. Goher, Tokhi and Siddique [9], designed a two wheeled robotic vehicle with virtual payload. In this paper, two types of control techniques are developed and implemented on the system. They are proportional-derivative control and fuzzy logic control systems. Also an external disturbance force is applied to the road. Finally, the results are analyzed. Grasser, D’arrıgo, Colombı and Rufer [10], had built a prototype of a revolutionary two-wheeled vehicle. Two decoupled state space controllers are used to control the system.

In this paper, adaptive-robust and fuzzy logic controllers are developed for balancing Segway robot. First adaptive-robust control system is designed for the Segway model. The Segway is based on the principle of inverted pendulum that will keep an angle of Zero degrees with vertical at all times. Fuzzy logic control system is

developed to keep the system in equilibrium. Then we introduce the two wheeled Segway robot and applied control laws to this model. Finally, results show that using adaptive-robust and fuzzy logic controller together, system gives better results.

2. Derivation of the Control Law In the absence of friction or other disturbances, Spong writes

the dynamic model of an n-link manipulator as [11];

M(q)q C(q,q)q G(q)+ + = τ (2.1)

where q denotes generalized coordinates, τ is the n-dimensional vector of applied torques (or forces), M(q) is the nxn symmetric positive definite inertia matrix, C ( q , q ) q is the n-dimensional vector of centripetal and Coriolis terms and G(q) is the n-dimensional vector of gravitational terms. Equation (2.1) can also be expressed in the following form.

Y(q,q,q)π = τ (2.2)

where π is a p-dimensional vector of robot parameters and Y is an nxp matrix which is a function of joint position, velocity and acceleration. For any specific trajectory, the desired position, velocity and acceleration vectors are qd, dq and dq . The measured

actual position and velocity errors are dq q q= − , and dq q q= − . Using the above information, the corrected desired velocity and acceleration vectors for nonlinearities and decoupling effects are proposed as:

r dq q q= − Λ ; r dq q q= − Λ (2.3)

Then, σ is given as [11];

rσ q q q Λq= − = + (2.4)

where Λ is a positive definite matrix. Then the following nominal control law is considered:

0 0 r 0 r 0

r r 0

τ M (q)q C (q,q)q G (q) Kσ = Y (q,q,q ,q ) π Kσ= + + −

−

(2.5)

The control input τ can be defined in terms of the nominal control vector 0τ

0 r r 0 r 0 r 0

r r 0

τ Y (q,q,q ,q ) u M (q)q C (q,q)q G (q) Kσ = Y (q,q,q ,q ) (π u) Kστ = + = + + −

+ −

(2.6)

14

mailto:[email protected]


where π0 ∈Rp represents the nominal parameters in dynamic model and Kσ is the vector of PD action.

0( )π = π − π ≤ ρ (2.7)

where ρ∈Rp, δ∈R are the upper uncertainty bound on the parametric uncertainty. Let us define the control input u

Theorem 1: [11]

TT

T

T2 T

Yˆ ve YY

uYˆ ve Y

σ−ρ σ > ε σ= σ−ρ σ ≤ ε ε

(2.8)

The Lyapunov function candidate is defined as;[11]

T T T1 1V σ M ( q ) σ q K q2 2

V 0

= + Λ

≥

(2.9)

Derrivative of the Lyapunov function is:

T T T T

T T

V q K q q K q + Y ( π u)

x Q x Y ( π u)

=− − Λ Λ θ +

=− + θ +

(2.10)

Where T T Tx [q ,q ]= and TQ diag( K ,K)= Λ Λ the rest of the proof is given in [11].

V 0≤ for x w⟩ where (2.11)

2m i nw /2 (Q)=ε ρ λ (2.12)

Where m i n (Q)λ denotes the minimum eigenvalue of Q. The argument proceeds as follows. Examining the second term in (2.10), we see that if then;[11]

( )

TT T

T

T

YY ( π u) Y πY

Y π 0

σ σ + = σ −ρ σ

≤ σ −ρ ⟨

(2.13)

from the Cauchy-Schwartz inequality TY σ ⟩ε and our

assumption on π . If TY σ ≤ε we have

TT T

T

TT T

T

YY ( π u) Y uY

YY YY

σ σ + ≤ σ ρ + σ

σ ρ ≤ σ ρ − σ εσ

(2.14)

This last term achieves a maximum value of /2ε ρ when TY /2σ =ε . Thus we have that

TV x Q x /2≤− +ε ρ (2.15)

To complete the proof, it suffices to notice the following. With class-K functions 1γ (.) and 2γ (.) such that

( ) ( )1 2x I M(q) x Iγ ≤ ≤γ (2.16)

it can be shown that there exist class-K functions 1α (.) and 2α (.) such that

( ) ( )1 2x V xα ≤ ≤α (2.17)

Equation (2.15) shows that: 2

3V x /2≤−α +ε ρ (2.18)

3. Fuzzy Logic Controller With fuzzy logic, like small, medium and large vague linguistic

expressions can be expressed as by membership functions. These membership functions are triangular, trapezoidal or bell curved shape. (Fig. 1). They take the values between [0,1].

Fig. 1 Different shapes of membership functions [12]

Fuzzification, Rule Evaluation and Defuzzification are the steps of the fuzzy logic control. In the first stage, membership functions are defined for the variables. Thus, certain values are converted to fuzzy values. The second stage is the rule evaluation. The rules have been prepared based on the knowledge of the system. And the output of the system is decided by the input of the system.

Fuzzy Logic Controller has two inputs and one output. These are error of theta, it’s derrivative and output is the control force respectively. Linguistic variables which implies inputs and outputs have been classified as: NB, NS, Z, PS, PB. Inputs and outputs are all normalized in the interval of [0, 1] as shown in Fig.2

Fig. 2 Membership functions of inputs (et, det) and output (u)

The linguistic labels used to describe the Fuzzy sets were “Negative Big” (NB), “Negative Small” (NS), “Zero” (Z), “Positive Small” (PS), “Positive Big” (PB). Rules are written in a rule base look-up table which is shown in Table 1

Table 1: Decision Table (et, det, u)

etheta\detheta NB NS Z PS PB

NB NB NB NS NS Z

NS NB NS NS Z PS

Z NS NS Z PS PS

PS NS Z PS PS PB

PB Z PS PS PB PB

15

4. Equations of Motion

Fig. 3 Schematics of Segway type mobile robot. [6]

w w

w w

M x = H+H

J rHφ = − + τ

(4.1)

The rotational angle of the wheel and the displacement of the robot have the following relationship:[6]

r =xφ (4.2) From Eqs. (4.1) and (4.2), the dynamic equations of the Segway

robot are; [6]

2ww p p p2

J(M M )x M lcos M lsinr r

τ+ + + θθ − θθ = (4.3)

2p p p p(J M l ) M lx cos M glsin+ θ + θ − θ = −τ (4.4)

where Mw is mass of wheel, Jw is the inertia of wheel, θ : Angle of pole, x is displacement of the robot, r: radius of wheel, Mp :Mass of center of gravity of pole, Jp Moment of inertia of center of gravity of pole and φ : Rotational angle of wheel.

Also the torques are represented in a matrix form like in (4.5)

11 12 11 12 11

21 22 21 22 21

M M C C Gx x xM M C C G

τ = + + θ θ θ

(4.5)

This new control law applied to two wheeled segway robot. Simulations have been done by using control law (2.8). We simulate the position and balance control of the Segway mobile robot using adaptive-robust and fuzzy logic controller together. The results of the angle of the pole, the angle error of the pole, the displacement, the change in the displacement are shown in Figures 4, 5, 6 and 7 respectively.

0 5 10-0.5

0

0.5θ

Time(sec)

Trac

king

erro

r(rad

)

0 5 10-0.5

0

0.5eθ

Time(sec)

Trac

king

erro

r(rad

)

0 5 10

-10

-5

0

5

10

X

Time(sec)

Dis

tanc

e(m

)

0 5 10-0.5

0

0.5eX

Time(sec)

Dis

tanc

e(m

)

Fig. 4 Response using the adaptive-robust and fuzzy logic control law when Λ=diag(20 20), K=diag(20 20 ). The target position is 10 [m].

0 5 10-0.5

0

0.5θ

Time(sec)

Trac

king

erro

r(rad

)

0 5 10-0.5

0

0.5eθ

Time(sec)

Trac

king

erro

r(rad

)

0 5 10-20

-10

0

10

20X

Time(sec)

Dis

tanc

e(m

)

0 5 10-0.5

0

0.5eX

Time(sec)

Dis

tanc

e(m

)

Fig. 5 Response using the adaptive-robust and fuzzy logic control law

when Λ=diag(50 50), K=diag(50 50 ), The target position is 10 [m].

0 5 10-2

-1

0

1

2θ

Time(sec)Tr

acki

ng e

rror(r

ad)

0 5 10-1

-0.5

0

0.5

1eθ

Time(sec)

Trac

king

erro

r(rad

)

0 5 10

-10

0

10

X

Time(sec)

Dis

tanc

e(m

)

0 5 10-1

-0.5

0

0.5

1eX

Time(sec)D

ista

nce(

m)

Fig. 6 Response using the adaptive-robust and fuzzy logic control law when Λ=diag(20 20), K=diag(20 20), The target position is 10 [m]. The reference rod is 1 rad.

0 5 10-2

-1

0

1

2θ

Time(sec)

Trac

king

erro

r(rad

)

0 5 10-1

-0.5

0

0.5

1eθ

Time(sec)

Trac

king

erro

r(rad

)

0 5 10

-10

0

10

X

Time(sec)

Dis

tanc

e(m

)

0 5 10-1

-0.5

0

0.5

1eX

Time(sec)

Dis

tanc

e(m

)

Fig. 7 Response using the adaptive-robust and fuzzy logic control law when Λ=diag(50 50), K=diag(50 50 ), The target position is 10 [m]. The reference rod is 1 rad.

5. Conclusion The aim of this study is to develop a novel fuzzy logic control

and adaptive-robust control law to minimize the trajectory tracking error and balance the rod. We develop adaptive-robust controller for position control then we design fuzzy logic controller for balancing

16

the rod. As seen in the figures 4 - 7, the optimal values for K and Λ system gives better results. The main important part of this study is the parameters of robot are assumed to be unknown.

6. References [1] Grepl R., “Balancing Wheeled Robot: Effective Modelling,

Sensory Processing and Simplified Control”, Engineering Mechanics, Vol.16, 2009, No. 2, p. 141–154.

[2] Kim H., W., and Jung S., “Fuzzy Logic Application to a Two-wheel Mobile Robot for Balancing Control Performance”, International Journal of Fuzzy Logic and Intelligent Systems, vol. 12, no. 2, June 2012, pp. 154-161.

[3] Sangfeel K., Eunji S., KyungSik K. and ByungSeop S., “Design of Fuzzy Logic Controller for Inverted Pendulum-type Mobile Robot using Smart In-Wheel Motor”, Indian Journal of Science and Technology, Vol 8(S8), 493-503, April 2015.

[4] Chiu C-H., and Peng Y-F., “Design and implement of the self-dynamic controller for two-wheel transporter”, 2006 IEEE International Conference on Fuzzy Systems Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada July 16-21, 2006.

[5] Xu J-X, Guo Z-Q and Lee T.H., “Design and Implementation of a Takagi–Sugeno-Type Fuzzy Logic Controller on a Two-Wheeled Mobile Robot”, IEEE Transaction on Industrial Electronics, Vol. 60, No. 12, December 2013.

[6] Kwak S. and Choi B-J., “Design of Fuzzy Logic Control System for Segway Type Mobile Robots”, International Journal of Fuzzy Logic and Intelligent Systems Vol. 15, No. 2, June 2015, pp. 126-131.

[7] Reid K., “Fuzzy Logic Control of an Inverted Pendulum Robot”, Electrical Engineering Department of California Polytechnic State University San Luis Obispo, 2010.

[8] Hadiya V., Rai A., Sharma S. and More A., “Design & Development of Segway”, International Research Journal of Engineering and Technology, Volume: 03 Issue: 05 May-2016.

[9] Goher K. M, Tokhi M.O and Siddique N.H., “Dynamic Modelling and Control of a Two Wheeled Robotic Vehicle with a Virtual Payload”, ARPN Journal of Engineering and Applied Sciences, Vol. 6, No. 3, March 2011.

[10] Grasser F., D’arrıgo A., Colombı S. and Rufer A., “JOE: A Mobile, Inverted Pendulum”, Laboratory of Industrial Electronics Swiss Federal Institute of Technology Lausanne EPFL CH-1015 Lausanne, Switzerland.

[11] Spong, M. W., “On the robust control of robot manipulators”, IEEE Trans. Automat. Cont., 37, 1992, pp. 1782-1786.

[12] Hacioglu, Y., “Bir Robotun Bulanık Mantıklı Kayan Kipli Kontrolü”, Yüksek Lisans Tezi, İstanbul Üniversitesi Fen Bilimleri Enstitüsü, 2004

[13] Lee S-H. and Rhee S-Y., “Dynamic modelling of a wheeled inverted pendulum for inclined road and changing its center of gravity,” J. of Korean Institute of Intelligent Systems, vol. 22, no. 1, pp. 69-74, 2012.

APPENDIX

w11 w p 2

12 21 p

222 p p

JM M Mr

M M M lcos

M J M l

= + +

= = θ

= +

11 21 22

12 p

C C C 0

C M lsin

= = =

= − θθ

11 12 21

22 p

G C C 0G M gl

= = == −

And some parameters of the Segway mobile robot are as follows:[13]

w5 2

w

p

2 2p

2

M 0.076kg

J 3.42x10 kgmM 0.6kg

J 1.34x10 kgm

g 9.81m / sr 0.03ml 0.15m

−

−

=

==

=

===

1 2

2 3 2

3

4

xM

c

x0 sC0 0

0 xG

π π = −π −π θ π θθ

= θ

= π θ

w1 w p 2 p2

23 p p 4 p

J(M M ) M lr

J M l M gl

π = + + π =

π = + π =

17

EULER BERNOULLI THEORY FOR A 3-DIMENSIONAL,VARIABLE-CURVETURE BEAM

L.Emir Sakman 1, Aşkın Mutlu 1

Faculty of Engineering, Department of Mechanical Engineering, Istanbul University, Turkey1


Abstract: The linear theory including the effects of bending-torsion coupling and rotatory inertia is used to derive the equations of motion for a space beam with variable curvature. The governing differential equations of motion are derived based on Euler-Bernoulli beam theory via Hamilton’s principle. The full, coupled system of governing partial differential equations has a total order of 12.

Keywords: EULER BERNOULLI THEORY, VARIABLE-CURVETURE BEAM

1. Introduction

While many of the curved elements used in engineering structures are very common shapes like circular arcs and helixes, arbitrarily shaped elements also find usage which may be expected to expand with the ever increasing complexity of mechanisms, aerospace and civil structures. The general equations for the small vibrations of an arbitrarily-shaped space beam were derived long ago; the definitive reference for this (and many other problems) is Love (1944) [1] according to whom the general formulation for arbitrarily-curved space beams is due to Clebsch (1862) [2].

2. Governing Equations Following Love [1], we denote the axis along the arc

length of the spatial curve formed by the centroids of the cross-sections (which will be called the wire axis) as z. X and y axes are chosen to be the principal axes of the cross-section (Fig. 1).

Fig. 1 Frenet vectors and coordinate system attached to beam axis

The xyz system is therefore attached to the wire axis with z denoting the tangent direction while x and y representing

the orientation of the cross-section with respect to z. The principal normal (N) and the binormal (B) at any point on the wire axis are within the cross-section, however, they do not coincide with x and y axes, in general. We denote the angle between N and y as γ. The change in γ as one moves along the main helix axis, /d dsγ is termed the torsional twist, where s is the arclength along z. The unit tangent along z is denoted T. These are related by the Frenet equations:

𝑑𝑑𝑻𝑻𝑑𝑑𝑑𝑑

= 𝜟𝜟 × 𝑻𝑻 (1a)

𝑑𝑑𝑵𝑵𝑑𝑑𝑑𝑑

= 𝜟𝜟 × 𝑵𝑵 (1b)

𝑑𝑑𝑩𝑩𝑑𝑑𝑑𝑑

= 𝜟𝜟 × 𝑩𝑩 (1c)

where is the principal curvature and τ is the torsion of the wire axis and

𝜟𝜟 = 𝜏𝜏 𝑻𝑻 + 𝜅𝜅𝑩𝑩 (2)

is the Frenet vector. It is the angular velocity of the TNB system as its origin moves with unit velocity along the wire axis. The xyz system differs from the TNB system by a rotation around T (z axis) through the angle γ between N and y; therefore

BNi γγ cossin −= (3a)

BNj γγ sincos += (3b)

Tk = (3c)

where 𝒊𝒊 , 𝒋𝒋 , 𝒌𝒌 are the unit vectors along xyz. The changes in these can be expressed as

𝑑𝑑𝒊𝒊𝑑𝑑𝑑𝑑

= 𝝎𝝎 × 𝒊𝒊 = 𝜆𝜆 𝒋𝒋 − 𝜅𝜅𝑦𝑦𝒌𝒌 (4a)

𝑑𝑑𝒋𝒋𝑑𝑑𝑑𝑑

= 𝝎𝝎 × 𝒋𝒋 = −𝜆𝜆 𝒊𝒊 − 𝜅𝜅𝑥𝑥𝒌𝒌 (4b)

𝑑𝑑𝒌𝒌𝑑𝑑𝑑𝑑

= 𝝎𝝎 × 𝒌𝒌 = 𝜅𝜅𝑦𝑦𝒊𝒊 − 𝜅𝜅𝑥𝑥𝒋𝒋 (4c)

where

𝝎𝝎 = 𝜟𝜟 + 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝒌𝒌 (5)

18

is the angular velocity of the xyz system as its origin moves with unit velocity along the wire axis; it differs from the Frenet vector by torsional twist. In the xyz system

kjiω λκκ ++= yx (6)

where

𝜅𝜅𝑥𝑥 = −𝜅𝜅 cos 𝑑𝑑 (7a)

𝜅𝜅𝑦𝑦 = 𝜅𝜅 sin 𝑑𝑑 (7b)

are the curvatures around x and y directions, and

𝜆𝜆 = 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

+ 𝜏𝜏 (8)

is the total twist with first term showing the torsional and the second the geometric twist. Also relations between geometric quantities are needed, i.e., between curvatures and twist of wire axis, before and after the loading.

Let 𝒊𝒊𝟎𝟎, 𝒋𝒋𝟎𝟎, 𝒌𝒌𝟎𝟎 denote the base vectors attached to a point on the wire axis before the deformation as explained before. After the deformation, the point moves to a new location and base vectors change to 𝒊𝒊 , 𝒋𝒋 , 𝒌𝒌 . The deformation vector is denoted as

𝐔𝐔 = 𝑈𝑈𝒊𝒊0 + 𝑉𝑉𝒋𝒋0 + 𝑊𝑊𝒌𝒌0 (9)

The point, initially located at 𝑹𝑹, moves to

URr += (10)

Differentiating this expression with respect to the arclength

𝑘𝑘 = 𝑘𝑘0 + 𝑑𝑑𝑼𝑼𝑑𝑑𝑑𝑑

(11)

where k r /d ds= , 0k R /d ds= . Since the bar is assumed to be unextended, it does not matter what arclength is meant by s. The relation between the base vectors of undeformed and deformed coordinate systems is written as

000 kjii 111 NML ++= (12a)

000 kjij 222 NML ++= (12b)

000 kjik 333 NML ++= (12c)

We find, from Eq. (12c),

𝐿𝐿3 = 𝑑𝑑𝑈𝑈𝑑𝑑𝑑𝑑− 𝜏𝜏0 𝑉𝑉 + 𝜅𝜅𝑦𝑦0 𝑊𝑊 (13a)

𝑀𝑀3 = 𝑑𝑑𝑉𝑉𝑑𝑑𝑑𝑑− 𝜅𝜅𝑥𝑥0 𝑊𝑊 + 𝜏𝜏0 𝑈𝑈 (13b)

𝑁𝑁3 = 1 + 𝑑𝑑𝑊𝑊𝑑𝑑𝑑𝑑− 𝜅𝜅𝑦𝑦0 𝑈𝑈 + 𝜅𝜅𝑥𝑥0 𝑉𝑉 (13c)

𝐿𝐿3 and 𝑀𝑀3 are ( )O U (assuming deformation and

deformation gradient are of the same small order) while 𝑵𝑵𝟑𝟑

is 𝑂𝑂(1). Since 2 2 2 2

3 3 3k 1L M N= + + = , substituting

from Eq. (A.16) and ignoring ( )O U terms,

13 =N (14)

and to ( u )O ,

𝑑𝑑𝑊𝑊𝑑𝑑𝑑𝑑− 𝜅𝜅𝑦𝑦0 𝑈𝑈 + 𝜅𝜅𝑥𝑥0 𝑉𝑉 = 0 (15)

which expresses that the wire axis is not extended. Thus, we have found how the tangent to the wire axis changes

( )0k k→ expressed in Eqs. (13a), (13b) and Eq. (14). To complete the transformation, we need another parameter. Love [1] takes the angle between x axes before and after the deformation and denotes the sine of this angle as , i.e.,

𝑀𝑀1 = 𝛽𝛽 (16)

The other entries in the transformation matrix Eq. (12) are found by requiring that the matrix is orthonormal; ignoring nonlinear terms,

11 =L (17a)

31 LN −= (17b)

𝐿𝐿2 = −𝛽𝛽 (17c)

12 =M (17d)

32 MN −= (17e)

Therefore, the complete transformation of base vectors during deformation is given in terms of u, v, w, 𝛽𝛽 as

𝑖𝑖 = 𝑖𝑖0 + 𝛽𝛽 𝑗𝑗0 − 𝐿𝐿3𝑘𝑘0 (18a)

𝑗𝑗 = 𝛽𝛽 𝑖𝑖0 + 𝑗𝑗0 −𝑀𝑀3𝑘𝑘0 (18b)

𝑘𝑘 = 𝐿𝐿3𝑖𝑖0 + 𝑀𝑀3𝑗𝑗0 − 𝑘𝑘0 (18c)

where 𝐿𝐿3 and 𝑀𝑀3 are given by Eqs. (13a) - (13b).

Using these in Eq. (4) we find the relations between curvatures and twist before and after the deformation:

𝜅𝜅𝑥𝑥 = 𝜅𝜅𝑥𝑥0 + 𝜅𝜅𝑦𝑦0 𝛽𝛽 − 𝑑𝑑 𝑀𝑀3𝑑𝑑𝑑𝑑

− 𝜏𝜏0𝐿𝐿3 (19a)

𝜅𝜅𝑦𝑦 = 𝜅𝜅𝑦𝑦0 − 𝜅𝜅𝑥𝑥0 𝛽𝛽 − 𝑑𝑑 𝐿𝐿3𝑑𝑑𝑑𝑑

− 𝜏𝜏0𝑀𝑀3 (19b)

𝜏𝜏 = 𝜏𝜏0 + 𝑑𝑑 Ɓ𝑑𝑑𝑑𝑑− 𝜅𝜅𝑥𝑥0𝐿𝐿3 − 𝜅𝜅𝑦𝑦0𝑀𝑀3 (19c)

3.Conclusion The equations of motion for an arbitrary three

dimensional beam, including bending-torsion coupling were derived.

4.References [1]Love,A.E.H., 1944. A Treatise On the Mathematical

Theory of Elasticity, Dover Publications, New York.

[2] Alfred Clebsch , 1862 (B. G. Teubner, 1862).Theorie der Elasticitat fester Körper, Leipzig,

19

VIRTUAL MODELING AND SIMULATION OF A CYLINDER BUNDLE VERTICAL AND ROTATIONAL DROP

Ass. Prof. Aleksandar Kostikj PhD, Prof. Milan Kjosevski PhD

Faculty of Mechanical Engineering, Ss. Cyril and Methodius University in Skopje, Republic of Macedonia

[email protected]

Abstract: A cylinder bundle is a portable assembly which consists of a frame and two or more cylinders, each of a capacity up to 150 l and with a combined capacity of not more than 3000 l, or 1000 l in the case of toxic gases, connected to a manifold by cylinder valves or fittings such that the cylinders are filled, transported and emptied without disassembly. The type approval of the cylinder bundle covers series of tests regarding its structure and its behavior during and after the tests. The research, presented in this paper, is focused on virtual testing, i.e. modeling and simulation of a cylinder bundle drop tests. First, a CAD model of a cylinder bundle which contains five cylinders is built, and then a vertical and rotational drop tests are simulated in virtual environment. The obtained results are analyzed in line with the demands defined in the international standard ISO 10961:2010(E).They could serve as a base for further improvement of the model and point out the possibility for validation of the virtual testing.

Keywords: CYLINDER BUNDLE, VIRTUAL MODEL, VIRTUAL TESTING, DROP TESTS

1. Introduction Cylinder bundles are portable assemblies which are widely used

for transport and storage of gases on sites, where the gases are further used. According to the international standard ISO 10961:2010(E), a cylinder bundle is a portable assembly which consists of a frame and two or more cylinders, each of a capacity up to 150 l and with a combined capacity of not more than 3000 l, or 1000 l in the case of toxic gases, connected to a manifold by cylinder valves or fittings such that the cylinders are filled, transported and emptied without disassembly. The exploitation of a cylinder bundle is preconditioned with its type approval. The type approval itself covers series of tests regarding the structure of the cylinder bundle and its behavior during and after the tests. The most demanding tests are the vertical drop test and the rotational drop test as defined in the international standard ISO 10961:2010(E) [7]. These tests have the following pass criteria: the primary frame structure shall not fail such that subsequent movement by fork-lift truck or slinging is not possible; the cylinders and manifolds shall remain constrained in the frame, though deformation of components is acceptable; the bundle shall not leak.

The research, presented in this paper, is focused on virtual testing [1, 2, 4, 5, 7] regarding the above mentioned tests. They are conducted on a model of a cylinder bundle which was already produced. The bundle contained five Vitkovice cylinders 690/150, intended for carriage of high pressurized gas (over 200 bar). The produced cylinder bundle is presented on fig. 1.

Fig. 1 Produced cylinder bundle

The model of the bundle is built in a CAD software package [6]. It is a relevant representative of the real bundle. The virtual model is presented on fig. 2.

Fig. 2 Virtual model of the cylinder bundle

The remainder of the paper is organized as follows: The virtual modeling and simulation of the cylinder bundle vertical drop test are presented in section 2. Section 3 presents the virtual modeling and simulation of the cylinder bundle rotational drop test. Finally the conclusions are laid down in section 4.

2. Virtual modeling and simulation of the cylinder bundle vertical drop test

The procedure of the vertical drop test prescribes that the bundle is dropped at a height of 100mm on a concrete surface. Also, the initial inclination of the bundle towards the surface should be at last 5˚.

The initial setup of the virtual testing is in line with the requirements defined in point 7.2.2.3.4 of the international standard ISO 10961:2010(E) [7]. The model is set on a height of 100mm from concrete surface and the initial inclination of the bundle towards the surface is set on 10˚ (fig. 3.).

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Fig. 3 Initial setup of the vertical drop test simulation

The virtual vertical drop test is conducted with two consecutive and connected simulations-analyses [3]. The first one is a transient structural analysis. It treats the free fall of the bundle till the impact with the concrete surface. The free fall lasts for 0.143s. The position of the bundle at different time moments is presented on fig. 4, fig. 5 and fig. 6. The second simulation is an explicit dynamics analysis. This simulation treats the impact of the bundle with the concrete surface and lasts for 30ms. The stress condition of the bundle is stable after this time period. The equivalent stresses which appear in the bundle at different time moments of the explicit dynamics analysis are presented on fig. 7, fig. 8 and fig. 9.

Fig. 4 Position of the bundle at time t=0.02s



Fig. 7 Equivalent stresses in the bundle at time t=0.0051s



21

The explicit dynamics analysis shows that the stresses in the bundle, which appear during the impact, are below the ultimate stress of the material. The maximum stress appears in the vertical beams of the bundle, in the impact zone. Its range is about 440N/mm2. The plastic deformations of the bundle during the impact are below 8.1% of the size of the model’s final elements.

Based on the results of the performed combined analyses it can be concluded that the bundle satisfies the requirements as defined in point 7.2.2.3.4 of the international standard ISO 10961:2010(E)[7], regarding the vertical drop test.

3. Virtual modeling and simulation of the cylinder bundle rotational drop test

The procedure of the rotational drop test prescribes that the bundle falls from a platform on a concrete surface. The platform has a minimal height of 1200mm. During the fall, the bundle rotates about point 2 (fig. 10).

Fig. 10 Rotation drop test – procedure (1 – platform, 2 – rotational point of the bundle, 3 – concrete surface)

The initial setup of the model, regarding the rotational drop virtual testing, is in line with the requirements defined in point 7.2.2.3.4 of the international standard ISO 10961:2010(E)[7]. The model is set on a height of 1200mm from concrete surface and the initial inclination of the bundle towards the surface is set on 35˚ (fig. 11.). This inclination is defined according to the bundle’s center of gravity and ensures rotational free fall of the bundle.

Fig. 11 Initial setup of the rotational drop test simulation

The rotational drop test alike the vertical drop test is conducted with two consecutive and connected simulations-analyses [3]. The first one is a transient structural analysis. It treats the rotational free fall of the bundle till the impact with the concrete surface. This free fall lasts for 1.318s. The position of the bundle at different time moments is presented on fig. 12, fig. 13 and fig. 14. The second simulation is an explicit dynamics analysis. This simulation treats the impact of the bundle with the concrete surface and lasts for 175ms. Within this time interval, the bundle has complete translational and rotational freedom. The time span of explicit dynamics analysis is sufficient to cover the dominant dynamics of the impact. The equivalent stresses which appear in the bundle at different time moments of the explicit dynamics analysis are presented on fig. 15, fig. 16 and fig. 17.



Fig.14 Position of the bundle at time t=1.318s


22



The explicit dynamics analysis points out that the total deformations during the impact jeopardize the space where the cylinder valves and the manifold are mounted (fig. 18). As a result, the valves and the manifold could be damaged and a gas leakage could appear.

Fig. 18 Space where the cylinder valves and the manifold are mounted at time t=0.175s of the explicit dynamics analysis

The equivalent stresses which appear in some segments of the bundle are over the ultimate stress of the material. The range of the maximal stresses at the end of the analysis is about 3000 N/mm2.

The maximal stresses, which appear in the vertical beams of the bundle, range between 417.34 N/mm2 and 614.46 N/mm2. Despite these high values, the maximal plastic deformations range between 10.27% and 20.989% of the size of the part’s final elements. These results show that during the impact there is no failure in the vertical beams structure, but on the other hand there is a failure in the connections between the front left beam, the upper rectangular frame and the middle side plate (fig. 19). This could lead to

significant cylinder movement, gas leakage and exclusion of the possibility for subsequent movement of the bundle by fork-lift truck or slinging.

Fig. 19 Failure of the front left beam connections

The impact of the bundle brings up to tearing of the pre-tensioning bolts or failure of the connection between the bolts and the pipes that secure the cylinders (fig. 20). The equivalent stresses in the bolts range up to 700 N/mm2 and the plastic deformations range up to 57% of the size of the part’s final elements.

Fig. 20 Plastic deformations of the front bolts and pipe

The highest equivalent stresses appear in the middle frame of the bundle in the areas where the cylinders lean on the frame. Their range in these areas is between 700 N/mm2 and 1100 N/mm2. The maximal equivalent stress is 3075.5 N/mm2. The range of the plastic deformations is between 50% and 82% of the size of the appropriate final elements. The maximal plastic deformation is 195.27% of the size of the appropriate final element. These results imply on crush of the middle frame in the areas where the cylinders lean on (fig. 21).

Fig. 21 Plastic deformations of the middle frame of the bundle

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The results of the performed analyses point out that the bundle does not satisfy the requirements as defined in point 7.2.2.3.4 of the international standard ISO 10961:2010(E), regarding the rotational drop test.

4. Conclusion The research presented in this paper produced numerous results

which serve as a base for the following conclusions. At this stage, without validation, the developed virtual model of the cylinder bundle can be used only in preliminary structural and dynamics simulations. The real cylinder bundle would satisfy the requirements as defined in point 7.2.2.3.4 of the international standard ISO 10961:2010(E), regarding the vertical drop test. Despite this, the real cylinder bundle would not satisfy the requirements as defined in point 7.2.2.3.4 of the international standard ISO 10961:2010(E), regarding the rotational drop test. Also, the results of the virtual testing pointed out the possible weaknesses of the structure of the bundle. They can serve as a base for further improvement of the model and ultimately of the real bundle too. The experimental tests of the real bundle should be conducted only after the model passes the virtual testing. This methodology saves time and resources. The results of the experimental tests could be further used in the validation process of the model and most important in the validation process of the virtual testing.

5. References [1] American Society of Mechanical Engineers (2006). “Guide for

Verification and Validation in Computational Solid Mechanics”, 2006. Standards Committee on Verification and Validation in Computational Solid Mechanics (PTC 60/V&10).

[2] Andre Eggers, Holger Schwedhelm, Oliver Zander, Roberto Cordero Izquierdo, Jesus Angel Garcia Polanco, John Paralikas, Konstantinos Georgoulias, George Chryssolouris, Dominic Seibert, Christophe Jacob, “Virtual Testing based Type Approval Procedures for the Assessment of Pedestrian Protection developed within the EU-Project IMVITER”, The 23rd International Technical Conference on the Enhanced Safety of Vehicles (ESV) Seoul, Republic of Korea, May 27-30, 2013.

[3] ANSYS Inc., Release 15.0, “ANSYS Mechanical User's Guide”, Southpointe 275 Technology Drive Canonsburg, USA, 2013.

[4] COMMISSION REGULATION (EU) No 371/2010 of 16 April 2010, replacing Annexes V, X, XV and XVI to Directive 2007/46/EC (Framework Directive).

[5] COMMISSION REGULATION (EC) No 631/2009 of 22 July 2009 laying down detailed rules for the implementation of Annex I to Regulation (EC) No 78/2009 of the European Parliament and of the Council on the type-approval of motor vehicles with regard to the protection of pedestrians and other vulnerable road users, amending Directive 2007/46/EC and repealing Directives 2003/102/EC and 2005/66/EC.

[6] Curtis Waguespack, “Mastering Autodesk Inventor 2014 and Autodesk Inventor LT 2014”, John Wiley & Sons, Inc., 2013.

[7] International standard ISO 10961:2010(E), Gas cylinders - Cylinder bundles - Design, manufacture, testing and inspection, Second edition, 2010-10-15.

24

РЕЛАТИВНО ИЗНОСВАНЕ НА ЛИФТЕРИ

INNOVATIVE RELATIVE WEAR OF LIFTERS

Стоименов Н. Институт по Информационни и Комуникационни Технологии, БАН, София, България

e-mail: [email protected]

Резюме: В настоящата статия са разгледани лифтери и нуждите от тях. Обърнато е внимание на релативното износване на лифтер с мелещи тела. Процесът е симулиран и моделиран в софтеур, работещ по метода на дискретните елементи (Discrete Element Method). Получените данни от симулацията са анализирани и сравнени със данни от друга симулация с друг тип лифтер.

Key words: лифтери, мелници, смилане, симулация.

1. Въведение В съвременните производствени условия топковите

мелници са един широк клас от машини, предназначени за раздробяване, смилане и/или смесване на материали, като за целта се използват метални или друг вид сферични тела, така наречената работна (мелеща) среда. В конструктивно отношение топковата мелница представлява относително просто устройство с проста конструкция, но за разлика от конструкцията има сложния характер на работния процес.

Топковата мелница представлява цилиндричен съд, монтиран върху фундамент, който позволява осъществяването на въртеливо движение на барабана посредством задвижване от електрически двигател със съответна трансмисия. Смилането и натрошаване на материали се осъществява най-често при топкови мелници. Най-разпространените топкови мелници са полу-автогенни или автогенни.

Най-често тези мелници се използват за процеси при обогатяването на руди, натрошаването и смилането на материали. Натрошаването и смилането се осъществява с помощта мелещи тела и на лифтери (облицовъчни плочи), които също са подложени на агресивна работа среда, освен самите мелещи тела. Този процес е изключително енергоемък (световно около 20% от енергията се използва за този процес). Поради тази причина е силно изследван. От голямо значение е правилното функциониране на мелницата, мелещите тела, лифтерите, оборотите и други фактори за постигане на добра работа и висока производителност[1-3].

Целта на настоящата статия е да се изследва относителното износване на лифтери.

2. Анализ на процеса Процесът на смилане при този тип мелници може да бъде

разгледан като процес на повишаване на сумарната площ на смилаемия материал. Повечето мелници са разделени на два стадия (грубо, и фино смилане на материал) като в повечето случаи има решетка между двата стадия на мелницата с определени отвори. Това е с цел да се осъществи преминаване само на частиците, които са смлени за следващ етап. Смилането се осъществява както с мелещи тела, така и с лифтери. Мелещите тела най-често са сферични стоманени топки с различни размери.

Процесът може да бъде осъществен при различни режими на работа на топковите мелници. Най-разпространените режими са каскаден, водопаден, центрофугиране (режим, който е изключително енергоемък и с повишено износване на мелещата среда) и др.

При лифтерите за по-грубото смилане се използват по-големи (фиг. 1), а за по-финото смилане по-малки, показани на фиг. 2. Лифтерите са разположени по вътрешната част на мелницата, като имат за цел при въртеливото движение на мелницата да спомагат за повдигането на материала и

мелещите тела до по-високи нива, за да се осъществи по-качествено смилане. От друга страна, лифтерите служат и за предпазване на вътрешната част на мелницата. Броят, размерите и самата форма също са от съществено влияние за производителността [2-4].

Основните параметри за производителност на топковите мелници са:

• Размери на мелницата – дължина и диаметър; • Тип на мелницата – преливен или диафрагмен; • Скорост на въртене; • Обем на товара; • Размери на частиците на входния материал и на

изходния продукт; • Работен индекс на материала; • Мощност на вала на мелницата; • Плътност на мелещите тела.

Фиг. 1. Лифтери [5].

Фиг. 2. Различни профили на лифтери [3].

3. Методика за симулация на износоустойчивост.

За изследване износоустойчивостта на лифтери, чрез симулационно моделиране със специализиран софтуер, работещ по метода на дискретните елементи е необходимо да се извършат последователно следните задачи:

25

1. Запознаване с нуждата от симулация и очакваните резултати и изходни данни.

2. Подбиране на подходящ модел (Hertz-Mindlin (no slip), Hertz-Mindlin (no slip) with RVD Rolling Friction, Hertz-Mindlin with JKR, Hertz-Mindlin with bonding, Hertz-Mindlin with heat conduction, Hysteretic Spring, Linear Cohesion, Linear Spring), по който ще се осъществи симулацията.

3. Задаване и определяне на нужните връзки между частици и геометрия.

4. Задаване на гравитация. 5. Задаване на материали на мелещи тела и геометрия. 6. Задаване свойства на материалите. 7. Задаване на връзки между различните материали. 8. Моделиране на 3D геометрични модели, необходими

за симулацията и определяне тяхните размери. 9. Вмъкване на 3D модели. 10. Задаване на динамични характеристики (в

конкретният случай - линейна ротация). Задаване на продължителност на действието.

11. Определяне посоката на действие по оси Х, Y, Z. 12. Определяне на необходимият брой частици, времето

за което ще се осъществи генерирането им, маса, брой. Време от което ще започнат да се генерират.

13. Задаване на параметри на частиците като тип, размер, позиция, скорости, ориентация, ъглова скорост и др.

14. Задълбочено анализиране на осъществената симулацията.

15. Експортиране на изходни данни от симулацията като скорости, ускорения, връзки, взаимодействия, сили и др.

Изпълнението и определянето на поставените задачи е персонално за всеки тип симулация. Горепосочените задачи са ключовите, от които следва разширяване на някои методи и създаване на нови.

4. Моделиране и симулиране на процеса. Прилагането на метода на дискретните елементи при

симулирането на процеса на работа на топкови мелници, както и изследването на техните режимите на работа позволява използването на EDEM Software. Софтуера има възможност за симулиране повърхнини и материали с различни коефициенти и свойства, позволява изследването на частици с различни геометрични форми, взаимодействията между тях, както и потока им. При подходящи параметри и оптимизации позволява симулирането на движението на голям брой частици. Друга интересна опция на този софтуер е отчитането на относителното износване на геометрията.

За симулирането е използван модел на лабораторна топкова мелница със следните размери: вътрешен диаметър D=305mm и дължина от L=305mm. Тази мелница максимално се доближава до габаритите на мелница на БОНД. Конструкцията на барабанната топкова мелница представляват три камерна конструкция с различна ширина – 150, 100 и 50mm. Страничните капаци са прозрачни, това позволява наблюдаване на различните режими на смилане. Мелницата има възможност за добавяне на лифтери, като техният брой е до 24. За случая на симулацията са използвани 12 лифтера.

На фиг. 3 е показана вътрешността на мелницата, като моделът е конструиран така, че да позволява бърза смяна на лифтерите с цел изследване на различни варианти. В случаят 3D модела е моделиран на три части – барабан, капаци и лифтери. На фиг. 4 а) са показани използваните лифтери в тази симулация. Лифтерите представляват цилиндрични пръти. Данните от симулацията ще бъдат сравнени със предишна симулации от иновативна форма лифтери. Иновативната форма се състои от глава, която представлява триъгълник със

сфероидални страни и заострен връх, тяло и основа (фиг. 4б). [6]

Фиг. 3. Моделирана топкова мелница.

а) Лифтери на лабораторната мелница.

б) Иновативна форма лифтер.

Фиг. 4. Лифтери на лабораторна мелница – а) тип на наличните лифтери от лабораторната мелница; б) иновативна форма на лифтер.

Относителното износване е отчетено като идентифициране на региони с повишена степен на износване на моделираните обекти. Изчислението се осъществява на относителната скорост и свързаните с тях сили между оборудването и мелещите тела. Чрез използването на този модел се получават данни, като се локализират регионите, където износването оказва влияние. Този метод осигурява количествени стойности

26

за сравнение между проектни взаимодействия, не може да определи като процент отнемането на материал [7, 8].

5. Анализ на получените резултати Данните получени от софтуера индексират равномерно

износване на лифтерите и повишено износване на областите между тях. Повишено износване се наблюдава в момента на генериране на мелещите тела, при първоначалния им контакт с вътрешността на мелницата, показано на фиг. 5.

Фиг. 5. Относително износване в начабото на симулацията.

Също така получената енергия от мелещите тела по мелницата в този момент на симулацията е 0,035J, която е по-малка от получената енергия при симулацията с иновативния вид лифтер, показана на фиг. 6 [9].

Фиг. 6. Относително износване в начабото на симулацията на нов тип лифтер.

Тази разлика при енергията може да бъде обяснена с формата на лифтера, като иновативната има за цел да разтрошава материалите по-агресивно, с цел намаляване времето за смилане.

Получената графика, показана на фиг. 7 от потенциална енергия при тази симулация също отчита завишени стойности в началото, където се осъществява първоначалия контакт с мелещите тела.

В краят на симулацията се наблюдава равномерно относително износване както на лифтерите, така и на вътрешността на мелницата, показано на фиг. 8. При този тип лифтери и тук енергията остава по-малка, сравнение с тази на иновативната форма.

Фиг. 7. Графика потенциална енергия.

Фиг. 8. Относително износване в края на симулацията.

6. Заключение От направената симулация се наблюдава повишено

износване в началото на симулацията. Това се дължи от височината на падане на мелещите тела.

При сравнението на лифтерите от лабораторната мелница и иновативната форма, се наблюдават по-завишени сили и енергии в полза на иновативната форма. Това се обяснява именно с ръбът, който служи за разтрошаване на частиците. От друга страна това означава по-бързо износване на лифтерите. Разглежда се възможността за прилагане на високотемпературни процеси с цел уякчаване на този ръб.

Симулацията позволява бързи промени на лифтерите, като по този начин могат да се търсят по-добри варианти за брой, големина и форма на лифтерите.

От направените симулации става ясно, че ако изсипването на материали за смилане и мелещи тела се осъществява възможно най-близо до вътрешният корпус на мелницата, това би спомогнало за запазване на вътрешността на мелницата. По този начин ще се повиши експлоатационноста и ще се намалят ремонтите и времената за ремонт на вътрешността на мелниците.

Благодарности Изследването в настоящата статия е осъществено с

подкрепата на проект “Изследване и оптимизация на процеси за смилане чрез иновативни форми на мелещи тела и среди.”, договор ДФНП-96/04.05.2016, финансиран от Българска Академия на Науките, програма за подпомагане на млади учени.

27

Литература 1. Жълтов А., Машини за строителни материали, София, Техника,

1980, 104-122 2. Денев С. Трошене смилане и пресяване на полезни изкопаеми,

София, Техника, 1964, 141-161 3. Цветков Х., Обогатителни машини, ДИ „Техника“, С., 1988г.,

229-252 4. D. Karastoyanov, M. Mihov, B. Sokolov., Optimization of the

Control System by Milling Processes., John Atanasoff Celebration Days, International Conference “Robotics, Automation and Mechatronics” RAM 2012, Sofia, 15-17 October 2012, ISSN 1314-4634

5. Timm D., HIRSCHI N., Moir T., Ecoff B., “MILL LINNER FOR A GRINDING MILL” Pub.No.: WO2011/037600 A1, Pub. Date: March 31, 2011

6. Карастоянов Д., Н. Стоименов, ЛИФТЕР, Заявка за патент на България, Рег. №112174, приоритет от 14.12.2015

7. D. Karastoyanov, B. Popov., Innovative Technology for High Temperature Production of Materials and Alloys., Int. Conf. High Technologies, Business Community 2016, March 14-14 2016, Borovetz, Bulgaria, ISSN 1310-3945, pp. 16-19

8. EDEM Software Platform – www.dem-solutions.com 9. Стоименов Н., Съботинков Н., Соколов Б., Изследване

износоустойчивостта на лифтери с EDEM Софтуер., International Conference Robotics, Automation and Mechatronics’16 RAM 2016, Byaga, Bulgaria, October 3-4, 2016, стр. 70-73, ISSN 1314-4634.

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http://www.dem-solutions.com/

COMPARISON OF NUMERICAL AND EXPERIMENTAL RESULTS OF STRESS-DEFORMATION STATE IN A PIPELINE BRANCH

Prof. dr Bajić D. PhD1, M.Sc. Ćulafić S.1 Faculty of Mechanical Engineering – University of Montenegro, Montenegro 1

[email protected]

Abstract: The subject of this paper is the analysis of stress distribution of the pipeline branch in hydropower. Pipe branches are widely used and very in complexity of the shape. Behaviour of the pipe branch subjected to the internal pressure was analyzed both numerically and experimentally. Analytical stress calculations are limited on the simpler forms of branches, so numerical calculations had to be used. Focus of numerical analysis was on determining critical locations and its values. Strain gauge method was used to measure greatest stress concentrations on the defined locations. Experimental results were very close to numerical calculations. Material used for manufacture of the pipeline branch is NIOVAL 47. This paper can be used as the base for the future researches concerning stress distribution in other branches among the pipeline both numerically and experimentally.

Keywords: strain gauges, pipeline branch, stress concentration factor, finite element method, numerical calculation

1. Introduction Reason for the detailed research of the A6 (Figure 1.) branch on

the C3 pipeline in the HP Perucica lies in the necesity of adding one generator and thus to increase the production capabilities of HP. It is necessary, among other, to perform detailed stress analysis, so the further activities can be planed. Installation of the generator would increase dynamic loads of the branch. This is why it is useful to have real image of the branch loads in static conditions, so it could be verified through the detailed calculation of dynamic loads if there is space for generator implementation.

Fig. 1 Branch A6 after reconstruction

Pipeline branch geometry is basically very complex as seen in Figure 2. This means that on the local level, on the some places of the branch, big geometric irregularities can be noticed. In places of branch geometric irregularities, when certain geometric values, which define branch geometry, suddenly change, also the values of the stress in the branch material changes.

Changing the internal pressure of the pipeline and branch, on the places of geometric irregularities stress values can't be controlled with known theoretical processes of the stress analysis. So, it is very important to try to define stress concentration factor.

Topic of this paper is the analysis of stress distribution of pipeline branch subjected to internal pressure.

Various analysis have to be performed in order to validate the integrity of real structures. These analysis depend on the criticality, loads, and geometry. In the case of branch designing many factors such as: branch shape, manufacturing materials, stress calculation etc., have to be considered. Stress calculation is possible only in the domain of the regular geometric shapes, and is defined by standards for pressure vessels.

Many engineers use various software packages for calculations based on finite element method. Paper [2] showed it was possible to easily implement elastic compensation method to any Finite Element Code in order to enable simpler determination of limit loads in complex structures. In papers [3] and [4], the authors

studied limit load solutions for branch connections (with straight branch to run angles) under different loads. In paper [5], static finite element method is performed for analysis of piping system and the pipe branch in order to determine extreme stress values. The most loaded parts of the pipe branch were analyzed by experimental tensometric method. This way, by combining numerical and experimental analysis, it was possible to obtain stress distribution of the whole pipeline. By analyzing obtained stress values, it was possible to evaluate stress concentration factor for the pipe branch model, which can be applied on the structures with similar geometry[1].

2. Finite element method Special attention during the preparation of this paper was

devoted to the analysis of branch with finite element method. From the accuracy of obtained data depends whether it can be expected that the real branch can be credibly displayed in the commercial software. This question has been raised because of the complexity of the geometry, irregularities and stress concentration, incomplete technical documentation, etc. If the comparative analysis of the obtained data show that the geometric model of real branch is acceptable, then it can be an important incentive for further research, because it does not have to be conducted on a real branch but can be used for the geometric model. Due to the size and inaccessible terrain on which branch is this may represent a significant contribution in the future. Branch A6 is made of a material Nioval 47. Basic dimensions of the branch at the entrance is D1 = 2500 mm, while the diameter of the branches at the exit: D2 = 2250 mm. Branch length L = 4300 mm, while the thickness is s = 36 mm. There are segments of the branch with thickness of 50mm, and for these segments are welded so called branch collars.

Fig. 2 Branch A6 tecnical documentation

Based on earlier researches [1] critical spots on the branch model are defined and experimental and numerical calculation of stresses in critical points (measured points) are conducted. Using the similarity, applied to pipelines under pressure when bending stresses are considered small, thus losing the non-linearity of the problem, it is possible to assume that the stresses at critical points are to be about the same on a real branch and branch model, if the

aa

aa a

ab b b b

d d

b b

bb

b

b

bb

gg

cc

e e

a a

aa

aa

ff

5

68

7

10

9

11

12 13

3

2

1

4

Ø250

036

50

36

36

Ø235

036

50 36

29

conditions of boiler formula are satisfied when creating branch model.

Fig. 3 FEM model of the branch

Geometrical modeling and stress deformation analysis is preformed using AUTODESK INVENTOR 2012 as FEM software.

Fig. 4 Critical strip of FEM branch model pressure 20 bars

Reviewing results of the analysis preented in the Figures 4, 5, 7, 8, it can be concluded that the biggest Von Misses stresses of branch apears in the area next to branch collar. Von Misses stresses are given in the table 1.


Fig. 6 Anchor of FEM branch model

Table 1: VonMisses stresses values for MP1

Pressure values [bar]

Maximum stress values for MP1 [MPa]

20 111

50 234

84 458


The results of numerical analysis of real branches shows that critical zones, when stress value is concerned, are exactly as the points obtained by branch model analysis [1] (with smaller geometry) both experimental and numerical method. This leads to the conclusion that the tests can be based on numerical methods and analysis models, without the necessary tests of the branch in real conditions. Dominant loads in all the tests that were performed figure as loads of stretching the material, which leads to the appearance of cracks in critical areas. This is also confirmed by the linear dependence of the critical stress loads, which means that bending loads of branch are not dominant.


3. Experimental measuring Experimental research on the branch model (Figures 9, 10, 11)

were conducted in order to verify the assumption that the real branch is possible to replace in analasys with the branch model. This can be carried out in strict compliance with the conditions defined by the boiler formula. Calculation of stresses in the branch structure analytically is possible and correct only on the cylindrical part of branch excluding stiffeners, ribs and holes. This calculation is defined also with the standards for pressure vessels. The formula by which calculationes of the stress is carried out in this case is called the boiler formula.

Boiler formula for calculating stresses on the cilinder loaded with internal pressure without ribs and holes is:

- cilinder circumferential direction tRpo ⋅

=σ

30

- cilinder longitudinal direction tRpp

⋅⋅

=2

σ

where: p [bar]- fluid internal pressure,

R [mm]- cilinder radius,

t [mm]- cilinder thickness.

From previous equations it can be seen that values of stress in circumferential direction twice bigger from the values in the longitudinal direction - po σσ 2= .

Fig. 9 Branch model with strain gauges

Branch model should give same stress as real branch. This is secured with the similarity method as follows:

elamod

elamodelamodo

tRp

t

Rp

tRp ⋅

=

⋅=

⋅=

10

52σ

Obtaining the values of the same stress is secured as follows:

2pp elamod =

5RR elamod =

10tt elamod =

Real branch: p = 50 bar, R = 1250 mm, t = 36 mm, σo = 174

MPa.

Branch model: p = 25 bar, R = 250 mm, t = 4 mm, σo = 156 MPa.

Fig. 10 Branch model in laboratory

This means that the branch modelfor twice the value of the pressure has twice the value of circumferential stress, or that branch model should be loaded with twice as less pressure to be correlated with the real branch. For creation and load of the model following relations are adopted. Since there was no sheet thickness of 3.6 mm, it was necessary to apply a sheet thickness of 4 mm. In this way, a smaller stress is obtained in the sheets of the newly selected thickness by about 10%. The stress on the anchor (ellipse) is same in the model and the real branch since the thickness are of 8 mm and 80 mm. Similarities method we could apply to this branch model, because in its structure there is very little presence of bending stresses which depend on the square of the material thickness (t2). Based on the reading of all the diagrams stress value is defined at all measurement locations for the pressure of 10 bar and they are given in table 2:

Table 2: Measuring results

Pres

sure

[bar

s]

Stress[kN/cm2] - Measuring point

MP1 MP2 MP3 MP4 MP5 MP6 MP7 MP8

10 11 7.5 5 - 1 0.5 4 3.3

Fig. 11 Measuring equipment

Stress values at any pressure until the limit of the strength of material is obtained in the way that values from the table are multiplied with the ratio of the desireable pressure and pressure of 10 bars. Research pressure is adopted as twice smaller than real branch exploatation pressure and limit of the materials strenght of branch model is S355J2+N (Č.0563) 36 KN/cm2 (KN/cm2=10MPa).

4. Discussion of the results Based on the previously presented data in the previous sections

of this paper, it is possible to reach the following conclusions:

Table 3: Comparison of obtained values

Measuring point No: M

P1

MP2

MP3

MP4

MP5

MP6

MP7

MP8

Experimental [MPa]

110 75 50 - 10 - 40 33

FEM branch model [MPa]

107 84 63 - 11 - 45 31

FEM real branch [MPA]

111 86 73 - 13 - 47 31

Places that includes a narrow strip at the junction of the anchor and pipe are recognized as places with a maximum intensity of stresses. This is confirmed by numerical analysis of branch model, and the real branch, and also at experimental measurments on the branch model which can be seen in the fugures.

Comparative results of all three studies are given in Table 3. The coincidence of the critical stress intensity in numerical analysis on the real branch A6 with the results obtained at experimental branch model analysis thus justifying the application of the boiler formula, based on which is shown geometrical similarity between the model and the real branch. As stated before, this similarity enables proper application of the proportionality of pressure to form the corresponding stresses, which are confirmed by numerical analysis of the branch model.

Analysis of the results presented in Table 3 leads to the conclusion that the results obtained by numerical methods correspond to the experimental measurements that were performed on the branch model.

31

5. Conclusions Following conclusions can be given:

• 3D model of the pipe branch was analyzed with finite element method. This allowed locating critical spots on the branch from the stress concentration point of view.

• Experimental measurements, conducted by the strain gauges, were compared to the numerical calculations. Locations with the greatest stress concentrations were determined. Numerical and experimental methods confirmed that plastic deformation would not occur on the pipe branch in the maximum regime of the hydropower's work.

• Numerical calculations of the branch can be compared with the numerical calculations of the branch model, and experimental results that were performed on the branch model.

The results presented in this paper could form the basis for future research. The fact that all tests on the branch can be replaced by tests on a branch model greatly facilitate future research and testing in the field of stress concentration, strains and deformations. Also, one of the aspects on which future research is based on that and all the other branches and critical points on the pipeline C3 in HP "Perucica" can be simulated in a similar manner. Through this work, among other things it is shown that whenever possible, especially in structures whose dimensions are large, the output should be sought in designing the model, which will faithfully reflect the behavior of the real object of research. Such a model, even analyzed through numerical methods, can be enough to pinpoint critical bands on which to focus in the research of the real object.

6. Literature [1] Bajic, D.; Momcilovic, N.; Maneski, T.; Balac, M.; Kozak,

D.; Culafic, S.: Numerical and Experimental Determination of Stress Concetration Factor for a Pipe Branch Model

[2] Plancq, D; Berton, M.N. Limit Analysis Based on Elastic Compensation Method of Branch Pipe Tee Connection Under Internal Pressure and Out - of - Plane Moment Loading. // International Journal of Pressure Vessels and Piping, 75(1998), pp. 819- 825.

[3] Kim, Y.J; Lee, K.H.; Park, C.Y. Limit Load for Piping Branch Junctions Under Internal Pressure and In - Plane Bending - Extended Solutions. // International Journal of Pressure Vessels and Piping, 85(2008), pp. 360- 367.

[4] Mkrtchyan, L. Scha, H. Hofer, D. Stress Indices for Branch Connections with Arbitrary Branch -To-Run Angles,// Transactions, SmiRT/ New Delhi, India, 21. November 2011, pp. 1-8.

[5] Jovanovic, M.; Milenkovic, D.; Petrovic, G.; Milic, P.; Milanovic, S. Theoretical and Experimental Analysis of Dynamic Processes of Pipe Branch for Supply Water to the Pelton Turbine. // Thermal Science, vol. 16, (2012), pp. S617-S629.

32

INFLUENCE OF TEMPERATURE ON DIELECTRIC BREAKDOWN OF WORKING FLUID VAPOR IN HEAT PIPE

M.Sc. Nemec P. PhD.1, Prof. RNDr. Malcho M. PhD.1, M. Sc. Palacka M. 1

Faculty of Mechanical Engineering – University of Zilina, the Slovak Republic 1

[email protected]

Abstract: The paper deal with heat pipe technology which is often used in electronic cooling from small voltage microchips to the high voltage electric elements. In case of cooling the high voltage electric elements have to be evaporator part and condenser part of heat pipe a separated by electrical nonconductive material, because the heat pipes are most often made of metallic materials, and thus, are electrically conductive. As a working fluids in this applications are used dielectric fluids such as fluorinert liquids. But there is still risk of the dielectric breakdown between evaporator and condenser of heat pipe. The task of the experiment is to find how the ambient temperature effect on dielectric breakdown of vapour phase of working fluid in heat pipe. In experiment was investigated dielectric breakdown between copper pipes inserted in to glass heat pipe in distance of 70 and 65 mm and temperature range -10 to -40°C. This distance simulate electric insulator distance of heat pipe used for real application of high voltage electric element cooling. For this experiment was used glass heat pipe with working fluid Fluorinert FC 72. The choice of this fluid is mainly due its excellent dielectric properties and unique combination of the thermodynamic and others properties, which makes the Fluorinert FC - 72 ideal fluid for electronic cooling used in many electronic applications.

Keywords: HEAT TRANSFER, ELECTRICITY, HEAT PIPE, DIELECTRIC BREAKDOWN

1. Introduction The cooling problems solution are currently still difficult,

especially when in cases of cooling the electrical and electronic equipment, because their size are still reducing, performance characteristics are still increasing so this create still more demanding requirements to cooling them and therefore are new types of the cooling possibility in electronic cooling still developing. The heat pipe technology seems to be a one from the new cooling possibility. The heat pipe technology is mainly used to heat removal from a heat sources where common cooling technologies cannot be used from various reasons (e.g. small space or difficult access) to the places, wherein the waste heat can be dissipated to surrounding. The heat pipes are develop with electronic devices developing and today are known many kinds with various shapes and design considering to the intended use [1].

The basic type of heat pipe is a hermetic sealed pipe with working medium inside (water, alcohol, freon, mercury, ammonia, helium, ethanol, toluene, sodium ...) at a given pressure. It is divided into three parts - evaporation, condensation and adiabatic (isothermal) part. The heat loaded to the evaporation section of the heat pipe causes the working medium in the liquid phase start evaporate due effects of increasing temperature at corresponding pressure. Vapor flows through the adiabatic part into the condensation part, where condenses to a liquid and release latent heat. Then the condensed liquid is returned to the evaporation part by gravity, capillary or centrifugal force, depending on heat pipe type. Thus is created a closed cycle flowing the working fluid in conjunction with the heat transfer. Since the heat pipe is mostly made from one piece of metal material, it becomes the good heat conductor as well as electrical conductor. If the heat pipe is used to heat remove from electric elements plugged to high electric voltage there is in case of electric short danger. If the evaporator is not electrically separated from the rest heat pipe parts by insulated material, the electric voltage can pass through the heat pipe container to the condensation part and this is undesirable in view of safety at work. In addition at heat pipes the electric voltage can pass through the working fluid. Therefore heat pipes used to heat remove from electric elements plugged to high electric voltage has evaporator separated from the rest parts by the insulator and as a working fluid are used dielectric substances. But there is still risk of the dielectric breakdown inside heat pipe container between evaporation and condensation part. This work deal about influence of ambient temperature and insulator length on dielectric breakdown through the vapor phase of working fluid inside heat pipe [2].

2. Working fluids selection This part deal about selection of the working fluid used for

experiment. There are described characteristics of various fluids commonly used in heat pipes for electronic cooling and compared its properties.

Selection of a suitable working fluid depends mainly on the type of application in which is used. In general, there are two cases, if the phase change in the application occur or does not.

Requirements that determine the intended use of the fluids:

1. Thermodynamic properties (density, pressure, specific heat capacity, thermal conductivity, latent heat of evaporation)

2. Physical properties (electrical properties, solubility in water and oils)

3. Chemical properties (flammability and explosiveness, stability, effects on construction materials and oil)

4. Physiological effects on the human body

5. Price

These requirements on substances potentially useful in application of cooling electrical and electronic equipment by heat pipes reduce substance selection to few substances with suitable parameters such as acetone, methanol, ethanol and fluorinert liquids.

Acetone

Acetone (systematically named propanone) is the organic compound with the formula (CH3)2CO. It is a colourless, volatile, flammable liquid, and is the simplest ketone. Acetone is miscible with water and serves as an important solvent in its own right, typically for cleaning purposes in the laboratory. It is a common building block in organic chemistry. Familiar household uses of acetone are as the active ingredient in nail polish remover and as paint thinner.

Acetone is produced directly or indirectly from propylene. Approximately 83% of acetone is produced via the cumene process as a result, acetone production is tied to phenol production. In the cumene process, benzene is alkylated with propylene to produce cumene, which is oxidized by air to produce phenol and acetone.

Acetone is a good solvent for many plastics and some synthetic fibers. It is used for thinning polyester resin, cleaning tools used with it, and dissolving two-part epoxies and superglue before they harden. It is used as one of the volatile components of some paints and varnishes. As a heavy-duty degreaser, it is useful in the

33

preparation of metal prior to painting. It is also useful for high reliability soldering applications to remove rosin flux after soldering is complete; this helps to prevent the rusty bolt effect. Acetone is used as a solvent by the pharmaceutical industry and as a denaturant in denatured alcohol. Acetone is also present as an excipient in some pharmaceutical drugs [3].

Methanol

Methanol, also known as methyl alcohol among others, is a chemical with the formula CH3OH (often abbreviated MeOH). Methanol acquired the name "wood alcohol" because it was once produced chiefly as a byproduct of the destructive distillation of wood. Today, industrial methanol is produced in a catalytic process directly from carbon monoxide, carbon dioxide, and hydrogen.

Methanol is the simplest alcohol, being only a methyl group linked to a hydroxyl group. It is a light, volatile, colorless, flammable liquid with a distinctive odor very similar to that of ethanol. At room temperature, it is a polar liquid, and is used as an antifreeze, solvent, fuel, and as a denaturant for ethanol. It is also used for producing biodiesel via transesterification reaction.

Methanol is produced naturally in the anaerobic metabolism of many varieties of bacteria, and is commonly present in small amounts in the environment. As a result, the atmosphere contains a small amount of methanol vapor. But in only a few days, atmospheric methanol is oxidized by sunlight to produce carbon dioxide and water.

Methanol is also found in abundant quantities in star forming regions of space, and is used in astronomy as a marker for such regions. It is detected through its spectral emission lines [4].

Ethanol

Ethanol is a volatile, flammable, colorless liquid with a slight chemical odor. It is used as an antiseptic, a solvent, a fuel, and due to its low freezing point, the active fluid in many alcohol thermometers. The molecule is a simple one, being an ethyl group linked to a hydroxyl group. Its structural formula, CH3CH2OH, is often abbreviated as C2H5OH, C2H6O or EtOH. Ethanol is slightly more refractive than water, having a refractive index of 1.36242 (at λ=589.3 nm and 18.35 °C or 65.03 °F). The triple point for ethanol is 150 K at a pressure of 4.3 × 10−4 Pa. It burns with a smokeless blue flame that is not always visible in normal light.

Ethanol is produced both as a petrochemical, through the hydration of ethylene and, via biological processes, by fermenting sugars with yeast. Which process is more economical depends on prevailing prices of petroleum and grain feed stocks.

Ethanol is an important industrial ingredient. Ethanol is used extensively as a solvent in the manufacture of varnishes and perfumes; as a preservative for biological specimens; in the preparation of essences and flavorings; in many medicines and drugs; as a disinfectant and in tinctures; and as a fuel and gasoline additive [5].

Fluorinert

Fluorinert is the trademarked brand name for the line of electronics coolant liquids sold commercially by 3M. It is an electrically insulating, stable fluorocarbon-based fluid, which is used in various cooling applications. It is mainly used for cooling electronics. Different molecular formulations are available with a variety of boiling points, allowing it to be used in "single-phase" applications, where it remains a liquid, or for "two-phase" applications, where the liquid boils to remove additional heat by evaporative cooling. An example of one of the compounds 3M uses is FC-72 (perfluorohexane, C6F14). Perfluorohexane is used for low-temperature heat-transfer applications due to its 56 °C (133 °F) boiling point. Another example is FC-75, perfluoro (2-butyl-tetrahydrofurane). There are 3M fluids that can handle up to 215 °C (419 °F), such as FC-70 (perfluorotripentylamine) [6].

Working fluid properties

In the figures 1, 2, 3 and 4 are compared main thermodynamic and physical properties of selected substances.

In the figure 1 are shown latent heat potential working fluids of heat pipe. Latent heat is thermodynamic properties which indicates the amount of heat that the substance is able to accept at the boiling or transmit at the condensation. Higher value means that the substance is able transmit more heat. This substance properties occur only at the phase change [7].

Fig. 1 Latent heat potential working fluids of heat pipe

In the figure 2 are shown specific thermal capacity potential working fluids of heat pipe. The specific thermal capacity is thermodynamic properties which indicate the amount of heat, which is necessary add to 1 kg of the substance to increase its temperature by 1 °C. The lower value mean that the substance is able absorb less heat [8].

Fig. 2 Specific thermal capacity potential working fluids of heat pipe

In the figure 3 are shown boiling points potential working fluids of heat pipe. The boiling point of the substance is the temperature at which the vapour pressure of the liquid equals the pressure of the surrounding atmosphere and phase change from liquid to vapour occur [9].

Fig. 3 Boiling point potential working fluids of heat pipe

34

https://en.wikipedia.org/wiki/Petrochemical

https://en.wikipedia.org/wiki/Fermentation_%28biochemistry%29

https://en.wikipedia.org/wiki/Yeast

In the figure 4 are shown dielectric constants potential working fluids of heat pipe. This constant indicate the ability of substance to create electrical bonds with other molecules, which means that it is capable eliminate the gravity of opposite charged surrounding ions.

Fig. 4 Dielectric constant potential working fluid of heat pipe

3. Experiment The experiment dielectric breakdown of vapour phase of

working fluid in heat pipe was performance on specific designed heat pipe shown in figure 5. It is gravity heat pipe made of a copper pipe, wherein the evaporation and the condensation sections are separated by glass tube of length L, which substitute electrical insulator. According above working fluid selection was the Fluorinert FC 72 choose as a working fluid. The choice of this fluid is mainly due its excellent dielectric properties and unique combination of the thermodynamic and others properties, which makes the Fluorinert FC - 72 ideal fluid for electronic cooling used in many electronic applications.

The experiment investigate influence of ambient temperature and insulator distance on dielectric breakdown of vapour phase of working fluid in heat pipe. There was choose two distances of electric insulator 70 and 65 mm and ambient temperature range from – 40 °C to – 10 °C.

Fig. 5 Model of gravity heat pipe with electric insulator

The real experimental heat pipe and dielectric breakdown measurement is shown in figure 6. The measurements were carried out in a thermostatic chamber with temperature regulation. To electric breakdown induction inside heat pipe was evaporator part plugged on the positive pole and condenser part plugged on the negative pole of the laboratory high voltage supply with operating range of 0 to 60 kV.

Fig. 6 Dielectric breakdown measurement

Than was continuously increasing electric voltage on the laboratory supply till the value when occur dielectric breakdown between evaporator and condenser. Dielectric breakdown was indicated by electric current fail on the laboratory supply and by flash between evaporator and condenser. The same measurement was performance at temperature -40, -30, -20 and -10°C.

4. Results In the figure 7 are interpreted results of the experiment

dielectric breakdown of vapour phase of working fluid in heat pipe depending on ambient temperature and insulator distance. There is seen that with the increasing temperature increase value of electric voltage which inducted the dielectric breakdown at booth insulator distances 75 and 60 mm. Investigation dependence of ambient temperature was limiting by voltage range on the laboratory supply, because the dielectric breakdown inducted by maximal electric voltage 60 kV of the laboratory supply occur already at the temperature – 10 °C.

Fig. 7 Dielectric breakdown of vapor phase of working fluid in heat pipe depending on ambient temperature and insulator distance

5. Conclusion Based on the results obtained from the experiment it can be

concluded that the heat pipe with electric insulator length approx. 60 - 75 mm and working fluid Fluorinert FC 72 is a suitable device to heat remove from the power electronic components works at high electric voltage and adverse (-40 to -10 °C) ambient temperature conditions.

Acknowledgment This work has been financially supported by the projects

APVV-15- 0778 Limits of Radiative and Convective Cooling through the Phase Changes of Working Fluid in Loop Thermosyphon (50 %) and KEGA 042ŽU-4/2016 Cooling on the basis of physical and chemical processes (50 %).

References [1] R. Nosek, M. Holubčík, Š. Papučík, Sci. World J., Vol.

2014, 2014, art. n. 487549. [2] R. Lenhard, K. Kaduchová, Š. Papučík, J. Jandačka, EPJ

Web of Conf., Vol. 67, 2014, art. n. 02067. [3] A. Klamt, COSMO-RS: From Quantum Chemistry to

Fluid Phase Thermodynamics and Drug Design, 2005, pp. 92–94. [4] D. R. Lide, CRC Handbook of Chemistry and Physics

(86th ed.), Boca Raton, CRC Press, 2005. [5] D. R. Lide, CRC Handbook of Chemistry and Physics (89

ed.), Boca Raton, CRC Press, 2008. [6] Product list 3M Fluorinert FC-70 Electronic Liquid. [7] J. Galliková, R. Poprocký, P. Volna, Diagnostyka, Vol.

17, 2016, no. 4 pp. 85-92. [8] P. Ďurčanský, Š. Papučík, J. Jandačka, M. Holubčik, R.

Nosek, Scient. World J., Vol. 2014, art. n. 138254. [9] R. Lenhard, K. Kaduchová. J. Jandačka, Advanced

Materials Research, Vol. 875-877, 2014, pp. 1693-1697.

35

INFLUENCE OF THE SOIL PARTICLES ON THE WEAR OF PLOUGHSHARES DURING PLOUGHING

Opačak I., mag.ing.mech. 1, Putnik I., mag.ing.mech. 1, Samardžić M. 1 Faculty of Mechanical Engineering, University of Osijek, Trg Ivane Brlić-Mažuranić 2, Slavonski Brod, Croatia 1

[email protected], [email protected], [email protected]

Abstract: Researchs of the influence of the soil particles were perfomed on the powder loamy soil to powder clay texture. Standard and welded ploughshares were tested. The standard ploughshares are made of steel 50Mn7. The welded ploughshares are made by applying C-Cr-Co-Ni-Si additional material on the steel 50Mn7. The ploughshares are tested on the plough roller machine. Researches were perfomed in periods of 120, 240 and 360 hours of ploughing, or 60, 120 and 180 work hours of each ploughshare. After 180 hours of work at least average reduction of the ploughshares lenght was at welded ploughshares and it amounted to 8,27 % of the initial length. At the same time reduced the average length of the top of the ploughshares with standard ploughshares amounted to 19,65 % of the initial length. It was concluded that the application of welded ploughshares can contribute to increased of the productivity.

Keywords: PLOUGHING, SOIL PARTICLES, WEAR OF PLOUGHSHARES, PRODUCTIVITY

1. Introduction While ploughing the soil certain parts of the plough wear,

mostly ploughshares. The most weared parts of the surface are the top and blade. They dull during the work, causing the loss of the mass and dimension changes of the ploughshares. Standard ploughshares which are supplied while buying ploughs do not meet the requirements of sustainability. Delays which are caused by wear and dull of the ploughshares require some time to replace with new ones. It increases the costs and reduces the efficiency of the tractor. One of the possible solutions to the wear problem of the ploughshares is the surfacing hard layers to the top of the blade. Wear problems of the tools for the soil ploughing was among the first engaged by the scientist Richardson [1]. He found that the soils contain abrasive particles with a hardness greater than the hardness of ploughshares. Further examinations of the ploughshares different hardnesses author notes that the surface hardness is one of the most important characteristics of resistance to wear during operation. In the nineteen seventies experiments with the application of the hard layers of the additional material on the blades for the soil ploughing began [2]. Conclusion was that on the sustainability and wear, significant influence has humidity and mechanical composition of the soil during ploughing. Natsis and colleagues [3] investigated the influence of type and soil moisture and the sharpening of ploughshares on power consumption, performance and quality of ploughing. They conclude that on the clay and loamy soils ploughshares wear decreases with increasing soil moisture, and that on the sandy soils wear increases with increasing moisture content. They note that during the work with the worn-dull blade of the ploughshares comes to increasing the necessary traction force for 62 %, and consequently to reduce the effect of efficiency for 30 %. Banaj and colleagues [4] analyzed the arrangement of the moisture in depth and found out that, depending of the soil type, the difference between the layer of 0 to 10 cm and 20 to 30 cm is around 5 %. Top of the ploughshares first dulls, and then other cutting surfaces [4, 5]. Aim of this research is, based on the comparision of the results of the welded and standard ploughshares, to find: change the basic dimensions of ploughshares, weight loss, and that based on these parameters define which of the tested ploughshares showed the best results.

2. Ploughshares materials and research methods Research was performed with two tractors (W1 and W2 )

power of 129 kW with drive to all four wheels and two rotational ploughs with working width of 120 cm. Two characteristic soil types were selected for the analysis.

For the analysis for the wear resistance during ploughing are selected: 1. standard ploughshares, manganese steel 50Mn7, test

sample mark „A“, 2. own welded ploughshares, an optional protective layer on the base material C-Cr-Co-Ni-Si on the basic material of manganese steel 50Mn7, test sample mark „B“.

2.1. Types of soil

Research on the influence of soil to wear of the standard and welded ploughshares was performed on silty loamy and silty clay soil. Research was performed from september to december. Pre-crop on plots on which was performed research were wheat and corn. Those pre-crops, due to the much larger soil compaction than after eg. turnip, affecting soil that has a higher resistance when ploughing [6]. The soil composition and the level of current humidity were tested, middle value on the depth from 0 to 30 cm, Table 1.

Table 1: Composition, humidity and textural mark of the soil.

Sample number

Moisture content,

%

Mechanical composition of the soil, % particle, mm

Big sand

Small sand

Total sand Dust Clay

Texture mark

of soil* 2 ÷

0,2 mm

0,2 ÷

0,05 mm

2 ÷

0,05 mm

0,5 ÷

0,02 mm

< 0,02 mm

1 19,32 0,25 0,93 1,17 67,95 30,88 PrGI

2 26,72 0,98 1,69 2,67 74,67 22,65 PrI

3 26,28 0,80 1,40 2,20 70,84 26,96 PrI

4 35,39 0,46 1,28 1,74 67,78 30,48 PrGI

5 26,13 0,89 1,64 2,53 69,51 27,96 PrGI

6 25,72 1,08 1,39 2,47 66,46 31,07 PrGI

7 23,99 0,37 1,08 1,45 65,06 33,49 PrGI

8 24,28 1,01 1,67 2,68 68,95 28,37 PrGI

9 32,37 0,70 1,13 1,83 66,50 31,67 PrGI

10 24,25 1,09 1,28 2,36 67,77 29,86 PrGI

11 21,41 0,92 1,70 2,61 71,24 26,18 PrI

12 24,76 1,35 1,64 2,99 71,67 25,34 PrI

13 21,24 0,34 2,05 2,39 69,35 28,26 PrGI

14 23,61 0,49 2,02 2,51 70,83 26,66 PrI

15 25,08 1,16 2,00 3,16 71,90 24,94 PrI *Soil mark: PrI - silty loam; PrGI - silty clay loam.

The smallest share of the current humidity is established on the land no. 1 (19,32 %), while the highest was on the no. 4 (35,39 %). It was found that the proportion of clay particles is in the range of 22,65 % on the land 2 to 33,49 % on the land. 7. On

36

this lands soil is silty loam (41,17 %) to sily clay loam texture (58,83 %). Percentage of particles of clay with silty loam soil texture ranged 22,65 % on the land 2 to 26,96 % on the land 3. In silty clay soil texture percentage of clay particles ranged from 27,96 % on the land 5 to 33,49 % on the land 7. Increased share of clay particles affects a range of chemical and physical properties of soil. The main characteristic of the clay is swellable, and when the soil is dry, it is shrinking and decreasing volume. Clay particles are impermeable to water, have very high plasticity and stickiness when wet and compact and hard when dry.

2.2. Material of the ploughshare

Standard ploughs, mark „A“ are made of the manganese steel 50Mn7. On experimental steels, standard ploughs and for making your own ploughshares chemical analysis was performed. Composition of both steel meets the requirements, Table 2.

Table 2: Chemical composition of the basic material and standard and own ploughshares.

Steel mark 50Mn7

EN 10025-2: 2004

Chemical composition of the basic material, %

C Si Mn S P Cr Ni Mo Cu N

Standard ploughshares

„A“

0, 45

0, 33

1, 78

0, 029

0, 024

0, 22

0, 13

0, 04

0, 02

0, 007

Own welded ploughshares

„B“

0, 55

0, 25

1, 63

0, 027

0, 030

0, 29

0, 12

0, 09

0, 03

0, 008

Top of the ploughshare is part of plough is most exposed to reducing the dimensions during ploughing [6]. Except top, wear is exposed to the back part of the ploughshare blade. For the continuation of studies were selected: - to weld the top of the ploughshare with electrode C-Cr-Co-Ni-Si, with hand-arc process, - to secure back part with inductive melted powder C-Cr-Co-Ni-Si. Hand-arc process is chosen because of complicated "the pointed" shape top of ploughshares (top triangle should be welded from the back side). The outer pard of the ploughshare is welded first, shaped in the letter „V“, and then fills the top of the triangle (dimensions ≈ 150 mm down part, b ≈ 120 mm upper part in shape of „V“). Back part of the ploughshare blade is welded with the inductive melted powder. Weld width is 20 mm, thickness is 3 mm. First, inductive device is welding the blade, and then with the hand-arc procedure is welded top from the front and the back side. The length of both sides of the top of ploughshares has the shape of a triangle side (≈ 50 mm). Inductive procedure is selected because of the possibility of achieving evenly distributed layer, evenly thickness and the speed of the melting procedure on such large lenghts (over 500 mm). Chemical composition of the additional material is shown in Table 3.

Table 3: Chemical composition of the electrode and metal powder of the additional material.

Chemical composition, % C Si Mn Cr Ni Mo Co

3,30 1,49 0,43 24,32 3,13 0,10 3,20

Analysis is performed with spectrometric method on the device SPECTRUMAT - 750 GDS. Characteristic dimensions of ploughshares are marked on Figure 1. By controlling the dimensions before, during and after the ploughing their wear will be followed. Measuring of the ploughshares „a“, „b“, „c“ and „d“ was performed with the caliper, measuring range 0 ÷ 200 mm with the accuracy of measurement (± 0,01 mm).

Mass of the tested ploughshares will be determined by weighing on an electronic scale with measuring range to 6000 g and accuracy ± 1 g.

Figure 1 The characteristic of ploughshares dimensional control: a - the length of the top of the ploughshare; b - hight of the ploughshare on front part ; c - hight of the ploughshare on middle part; d - hight of the ploughshare on back part; l1 - lenght of back part of blade; l2 - lenght of upper part of ploughshare.

2.3. Making of test ploughshares

For the purposes of this research are purchased/constructed two sets of ploughshares, 8 ploughshares on every plough. Total of 16 ploughshares. One set of standard ploughshares was purchased (mark „A“) and one set of own ploughshares with the surface layer of the additional material „B“ was made, with same dimensional characteristics like standard one. Standard ploughshares are purchased from suppliers and on them were performed tests of the chemical composition, hardness, dimensional and mass control. With hand arc procedure top of the ploughshare was welded, and with inductive melting powder procedure back part of the ploughshare was surfaced. Surface preparation was performed before welding procedure. In arc welding process: sanding and degreasing, and in inductive process: milling of the surface prior to welding. For inductive welding of the ploughshare metal powder was used, and for arc welding the diameter of the electrode was ø 4,5 mm. Thickness of the additional material is around 3 mm. Average surface hardness of the standard ploughshares „A“ is 44 HRC, while on the welded ploughshares „B“ average hardness is around 46 HRC. The characteristic appearance of standard ploughshares „A“ is showed in Figure 2, own welded „B“ in Figure 3.

Figure 2 Standard ploughshares „A“ before ploughing.

Figure 3 Welded ploughshares „B“ with basic material 50Mn7, before ploughing.

3. Test results Researchs were performed on both sets of the ploughshares, 8

ploughshares on every plough. During the reasearch roller ploughs were used. Average start lenght of the top „a“ of standard ploughshares „A“ was 198,50 mm, width „b“ 142,13 mm, „c“ 127,63 mm, „d“ 121,25 mm, while the average lenght of the top „a“ of welded ploughshares „B“ was 199,63 mm, width „b“ 143,75 mm, „c“ 132,13 mm and „d“ 125,63 mm. Control of dimension change and mass loss of the ploughshare „A“ and „B“ was performed in three periods: 120, 240 and 360 working hours.

So, the roller plough was used, every ploughshare is controlled after 60, 120 and 180 hours of work. Before starting and in any defined time of the research measurement was

Upper side

Down side

Upper side

Down side

37

performed in order to determine size and weight. Results of change of characteristic dimension are shown in Table 4, and results of weight loss in Table 5. Figure 4 and 5 show ploughshares after testing/ploughing.

Figure 4 Standard ploughshares „A“ after ploughing.

Figure 5 Welded ploughshares „B“ on basic material 50Mn7, after ploughing.

Table 4: Average dimension reduce of 8 ploughshares during ploughing. Average reduction of characteristic dimensions

Ploughshares type

After 60 hours of work

After 120 hours of work

After 180hours of work

Nominal dimension a

Wear Wear Wear

mm % mm % mm % Standard „A“ 16,13 8,12 27,38 13,79 39 19,65 Welded „B“ 6,25 3,14 12,13 6,07 16,5 8,27

Nominal dimension b Standard „A“ 5,63 3,97 9,25 6,51 13,63 9,59 Welded „B“ 3,13 2,18 6 4,18 8,13 5,66

Nominal dimension c Standard „A“ 6,88 5,39 10,5 8,23 14,13 11,07 Welded „B“ 5,75 4,35 8,75 6,63 10,75 8,14

Nominal dimension d Standard „A“ 6,13 5,04 10,25 8,35 14,38 11,85 Welded „B“ 5,13 4,08 8,25 6,57 10 7,95

Table 5: Average weight reduce of standard and welded ploughshares.

Ploughshares type

After 60 hours

After 120 hours

After 180 hours

Weight loss Weight loss Weight loss g % g % g %

Standard „A“ 355 9,04 678, 75

17, 29

1. 032,50 26,29

Welded „B“ 381, 25 8,82 708,

75 16, 39 971,25 22,45

During research average speed of all tractors was monitored with chronometer in lenght of 100 m. In all tests the speed of the tractor is set to 7 km/h. The optimal speed is selected to obtain a good turn of the furrows. („that the ridges along as sheets of the book“), and to obtain appropriate tempo of ploughing. In the event of an increase in the occurrence of resistance of soil sensor in the transmission registers it. The automatic transmission shifts gears in the lower level of the movement, and has avoided the manual gear changes. The monitoring has found that during the experiment speed of tractors ranged from 6,8 to 7,2 km/h. The controller of high pressure pump adjusts engine speed and in terms of the major resistance it increased to a maximum of 200 r/min. Size of treated surface is measured with the measuring tape, and work hours of tractor are measured with the chronometer, Table 6.

Table 6: Size of treated surface and work hours of tractor.

Work time, h Treated surface, ha Time of tractors

clean work, h Standard ploughshares „A“

120 119,23 120 240 110,23 120 360 101,79 120

Welded ploughshares „B“ 120 127,36 120 240 113,92 120 360 107,60 120

Plough depth (ho) was determined with depth sonar, while the plough width (bo) was determined with measure tape, Table 7. Measures are in both cases performed 30 times with 3 repeats (total of 90), and it determined the average of depth and width of plough.

Table 7: Middle values of the depth and width of ploughing.

Tractor’s work time, h

Depth and width of plough, cm Standard

ploughshares “A” Welded

ploughshares “B” ho bo ho bo

120 29,17 163,68 29,67 163,90 240 29,11 163,43 29,57 163,30 360 29,03 163,41 29,93 163,09

4. Analysis of the results and conclusion Average depth of plough with the standard ploughshares is

29,10 cm. For welded ploughshares „B" average depth of ploughing was 29,71 cm. Analysis of the average reduction of ploughshares on characteristic parts (Table 4) determined significantly higher reduction of average dimension of standard ploughshares „A“ in comparision with the welded ploughshares „B“. The average weight of standard ploughshares „A“ before starting the work was 3.927,50 g, and welded ploughshares „B“ 4.330,00 g. Average reduction of weight on standard ploughshares „A“ and welded ploughshares „B“ after 60, 120 and 180 hours was shown in Table 5. On welded ploughshares „B“ whose surfaces were welded with combined technique of welding, there was less wear compared with the standard ploughshares „A“. Wear of ploughshares in sandy clay PrI is higher than in silty clay loam PrGI. This is consistent with the results [7] where is stated that the weight reduction of ploughshares in sandy soil was 30 to 150 g/ha, while the weight loss of ploughshares in clay soil was 5 to 30 g/ha. The intensity of the wear of ploughshares during ploughing increases with increasing the share of sand in the soil and ranges from 90 to 210 g/ha [8, 9].

Table 8: Treated surface, working time and coefficient of utilization of working time.

Tractor's working time, h

Treated surface,

ha

Time of tractors clean

work, h

Loss of tractor's working time, h

Total working time, h

Utilization of working

time, %

Standard ploughshares „A“ 120 119,23 120 78,39 198,39 0,60 240 110,23 120 74,70 194,70 0,62 360 101,79 120 93,10 213,10 0,56

Welded ploughshares „B“ 120 127,36 120 50,17 170,17 0,71 240 113,29 120 47,54 167,54 0,72 360 107,60 120 51,74 171,74 0,70

Natsis and colleagues [3] indicate that the ploughing performance is decreased for 30 % when the thickness of the ploughshare on blade during wear increases from 1 mm to 6 mm.

Upper side

Down side

Upper side

Down side

38

Longer life of ploughing tools increases the performance and the productivity. One of the reasons is less loss of work time due to frequent changes of the ploughshares [10]. Coefficient of utilization of working time with standard ploughshares „A“ was 0,60 %, 0,62 % and 0,56 %. When ploughing with welded ploughshares „B“ coefficient of utilization of working time (at all measures 120, 240 and 360 hours) was 0,71 %, 0,72 %, 0,70 %, Table 8. Based on these preliminary results, an advantage in the application should be given to the welded ploughshares. Continuation of research through analysis of relations of influence of the structure of surface layers of ploughshares should point out the ratio of carbide in dull core, in order to get higher performance. We should not leave out either the economic effects that include not only the direct costs of development/acquisition of new ploughshares, but also possible indirect tribological "losses".

5. References [1] Richardson, R. C. D.: The wear of metallic materials by soil - Practical phenomena, Journal of Agricultural Engineering Research 12 (1967) 1, 22-39. [2] Xiaogang, Z.; Zebing, X.: Abrasive wear resistance property of surfacing cladding hard alloy on tillage components, Agricultural Equipment & Vehicle Engineering, 5 (2014). [3] Natsis, A.; Papadakis, G.; Pitsilis, J.: The influence of soil type, soil water and share sharpness of a mouldboard plough on energy consumption, rate of work and tillage quality, Journal of Agricultural Engineering Research, 72 (1999) 2, 171-176. [4] Banaj, Đ.; Duvnjak, V.; Tadić, V.; Kanisek, J.; Turkalj, D.: Tehničko-tehnološki aspekti primjene novih oblika lemeša pluga, Poljoprivreda, 14 (2008) 1, 1-8. [5] Filipović, D.; Banaj, Đ.; Košutić, S.; Josipović, M.; Šimić, B.: Comparison of the protected and unprotected plough share wear by the abrasion of the soil particles, Strojarstvo, 45 (2003) 1-3, 17-23. [6] Owsiak, Z.: Wear of symmetrical wedge-shaped tillage tools, Soil Tillage Res., 43 (1997) 3-4, 295-308. [7] Miloš, B.; Pintarić, A.; Buljan, G.: Abrasive wear of agricultural machinery parts, Proceedings of the International conference „Tribology in Agriculture“, 1993., 44-48. [8] Bobobee, E. Y. H.; Sraku-Lartey, K.; Fialor, S. C.; Canacoo, E. A.; Agodzo, S. K.; Yawson, A.: Wear rate of animal- drawn ploughshares in selected Ghanaian soils, Soil Tillage Res., 93 (2007) 2, 299-308. [9] Bayhan, Y.: Reduction of wear wia hardfacing of chisel ploughshare, Tribol. Int., 39 (2006) 6, 570-574. [10] Ferguson, S. A.; Fielke, J. M.; Riley, T. W.: Wear of cultivator shares in abrasive South Australin soils, Journal of Agricultural Engineering Research, 69 (1998) 2, 99-105.

39

ЗЪБНА ПРЕДАВКА С ПРОМЕНЛИВО ПРЕДАВАТЕЛНО ОТНОШЕНИЕ

GEAR TRANSMISSION WITH VARIABLE GEAR RATIO

ас. инж. Георгиев И. Technical University of Gabrovo, Bulgaria

[email protected]

Abstract: В настоящия доклад се разглежда разработване на двустепенни, тристепенни и четиристепенни зъбни вариатори с асиметричен профил на зъбите които са оборудвани с еднакво високи зъби на пълна и не пълна дължина, разположени по протежение плоски или пространствени криви, които представляват функция на съотношението на променливата скорост.

Keywords: asymmetric tooth profile, variable speed ratio, gears variators

1. Въведение В съвременните машини и оборудване често се налага да се

осъществява движение на изпълнителните органи по предварително зададен закон за променливо предавателно отношение.

За решението на тези задачи се използват зъбни предавки с некръгли колела. За техни недостатъци се считат променливото предавателно отношение и динамичното натоварване на предавката, а също и трудността при изработката на некръглото зъбно колело.

Цел на настоящия доклад е да се предостави възможност за реализацията на вариатори чрез сферично и елиптично зъбно колело с асиметричен профил на зъбите.

2. Изложение Вариаторите са зъбни механизми, които могат да бъдат

реализирани с една или повече степени чрез зъбни колела с криволинейни зъби.

Двустепенен вариатор на скоростта (фиг.1) се състои от водещо тороидално 1, промеждутъчно сферично 3 и елипсовидно 2 и задвижвано тороидално 4 колело. Колела 2 и 3 са захванати подвижно с възможност за въртене на неподвижната ос 5. Колела 1 и 4 са снабдени с равни по височина прави зъби 6 които са с асиметричен профил. На колела 2 и 3 са изработени прави зъби с асиметричен профил, като 7 и 8 са с непълна дължина, които представляват зададената функция на променливото предавателно отношение[1,2,3,4,5,6].

Предавателното отношение има вида:

(1) 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑅𝑅2𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑2𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚

. 𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚𝑅𝑅3𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑 2

= 𝑅𝑅2𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑2𝑅𝑅3𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑3

. 𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚



= 𝑅𝑅2𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑2𝑅𝑅3𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑3

. 𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚

Диапазонът на регулиране е равен на:

(3) 𝐷𝐷 = 𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚

,

Тристепенният вариатор на скоростта (фиг.2) се състои от задвижващо тороидално колело 1, промеждутъчно сферично или елипсовидно колело 2, промеждутъчни тороидални колела 3 и 4, които са съединени посредством валове 5 и 6 с кръгли конични колела 7,8,9 и 10, вал 11 и задвижваното сферично или елипсовидно колело 12. Колело 2 е свободно лагерувано на неподвижната ос 14. Колела 1,3 и 4 са снабдени с равни по височина прави зъби с асиметричен профил и пълна дължина, а колела 2 и 12 са снабдени с равни по височина прави зъби с асиметричен профил. Колела 16 и 17 имат зъби с непълна дължина, които са разположени на криви 18 и 19, които представляват зададената функция на променливо предавателно отношение.

Предавателно отношение

(4)𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑅𝑅2𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑2𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚

. 𝑟𝑟3𝑚𝑚𝑚𝑚𝑚𝑚𝑅𝑅2

. 𝑅𝑅12𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑12𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚

=

= 𝑟𝑟3𝑚𝑚𝑚𝑚𝑚𝑚𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚 𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚

𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑2. 𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑12

(5) 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑅𝑅2𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚


. 𝑅𝑅12𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚

= 𝑟𝑟3𝑚𝑚𝑚𝑚𝑚𝑚𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚 𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚

. 1𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑 2

Диапазон на регулиране:

(6) 𝐷𝐷 = 𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟3𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟3𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚

. 𝑐𝑐𝑐𝑐𝑐𝑐2𝜑𝜑2. 𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑12 ,

Четиристепенният вариатор на скорост (фиг.3) се състои от задвижващо 1, междинни 2 и 3, както и задвижвано 4 тороидално колело. Междинните сферични или елипсовидни колела 5 и 6, които са с възможност за въртене и са закрепени неподвижно на ос 7. Колела 1,2 и 6 са снабдени с равни по височина прави зъби 8 с непълна дължина, които са разположени на пространствените криви 9,10 и 11 които представят зададената функция на променливото предавателно отношение. Колела 3,4 и 5 са снабдени с равни по височина прави зъби с асиметричен профил 12, които са с пълна дължина. Колела 2 и 3 са свързани чрез валове 13,14 и 15, и сферични конични колела 16,17,18 и 19.

Предавателно отношение има вида:



. 𝑅𝑅6𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑6𝑟𝑟3𝑚𝑚𝑚𝑚𝑚𝑚


=

= 𝑟𝑟2𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚 𝑟𝑟3𝑚𝑚𝑚𝑚𝑚𝑚

𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑5. 𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑6

(8) 𝑈𝑈𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑅𝑅5𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚

. 𝑟𝑟2𝑚𝑚𝑚𝑚𝑚𝑚𝑅𝑅5𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑5

. 𝑅𝑅6𝑟𝑟3𝑚𝑚𝑚𝑚𝑚𝑚

. 𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚𝑅𝑅6.𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑6

=

= 𝑟𝑟2𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚 𝑟𝑟3𝑚𝑚𝑚𝑚𝑚𝑚

. 1𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑 5.𝑐𝑐𝑐𝑐𝑐𝑐𝜑𝜑6

Диапазонът на регулиране, е:

(9) 𝐷𝐷 = 𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟2𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟3𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚𝑟𝑟1𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟2𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟3𝑚𝑚𝑚𝑚𝑚𝑚 .𝑟𝑟4𝑚𝑚𝑚𝑚𝑚𝑚

. 𝑐𝑐𝑐𝑐𝑐𝑐2𝜑𝜑5. 𝑐𝑐𝑐𝑐𝑐𝑐2𝜑𝜑5

Ако е необходимо задвижваните колела и валове на зъбните предавки с променливо предавателно отношение да извършват въртеливо движение с постоянна ъглова скорост, то равните по височина зъби с асиметричен профил и непълна дължина се разполагат на крива, която се състои от части с изменящи се и постоянни радиуси.

Ако е необходимо задвижваните колела и валове на предавките да осъществят различни закони на предавателно отношение, то зъбите с непълната дължина се разполагат на различни криви, които представляват различни функции на зададеният закон за променливо предавателно отношение. Кривата съставена от части, съответстващи на различни

40

функции на променливото предавателно отношение се разполагат на началната повърхност на задвижващото или задвижваното колело.

Двустепенният вариатор на скоростта (фиг.1) се задвижва от колело 1 с постоянна ъглова скорост. Посредством страничните повърхности на зъбите с асиметричен профил на колела 6 и 7 които имат пълна крива на зацепване и колела 1 и 2, които имат непълна крива на зацепване извършват въртеливо движение с променлива ъглова скорост която се предава на неподвижно съединеното колело 3 посредством страничните повърхности на зъбите с асиметричен профил. В последствие движението се предава на колела 8 и 6 които са с непълна крива на зацепване и колела 3 и 4 които са с пълна крива на зацепване, като колело 4 извършва просто движение на сумарно променливата ъглова скорост.

Фиг.1 Двустепенен вариатор

Фиг. 2 Тристепенен вариатор

Тристепенният вариатор на скоростта (фиг.2) се задвижва от колело 1 и предава въртеливото движение с постоянна ъглова скорост посредством зацепване с колела 15 и 17, които имат непълна крива на зацепване. В последствие се зацепват

колела 1, 2 и 3 като колело 3 извършва въртеливо движение с променлива ъглова скорост и посредством валове 5, 6 и 11 и колела 7, 8, 9 и 10 се осъществява зацепване с непълна крива на колела 15 и 17 които предават въртеливото движение на колела 4 и 12, като колело 12 извършва просто движение със сумарна променлива ъглова скорост.

Четиристенният вариатор (фиг. 3) се задвижва чрез колело 1 предаващо въртеливо движение с постоянна ъглова скорост. Посредством зацепване с колела 12 и 8 които имат пълни криви на зацепване се предава въртеливо движение на колела 1, 5 и 2, като колело 2 извършва въртеливо движение с променлива ъглова скорост. То посредством валове 13, 14 и 15 и колела 16, 17, 18 и 19 осъществява предаване на движението на колела 12 и 8, както и на колела 3 и 6, както и на колела 6 и 4, които предават въртеливо движение на задвижваното колело 4, което извършва просто движение със сумарна променлива ъглова скорост.

Фиг. 3 Четиристепенен вариатор

Ъглите на зацепване при асиметричен профил (αw и α*w) се определят от следната трансцедентна система:

(10)

( ) ( )

*

*

*12

*12*

coscos

coscos

..2

ww

ww

invinvzz

tgtgxxinvinv

αα

αα

αα

αααα

=

++

+±

+±=+

.

където α и α* – профилните ъгли на инструмента;

x1 и x2 – коефициентите на изместване на инструмента за колелата от предавката, като за колелото с вътрешни зъби се приема коефициентът на изместване на еквивалентното колело с външни зъби.

Зъбодълбачното колело представлява инструмент за нарязване на колелата, в основата на което е теоретичното производящо колело. Производящия контур на зъбодълбачното колело може с достатъчна за практиката точност да се счита за еволвентен при разглеждане на ортогоналната проекция на режещите му ръбове на равнина, перпендикулярна към оста на колелото. Следователно геометричния синтез на предавка с асиметричен профил на зъбите, която е произведена със

41

зъбодълбачно колело, се извършва при разглеждане на зацепване единствено между зъбни колела. Следователно геометричните параметри на инструменталното зацепване се определят от теоремата за реверсиране посоката на движение [7]:

− за I-ва възможност на образуване:

(11)

( )( )

*w

*b

w

b

*01

*01*

ww

0

0,1

0

0,1

00

cos

d

cos

d

invinv

zztgtg.xx.2

invinv

α=

α

α+α+

+±

α+α±=α+α

където αwo и α*w0 са ъглите на инструментално зацепване между колело 1 и зъбодълбачното колело;

х1 и х0 са коефициентите на изместване на колело 1 и зъбодълбачното колело;

z1 и z0 – броят зъби на колело 1 и зъбодълбачното колело;

db1 и db0 – диаметрите на основните окръжности на колело 1 и зъбодълбачното колело.

В зависимост (12) знакът (+) се отнася на външно инструментално зацепване, а знакът (-) за вътрешно инструментално зацепване. По аналогичен начин се определят и ъглите на инструментално зацепване за колело от предавката.

− за II-ра възможност на образуване:

(12)

( )

( )( )

0

0

0

0,1

0

0,1

0

w*

01

*01*

w

*w

*b

w

b

01

01w

invinvinv

zztgtg.xx.2

inv

cos

d

cos

d

invzz

tg.xx.2inv

α−α+α+

+±

α+α±=α

α=

α

α+±

α±=α

При II-ра възможност на образуване на профила се наблюдава вариране на профилния ъгъл на инструмента α* в рамките на приетата пропорционалност между основните окръжности db1,2 и d*

b1,2. Неговата стойност се определя единствено от трансцедентната система (12) и е невъзможно тя да остане променлива при определяне геометричните параметри на зацепването. Следователно за определяне ъглите на зацепване αw и α*w, за колелата от предавката с асиметричен профил се използва следната трансцедентна система, независимо от възможността на образуване:

(13)

( )( )

*w

*b

w

b

*12

*12*

ww

cos

d

cos

d

invinv

zztgtg.xx.2

invinv

2,12,1

α=

α

α+α+

+±

α+α±=α+α

При проектиране на зъбна предавка със зъбодълбачно колело е необходим профилния ъгъл в долната гранична точка

νl0, който за симетрични стандартизирани зъбодълбачни колела се дава от производителя.

Поради липса на такива с асиметричен профил в настоящата работа тези гранични профилни ъгли се определят от параметрите на червячната фреза, с която се изработва зъбодълбачното колело, по следната зависимост:

(14)( )

α−−

−α=α2sin.z

xhh.4tgtg0

0*

0a*0l

0l

където h*lo е коефициентът на височината на

праволинейния участък на изходния контур за нарязване на зъбодълбачно колело.

3. Заключение Разработена е конструкция на зъбни предавки,

позволяваща да се намалят динамичните характеристики и натоварване на зъбите.

Значително се опростява процеса на изготвяне на зъбни предавки с асиметричен профил на зъбите чрез използване на стандартно серийно оборудване и метод на копирането.

Зъбните предавки с асиметричен профил на зъбите позволяват конструиране на нови механизми за вариране на предавателното отношение чрез разполагане на зъбите по взаимно спрегнати криви.

4. Литература 1. Варсимашвили Р.Ш. Теория зацепления зубчатых

передач с переменным передаточным отношением / Р.Ш. Варсимашвили / «Технический университет». – Тбилиси, 2008. – 497 с.

2. Кожевников С.Н. Механизмы / С.Н. Кожевников, Я.И. Есипенко, Я.М. Раскин. – Москва: «Машиностроение», 1976. – С. 329-330: рис. 5.18; с. 331-332, рис. 5.21.

3. Литвин Ф.Л. Теория зубчатых зацеплении / Ф.Л. Литвин. – Москва: Наука, 1968. – 484 с.

4. Зубчатая передача: патент 2864В (Грузия) / Варсимашвили Р.Ш., Варсимашвили З.Р. - Опубл. Б.И. 2002, № 24.

5. Варсимашвили Р.Ш. Приказ о выдаче патента 651/01 от 17.08.2012. / Р.Ш. Варсимашвили, М.Р. Кахиани; Сакпатент, Грузия.

6. Варсимашвили Р. Ш., М. Р. Кахиани, З. Р. Варсимашвили, новыезубчатыепередачи с переменным передаточным отношением Прогресивні технології і системи машинобудування Вип. 1(45)-2 (46), 2013 Грузинский технический университет, Грузия Инженерная академия Грузии.

7. Симеонов С., Г. Цветанов. Теорема за реверсиране посоката на движение при еволвентни цилиндрични зъбни предавки с асиметричен профил на зъбите, Известия на ТУ-Габрово, УИ – „Васил Априлов”, №32, Габрово, 2005, ISSN 1310-6686.

42

КОНСТРУКТИВНИ И КИНЕМАТИЧНИ ОСОБЕНОСТИ НА ПЛАНЕТНАТА ПЛАВНОРЕГУЛИРУЕМА ЗЪБНА ПРЕДАВКА

CONSTRUCTIVE AND KINEMATIC FEATURES FOR PLANETARY VARIABLE GEAR DRIVE

ас. инж. Георгиев И.

Technical University of Gabrovo, Bulgaria [email protected]

Abstract: В настоящия доклад се разглежда на базата на три основни принципа на съществуване на зъбен вариатор с планетни колела. Установени са основните източници на кинематична грешка в непрекъснато променливата планетна плавно регулируема предавка. Дадени са мерки за осигуряване на нормалното функциониране на предавката.

Keywords: Infinitely adjustable planetary gear, gears variator, asymmetric tooth

1. Въведение Въпреки растящата конкуренция между регулируеми

електрически и високомоментни електродвигатели, най-голям обем от световното производство е в изработването на зъбни предавки. Това в не малка степен спомага за усъвършенстване на конструкциите им и експлоатационните им характеристики във водещите технически развити страни. Класическата зъбна предавка може да има уникални свойства, заключаващи се в плавно регулиране на предавателното отношение и възможност за реализация на съставни много секторни зъбни колела [1], схемата на която е изобразена на фиг. 1. В конструкциите на тази предавка се реализират три принципа, на база които може да се създаде едноконтурна (недиференциална) и следователно имаща минимум елементи на преобразуване плавно регулируемата зъбна предавка.

Цел на настоящата статия е да се проектира планетна плавно регулируема предавка, която има следните особености:

- Разделя потока на мощността; - Осъществява независимо функциониране на силовите

потоци; - Осъществява твърда кинематична връзка между

преместванията на всички елементи [2].

2. Изложение Планетна плавно регулируема предавка е представена на

фиг.1

а)

б)

Фиг. 1 Планетна плавно регулируема предавка – разрез В-В

при максимален радиус на сателита; б – разрез по В-В при минимален радиус сателита

Основната конструкция се явява високо преобразуваща ексцентрична планетна предавка [3], в която централното зъбно колело е изпълнено със съставни сектори, а величината на ексцентрицитета на сателита може да се изменя. Съставните секторни зъбни колела с външни зъби променят началния диаметър, който се изменя в широк диапазон. В дадения случай се създава възможност за изменение началния диаметър на колелата с вътрешни зъби така, както е показано на фиг. 1а, б. Това се постига чрез реализация на централното колело, като съставно от сектори 2 и 3, образуващи два силови потока, всеки от които се състои от три сектора.

Сектори с различни силови потоци са захванати един към друг челно и дефазирани един спрямо друг на ъгъл φ. В зацепване с централното колело се намира двустепенен сателит 4. Той съдържа идентични зъбни венци и сектори като един от тях може е закрепен еластично и се движи относително спрямо другия в окръжно направление на величина не по-голяма от половин стъпка на зъбите, което позволява да се избегне заклинване. Всеки от венците взаимодейства със сектора на своя силов поток, при което се получава челно припокриване на зъбите на зъбните венци на сателита 4 и секторите с различни силови потоци на централното зъбно колело. Синхронните радиални премествания на сектора се осигуряват с едновременно завъртане на гърбица, което взаимодейства с междузъбието, образувано в телата на сектори 2 и 3, и установено в опорни колела 9, монтирани в корпуса на предавката. Чрез завъртането на всички гърбици се предава движение на управляващ вал чрез зъбните предавки, включващи зъбните колела, както с външни така и вътрешни зъби, монтирани на опорни колела 9. Радиалните премествания на сектори 2 и 3 трябва да съответстват на равните им радиални премествания на сателит 4, довеждащи към изменение на неговия ексцентрицитет спрямо оста на предавката. Те се осигуряват чрез гърбица, която ги затваря геометрично и има диапазон, взаимодействащ с плъзгач, приемайки формата на отвор и осигуряващ равенство на преместването на секторите и сателитите. Плъзгачът е закрепен на бутало, преместващо се по направляващи, изпълнени на челния водещ вал. На буталото е неподвижно закрепен вал, на който с възможност за завъртане е установен сателит 4. Упоменатите особености се състоят в това, че управляващото движение на гърбицата е необходимо движение с управляващия вал в процеса на съвместно въртене на гърбицата и водещия вал. С тази цел гърбицата е снабдена със зъбен венец, а на вала неподвижно е закрепено зъбно колело с такива зъби. Освен това на вал с възможност за въртене е установено водило, на което са установени сателитите. Сателитите се намират в зацепване със зъбното колело и са неподвижно закрепени на корпуса, като предават движение на зъбното колело. В такъв вид, колелото с външни зъби и сателита образуват управляваща планетна предавка, осигуряваща съвместното въртене на гърбицата и вала. Предавателното отношение на плавно регулируемата планетна предавка е равно на отношенията на броя зъби на сателита 4 към разликата на условния брой зъби на секторното зъбно колело и сателита 4 и при минимален радиус на зъбните

43

сектори 2 и 3 относно оста на предавките. При необходимост да се измени предавателното число на скоростната кутия се задава въртеливо движение на вала, който едновременно предава движение на гърбицата и коляното, благодарение на което радиусите на сектори 2 и 3 спрямо оста на симетрия на централното зъбно колело се изменят в такъв вид, че зъбите на венците на сателита 4 не излизат от зацепване със зъбите на централното зъбно колело. Сателит 4 и изходящия вал имат допълнително назъбване, при което допълнителните назъбвания се намират в зацепване със зъбно колело. В такъв вид, въртенето на сателит 4 ще се предава на изходящия вал при произволно значение на ексцентрицитета на сателит 4, а водилото прави ротационно движение с честотата на въртене на задвижващия вал. Така зъбните колела образуват изходната планетна предавка, която може да варира и ще определя нужната кинематична характеристика на плавно регулируемата предавка в цялост. При равен брой зъби на зъбните колела предавателното отношение на изходната планетна предавка е равно на 1.

От кинематичните възможности на описаната планетна предавка при зададени брой зъби на сателита Zsat ще се определят шест главни параметри. В такъв вид, основните параметри на планетната плавно регулируема предавка могат да бъдат определени от резултатите на решението на задача за синтез и анализ на нейното съставно централно зъбно колело. Задачата за синтеза на такова колело определя неговите максимален брой зъби Zmax при зададени минимални брой зъби Zmin, модула на зацепване m и брой зъбни сектори is в два силови потока. Задачата за анализ на съставно зъбно колело се явява определяне при зададени модули на зацепване m, максимален брой зъби Zmax, брой зъбни сектор is, значението на коефициента εs на челно припокриване на секторите на съставното централно зъбно колело е минимално възможно на неговите брой зъби Zmin. Алгоритмите на решение на тези са показани в [4].

Предимството на описаната планетна плавно регулируема предавка се явява конструктивно просто, неподвижността на регулируемото съставно зъбно колело, благоприятна форма на централното зъбно колело, способстваща изключване на заклинване на сателита без корекция на параметрите на изходния контур при малки разлики в броя на зъбите. Конструктивните проблеми на подобни предавки се явяват необходимостта от балансиране на сателита и синхронизирането на радиалните премествания на сателита и зъбните сектори на централното зъбно колело, а също и ротационното движение със сателита и задаващо въртеливо движение на неговия задвижван вал при произволно значение на предавателното отношение.

Кинематиката [5] на тази предавка далеч не е идеална, затова без компенсатори не може да съответства на своето функционално предназначение.

В съответствие с фиг.2 максималната ъглова грешка на положението на зъбния сектор, относително съответства на зъбите на условното зъбно колело и се определя по формулата:

(1) ∆= � 2𝜋𝜋𝑧𝑧𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

− 2𝜋𝜋𝑧𝑧𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

� . [𝑧𝑧𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

]

n - брой на секторите.

Където Zpref- брой зъби на заготовката на изготвяне сектора на централното зъбно колело; Zcond - настояща стойност на броя зъби на условното цяло централно зъбно колело.

Определяме грешката на ъгъла на завъртане на сателита за случая, когато:

- Максимално значение на броя на зъбите на условното цяло централно зъбно колело Zcondmax= 60 (n.zsect.=60)

- Минимално значение на броя зъби на условнотоцяло централно зъбно колело Zcondmin=36 (n.zsect.=36)

- Текущо значение на броя зъби на условното цяло централно зъбно колело Zcond=40

- Предвижването на всеки сектор става диаметрално по оста на междузъбието разполовяващо сектора

- Брой зъби на заготовка за изготвяне на сектори на централното зъбно колело Zpref=60

- Брой зъби на сателита Zsat=30 - Модул на зацепване m=3mm - Зъбни колела с прави зъби и нарязани без изместване

на инструмента

Грешката в ъгъла на въртене на сателита около собствената ос, се определя в относителното изходно положение, в която оста на симетрия на зъбите на сателита съвпада с оста на симетрия на върховия сектор фиг. 2 и зависимост (1).

Фиг.2 Грешно ъглово положение на зъбния сектор на

централното зъбно колело

Фиг.3 Схема на определяне грешката на ъгъла на

завъртане на сателита при изместване на зъбни сектори и различен силов поток

Ще разгледаме схемата на зацепване на зъбите на двупоточния сателит и централното зъбно колело в областта на изместване на секторите на различни силови потоци при техните взаимодействия със сателита е равен на φ1. Проекцията на условните граници между законите на зацепване на върха и горните десни сектори в равнина, перпендикулярна на оста на задвижващия и задвижвания валове, разположени под ъгъл φ към хоризонталната ос на предавката. Ъгълът на въртене на

44

задвижваното по часовниковата стрелка колело е равен на φ1, т.е. проекциите на осите на валовете и сателита разположени на границата между зоните на зацепване. При това предавателното отношение на предавката при предаване на движение от водещия вал към сателитите при неподвижно централно колело е равно на:

(2) 𝑖𝑖𝑙𝑙𝑝𝑝𝑙𝑙𝑐𝑐 −𝑠𝑠𝑙𝑙𝑠𝑠𝑐𝑐 = −𝜔𝜔𝑙𝑙𝑝𝑝𝑙𝑙𝑐𝑐𝜔𝜔𝑙𝑙𝑝𝑝𝑐𝑐

= − 𝑍𝑍𝑠𝑠𝑙𝑙𝑠𝑠𝑍𝑍𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 −𝑍𝑍𝑠𝑠𝑙𝑙𝑠𝑠

,

А ъгъла на въртене на сателита около своята ос обратно на часовниковата стрелка се определя като разлика между броя зъби (𝑍𝑍𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 − 𝑍𝑍𝑠𝑠𝑙𝑙𝑠𝑠 ).

В зоната на изместване на секторите от техните твърди конструкции при значение на диаметър на условната начална окръжност на централното зъбно колело, по-малко от неговото значение за колелата – заготовки, създават обективно предпоставки за грешка в ъгъла на въртене на сателита. Ще определим теоретичната (номинална) величина на тези грешки за случая, когато зъбния венец на втория силов поток на сателита взаимодейства със зъбните сектори на втория силов поток на централното зъбно колело.

В триъгълника АООsec ще намерим относително ъгъл δ.

(3) 𝛿𝛿 = � 2𝜋𝜋𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

. �𝜋𝜋𝑐𝑐𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

2𝜋𝜋�� − 𝜋𝜋

2𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝− 𝑖𝑖𝑐𝑐𝑖𝑖𝑖𝑖 Δ𝐴𝐴𝐴𝐴𝐴𝐴 +

+ 𝑖𝑖𝑐𝑐𝑖𝑖 �𝑙𝑙𝑝𝑝𝑐𝑐𝑐𝑐𝑐𝑐𝑠𝑠 𝑝𝑝𝑏𝑏𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑙𝑙𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

�

(4) 𝛿𝛿∗ = � 2𝜋𝜋𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

. �𝜋𝜋𝑐𝑐𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

2𝜋𝜋�� − 𝜋𝜋

2𝑍𝑍𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝− 𝑖𝑖𝑐𝑐𝑖𝑖𝑖𝑖∗Δ𝐴𝐴𝐴𝐴𝐴𝐴∗ +

+ 𝑖𝑖𝑐𝑐𝑖𝑖 �𝑙𝑙𝑝𝑝𝑐𝑐𝑐𝑐𝑐𝑐𝑠𝑠𝑝𝑝𝑏𝑏𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝∗

𝑝𝑝𝑙𝑙𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝�

(5) 𝑝𝑝𝑏𝑏𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = 𝑚𝑚 𝑧𝑧2𝑐𝑐𝑐𝑐𝑠𝑠𝑖𝑖

(6) 𝑝𝑝∗𝑏𝑏𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 = 𝑚𝑚 𝑧𝑧2𝑐𝑐𝑐𝑐𝑠𝑠𝑖𝑖∗

Където rbpref - радиус на основната окръжност за зъбното колело;

rapref - радиус на окръжността на върха на зъбното колело;

α и 𝑖𝑖∗ - ъгли на зацепване.

След това намираме отрязъка ОА

(7) ∠𝐴𝐴𝐴𝐴 = �𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐𝐴𝐴2 + 𝐴𝐴𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐2 − 2𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐 𝐴𝐴.𝐴𝐴𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐 . 𝑐𝑐𝑐𝑐𝑠𝑠𝛿𝛿

(8) ∠𝐴𝐴𝐴𝐴∗ = �𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐∗ 𝐴𝐴2 + 𝐴𝐴𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐2∗ − 2𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐∗ 𝐴𝐴.𝐴𝐴𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐∗ . 𝑐𝑐𝑐𝑐𝑠𝑠𝛿𝛿∗

След това ъгъл АООsec и ∠𝐴𝐴𝐴𝐴𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐∗

(9) ∠𝐴𝐴𝐴𝐴𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐 = 𝑙𝑙𝑝𝑝𝑐𝑐𝑠𝑠𝑖𝑖𝑐𝑐 𝐴𝐴𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐 .𝑠𝑠𝑖𝑖𝑐𝑐𝛿𝛿𝐴𝐴𝐴𝐴

(10) ∠𝐴𝐴𝐴𝐴𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐∗ = 𝑙𝑙𝑝𝑝𝑐𝑐𝑠𝑠𝑖𝑖𝑐𝑐 𝐴𝐴𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐∗ .𝑠𝑠𝑖𝑖𝑐𝑐 𝛿𝛿∗

𝐴𝐴𝐴𝐴

Тогава

(11) ∠𝐴𝐴𝐴𝐴𝐴𝐴 = 𝜋𝜋2− ∠𝐴𝐴𝐴𝐴𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐

(12) ∠𝐴𝐴𝐴𝐴𝐴𝐴∗ = 𝜋𝜋2− ∠𝐴𝐴𝐴𝐴𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐∗

(13) ∠𝐴𝐴𝐴𝐴𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠 = ∠𝐴𝐴𝐴𝐴𝐴𝐴 − 𝜑𝜑2 (14) ∠𝐴𝐴𝐴𝐴𝐴𝐴𝑠𝑠𝑝𝑝𝑐𝑐∗ = ∠𝐴𝐴𝐴𝐴𝐴𝐴∗ − 𝜑𝜑2 Представя се възможността от триъгълника АООsat да се

определи радиуса OsatA принадлежащ на точка А на контактите на зъбите

(15) ∠𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠 𝐴𝐴 = � 𝐴𝐴𝐴𝐴2 + 𝐴𝐴𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠 −2𝐴𝐴𝐴𝐴.𝐴𝐴𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠 . cos(𝐴𝐴𝐴𝐴𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠 )

(16) ∠𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠 𝐴𝐴∗ = � 𝐴𝐴𝐴𝐴∗2 + 𝐴𝐴𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠∗ −2𝐴𝐴𝐴𝐴∗.𝐴𝐴𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠∗ . cos(𝐴𝐴∗𝐴𝐴𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠∗ )

Ако се определят ъглите АОsatE и 𝐴𝐴𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠∗ 𝐸𝐸по формулите

(17) ∠𝐴𝐴𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠 𝐸𝐸 = � 2𝜋𝜋𝑍𝑍𝑠𝑠𝑙𝑙𝑠𝑠

.𝑍𝑍𝑔𝑔𝑝𝑝𝑙𝑙𝑝𝑝𝑖𝑖𝑐𝑐𝑔𝑔 � + 𝜋𝜋2𝑍𝑍𝑠𝑠𝑙𝑙𝑠𝑠

+ 𝑖𝑖𝑐𝑐𝑖𝑖𝑖𝑖 −

− 𝑖𝑖𝑐𝑐𝑖𝑖(𝑙𝑙𝑝𝑝𝑐𝑐𝑐𝑐𝑐𝑐𝑠𝑠 𝑝𝑝𝑏𝑏𝑠𝑠𝑙𝑙𝑠𝑠𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠 𝐴𝐴

)

(18) ∠𝐴𝐴𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠∗ 𝐸𝐸 = � 2𝜋𝜋𝑍𝑍𝑠𝑠𝑙𝑙𝑠𝑠

.𝑍𝑍𝑔𝑔𝑝𝑝𝑙𝑙𝑝𝑝𝑖𝑖𝑐𝑐𝑔𝑔 � + 𝜋𝜋2𝑍𝑍𝑠𝑠𝑙𝑙𝑠𝑠

+ 𝑖𝑖𝑐𝑐𝑖𝑖𝑖𝑖∗ −

− 𝑖𝑖𝑐𝑐𝑖𝑖(𝑙𝑙𝑝𝑝𝑐𝑐𝑐𝑐𝑐𝑐𝑠𝑠 𝑝𝑝𝑏𝑏𝑠𝑠𝑙𝑙𝑠𝑠∗

𝐴𝐴𝑠𝑠𝑙𝑙𝑠𝑠∗ 𝐴𝐴

)

Където Zgearing – брой винаги зацепени зъбни двойки.

Аналогично можем да определим ъгъла на въртене на сателита при взаимодействието на неговите зъби в зоната на изместване на секторите със зъбите на зъбния сектор на първия силов поток, като грешката на този ъгъл по отношение на номиналното значение е значително по-малко от 1𝑐𝑐 , но все още е много съществена. В качество на една от мерките за изравняване на отрицателните последствия на кинематичната грешка, свързана с особеностите на функциониране на предавките, може да бъде препоръчано фланкиране на зъбите.

Друг метод за отстраняване на кинематичната грешка в точността на предаване на ъгъла на завъртане е чрез създаване на безхлабинни конструкции или предварително еластични конструкции чрез еластично разделяне на зъба в радиална и диаметрална посока.

3. Заключение Разработени са принципи за създаване на планетен плавно

регулируем вариатор с асиметричен профил на зъбите осигуряващ работоспособна конструкция с достатъчно зацепени брой зъби при неговата работа и вариране на броя сектори и броя зъби на централното зъбно колело.

Оценена е кинематичната точност на планетен вариатор с асиметричен профил на зъбите като е получена относителна ъглова грешка изразена в ъглова стъпка и едновременно зацепени двойки зъби.

В бъдещи разработки ще бъде разгледан случаят с изместване на инструмента и компенсиране на мъртвия ход при асиметричен профил на зъбите.

4. Литература 1. Даньков, А. М. Сборка составных зуб- чатых колес для

регулируемых зубчатых передач / А. М. Даньков // Сборка в машиностроении, приборостроении. – 2002. – № 11. – С. 7–10.

2. Даньков, А. М. Сборка и регулировка основных модификаций плавнорегулируемой зубчатой передачи / А. М. Даньков // Сборка в машиностроении, приборостроении. – 2005. – № 10. – С. 38–43.

3. Литвин, Ф. Л. Проектирование меха- низмов и деталей приборов / Ф. Л. Литвин. – Л. : Машиностроение, 1973. – 320 с.

4. Даньков, А. М. Синтез и анализ составного центрального зубчатого колеса планетарной плавнорегулируемой передачи нового типа / А. М. Даньков, А. З. Иоффе // Механика машин, механизмов и материалов. – 2009. – № 2. – С. 38–42.

5. А. З. Иоффе, А. М. Даньков. Конструктивные и кинематические особенности плавнорегулируемых зубчатых передач //Вестник Белорусско-Российского университета. 2011. № 1 (30)

45

MINIATURE DEVICE FOR ENERGY CONVERSION – BASIC BUILDING ELEMENTS IN MECHATRONICS

Assoc. Prof. Abadjieva E. PhD.1,2, Prof. Naganawa A. PhD.1, Prof. Abadjiev V. PhD., D.Sc.2

Graduate School of Engineering Science, Faculty of Engineering Science, Akita University, Japan1 Institute of Mechanics, Bulgarian Academy of Sciences, Bulgaria 2

[email protected]

Abstract: A prototyping of miniature hyperboloid gear drives and ultrasonic motors is presented. A new type ultrasonic motor is experimentally tested.

Keywords: MECHATRONICS, HYPERBOLOID GEARS, ULTRASONIC MOTORS

1. Introduction Mechatronics is the leading direction in contemporary

industrial sciences and approach to the creation of products in the direction of synergistic integration of various branches of science and techniques as mechanics, electronics, electrical engineering, control theory and computer science.

This work has for objects of research multibody systems mechanics, which are mechatronics modulus. It contains a brief review of the development and improvement of the approaches for studying of the energy transformation processes, in order to achieve a regularly defined motions.

The multibody systems with force (regular) determined relations and interactions are developed in such way, so that they as a whole or separate bodies (body parts, respectively) of them to realize a law of energy transformation. In this case, the relations and interactions between bodies exist unlimited in time or duration of their existence is precisely defined. The predominant mechanical motions transformers and energy convertors and machines belong to these systems.

The mechanical miniature multibody systems, which purpose are to realize a preliminary defined law of energy transformation, which are the study objects are as follows:

• miniature hyperboloid gear drives; • miniature ultrasonic motor.

2. Miniature Hyperboloid Gear Drives 2.1. Background

Typical products of mechatronics are bio-robots. Their transmissions as a rule include miniature transformers of motions and energy (see Fig. 1,a) [1, 2].

Fig. 1. Model of robot hand: a) whole hand; b) bevel gear with straight teeth with 412 =i ; 101 =z ; 402 =z ; 5,0=m mm

The current work aims to present the realized by authors activates related with improvement of exploitation properties of the bio-robot hand shown on Fig. 1 [1 - 3]. The tasks related to the mentioned above goal is to find out a solution to the problems connected to the increment of the number of simultaneously contacting active tooth surfaces and also to create preconditions for controlling the backlash between mating gears which are implemented into the fingers of this hand. This is achieved when a plane bevel gear (Fig. 1b) is replaced with kinematically equivalent miniature spatial gear drive of type Spiroid or Helicon [3 - 5] (Spiroid and Helicon are registered trade mark of Illinois Tool Works, Chicago, Illinois.).

2.2. Synthesis and Prototyping.

The gear drives shown in Fig. 2 - Fig. 5 are specially synthesized by choosing the optimal structure and geometrical characteristics and they are CAD modelled. From an exploitation view point these gear drives are suitable for integration into already existing robot hand, which will result in its technical precision.

Fig. 2. Spiroid gear drive with offset 3,25 mm, gear ratio 32/8 (axial module 0. 5 mm): a) 3D CAD model; b) 3D printed model (the shown scale is in mm)

Fig. 3. Helicon gear drive with offset 3,25 mm, gear ratio 32/8 (axial module 0. 5 mm): a) 3D CAD model; b) 3D printed model (the shown scale is in mm)

The novelty of this design solution is that developed Helicon and Spiroid gears have a boundary small gear ratio. This is a

46

challenge both for their optimization synthesis and design in terms of their technical realization. The reason for this is that these gear pairs usually ensure rotations transformation with gear ratio more than 10 [6].

Fig. 4. Spiroid gear drive with offset 4 mm, gear ratio 40/10 (axial module 0. 5 mm): a) 3D CAD model; b) 3D printed model (the shown scale is in mm)

Fig. 5. Helicon gear drive with offset 4 mm, gear ratio 40/10 (axial module 0. 5 mm): a) 3D CAD model; b) 3D printed model (the shown scale is in mm)

The extreme difficulty of elaboration with available technical and technological device and the high manufacturing cost, define the reason to use 3D software technology for the elaboration of the above mention gear transmission (see Fig. 2 - Fig. 5).

We will mentioned, that the applied by authors, 3D software technology include the following stages:

- mathematical modeling for optimization synthesis of skew-axes gears upon a „pitch contact point“ [6, 7];

- development of a mathematical model for synthesis upon a „mesh region“[6] (development of a 3D CAD model);

- 3D printing of the synthesized gear drives.

Fig. - Fig. 5 illustrate the last two stages of the 3D software technology.

The use of this technology is a guarantee of :

- Shortening of the cycle "innovative idea - innovative product" ; - Impetus of the innovative strategies development and

increasing the actual quality of the created prototypes by improving their accuracy and a fast realization of various modifications (variants) of a physical prototype;

- Impetus to the process of building a competitive environment; - Stimulation of the inventive and innovative activity of

engineers, designers and scientists. An essential problem, related to the 3D technology of

manufacturing is the optimal choice of 3D printers and materials for the gear sets elaboration. The quality solution of these tasks is a

guarantee for the optimal teeth strength, optimal smoothens and hardness of the active tooth surfaces.

2.3. Conclusion

The mathematical models of two Spiroid and Helicon gear drives for incorporation into the robot-hand are elaborated, based on the presented approach. An experimental printing with different alternatives material is forthcoming.

3. Miniature Ultrasonic Motor with a Metallic Plate

3.1. Background

Ultrasonic motor is a mechanical system for transforming an electric energy into a mechanical one. It is a type of electric motor powered by the ultrasonic vibration and friction of a component – the stator, placed against another component – the rotor or slider depending on the scheme of operation (rotation or linear translation). The ultrasonic vibration is generally generated by a piezoelectric element. The first applied in practice, ultrasonic motor is of a rotational type and it is developed in Japan in 1986 [8, 9]. Other motors with different working principle are elaborated after it, but in most cases it is difficult to be downsized [10 - 12].

This study presents a new miniature ultrasonic motor, which combines the operating of the ultrasonic motor with a metal plate [13]. The new ultrasonic motor is characterized with a simple construction, small dimensions and mass. The action of the created prototype is under testing.

3.2. Structure of the Мotor.

In Fig. 6 are shown the device and basic dimensions of the stator of the new ultrasonic motor )2,15,267,2( mmmmmm ×× . Stator’s structure includes a piezoelectric element and a J-shaped metal plate. The piezoelectric element is a multilayer – type AM1 (with dimensions mmmmmm 47,22,12,1 ×× ) and it is elaborated by NEC/Tokin Corp., Japan. The material of the metal plate is phosphor bronze having a thickness of board mm1,0 . Fig. 7 shows the result of the vibration mode by finite element method (FEM) analysis (the first frequency vibration mode is kHz7,4 and the second mode is kHz6,51 ). Through experiments it is verified the obtained rotation of the lowest frequency to high frequency.

The displacement characteristics are measured by the experiment. It is generated a 1 Hz trapezoidal wave from a function generator and it is applied as the driving signal by its amplifying with an amplifier. The horizontal displacement is detected by a laser sensor, and the data are recorded with an oscilloscope. When the voltage of V4± was applied, the maximum displacement was

mµ26,0 in the horizontal direction.

Fig. 6. Structure of the stator

47

Fig. 7. Vibrational modes of the stator

3.3. Operating Principle

On Fig. 8 is shown the operating principle of the new ultrasonic motor. When a driving signal is inputted into the piezoelectric element, the voltage causes the piezoelectric element to stretch in horizontal direction. The extension drives the metallic plate. On Fig. 9 is shown a driving signal: (a) the driving wave for the rotation in the counterclockwise direction; (b) driving wave for the rotation in clockwise direction. The signal is saw-tooth shaped wave and the ratio of the voltage is 1: 8: 1 (see Fig. 9).

Fig. 8. Operating principle

Fig. 9. Driving wave

3.4. Experiment

The equipment for the experiment is shown on Fig.10. A rotor is used to verify the rotation characteristics of the stator. The rotor has the miniature bearing with the diameter 3 mm which is made by the stainless. The video image is analyzed in order to measure the rotational speed. Since the bearing is so small, there are is not a measurement method.

Fig. 10. Experimental equipment: (a) Comparison of the size of the stator with a coin; (b) A miniature ultrasonic motor

The conducted experiment is realized by changing the applied voltage to a piezoelectric element: VVV 4;3;2 ±±± . Fig. 11 shows the results from the experiment, when the rotor is rotating in clockwise direction. The vertical axis shows the rotor’s rotational speed analyzed in the video image. It is found that when the driving frequency applied to the stator is higher, the resulting rotational speed of the rotor is higher. The maximum speed of rotation is around 360 1min− , when the applied voltage is V4± . The miniature motor has a rotation speed of 60-110 1min− (by driving frequency of kHz17585 − ), and it can driven even with a very low voltage of V2± .

Fig. 11. Results of the experimental test (rotation into clockwise direction)

3.5. Conclusion

The study of new miniature ultrasonic motor is presented. Its structure combines multilayer piezoelectric element with a metal plate. It can realize a rotational speed of the rotor over 360 1min− . The futures studies will examine the motor torque by using a force sensor.

4. Generalized Conclusion The study is dedicated to the offered and applied by the authors

of this work, two type miniature mechatronics modulus:

• miniature hyperboloid three-links transmissions with face mating gears of type Spiroid and Helicon, intended for incorporation into bio-robots;

• miniature ultrasonic motor with a driving metal plate, implanted in its stator;

The study contains information about the developed constructions, approaches to the synthesis, prototyping and experimental testing. The perspectives for the development of the created modules, as well as the possibility for their combining in order to establish a mechatronic systems, are declared.

48

References 1.Mouri, T., T. Endo, H. Kawasaki Review of Gifu Hand and its Application, An International Journal Mechanics Based Design of Structures and Machines, Publisher Taylor and Francis, London UK, 2011, pp. 210-228

2. Mouri, T., H. Kawasaki, S. Nakagawa, T. Miura in: High Power Humanoid Robot Hand, Proc. of RSJ2012, No RSJ2012AC202-3, Sapporo, Japan, 2012, (in Japanese)

3. Abadjiev, V., E. Abadjieva, H. Kawasaki, T. Mouri Computer Synthesis Approaches of Hyperboloid Gear Drives with Linear Contact, Journal of Theoretical and Applied Mechanics, Institute of Mechanics, Sofia, vol. 44, No. 3, 2014, pp. 8-10

4. Abadjieva, E., V. Abadjiev, H. Kawasaki, T. Mouri in: On the Synthesis of Hyperboloid Gears and Technical Applications, Proceedings of ASME 2011 International Power Transmissions and Gearing Conference, IDETC/CIE 2013, 4-7 August 2013 Portland, Oregon, USA (published on CD), 2013

5. Abadjiev, V., E. Abadjieva, H. Kawasaki, T. Mouri, D. Petrova, in: Some Principles of Mathematical Modelling and Computer Synthesis of Hyperboloid Gears with a Conjugate Linear Contact. 2014 International Conference on Information Science, Electronics and Electrical Engineering, ISEEE 2014, April 26-28. 2014. Sapporo City, Hokkaido, Japan, 2014, (published on CD)

6. Abadjiev, V., Mathematical Modelling for Synthesis of Spatial Gears, Journal of Process Mechanical Engineering, Proceedings of the Institution of Mechanical Engineers, Part E, Vol 216, 2002¸ pp. 31-46

7. Litvin, F., Gear Geometry and Applied Theory, PTR Prentice Hall, A Paramount, 1994 8. Sashida T., T. Kenji, An Introduction to Ultrasonic Motor, Oxford, Oxford University Press, 1993

9. Maeno T., Ultrasonic Motors, Journal of the Robotics Society of Japan, 21, 2003, pp. 10-14 (in Japanese).

10. Chen T., C. Yu, M. Tsai, A New Driver Based on Dual-Mode Frequency and Phase Control for Traveling-wave type ultrasonic motor, Energy Conversion and Management, 49, 2008, pp. 2767-2775.

11. Okamoto Y., R. Yoshida, H. Sueyoshi, The Development of a Smooth Impact Drive Mechanism (SIDM) Using a Piezoelectric Element, Konica Minolta Technology Report, 1, 2004, pp. 23-26 (in Japanese).

12. Pan Q., L. He, C. Pan, G. Xiao, Zhi Hua Feng, Resonant-Type Inertia Linear Motor Based on the Harmonic Vibration Synthesis of Piezoelectric Bending Actuator, Sensors and Actuators A: Physical, 209, 2014, pp.169-174.

13. Naganawa, A., K. Komatsu, H. Ito, Development of an Ultrasonic Motor That Uses an Inchworm Shaped Deformation of a Metallic Plate, World Journal of Engineering and Technology, 4, 2016, pp.100-106.

49

МОДЕРНИЗАЦИЯ РАЗГРУЗОЧНОГО УСТРОЙСТВА БЕГУНОВ МОКРОГО ПОМОЛА С ЦЕЛЬЮ ПОВЫШЕНИЯ ЭФФЕКТИВНОСТИ РАБОТЫ

MODERNIZATION OF THE DISCHARGING DEVICE RUNNERS WET MILLING TO IMPROVE THE

EFFICIENCY WORK

Казак Ирина Александровна, к.п.н. Инженерно-химический факультет – Национальный технический университет Украины «Киевский политехнический институт

имени Игоря Сикорского», Украина E-mail: [email protected]

Резюме: В тезисах представлен один из способов модернизации разгрузочного устройства бегунов мокрого помола с целью повышения эффективности работы их системы разгрузки за счет замены обычной конструкции тарельчатого питателя на тарельчатый питатель с обоймой и скребком. Предложенная конструкция тарельчатого питателя позволяет повысить эффективность прохождения сыпучих материалов с тарелки для разгрузки бегунов. КЛЮЧЕВЫЕ СЛОВА: БЕГУНЫ, РАЗГРУЗОЧНОЕ УСТРОЙСТВО, ТАРЕЛЬЧАТЫЙ ПИТАТЕЛЬ, ОБОЙМА, СКРЕБОК, ЭФФЕКТИВНОСТЬ, РАЗГРУЗКА

1. Введение Одной из важнейших отраслей современности является

изготовление строительных материалов, таких как кирпич, цемент, стекло и других. В производстве этих материалов используются машины для измельчения сырья: дробилки, мельницы, бегуны.

По сравнению с другими машинами для измельчения материала, например, валковыми дробилками, бегуны менее эффективны. Поэтому их следует применять только тогда, когда это предусмотрено специальными технологическими требованиями, когда наряду с измельчением необходимо обеспечить уплотнение, растирание, например, при переработке глины.

В работе исследуется проблема эффективности работы бегунов мокрого помола. Объектом исследования в данной работе является разгрузочное устройство бегунов мокрого помола - тарельчатый питатель, который обеспечивает выгрузку измельченного материала из бегунов мокрого помола. Целью исследования является повысить эффективность разгрузки бегунов мокрого помола на основе модернизации конструкции тарельчатого питателя, от эффективной подачи которого в разгрузочный лоток полученного измельченного материала зависит в том числе и количество готового продукта на выходе из бегунов мокрого помола.

2. Предпосылки и средства для решения

проблемы

Бегуны широко используются в различных отраслях промышленности строительных материалов: керамической, огнеупорной, стекольной, асбестоцементной и др. Бегунами называют машины, которые имеют чашу с установленными на ней катками. Они предназначены для мелкого дробления (до 3...8 мм) и грубого помола (0,2...0,5 мм) сырьевых материалов [1]. Измельчение в бегунах осуществляется в результате раздавливания с одновременным истиранием между цилиндрической поверхностью катков и плоской поверхностью чаши (пода) бегунов, по которой перекатываются катки. В бегунах измельчают такие материалы, как доломит известняка, сухая глина, кварц, бой керамической продукции, шамот и др. В асбестоцементной промышленности их широко используют для первой стадии разрыхления асбеста.

Существующие типы бегунов могут быть классифицированы по способу действия, технологическому назначению, конструктивному оформлению, способу разгрузки.

По способу действия: периодического и непрерывного действия.

По технологическому назначению: для мокрого, сухого и полусухого измельчения; для измельчения и перемешивания и только перемешивания; для брикетирования сырьевой смеси; с металлическими катками и металлическим подом; с каменными катками и каменным подом.

По конструктивному оформлению: с неподвижной чашей; с вращающейся; с верхним и нижним приводом (при нижнем приводе сложнее разборка, длительнее ремонт, но масса не загрязняется); с катками, опирающимися на материал своей массой или с дополнительным гидравлическим, пневматическим или с пружинным нажатием на катки. В бегунах с вращающимися катками вокруг вертикальной оси центробежные силы стремятся сорвать катки, а в случае их неуравновешенности вертикальный вал может изогнуться, но центробежные силы при этом не оказывают влияния на материал, находящийся в чаше.

У бегунов с вращающейся чашей более спокойный ход, но центробежные силы отбрасывают материал к периферии, кроме того, у этих бегунов большая нагрузка на упорный подшипник за счет массы катков и чаши.

По способу разгрузки: с ручной разгрузкой; продавливанием через подовую решетку; с центробежной разгрузкой; с разгрузкой через периферическую подовую решетку и с разгрузкой по опускающемуся в чашу отвалу.

В зависимости от материала, из которого изготовлены катки, бегуны могут оснащаться металлическими или каменными катками. Каменные катки применяют тогда, когда в измельчаемом сырье нет металлических включений. При этом необходимо облицевать чашу каменными плитами (из гранита, кварцита и др.) [1].

Достоинства бегунов по сравнению с валковыми дробилками: можно загружать значительно большие куски материала, проще регулировать тонкость измельчения, улучшать пластические свойства глиняных материалов из-за многократного воздействия катков на них. Недостатки бегунов: громоздкость, более сложный ремонт, повышенный удельный расход энергии на единицу массы перерабатываемого материала [2].

Бегуны мокрого помола предназначены для измельчения путем раздавливания тяжелыми катками, растирания, а также для перемешивания компонентов пластичной массы. Рассмотрим на фигурах 1 и 2 конструкцию и принцип работы бегунов мокрого помола на примере бегунов мокрого помола типа СМ-21Б [3].

Даная конструкция бегунов мокрого помола работает таким образом. Чаша 5, которая вращается вместе с осью 7, под действием сил трения приводит во вращение катки 10 и 12, установленные свободно на валу 16, который в зависимости от толщины слоя материала может вместе с катками перемещаться по вертикали. Поддон в центральной части выполнен из

50

сплошных плит, а по его периферии расположено кольцевое сито 9. Материал, прошедший сквозь сито 9, выпадает на диск (тарельчатый питатель) 13, из которого скребком 14 сбрасывается в разгрузочный лоток 15 [4].

Фиг. 1. Конструкция бегунов мокрого помола СМ-21Б 1 – фрикционная муфта; 2 – редуктор; 3 – цилиндрическая шестерня; 4 – зубчатое колесо; 5 – вращающаяся чаша; 6 – подшипники качения с витыми роликами; 7 – ось чаши; 8 – внутренние цельные плиты; 9 – внешние дырчатые плиты; 10 – каток; 11 – скребки; 12 – каток в разрезе; 13 – диск (тарельчатый питатель); 14 – скребок; 15 – разгрузочный лоток

Фиг. 2. Поперечный разрез бегунов мокрого помола СМ-21Б

16 – горизонтальный вал; 17 – коленчатые оси; 18 – рессоры

В строительной и химической отраслях получено очень широкое применение бегунов мокрого помола. Исследованиями данной машины занимались авторы в работах [1, 2, 5, 7]. Они рассматривали вопросы по усовершенствованию громоздкости, сложного ремонта, повышенного удельного расхода энергии на единицу массы перерабатываемого материала, влияние гигроскопического эффекта материала в бегунах мокрого

помола. Все эти исследования по устранению перечисленных недостатков доказывают актуальность повышения эффективности работы бегунов мокрого помола в различных отраслях.

3. Решение рассматриваемой проблемы

В данной работе основное внимание уделяется еще одному из актуальных вопросов - модернизации разгрузочного устройства бегунов мокрого помола с целью повышения эффективности их работы по выгрузке измельченного материала. На фигуре 1 в представленной конструкции бегунов мокрого помола разгрузочным устройством выступает диск - тарельчатый питатель 13, с помощью которого размолотый материал в бегунах скребком 14 подается в разгрузочный лоток 15 [1]. Преимущества тарельчатых питателей - компактность и плотность установки. Недостатки - ограниченная область применения по характеристикам материала. Например, недостаточно качественная выдача увлажненных материалов с тарельчатого питателя и способ для устранения этого недостатка, исследовались в работах [6, 7]. Качество подготовки измельченного материала в условиях использования увлажненных материалов зависит от технических возможностей тарельчатых питателей, которые отвечают за точность дозирования и выгрузки материала с тарелки. Не смотря на высокую технологичность управления работой тарельчатого питателя, он не обеспечивает качественную выдачу материалов с повышенной влажностью (больше 9 %), склонных к агрегации и уплотнению, что и обуславливает существенный недостаток тарельчатого питателя, который снижает его технологические возможности [7].

Для выбора варианта модернизации разгрузочного устройства бегунов мокрого помола выполнен литературно-патентный обзор конструкций тарельчатых питателей, которые могут использоваться в бегунах мокрого помола. В результате литературно-патентного поиска выявлено, что существует достаточно много конструкций тарельчатых питателей, которые преимущественно применимы только для сухих сыпучих материалов, а вот для увлажненных материалов предлагается мало таких конструкций тарельчатых питателей. Выбран вариант модернизации тарельчатого питателя для увлажненных сыпучих материалов после измельчения в бегунах мокрого помола на основе конструкции тарельчатого питателя с обоймой, в которой имеется сегментный вырез и скребок [8]. Задачей предлагаемой модернизации тарельчатого питателя является повышение эффективности выгрузки измельченного материала из бегунов мокрого помола.

4. Результаты

Рассмотрим конструкцию и принцип работы

модернизированного тарельчатого питателя подробнее, представленного на фигурах 3 и 4. Конструкция модернизированного тарельчатого питателя содержит обойму для сыпучих материалов 11, смонтированную на тарелке 14 с возможностью вращения, и скребок 15. Обойма выполнена в виде цилиндра 11, жестко соединена с тарелкой 14 и имеет сегментный вырез, образованный двумя радиальными вертикальными стенками 12 и 13 с центральным углом от 90º до 180 °, в одной из стенок сегментного выреза выполнено выгрузочное окно 16, перекрываемое дозирующей заслонкой 18, установленной с возможностью вертикального перемещения.

Модернизированный тарельчатый питатель работает следующим образом: обойма, выполненная в виде цилиндра 11 заполняется сыпучим материалом. При вращении тарелки 14 сыпучий материал выносится через выгрузное окно 16, выполненное в вертикальной радиальной стенке 12. Скребок 15, сбрасывает сыпучий увлажненный материал из вращающейся тарелки 14. Производительность тарельчатого

51

питателя регулируется изменением частоты вращения тарелки 14 и вертикальным перемещением дозирующей заслонки 17, при этом меняется скорость и поперечное сечение потока измельченного материала. Центральный угол β от 90 ° до 180 ° между радиальными вертикальными стенками 12 и 13 сегментного выреза обоймы 11 обеспечивает лучшие условия для работы устройства. При угле β <90 ° происходит скопление материала перед скребком 15, а при угле β > 180 °- снижается производительность тарельчатого питателя, вследствие уменьшения объема обоймы. Работа тарельчатого питателя рассмотрена на фигуре 4 при оптимальном угле β = 120 °. Выгрузное окно 16 выполнено в радиальной вертикальной стенке 12, перекрыто дозирующей заслонкой 17, что позволяет регулировать высоту измельченного материала на тарелке и обеспечить более равномерную выгрузку измельченного материала.

Фиг. 3. Модернизированная конструкция тарельчатого питателя с обоймой, имеющей сегментный вырез, и скребок

Фиг. 4. Вид сверху (А-А) и продольный разрез (Б-Б) модернизированного тарельчатого питателя с обоймой,

имеющей сегментный вырез, и скребок

Центральный угол β от 90 ° до 180 °, между радиальными вертикальными стенками 12 и 13 сегментного выреза цилиндра 11, обеспечивает лучшие условия для работы

устройства. При угле β <90 ° происходит скопление сыпучего материала перед скребком 15, а при угле β > 180 ° снижается производительность тарельчатого питателя вследствие уменьшения объема сыпучего материала на тарелке. Работа тарельчатого питателя рассмотрена на фигуре 4 при угле β = 120 °. Выгрузное окно 16 выполнено в радиальной вертикальной стенке обоймы 12, которое может перекрываться дозирующей заслонкой 17, что позволяет регулировать высоту сыпучего материала на тарелке и обеспечить более равномерную выгрузку влажных сыпучих материалов.

Данная конструкция модернизированного тарельчатого питателя позволяет эффективно разгружать бегуны мокрого помола за счет регулирования разгрузки материала из сегмента тарелки от 90º до 180 °, где в одной из стенок сегментного выреза выполнено выгрузное окно, перекрываемое дозирующей заслонкой, установленной с возможностью вертикального перемещения.

5. Заключение

Таким образом, предложенная модернизация конструкции тарельчатого питателя влажных сыпучих материалов бегунов мокрого помола, позволяет обеспечить более равномерную выдачу измельченного материала в широком диапазоне их влажности (9-14 %) [8], что обеспечивает более эффективную выгрузку материала из бегунов мокрого помола.

6. Литература

1. Коваленко, І.В. Основні процеси, машини та апарати

хімічних виробництв. Підручник. / І. В. Коваленко, В. В. Малиновський. – Київ: Інрес, 2006. – 264с.

2. Сапожников, М.Я. Механическое оборудование предприятий строительньгх материалов, изделий и конструкцій. Учебник для строительньїх вузов и факультетов. / М.Я. Сапожников – М.: Высшая школа, 1971 – 382с.

3. Тимонін О.М. Обладнання хімічних виробництв та підприємств будівельних матеріалів: Атлас конструкцій. – Розділ I. Обладнання для подрібнення, класифікації та змішування. / О.М. Тимонін, В.Г. Нестеров, В.В. Малишев. – К.: Університете «Україна», 2007. – 73 с.

4. Бігуни. Для дрібного подрібнення (кінцевий розмір зерен 3...8 мм) і грубого [Електронний ресурс]. – Режим доступу: http://helpiks.org/6-18623.html Назва з екрана

5. Кошляк, Л.Л. Калиновский В.В. Производство изделий строительной керамики. / Л.Л. Кошляк, В.В. Калиновский. – М.: Высшая школа, 1985. - 189 с.

6. Живильник для зволожених сировинних матеріалів [Текст]: Патент №89586 UA, МПК C22B 1/16 / С.Є. Суліменко, В.В. Бочка, А.С. Суліменко – Опубл. 25.04.14.

7. Богацкая, И.Г. Гигроскопический эффект в бегунах для измельчения строительных материалов. / И.Г. Богацкая, А.В. Боровских. – Журнал «Механизация строительства», №12(834), 2013. – С. 20-22

8. Тарельчатый питатель [Текст]: Патент № 113833 RU, МПК G01F 11/24 / Ермолин А.Ю., Кравченко И.А., Краснов И.Н. – Опубл. 27.02.12.

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http://helpiks.org/6-18623.html

ESTIMATION OF ULTIMATE LOADS FOR CLIP CONNECTION WITH PARTIAL SWEEP OF SHAFT

Ass. Prof. PhD Ropyak L.1, Prof. DSc Shatskyi I.2, Ass. Prof. PhD Velychkovych A.1

Ivano-Frankivsk National Technical University of Oil and Gas1, Ukraine, Ivano-Frankivsk branch of Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS of Ukraine2, Ukraine

Е-mail: [email protected], [email protected], [email protected]

Abstract: The paper describes promising structures of clip (friction-screw) connections with incomplete sweep of shaft used in the axial fans of pressurization of gas pumping units. The contact problems of interaction between semi-hubs and shaft for the generally asymmetric relatively the joint bolt connections are formulated. Two types of interaction are investigated: with and without lateral displacement. Based on a priori assumption about the distribution laws of contact pressure accepted in traditional courses of “Machine Details” an engineering method for calculating of clip connections is developed. Herewith different types of details coupling (with a gap, matched, with tightness) correspond to concentrated, cosine and sustainable (linear) distributions of contact stresses. There are determined an analytical dependences of limited moments and breakloose forces on spanning angles, bolt tightening force and tribological properties of joined parts of subassembly. The examples of comparative calculation for the variants of clip connection have been presented.

Keywords: CLIP CONNECTION, PARTIAL SWEEP OF SHAFT, CALCULATION

1. Introduction Clip (screw and friction) connections belong to the class of nominally fixed friction joints, in which required normal pressure is created by tightening bolts. There are designs with split and one-piece hub. Traditionally units with complete sweep of shaft are commonly used. But sometimes in structural considerations applicable are coupling in which semi-clips cling the part of cylindrical surface of shaft. Such a situation arises from the need to regulate the angle of parts fixing. An example of such a unit is combination of blades with hub in the axial fans of pressurization of gas pumping units. In Fig. 1 typical construction of such a pinch is shown. Necessity in regulation of fan blades impinging angle depending on season temperature in room has resulted to using of split joints and become key motivation for our research.

The methods of typical calculations of most commonly used clip connections with complete sweep of shaft are worked out in details today [1…4]. Instead, the quality issues of gathering of clip connections with partial sweep of shaft are in fact unexplored. Especially it concerns the units, that are asymmetric relatively the joint bolt.

In the article the theoretical aspects of modeling the interaction of elements of detachable clip connections with incomplete sweep of shaft are considered. Aim of the research is to develop methods of engineering evaluation of bearing capacity of structures for different types of details coupling. The declared simplicity of calculations is that they are held not on the basis of rigorous solutions of contact problems, but on the basis of intuitive a priori assumptions about the contact pressure distribution law as it is done in traditional courses of “Machine Details” while calculation the detachable clips with complete sweep of shaft. Here we also develop and specify some results [5].

2. Formulation of problem We consider split clip connections (Fig. 2). They consist of semi-hubs sweeping the shaft with diameter RD 2= in areas with angles of inclination β2 and βα + respectively in symmetric and asymmetric versions. Suppose angles α and β are acute, so every single arc of contact is no longer than semicircle: πβ ≤≤ 20 ,

πβα ≤+≤0 . Connection is tightened with through-bolt so that the main vector of bolt tightening forces is P and passes through the axis of the shaft. Let’s find the dependency of friction torque form tightening force.

Symmetric and asymmetric connections including the different character of parts coupling (with a gap, adjusted and with tightness) let’s consider separately. Let's start with the simplest situations.

Fig. 1 The design of the axial fans of pressurization: built-up (at the top) and laid-up (at the foot)

53

3. Calculation of symmetric connection Running polar angle ϑ is measured from the vertical axis of symmetry clockwise (Fig. 2, a). So for the upper semi-hub the dense clinging of shaft is possible on area ),( ββϑ −∈ .

Fig. 1 Scheme of clip connection with split hub that partially sweep the shaft: symmetric (a) and asymmetric (b) versions

Let )(ϑq is contact pressure that in this case is π-periodic even

function. The main vector of contact stresses applied to, for example, upper semi-hub has to be balanced by tightening force is

( )cos 0iY R q d Pβ

β

ϑ ϑ ϑ−

= − =∑ ∫ .

Hence

(1) 0

2 ( )cosP R q dβ

ϑ ϑ ϑ= ∫ .

Let’s find the moment of friction forces M acting on the shaft while attempting to turn it at two semi-hubs:

(2) 0

2 ( ) 2 ( )M R fq Rd fD R q dβ β

β

ϑ ϑ ϑ ϑ−

= = ⋅∫ ∫ ,

f is dry friction coefficient.

Comparing (1) and (2), we find

(3) 0

0

( )

( )cos

q dM fPD

q d

β

β

ϑ ϑ

ϑ ϑ ϑ=

∫

∫.

Postulating in (3) contact pressure distribution laws for a particular character of coupling, we obtain the dependences of moment from the force P and the angle β .

When planting clip with large clearance ( RRcl > ), when contact of semi-hub with the shaft passes through the generating

line 0=ϑ and after tightening of bolts – a narrow strip, the contact pressure was approximated by concentrated force per unit length

( ) ( ) /q p Rϑ δ ϑ= ,

where ( )δ ϑ is Dirac function, /p P L= , L is strip contact length (deep into Fig. 2).

Then the numerator and denominator in (3) are the same constants, and (4) M fPD= .

When adjusted (agreed) planting in conditions of equality of radii of the shaft circles and semi-hub the contact pressure distribution is taken close to the cosine: max( ) cosq qϑ ϑ= ,

( , )ϑ β β∈ − . By calculating the integrals in (3)

(5) 4sin2 sin 2

M fPD ββ β

=+

.

The presence of tightness ( clR R< ) in untensioned condition in fact means the presence of gap at small ϑ and the point of contact at ϑ β≈ ± . When tightening the bolt the contact pressure localizes at the edges around of angles: ϑ β= ± , but after tightening mentioned gap is eliminated and further growth of P leads probably to equalization of contact pressure. So in this case let be ( )q q constϑ = = and after calculating integrals in (3)

(6) sin

M fPD ββ

= .

4. Calculation of asymmetric connection Let ),( βαϑ −∈ be the arc of probable contact and )(ϑq be the contact pressure that in this case is π -periodic function (Fig. 2, b).

Calculating the vertical component of vector of contact stresses and the main moment of friction forces instead of (1) and (2) we obtain respectively

(7) ( )cosP R q dβ

α

ϑ ϑ ϑ−

= ∫ ,

(8) ( )M fDR q dβ

α

ϑ ϑ−

= ∫ .

From (7) and (8) it is easy to find out the dependence between the friction torque and the total strength of bolt tightening

(9) ( )

( )cos

q dM fPD

q d

β

αβ

α

ϑ ϑ

ϑ ϑ ϑ

−

−

=∫

∫.

The feature of asymmetric connection is that depending on the way the semi-hubs are mounted by bolt there are two possible situations: 1) fixed connection without mutual horizontal displacement of semi-hubs; 2) free connection with the possibility of mutual lateral displacement of parts.

In first case the relative horizontal displacement equals zero and horizontal component of the contact stresses vector is unknown. And vice versa in second case the relative horizontal displacement is unknown and the projection of the main contact stresses vector on horizontal axis is zeroed:

(10) ( )sin 0iX R q dβ

α

ϑ ϑ ϑ−

= =∑ ∫ .

The last condition is used to establish the degree of asymmetry of contact pressure distribution.

Depending on the character of semi-hub coupling with the shaft let's obtain the different expressions for the friction torque in asymmetric clip connection.

When planting the clip with a gap regardless of presence or absence of lateral displacement the contact pressure is concentrated in 0ϑ = . Then from (9) also can be obtained (4).

In case of agreed contact for the task without lateral displacement we postulate the law: ϑϑ cos)( maxqq = . Calculating integrals in (9)

(11) 4(sin sin )2( ) sin 2 sin 2

M fPD α βα β α β

+=

+ + +.

In case of presence of lateral displacement we accept cosine distribution of contact pressure with displaced maximum (12) max 0( ) cos( )q qθ ϑ ϑ= − , where the angle 0ϑ can be calculated from (10).

54

Calculating quadratures in (9) and (10) after simple transformations

0 0

0 0

(sin sin )cos (cos cos )sin4

(2( ) sin 2 sin 2 )cos (cos 2 cos 2 )sinM fPD

α β ϑ β α ϑα β α β ϑ β α ϑ

+ − −= ⋅

+ + + − −,

0cos 2 cos 2tg

2( ) sin 2 sin 2β αϑ

α β α β−

=+ − −

.

It is easy to ensure that 00 >ϑ if βα > .

Excluding 0ϑ finally we get

(13) 2 2

2(sin sin ) ( sin( ))( ) ( )(sin 2 sin 2 ) sin ( )

M fPD α β α β α βα β α β α β α β

+ − + − +=

+ − + + − +.

In order to guarantee the correctness of obtained result the inequality performing should be provided in (12)

( ) 0q ϑ ≥ , ( , )ϑ α β∈ − .

This inequality is performed if 0cos( ) 0α ϑ− − ≥ . Hence

02πα ϑ≥ − ,

or

(14) 02( ) sin 2 sin 2tg ctg

cos 2 cos 2α β α βα ϑ

β α+ − −

≥ =−

are the conditions under which it is possible to use of formula (13) when α β> . In other words β does not have to be less than α , then the area of contact covers the entire range ( , )α β− . In violated inequality (14) in some areas ( 1,α α− − ) the contact is broken, then instead α in (13) it should be taken 1( )α α β= , where 1α is the root of the transcendental equation

1 11

1

2( ) sin 2 sin 2tgcos2 cos2

α β α βαβ α

+ − −=

−.

Let’s finally consider the asymmetrical coupling with tightness. In the absence of lateral displacements we accept: ( )q constϑ = ,

( , )ϑ α β∈ − . Then from (9)

(15) sin sin

M fPD α βα β+

=+

.

To connect with an additional degree of freedom in the horizontal direction let's assume that the contact pressure is

distributed linearly (16) ( )q A Bϑ ϑ= + , ( , )ϑ α β∈ − .

Then 2 2( ) ( ) / 2

(sin sin ) ( sin cos )A BM fPD

A Bα β β α

α β α α β+ + −

=+ − +

,

where from (10) sin sin cos cos 0

cos cosAB

α β α α β ββ α

+ − −= >

−.

Excluding the value /A B finally we get

(17) 2(sin sin ) ( )(cos cos )2 2 2cos( ) ( )sin( )

M fPDα β α β α β α βα β α β α β

+ + − + +=

− + − + +.

Checking in (16) inequality 0q > we find the condition of result (17) applicability

0A Bα− ≥ ,

(18) sin sin cos coscos cos

α β α α β βαβ α

+ − −≤

−.

If α is too high and (18) is violated, then again in (17) it should be taken 1( )α α β= where 1α is the root of the transcendental equation that depends from β

1 11

1

sin sin cos coscos cos

α β α α β βαβ α

+ − −≤

−.

In this case the contact happens only on the area: 1( , )ϑ α β∈ − .

5. Analysis of results The final formulas for the calculation of limit values of moments that can be transmitted by connections with incomplete sweep of shaft are consolidated in Table.

The ultimate loads for the symmetric clip connection calculated using formulae (4)–(6) are given in the Fig. 3. The similar results for asymmetric connection without lateral displacement of semi-hubs obtained using formulae (4), (11) and (15) are exhibited in the Fig. 4–6.

In the case of mutual displacement of components additionally by axial force Q (perpendicular to the plane of Fig. 2) in the last column of the table and on the diagrams M should be replaced by

2 2( )M QR+ .

Table 1: Summary table

Type of connection

Character of coupling

Contact pressure distribution Friction torque

Symmetric

with a gap concentrated force M fPD=

adjusted cosine 4sin

2 sin 2M fPD β

β β=

+

with tightness uniform sin

M fPD ββ

=

Asymmetric without lateral

displacement of semi-hubs


adjusted cosine 4(sin sin )

2( ) sin 2 sin 2M fPD α β

α β α β+

=+ + +

with tightness uniform sin sin

M fPD α βα β+

=+

Asymmetric with lateral

displacement of semi-hubs


adjusted cosine with displaced maximum 2 2

2(sin sin ) ( sin( ))( ) ( )(sin 2 sin 2 ) sin ( )

M fPD α β α β α βα β α β α β α β

+ − + − +=

+ − + + − +

with tightness linear 2(sin sin ) ( )(cos cos )

2 2 2cos( ) ( ) sin( )M fPDα β α β α β α β

α β α β α β+ + − + +

=− + − + +

55

Fig. 3 The ultimate loads for the symmetric clip connection: lines 1, 2 and 3 correspond to couplings with a gap, matched and with tightness respectively

Fig 4 The ultimate load for asymmetric clip connection without lateral displacement of semi-hub and with a gap coupling

Fig 5 The ultimate load for asymmetric clip connection without lateral displacement of semi-hub and with matched coupling

Fig 6 The ultimate load for asymmetric clip connection without lateral displacement of semi-hub and with tightness coupling

6. Conclusions On the basis of a priori assumptions about the distribution of contact stresses analytical dependences of ultimate moment and breakloose forces in detachable clip connection on spanning angles, bolt tightening force and tribological properties of details surfaces are determined.

The coupling with tightness and with big angle of sweep of shaft has proved to be the most effective. Some asymmetry in the contact increases the ultimate load too.

The degree of adequacy of the results is advisable to find out using numerical analysis of contact problems of elasticity theory.

7. References 1. Blake A. Design of mechanical joints. – New York:

M. Dekker, 1985. – 553 p. 2. Korovin Yu. V., Shamsutdinov I. R. Connections shaft-hub.

Calculations and projecting. – Moscow: Mashynostroienie, 2000. – 55 p. (in Russian).

3. Springer Handbook of Mechanical Engineering / ed. by K.-H. Grote, E. K. Antonsson. – New York: Springer Science-+Business Media, 2009. – 1580 p.

4. Contact problems between the hub and the shaft with a three-angular shape of cross-section for different angular positions / M. Dudziak, G. Domek, A. Kołodziej, K. Talaśka // Procedia Engineering. – 2014. – Vol. 96. – Pp. 50–58.

5. Shatsky I. P., Ropyak L. Ya. Elementary calculation of clip connections with incomplete sweep of shaft // Odes’kyi Politechnichnyi Universytet. Pratsi. – 2015. – Issue 2(46). – Pp. 51–56.

56

INVESTIGATION OF HEAT PIPE'S PERFORMANCE PARAMETERS DEPENDING ON DIFFERENT CONDITIONS

Radovan Nosek1, Jan Siazik1, Michal Holubcik1,

Jozef Jandacka1 Department of Power Engineering, Faculty of Mechanical Engineering, University of Zilina1

[email protected]

Abstract: The article deals with effect of the nano-fluids on the performance parameters of heat pipes. Stainless steel heat pipe was filled with a nano-fluid, a solution of copper sulphate and ferric chloride, up to 20% of the total volume of the heat pipe. Solutions of the nano-fluids were produced in the following concentrations: 1%, 2%, 3%, 4% and 5%. The performance parameters were measured on the experimental setup. The experimental measurements were carried out for different operating temperature and measured results show that the concentration of working fluid has effect on performance of the heat pipe..

Keywords: NANO-FLUID, COPPER SULPHATE, FERRIC CHLORIDE, PERFORMANCE PARAMETERS

1. Introduction Rising energy costs and tightening the standards for reducing

CO2 emissions requires more particularly in areas of high energy efficient solutions. Effective option is energy recovery of waste heat [1]. Waste heat is produced by various technological processes in industrial and energy production. To recover waste heat is necessary to choose the right type of technology, which mainly depends on the type of uses and applications of such a device. For efficient use of waste heat are also used heat pipes [2]. Heat pipes are used for efficient transfer of heat while maintaining low temperature differences. Therefore, the development and optimization of the key to greater efficiency and broader application of heat pipes. The advantage of the heat pipe is that even with small dimensions can transfer high thermal performance while its construction is simple with a long life, reliability and durability [3]. Different types and quantities of substances affect labor transfer characteristics of the heat pipe. It is therefore important that a well working medium and the type of material used, in view of the used application. In this so that we can re-use the waste heat, are usually used heat exchangers of gravity or capillary heat pipes [4].

2. Theoretical analysis of gravitational heat pipes The heat pipe is a device that is widely used as a heat

exchanger. It has several advantages such as simple structure, long life, high efficiency and easy maintenance. Its performance parameters affect various factors, but in particular the working fluid, amount of the workload and filling process. The heat pipe comprises a closed outer shell and a working fluid provided within the pipe. The pipe operates in a vertical or slightly sloping position of each coupling portion located above the evaporation portion. In the vapour of the working fluid evaporates and condenses the condensation part. [4] The condensate then flows into the evaporator section by the action of gravity along the smooth inner wall. (Fig.1)

Fig. 1 Function of gravitation heat pipe

The transferred heat flow depends on the thermal resistance of the liquid film on the wall of the condensation part. Correct operation of the tube is conditioned in such a dosing quantity of working fluid, in the range of operating parameters to avoid insufficient wetting of the surface evaporation and thus decreased performance [5]. Conversely, too much excess liquid in the vapour of boiling over leads to the release of large steam bubbles when surging phenomena. Heat transfer between the vapour phase of the working fluid and the inner wall of the tube is mainly influenced by the character of the flow of the falling film of liquid.

3. Production gravitational heat pipes The heat pipe was made of several parts. All the parts were

made of stainless material. Casing pipe forms a hollow round bar stainless steel AISI 304, cut to a length of 500 mm with an inner diameter of 10 mm and a wall thickness of 1 mm (Fig 2). The bottom of the pipes (plugs) were turned off round bar of stainless material (304) to the required size (Fig. 2). Into the centre of the end caps were drilled holes with a diameter of 1.4 mm, where was subsequently placed a needle designed for filling process. All these parts were bonded by soldering (Fig. 2). By this process was made stainless gravitational heat pipe before filling the working substance.

Fig. 2 Stainless steel pipe, cap, closed end of the tube (respectively from left to right side)

In this research are presented experiments with heat pipe filled by the working substance to 20%. The amount of working fluid was determined based on previous research. These results shows, that optimal amount of working medium is 20-25% of the total heat pipe volume.

The heat pipes were weighed before and after filling the working substance at 22% of its capacity. The evaporation of the working medium was carried out by fast heating of the jacket pipe. The evaporation of the working fluid took place up to 20% filling, the filling needle was then closed with metal tongs and end of the needle has entered into a joint using a silver solder and flame.

Working medium – nano-fluid

As a working medium were chosen following nano-fluids: solution of distilled water with ferric chloride and solution of distilled water with cooper sulphate. These solutions should provide higher heat transfer of the heat pipe in comparison with distilled water.

57

In order to determine the optimum performance, the solutions were prepared in concentrations from 1% to 5%. Ferric chloride (FeCl3) is a yellow-brown but the transmitted light as a purple red hygroscopic inorganic compound (darkness of the colour depends on the degree of oxidation by oxygen), which is under the action of atmospheric moisture flow able self. Copper sulphate (CuSO4) is is an inorganic compound that combines sulfur with copper (anhydride), which turns blue water intake.

Fig. 3 Five percent solution of FeCl3 (left) and CuSO4 (right)

4. Experimental setup The measurement was carried out on an experimental setup

(Fig. 4), where the gravitational heat pipe was placed. Evaporating part of the heat pipe was heated with water in the range from 40 °C to 90 °C and the condensation part was cooled with water at 20 °C. In total were done six measurements and the temperature difference between the tests was 10°C.

For a correct analysis of the performance parameters of the heat pipe was needed precisely defined following values:

- Water temperature at the inlet and outlet of cooling (°C)

- Flow rate of the refrigerant circuit (l/ min).

In order decrease heat loses, the evaporation part of the pipe was insulated with glass wool into the environment. The measured values were recorded at 5 second intervals for one hour by means of sensors. Data from the sensors were transmitted through the measuring panel to the software AMR WinControl from AHLBORN installed in the notebook. The measured values were out of the program AMR WinControl from AHLBORN exported to Microsoft Excel, where the values were then processed and analyzed. The actual determination of the performance of the heat pipe is based on the difference of input and output temperatures of the cooling water passing through the cooling device positioned on the condensing section of the heat pipe.

Fig. 4 The scheme of experimental setup (1-Heat pipe, 2-Heating circulators, 3- Refrigerated circulator, 4-Data logger)

5. Results and discussion Inlet temperature in the heated part of the heat pipe device

greatly impacts the performance. The value of power was growing with increasing value of the operating temperature. The performance data of individual samples heat pipes were highest at a temperature gradient 90/20 °C. In general, the tested heat pipes began to work effectively in different temperature. This is due to the pressure difference inside the pipes.

The results in Tab. 1 and 2 show that using FeCl3 and CuSO4 nano-fluids reaching peak output of pipe with a 1% concentration. Its output grew approximately linearly with increasing temperature. The heat pipes work effectively at lower temperatures. In the case of samples with other concentrations, the heat pipes started to work effectively between 70 and 80 ° C. The lowest performance was measured for 3% concentration of the nano-fluid. This could be due not only to different strengths, but also a way of filling and sealing of heat pipe in which may have been deflated respectively aspiration of air.

Table 1: Power dependence on temperature and the concentration of the FeCl3 nano-fluid

FeCl3 40°C 50°C 60°C 70°C 80°C 90°C 1% 46 W 59 W 180 W 250 W 326 W 382 W 2% 14 W 41 W 148 W 213 W 285 W 359 W 3% 9 W 12 W 42 W 96 W 187 W 240 W 4% 20 W 95 W 147 W 198 W 260 W 315 W 5% 25 W 94 W 155 W 221 W 288 W 351 W

Table 2: Power dependence on temperature and the concentration of the CuSO4 nano-fluid

CuSO4 40°C 50°C 60°C 70°C 80°C 90°C 1% 15 W 37 W 53 W 201 W 342 W 431 W

2% 5 W 1 W 10 W 39 W 164 W 246 W

3% 20 W 22 W 22 W 39 W 261 W 368 W

4% 14 W 34 W 125 W 255 W 313 W 376 W

5% 34 W 62 W 101 W 182 W 300 W 405 W

6. Conclusions Currently, only a few publications present nano-fluids and this

research topic has considerable potential. Nano-fluid seems to be as interesting alternative working substance that can easily and efficiently achieve performance increase heat pipe. The article deals with nano-fluids ferric chloride and cooper sulphate at concentrations of from 1% to 5% and describes the method for producing stainless steel gravitational heat pipes that have been made for this test. The achieved results show the increase of heat pipe performance by about 5% in comparison to other working fluid (water, ethanol). In order to observe more accurate results it is necessary to improve the filling process and insure uniform pressure and the same amount of working medium in all samples.

Acknowledgement This article is supported by the financial assistance of the

project KEGA No. 042ŽU-4/2016 ”Chladenie na základe fyzikálnych a chemických procesov”.

References [1] REAY,D. A., KEW, P. A. Heatpipes, Theory, Design and

Applications, FifthEdition,USA,2006

[2] NEMEC, P., ČAJA, A., MALCHO, M. Mathematical model for heat transfer limitations of heat pipe, Mathematical and computer modeling Volume: 57 Issue: 1-2 Pages: 126-136, 2013

58

[3] LENHARD, R., KADUCHOVÁ, K. and PAPUČÍK, Š., Analysis of the fill amount influence on the heat performance of heat pipe. IN: International Conference on Application of Experimental and Numerical Methods in Fluid Mechanics and Energetics 2014, XIX.AEaNMiFMaE 2014; Liptovsky Jan; Slovakia; 9 April 2014 through 11 April 2014; Code 107300, ISBN: 978-073541244-6, DOI: 10.1063/1.4892724

[4] VANTÚCH, M., HUŽVÁR, J. and KAPJOR, A., Heat transfer from oriented heat exchange areas [Prenos tepla z orientovaných teplovýmenných plôch] In: EPJ Web of Conference [elektronický zdroj]. - ISSN 2100-014X. - Vol. 67, art. no. 02122 (2014)

[5] FAGHRI, A. Heat Pipe Science and Technology. Washington DC. Taylor & Francis, 1995.

59

ОТНОСНО БЕЗОПАСНАТА ЕКСПЛОАТАЦИЯ НА АСАНСЬОРИ

ABOUT THE SAFE OPERATION OF LIFTS

Assoc.Prof. Dr. Krasimir Krastanov Faculty of Machinery and Construction Technologies in Transport –Todor Kableshkov University of Transport, Republic of Bulgaria

[email protected]

Abstract: Compliance with safety measures for the operation of lifts is important to preserve the health and lives of the people using them. Because of the risk factors associated with lack of control devices load or idle ones; lack or wear buttons; poor alignment with the floor landings; friction washers worn and need replacing, oil leakage and other important proper maintenance of lifts and possibly risk assessment for future exploitation. The possible causes of accidents with lifts are analysed. The possible solutions to increase safety in the operation of lifts in compliance with legal requirements are presented. The possibilities for evaluation and assessment of risk in the operation of lifts are offered two.

Keywords: SAFETY, LIFTS, ASSESSMENT ON RISK, CONTROL THE LEVEL OF RISK

1. Въведение Повечето случаи на аварии с асансьори, свързани с

наранявания на хора и смъртни случаи са причинени основно поради технически неизправности в конструкцията и човешки грешки породени от неправилна експлоатация и неспазване на правилата за безопасност. Това налага да се търсят ефективни методи и подходи и чрез оценка на риска за повишаване безопасността на този тип машини.

По данни на ДАМТН /Държавна агенция за метрологичен и технически надзор/ 98 000 са регистрираните асансьори у нас, които подлежат на технически надзор от ДАМТН и лица (или структурно обособени части на предприятия или организации), получили лицензия от Председателя на ДАМТН. До 1 декември 2016 г. са проверени 7063 асансьора, като от тях 508 при внезапни технически прегледи. Спрени са 299, а издадените предписания в ревизионните книги от извършените проверки са 4034 [5].

Най-често срещаните проблеми на асансьорите в България са свързани с:

- липсва на устройства за контрол на товара, или с неработещи такива;

- повече от асансьорите са с полуавтоматични етажни врати и без кабинни врати. Това е една от причините за честите повреди, инциденти, наранявания и смърни случаи;

- нарушена цялост или наставяне на флексир кабелите; - липса или износване на бутоните по бутониерите на

асансьорните кабини и на етажните площадки, което от своя страна излага на показ необезопасени жици, които могат да бъдат докосвани от всеки;

- недобро изравняване с етажните площадки; - износени фрикционни шайби и необходимост от

подмяна; - течове на масло; - други

2. Анализ на авариите и злополуките с асансьори през последните години.

През 2013 г. от ГД ИДТН са регистрирани 20 сигнала за

аварии и злополуки с асансьори [7]. Вследствие обследването на причините за инцидентите е

установено, че 12 от възникналите аварии се дължат на грубо неспазване на инструкциите за безопасна експлоатация на асансьорите, 8 се дължат на настъпила техническа повреда при експлоатация на асансьорите.

В резултат на авариите или злополуките са нанесени материални щети на 20 обекта, ранени са 20 души и са загинали трима души.

През 2014 г. от ГД ИДТН са регистрирани 25 сигнала за възникването на аварии и злополуки с асансьори.

Вследствие обследването на причините за възникването на инцидентите е установено, че 20 от авариите се дължат на грубо неспазване на инструкциите за безопасна експлоатация, 5 се дължат на настъпила техническа повреда при експлоатация на съоръженията.

В резултат на възникналите аварии или злополуки са нанесени материални щети на 5 обекта, ранени са 13 души и са загинали трима души.

През 2015 г. от ГД ИДТН са регистрирани 18 сигнала за възникването на аварии и злополуки с асансьори.

Вследствие обследването на причините за възникването на инцидентите е установено, че 13 от авариите се дължат на грубо неспазване на инструкциите за безопасна експлоатация, 5 се дължат на настъпила техническа повреда при експлоатация на съоръженията.

В резултат на възникналите аварии или злополуки са нанесени материални щети на 5 обекта, ранени са 10 души и са загинали двама души.

През 2016 г. от ГД ИДТН са регистрирали 21 сигнала за възникването на аварии и злополуки с асансьори.

Фиг. 1 Сигнали за аварии с асансьори за периода 2013-2016 г.

Фиг.2 Брой аварии с асансьори за периода 2013-2015, поради неспазване на инструкциите за безопасност

60

Фиг.3 Брой ранени при аварии с асансьори за периода 2013-2015

3. Възможни решения за повишаване на безопасността при експлоатация на асансьори

Във връзка с повишаване на мерките за безопасност при експлоатацията на асансьори в Р. България неотдавна с промени в Наредбата за безопасна експлоатация и техническия надзор на асансьорите бяха одобрени 10 задължителни технически изисквания за обезопасяване на старите асансьори, пуснати на пазара преди 2002 г.

Има редица други изисквания по отношение осигуряване на безопасността при експлоатация на асансьори. Някой от тях са свързани с това, че при проектиране, изработване и монтиране трябва да не се допуска потегляне на кабината при недопустимо превишаване на номиналната товароподемност.

Асансьорите трябва да са оборудвани с ограничител за превишена скорост. Изискването за това не се отнася за асансьори, чиято конструкция на задвижването не допуска превишаване на скоростта.

Високоскоростните асансьори трябва да са оборудвани с устройство за следене и ограничаване на скоростта.

Най-малко 2000 асансьора в страната нямат система за контрол на товара. Съществува изискване такова устройство да се инсталира за да не може асансьорът да потегля при претоварване. Другият вариант пък е в кабината да се монтира допълнителна врата или да се намали площта им, за да ограничи броя на пътниците.

Фиг. 4 Решения за повишаване на безопасността на асансьори

Инсталирането на допълнителна спирачка може да повиши безопасността при работа при внезапен отказ на съществуващата спирачка. Модерните спирачни системи имат две спирачки работещи независимо електрически една от друга.

Инсталирането на устройство за автоматично отваряне на вратите , позволява освобождаване и евакуиране на пътниците в кабината при авария. Монтирането на разговорно устройство стана задължително от началото на 2017 г. Продължителността на работа на средството за връзка и на аварийното осветление трябва да е достатъчно голяма, за да се даде възможност за нормално извършване на процедурата за спасяване на пътниците в случай на авария е важно съгласно изискванията на Наредбата за съществените изисквания и оценяването на съответствието на асансьорите и техните предпазни устройства [1].

Инсталирането на предпазно устройство, предотвратяващо свободното падане и неконтролируемото движение на кабината нагоре при прекъсване на електрозахранването или при повреда на някоя от съставните й части също е важно за безопасността на асансьорите [3].

Асансьорите трябва да имат и поне едно предпазно устройство, което да не допуска по време на нормална експлоатация:

- случайно или умишлено пускане в движение на кабината, ако не са затворени и заключени всички врати на шахтите;

- отварянето на вратите на шахтите, когато кабината е в движение и е извън зоната на отключване на вратата; допуска се придвижване на кабината при отворена врата на шахтата в зоната на отключване при намалена и контролирана скорост на движение.

Една от мерките свързана с безопасността на асансьорите е монтирането на предпазен щит под кабината.

По време на експлоатацията си асансьора може да заседне. Когато това се случи често пъти пътниците сами се опитват да напуснат асансьорната кабина, която в повечето случаи е разположена между два етажа. Повечето стари асансьори са оборудвани с много малък предпазен щит с размер не по-голям от 20 до 30 см., намиращ се непосредствено под кабината.

Докато пътникът се опитва да напусне кабината има вероятност да загуби равновесие и вместо да стъпи на площадката под него, съществува голяма вероятност да пропадне в асансьорната шахта.

За да бъде ограничен този риск под кабините трябва да бъде монтиран достатъчно голям предпазен щит. Височината на предпазния щит трябва да бъде поне 75 см. Това трябва да стане в срок до 31 декември 2023 г. - за жилищните кооперации и до 31 декември 2018 г. - за административните сгради.

Износването на въжетата при експлоатация на асансьорите е една от основните причини за разрушаването им.

Асансьорните въжета са носещи носещи, т. е. на тях се окачват кабината и противотежестта и служат за предаване на праволинейно движение към последните от повдигателния механизъм, или като помощни - за задвижване на ограничителя на скоростта и централния етажен превключвател, в някои конструкции шахтови врати и др.

При асансьорите най-голямо приложение са получили стоманените въжета с двойна оплетка. Обикновено общият брой на жич¬ките във въжето е 114, оплетени в 6 снопчета по 19 жички във всяко (6 х 19 = 114), но се използват и въжета с 222 съставни жички (6 снопчета по 37 жички във всяко или 6 х 37 = 222).

Кръстосано усуканите асансьорни въжета са по-трайни в клиновидните канали на фрикционните шайби. Това се дължи на по-доброто, почти успоредно разположение на жичките спрямо оста на въжето.

Трайността на стоманените въжета до голяма степен зависи от броя на прегъванията по шайбите и ролките, през които преминават при работа. Особено неблагоприятни са обратните прегъвания. Във връзка с това стремежът е да се намалят до

61

минимум прегъванията чрез правилен подбор на необходимата кинематична схема (по възможност с най-малко отклонителни ролки).

Асансьорните въжета са подложени на : а) напрежения на опън, които се предизвикват от полезния

товар; б) напрежения на огъване, които се появяват при

преминаване на въжето при работа от право в огънато положение по фрикционната шайба или барабана и по отклонителните ролки;

в) допълнителни напрежения на огъване, срязване и усукване, които се явяват в резултат на технологичната обработка на въжето, а също и на взаимодействието на жичките под влияние на товара;

г) напрежения на натиск в част от жичките, които се опират към повърхността на каналите, през които минават;

д) напрежения, предизвикани от силите на триене между въжето и каналите на фрикционната шайба и отклонителните ролки.

По изискване на Стандарт БДС ЕN 81-1:1998+А3:2010, т. 9.2.1 - отношението между делителния диаметър на триещите шайби, барабаните и ролките на въжетата и номиналния диаметър на носещите въжета трябва да е най-малко 40, независимо от броя на телените снопове [4].

3. Оценка и преценяване на риска при експлоатация на асансьори

Анализът на риска представлява последователност от действия, позволяващи да се анализират видовете опасности, техните причини и бъдещите последствия от тези опасности.

Съществуващите асансьори могат да останат в експлоатация само след извършен анализ и оценка на риска.

Управлението на риска може да се раздели на две фази: оценка на риска и контрол на нивото на риска.

С цел осигуряване на последователност в наблюдението на процеса за ограничаване на риска, както и последващо управление на риска, мерките които могат да се приложат при оценка на риска при експлоатация на асансьори са следните:

- поддържане на база данни за риска /възможни рискови аварии на асансьора/;

- осъществяване на дейности, които преразглеждат управлението и ограничаването на риска /различни видове превантивни действия, монтиране на предпазни устройства и т.н.

Таблица 1 Определяне нивото на риска [6]

Степен на вероятност

Ниво на тежест

1 - високо 2 - средно 3 - ниско 4 - незначително

А – много вероятно 1А 2А 3А 4А

В – вероятно 1В 2В 3В 4В С - случайно 1С 2С 3C 4С D – малко вероятно 1D 2D 3D 4D

Е - невероятно 1Е 2Е 3Е 4Е F - невъзможно 1F 2F 3F 4F

Таблица 2 Оценка на риска

Група на риск Нива на риска Мерки, който трябва да се вземат

I 1А, 1В, 1С, 1D, 2А, 2В, 2С, 3А, 3В

Необходими зашитни мерки за намаляване на риска

II 1Е, 2D, 2Е, 3С, 3D, 4А, 4В

Изисква се анализ за определяне необходимостта от защитни мерки, като се взема под внимание решението и обществената полза1

III 1F, 2F, 3Е, 3F, 4С, 4D, 4Е, 4F Не се изискват защитни мерки

1 Необходимо е да се има впредвид, че практически някой защитни мерки могат да направят невъзможно използването на асансьора.

Трябва да се вземат под внимание следните фактори при определяне на вероятността от повреда:

a) излагане на опасности на хората, обслужващи асансьора или използващи асансьора. Излагането на опасности трябва да се определя за всеки асансьор индивидуално.

b) излагането на опасност може да бъде постоянна. Пример: Опасност, която може да доведе до падение на

човека при препъването му при влизане или излизане от кабината дори когато кабината спира на етажа при изравняване с етажната площадка.

c) постоянно съществуващи опасни ситуации. Въпреки това, опасността от излагане може да бъде много рядко или да продължи много кратко време, което намалява вероятността от увреждане.

Пример: Нерегламентирано движение на кабината на асансьора в шахтата при работа на обслужващия персонал върху нея. Въпреки това, излагането на този риск е рядко, трае относително кратко, тъй като нечесто се извършват ремонти на покрива на кабината и кабината не винаги се движи.Обучения за повишаване осведомеността на персонала може значително да се намали вероятността от опасни събития и техните последствия.

d) излагането на опасност може да бъде рядко, но времето за въздействие може да бъде различна.

Пример: Ако силата на отваряне на вратата е недостатъчна, за да издържи на натоварването от въздействието едно лице опитващо се да я отвори, вратата може да бъде повредена от такъв удар и лицето може да падне в шахтата с тежки последици за него.

e) като цяло, при определяне на честотата и продължителността на излагане на рискове трябва да бъдат взети под внимание всички възможни фактори, като например честотата на аварии в опасните места и продължителността на аварията, в тези места.

ЗАКЛЮЧЕНИЕ Използването на различни мерки за подобряване на

безопасната работа на асансьорите е важно за бъдещата им експлоатация. Имайки предвид случващите се аварии с тези устройства, можем да кажем че не толкова повреди в елементите и механизмите им са основната причина за наранявания и жертви, а по-скоро неправилната им експлоатация и поддържане. Необходимо е точно да се спазват приетите нормативни документи в страната по отношение на тези устройства и редовно да се правят оценки на възможните рискове при тяхната експлоатация.

ЛИТЕРАТУРА [1] Наредбата за съществените изисквания и оценяването

на съответствието на асансьорите и техните предпазни устройства, Обн. - ДВ, бр. 23 от 25.03.2016 г., в сила от 20.04.2016 г. Приета с ПМС № 47 от 15.03.2016 г.

[2] Наредба за безопасната експлоатация и техническия надзор на асансьори, Приета с ПМС № 75 от 1.04.2003 г.,изм и доп. ДВ бр. 88 от 24.10.2014 г.

[3] Guidelines for Modernising Existing Lifts, Electrical and Mechanical Services Department, Hong Kong, 2016

[4] ЕN 81-1:1998+А3:2010 Правила за безопасност за конструиране и монтиране на асансьори. Част 1: Електрически асансьори

[5] www.damtn.government.bg - Държавна агенция за метрологичен и технически надзор (ДАМТН)

[6] БДС EN ISO 14798:2013 Асансьори, ескалатори и подвижни пътеки. Методология за оценяване и намаляване на риска (ISO 14798:2009).

[7] Статистически данни от ДАМТН

62

http://www.damtn.government.bg/



VIBRATION CHARACTERISTICS OF QUARTER CAR SEMI-ACTIVE SUSPENSION MODEL - NUMERICAL SIMULATIONS AND INDOOR TESTING

Assist. Prof. Eng. Pavlov N. PhD., Eng. Sokolov E. PhD

Faculty of Transport, Technical University of Sofia, Bulgaria


Abstract: This paper describes the results of numerical simulations and laboratory experiments of quarter car semi-active suspension model. Elastic characteristic of the coil spring and damping characteristics of the shock absorber in various operating modes are determinate. The amplitude-frequency characteristics and transfer function of the system with various damping coefficient are obtained. The results can be used to design semi-active suspension control strategy for improving ride comfort and road holding of ground vehicles.

Keywords: VEHICLE, SEMI-ACTIVE SUSPENSION, DAMPING, QUARTER CAR MODEL, RIDE COMFORT

1. Introduction Automotive suspension there is many conflicting requirements.

The suspension characteristics must provide good comfort to passengers when driving on uneven road and at the same time good stability when cornering and braking. Furthermore, it is necessary to ensure optimum contact between the wheels and the road under different driving conditions to achieve maximum safety. Passive suspension used in most modern cars don't provide great opportunities for these conflicting requirements and applying controlled suspension with variable characteristics increase.

By using mechatronic systems with active hydraulic or electric actuators and feedback control is possible to realizate an active suspension which ensures optimum performance in all ride modes [5]. But such type of suspension is more complicated and more expensive than passive, has a high energy consumption and low reliability. Compromise between passive and active is a semi-active suspension, also known as suspension with active damping. This type of suspension consists of a hydraulic controlled damper with variable coefficient of damping and passive elastic element - usually a metal spring. It has reliability close to that of the passive, but offers adaptability of active suspension, with much lower power consumption [3, 10]. Damping characteristics are changed by changing the passage section of the throttling orifice or by changing the viscosity of the hydraulic fluid.

In order to create an algorithm for optimal control of semi-active suspension for various modes of ride and different input disturbance first necessary should to determine the characteristics of its components - springs and adjustable dampers, and vibration characteristics of sprung and unsprung masses.

In this regard, the objective of this publication is the first with the help of laboratory experiments to determine the characteristics of the elements of the suspension and the second using numerical simulations, computer modeling and laboratory experiments on real physical model of the quarter car to determine its vibration characteristics.

2. Spring and damping characteristics

2.1. Spring characteristic

The spring stiffness characteristic has been received on the electro-hydraulic test bench shown in Fig. 1. The test bench is equipped with a force sensor and displacement sensor.

Analysis of the characteristic (Fig. 2) shows that in the separate points, the coefficient of elasticity is obtained between 19,5 and 20,5 kN/m i.e. it can be considered linear. The average value of the spring ratio on five points:

𝑐𝑐 =𝐹𝐹𝑠𝑠𝑧𝑧

= 20 𝑘𝑘𝑘𝑘/𝑚𝑚

Fig. 1. Spring characteristic test bench.

Fig. 2. Spring stiffness characteristic.

2.2. Shock absorber characteristics To obtain force-displacement and force-velocity characteristics

of the shock absorber, was used electro-mechanical shock tester, make from Intercomp®, model Shock Dyno - Hi Speed (Fig. 3).

Fig. 3. Shock absorbers tester.

1. Adjustable shock absorber; 2. Shock tester; 3. Stabilized DC power supply, U = 12 V; 4. Board with a set of

switchable resistors; 5. Laptop.

63


The stand is factory equipped with displacement sensor, force sensor as well as analog-digital device for collecting data type USB-6009 DAQ from National Instruments®. Visualization and recording the shock absorber characteristics was done using a laptop with special software. The methodology for the obtaining of the characteristics is described in detail in work [8].

Fig. 4 shows the characteristics of the shock absorber tests at different values of current flowing through the solenoid coil (Is). Selected stroke is ± 2,5 cm, and the speed is varied by the step 10 cm/s in the range from 0 to 100 cm/s

Fig.4. Characteristics of the adjustable shock absorber with different values of Is.

In the special literature [7, 3, 11] recommended in initial design

calculations of automotive suspension to use damping coefficient at piston speed v = 0,52 m/s. Fig. 5 shows displacement-force diagram for tested shock absorber on piston speed of 52 cm/s and move ± 2,5 cm.

Fig. 5. Displacement-force characteristic of adjustable shock absorber in piston velocity v = 52 cm / s and different values of Is.

The calculation damping coefficient of the shock absorber β, is obtained as the arithmetic average of the resistive force of the shock absorber Fav, divided by the velocity of the piston, which in this case is 0,52 m/s:

𝛽𝛽 =𝐹𝐹𝑎𝑎𝑎𝑎𝑎𝑎

𝐹𝐹𝑎𝑎𝑎𝑎 =

𝐹𝐹𝑐𝑐 + 𝐹𝐹𝑟𝑟2

Where 𝐹𝐹𝑐𝑐 and 𝐹𝐹𝑟𝑟 are respectively the resistance forces of the

shock absorber during compression and rebound, N. Asymmetry ratio is:

𝑘𝑘𝑎𝑎 =𝐹𝐹𝑟𝑟𝐹𝐹𝑐𝑐

The parameters of the shock absorber, when the piston speed is

𝑎𝑎 = 0,52 𝑚𝑚/𝑠𝑠 and different amperage are shown in Table 1.

Table 1: Shock absorber parameters in piston velocity mode v=0,52 m/s and different values of current Iс.

Is. A Fav, N β, (N.s)/m ka, -

0,85 1425 2740 1,7

1,30 2025 3895 2,2

1,55 2150 4135 2,3

1,80 2475 4760 2,4

2,00 2575 4950 2,4

3. Mechano-mathematical quarter car model Ride comfort of the car and its operational safety is largely

determined by the characteristics of the suspension [9]. Key indicator determining the comfort of motion is the RMS value of the vertical acceleration of the sprung masses zσ . As additional indicators are used magnitude of maximum vertical acceleration maxz± [2].

RMS value of acceleration of unsprung masses is an important indicator of road holding as giving us information about dynamic wheel load [9].

To identify these indicators and set at the stage of designing the car it needs to be represented by its mechano-mathematical model. For the modeling of the vehicle vertical oscillations, the most commonly used models shown in Fig. 1. The simplest model is the one with 1 degree of freedom (fig. 1, а). It takes account unsprung mass m acting on a one wheel (1/4 of the car mass).

q

c

m

z

q

c

m

z

t

a) b)

ct

zt

mt

Fig. 6. 1DOF (а) and 2DOF (b) quarter car model.

More complex is dual mass plane model with two degrees of

freedom (фиг. 1, b). It consists of two bodies – sprung mass m and unsprung mass mt and two elastic elements c and ct, representing respectively the elasticity of the main elastic element and the tire elasticity. Dissipative elements are β and βt and represent the main dissipative elements (dampers) and tire dissipation. Through this model we receive results for the characteristics of the sprung and unsprung masses.

The basis of the method is Lagrange equation of the second order:

QqR

qqqdtd

iiii

=

∂∂

+

∂Π∂

+

∂Τ∂

−

∂Τ∂

wherein Т and П are the kinetic and potential energy of the system;

R – Rayleigh dissipation function;

iq , iq - vector of generalized coordinates and velocities; Q – kinematic disturbance; t – time. For the model of Fig. 1, a) generalized coordinate and it

derivatives are:

zq = , zq = , zq = .

64

Differential equation describing the vibration of the system is:

cqqczzzm +=++ ββ

Apply the transformation of Laplace with zero initial conditions

and receive operator images of equation:

)()()()()()( 2 pQcppZcppZcpmp t +=+−++ βββ

where )( pZ and )( pQ are the Laplace transforms (images) of the functions )(tz and )(tq ; p - complex variable.

It is known that the transfer function of a linear system is the ratio of the Laplacian image to the output variable to the Laplacian image for the input variable, with zero initial conditions [1]. Then the transfer function of the displacements of the sprung and unsprung masses of the system of Fig. 1, a) is given:

cpmpcp

pQpZpWz ++

+==

ββ2)(

)()(

The term transfer function is closely related to the term

frequency response (amplitude-phase characteristic [1]). Frequency response of a linear dynamic system is called the transfer function for purely imaginary values of the argument p , i.e. in case of

νip = , where i is the imaginary unit, and ν is the frequency in rad/s. Then the frequency characteristics are:

( )

( ) ( ) ciimci

iQiZiWz ++

+==

νβννβ

ννν 2)(

)()(

Spectral densities of the displacements and accelerations of the

sprung masses are:

)()()( 2 ννν qzz SiWS =

)()()( 24 νννν qzz SiWS =

wherein )(νqS is the spectral density of the input disturbance.

For the model of Fig. 1 b) generalized coordinates and their derivatives are:

{ }

=

tzz

q ; }{

=

tzz

q

; }{

=

tzz

q

.

Differential equations describing the oscillations of the system are:

0)()( =−+−+ tt zzzzczm β qqczzzzczzczm tttttttttt βββ +=+−−+−− )()(

After detecting parentheses members are grouped as follows:

qcqzcczzmczzczzczzzm

tttttttt

tt

+=++++++−=+−++

ββββββ

))()(()(0)()(

Apply the transformation of Laplace with zero initial conditions and

operators receive images of equations:

)()()())(()()(0)()()()(

2

2

pQcppZccppmpZcppZcppZcpmp

tttttt

t

+=++++++−

=+−++

ββββ

ββ (1)

where )( pZ , )( pZt and )( pQ are the Laplace transforms

(images) of )(tz , )(tzt и )(tq .

Then the transfer function of the displacements of the sprung and unsprung masses of the system of Fig. 1, b) as follows:

)()()(

pQpZpWz = ;

)()()(

pQpZpW t

zt = .

To solve the system (1) using the formulas of Kramer for solving

systems of linear equations can be written:

∆∆

= zpZ )( ; ∆∆

= ztt pZ )( ,

where ∆ is the main determinant;

z∆ - determinant obtained from ∆ , by replacing the column of the coefficients before )( pZ with the column of free members (right parts of equations);

zt∆ - determinant obtained from∆ , by replacing the column of the

coefficients before )( pZt with the column of free members. Determinants are the following:

))(()()()(

2

2

ttt ccppmcpcpcpmp

+++++−+−++

=∆βββ

ββ

))(()()(0

2ttttt

z ccppmcpcp

++++++−

=∆βββ

β

)()(0)( 2

ttzt cpcp

cpmp++−

++=∆

βββ

For the transfer functions are obtained:

222 )())()(())((

)()()(

cpccppmcpmpcpcp

pQpZpW

ttt

ttz +−++++++

++==

ββββββ

222

2

)())()(())((

)()(

)(cpccppmcpmp

cpcpmppQpZ

pWttt

tttzt +−++++++

+++==

ββββββ

Then the frequency characteristics are:

)()()(

ννν

iQiZiWz = ;

)()()(

ννν

iQiZiW t

zt = .

Spectral densities of the displacements and accelerations of the

sprung masses are:

)()()( 2 ννν qzz SiWS =

)()()( 24 νννν qzz SiWS =

For the unsprung masses:

)()()( 2 ννν qztzt SiWS =

)()()( 24 νννν qzttz SiWS =

4. Numerical experiments 4.1. 1DOF model Numerical experiments were conducted in MATLAB. The spring

ratio of the spring is obtained in section 2.1 - c=20 kN/m, damping parameters are given in Table 1, sprung mass m varies in the range of 100-400 kg.

65

Fig. 7. Oscillogram of 1DOF model damping oscillations at m = 400

kg, and different damping coefficient β.

Fig. 8. Amplitude-frequency and a phase-frequency response of

1DOF model at m = 400 kg, and different coefficients β.

4.2. 2DOF model Unsprung mass is mt=30 kg, tire spring ratio ct=150 kN/m, tire

damping βt=50 N.s/m. The other parameters are as 1DOF model.

Fig. 9. Amplitude-frequency and a phase-frequency response of 2DOF

model at m = 400 kg, and different coefficients β.

Peak of frequency response are at frequencies close to the natural frequency of sprung and unsprung masses.

In a study of random vibrations spectral density of road bumps is set with the [4]:

( )( )22 .5,11..5,1.75,0.000203,0

ϑνπϑν

+=qS

where ν and ϑ are respectively the frequency and velocity of the

transport unit.

Spectral density of the calculations in vehicle speed 5 m / s are shown below:

Fig. 10. Spectral density of acceleration of the sprung mass at

different values of β.

Fig. 11. Spectral density of acceleration of the unsprung masses at

different values of β.

Increasing the damping coefficient of the shock absorber increase the accelerations of the sprung mass in the resonance and the after resonant region, and slightly reduces the acceleration before the region of resonant frequency.

By accelerations of unsprung masses noticed a significant reduction in high rates of damping to given frequency range. The most obvious is the reduction of the accelerations at the resonant frequency of these masses. Small accelerations testify to small intensity of vibration of the wheels. This is expressed conflicting demands on damping and the need to reduce the coefficient β for maximum comfort and it increasing when we need maximum contact between tire and the road. 5. Suspension indoor testing

a) b)

Fig. 12. Test bench for obtaining vibration characteristics with a load of 100 kg (a) and 160 kg (b).

66

Fig. 13. Acceleration of the sprung mass and the relative displacement

of vibration platform of the test bench with load of 100 kg and a growing frequency from 1to 20 Hz and decreasing from 20 to 1Hz.

Fig. 14. Acceleration of the vibration platform of the test bench, acceleration of the sprung mass and the relative displacement of platform with load of 100 kg and frequency of 3 Hz. The coefficient β changes from

2740 to 4950 (app.10 s) and from 4950 to 2740 N.s / m (app. 20 s).

Fig. 15. Acceleration of the vibration platform of the test bench, acceleration of the sprung mass and the relative displacement of platform with load of 160

kg and frequency of 8 Hz. The coefficient β changes from 2740 to 4950 (app.10 s) and from 4950 to 2740 N.s / m (app. 20 s).

Fig. 16. Acceleration of the vibration platform (аq)

and sprung mass (az), at frequency 8 Hz, m=160 kg and amplitude q0=4 mm, numerical modeling (a) and laboratory experiment (b).

Analysis of the results indicates that the system is linear. Since

the gradual increase in the frequency of interference and consequent reduction, the maximum amplitude of resonant modes is approximately equal (Fig. 13). On the same figure is significantly shifting the zero line of oscillations in after resonance mode. It is due to the gravity of the sprung mass down, due to the asymmetric damping. As a result, the dynamic vertical coordinate of the sprung masses (car body) is reduced and increases the likelihood of impact of the suspension travel of the vehicle and of appearance so-called "jerk" in the suspension, which is felt by the driver and passengers in the car as a hard impact when ride through bumps.

Fig. 14 and Fig. 15 show changes that occur in the same size and frequency of disturbance and changing the resistance coefficient of the shock absorber. Unsprung mass acceleration variation is more significant at high frequencies and observes the "pull" of unsprung mass down at a high coefficient of damping, again more noticeable at high frequencies of disturbance. At 8 Hz (Fig. 15) its value is about 1,5 cm.

Fig. 16 shows a better comparability of results of numerical and laboratory experiments using deterministic sinusoidal disturbance.

5. Conclusion The considered models and presented laboratory equipment,

enable to determine series of vibration characteristics of semi-active suspension. Results for waveforms for free damped oscillations amplitude- and phase-frequency characteristics, spectral density of acceleration and other characteristics of the forced vibrations with deterministic or random nature are received. The results of numerical modeling have good compatibility with those of laboratory experiments and can be used to compile algorithms and control strategies of semi-active suspension to improve the comfort and road holding of the road vehicles.

Acknowledgement

The research presented in this article was carried out with financial support from the Scientific and Research Sector of the Technical University of Sofia – Internal Funding Session 2016. Grant No. 161ПР0002-04.

67

References: [1]. Ishtev. K.G Control Theory. TU-Sofia, 2007. (In Bulgarian) [2]. Kunchev, L. P. Vehicle Dynamics. Laboratory exercises. TU-

Sofia, 1997. (In Bulgarian) [3]. Telescopic Hydraulic Shock Absorbers for Automobiles - Bench

Test Methods. Sofia, Standardization Publishing, 1983. (In Bulgarian) [4]. Uspensky, I. N. , A.A. Melnikov. Design of Vehicle Suspension.

Mashinostroenie, Moscow (1976). (In Russian) [5]. Fijalkowski B. T. Automotive Mechatronics: Operational and

Practical Issues: Volume II. Springer, 2011. [6]. Guglielmino, E., T. Sireteanu. Semi-active Suspension Control:

Improved Vehicle Ride and Road Friendliness. Springer, 2008.

[7]. Heißing, B. Chassis Handbook: Fundamentals, Driving

Dynamics, Components, Mechatronics, Perspectives. Wiesbaden, Vieweg+Teubner Verlag, 2011.

[8]. Pavlov, N. A Method and Test Equipment for Obtaining Characteristics of Controlled Hydraulic Shock Absorbers. EKO Varna, 2015. (In Bulgarian)

[9]. Robert Bosch GmbH, Automotive Handbook, 2002. [10]. Sireteanu, T., N. Stoia. Damping Optimization of Passive and

Semi-active Vehicle Suspension by Numerical Simulation. Proceedings of the Romanian Academy, 2003.

[11]. ZF Sachs: Technisches Handbuch für den Konstrukteur (Kraftfahrzeugstoßdämpfer).

68

EXPERIMENTAL STUDY TO THE MACHINE FOR DRESSING OF WATER HOLDING MATERIALS INTO THE SOIL

Mitev. G.V., Kr. Bratoev

“Angel Kanchev” University of Ruse

Abstract: We examined a machine for depositing the water storage materials layer by layer while in subsoil soil. As a result of this

activity, improve physical and chemical properties of the soil, and yields have tended to increase sustainable. The article justified basic technological parameters of the machine to achieve the best results. The inclusion of such a machine technology for growing crops tasked along with higher yields reduce the negative impact of the processes that lead to soil degradation.

KEYWORDS: SOIL PRODUCTIVITY, WATER HOLDING MATERIALS, AGRICULTURAL MACHINES

Introduction Soil degradation is due to a combination of factors. One of them is their annual deep plowing. By this way the soil leave for several months exposed to the vagaries of nature. Rainfall represented by raindrops and their energy, destroying the structure and by activating anthropogenic erosion. In intensive tillage to reverse the plow layer mobilize a number of other processes in which oxidizes and burns organic matter and organic matter content in the soil is constantly decreasing. The use of large quantities of fertilizers has an indirect negative impact as mineral nutrition is not powered soil and direct food plants. Additional commercialization of crop rotation (their deliberate distortion to produce crops that have higher purchase prices), also lead to negative effects, one of the main signs is destroying the structure of soil aggregates. It has been found that the application of fertilizers and water into the subsoil layers contributes to the enhanced development of the root system of the plants, which is a factor for sustainable development, especially in case of strong drying soil. This is mainly due to the accumulated in soil layers deep the productive moisture, whereby the roots of the plants easily derive nutrients from the soil. Thereby avoiding stress on the development of plants during the dry period, and it provides resistance yields. The purpose of this study is to justify and determine the values of the main technical parameters of the machine for laying deep the water storage materials (VSM). In relation to the target are resolved following tasks: • Experimental study of a machine for applying VSM soil • Optimization of the process parameters of a machine for applying VSM soil Decision examined problem To carry out the experimental studies using presented in Figure 1 test machine for laying the water storage substances in the depth of tillage.

Figure 1. Experimental machine

By three-point lifting mechanism experimental machine is aggregated with a tractor with a power of 260 kW, which is equipped with autopilot and navigation system. On the machine frame symmetrically there are three working stations. The width of the machine is equal to 1,4 m, while its working width is equal to 2,1 m. Working sections are composed of three located one behind the other subloil working tools. Each of them worked at various depths, which from the first to the last amended in × 0.10 m, starting of 0.40 m and up to 0.60 m. The tines are of the type with a subsurface structure, which allows after each of them in the soil to form a channel which is filled with a water storage material fed from the metering apparatus. A metering unit feeds material only those who work at the same depth. The appliances are of grooved type, whose dose can be changed by modifying the volume of the grooves therein. The relationship between dosing apparatus and subsoilers authorities by means hose diameter ∅50 mm. The length of the hose coming out of a machine is the same for all three working bodies that are powered by the given system. With the above described test machine is intended uniformly laying the water storage substances in the root layer of soil in which the plants to be secured with the necessary moisture during the growing season. Tillage without turning the plow layer it is known and applied in cases where its subsoil layer is sealed over acceptable values and the water erosion is strong and yields progressively reduced. The potential of this type of treatment, combined with innovative technical solutions and appropriate technology can be used to solve many problems relating to maintaining and increasing soil fertility. In accordance with the tasks conducted active experiment. By its nature, it is a multifactor regression analysis conducted during the field operations. To carry out the regression experiment as control factors are involved: the speed of the machine and the soil moisture. It is known that the nature of the phenomena that occur in the process of deformation of soil affect multiple and elusive factors, but selected two have a strong influence on them. Accepted levels of control factors are consistent with the recommended values that are given to them in the literature. The task in the conduct of these trials is to assess the quality of the effort in soil water storage materials and on this basis to optimize machine operation. Performance (optimization parameters), which was performed this assessment are: 𝑌𝑌1- depth of water retention groove; 𝑌𝑌2 −maintain the set norm. The study used the cyber approach. This approach allows to study and manage an object only in its effects arising from the exercise on it called externalities factors - steered ( mxxx ,..., 21 ) and unmanaged (( qwww ,..., 21 ).). In the fixed values of control factors xi (i = 1,2 ...,

m), by the action of the unguided (disturbing) factors Wk (k = 1,2 ..., q) each of the parameters (responses) Yj (j = 1 2 ..., p) the output will be random in nature. If controllable factors are quantitative (measurable) general appearance of the relationship between parameters Yj (j = 1,2 ..., p) and control factors is represented by the so-called. "Function response":

69

[ ] ( )mmj xxxxxYE ,...,,...,/ 211 ϕ= , (1)

where [ ]mj xxxYE ,...,/ 21 is the conditional mean value of the

parameter Yj. The equation (1) is called the regression equation, and the surface that it describes the - surface of the response. The type of function ( )mxxx ,..., 21ϕ depends on the nature of change of the

parameter jY in the selected area of climate factors mxxx ,..., 21 . In

carrying out the multi-factor experiments, which are in the nature of the optimization problems for obtaining the type of the equation (1) using a polynomial model of the second level which, when the mfactor has the form:

∑∑∑===

++=m

iiii

m

kikiik

m

iii xxxxy

1

2

1,0

~ βββ , (2)

Where: mβββ ,...., 10 the parameters of the model. It should be borne in mind that the polynomial model simply

approximated with some accuracy the function ( )mxxx ,..., 21ϕ

in a relatively not big range of variation of control factors. One of the major tasks of any experimental research is the search for a zoom function response based on the received experimental data. To make good this approximation should attempts be held under a special scheme - run the experiment. With many good properties are the plans of type Bm. In order to simplify recording the conditions of the experiment and to ease processing of the experimental data for the planning of experiment plans using the encoded values of the factors. If the factor xj, j = 1, 2, ..., m varies at three levels - lower, middle and upper encoded have the value of these levels will be respectively -1, 0, and + 1s. Since the selected control factors are quantitative in finding a mathematical model of the processes studied using regression analysis, [11]. In conducting multi-factor experiment was monitored climate parameters optimization (Y1 и Y2) in case and two controllable factors (х1 and х2) and the second in changing only the speed of the machine and the depth of processing. Because of the possibility of error in experimental data and because of their finite number are determined not true

mβββ ,...., 10 model

parameters and their estimates Therefore, to describe the area of optimum parameters optimization separately for each expression is represented in the form:

∑∑∑===

+++=m

iiii

m

kikiki

m

iii xbxxbxbby

1

02

1,

00

,1

0

0ˆ , (2)

where

0b , ib ,

kib ,, and

iib are experimental coefficients of the

equation. For finding a polynomial of the type (2) related to the series of experiments used term of the second order B2 [2.4], which is recorded in Table 2. The use of such compositional plans to study the test machine allows you to search and optimal operation. To determine the optimal operation of the machine using the methods of optimization by using the function of desirability. For this purpose, the target functions Y1 and Y2 are represented by generalized function of desirability that parameter is Y1 type:

21.ddD = , (3) Where 1d and 2d are private functions desirability defined by the

equation: ( )[ ]`expexp iYd −−= , (4)

And for the parameter Y2 is as follow: d = exp �−�−Yi

`�n� (5)

In determining the function of desirability are used restrictions such as: minYYi ≥ and Ymin ≤ Yi ≤ Ymax . For the indicator Y1 lower limit of the limit is 75%, which provide the necessary dimensions shaped by the machine grooves. In the indicator Y2 lower limit of the limit is 31,5 m3 ha⁄ and 38,5 m3 ha⁄ , which are a prerequisite for even applying the water storage materials in depth. The summary function of desirability is determined for two series of experiments. Thus, from the values obtained for her look the most and determine the optimum values of factors. The possible values for summary function of desirability are listed in Table 1. Table 1. Values on the scale of desirability

Des i rab i l i t y Values on the scale of desirability

Exc el l en t Ve r y g o od

Go od Sa t i s f i ed

Not sa t i s f i ed Bad

Ver y b ad

1 ,0 0 1 ,0 0 -0 ,8 0 ,8 -0 ,6 3 0 ,6 3 -0 ,4 0 ,4 -0 ,3 0 ,3 -0

0 For each of the two generalized functions of desirability seek appropriate regression model and using it are optimum values of control factors. With the resulting optimal values of the factors are calculated each indicator. The processing of all results of experiments and numerical determination of the required characteristics of the studied parameters was carried out with the help of specialized software "Statistica" 10 [11]. Essential to the reliability of the test results is the exclusion of conflicting mode of study experienced machine. Such a regime at the trials is the process of scratching ripening tools working to a depth of 0.60 m. Determine the length of this section are the way of the detachable machine to the linkage of the tractor and constructive set back corner of the working bodies of the last row of the machine. This mode is removed in the region corresponding to the path of scratching of ripening tools not conducting measurements. The duration in various attempts multifactor experiment at a constant length of the test section is amended in the range of 95÷150s depending on the set speed of the unit. Within this interval, the experimental installation process strips right have 142.8 m length of which in 5 m is done through reporting parameters such as initial 5 m are not involved in measurements due to the above mentioned reasons. Experiments were carried out in areas of the field from which it is retracted and no previous culture performed after this treatment of the soil. Using a simulator for intense rainfall are handled certain parts of the field so that the absolute humidity of the soil in them to reach the required attempts upper level. Reporting humidity is performed with moisture to soil. For reached the upper level of the absolute humidity is assumed that its value corresponds to about 70% of FC soil type in the box. Determining the type of soil is done according to its mechanical composition [43]. By using a device whose principle use is shown in Figure 3 is taken into account the distance from the "notional line" to the soil surface -h (t).

Figure 3. Principle of the notional line

70

Reporting h(t) is carried out in two points of the profile of the right of each of the parallel trials. One point is at the bottom of the open groove and the second is at the cutting edge of the furrow. In the reported results are calculated, their coefficient of variation from which to judge the depth of the open groove. In the hopper of the machine is mounted a device for monitoring the level of material therein. It consists of a tube, graduated divisions over 0.01 m, in which slide "cap" (horizontal plane), located in constant contact with the material. Upon reaching the point of parallel experiments in a series of rock pipe into account the thickness of the layer material leaked from the bunker. The result is then used to calculate the volume of imported soil VSM. The results for both parameters optimization (Y1 and Y2) at the respective levels of the factors and output matrix of the experiment are shown in Table 2. The graphical representation of these results include relevant surfaces of response and lines at the same level shown in Figure 2. Table. 2. Levels of factors matrix experiment and results of research conducted by B2 plan to process with software "Statistics"

Leve ls

Factors Working

speed 1x – кm/h

Soi l moisture

x2 -% Down (-1) 6 16

Average (0) 7 18

Upper (+1) 8 20

Factors in code Indicator Y

№ х0 х1 х2 %,1Y damY 3

2 ,

1 1 +1 +1 0,15 1,86

2 1 -1 +1 0,15 4,27

3 1 +1 -1 0,17 2,08

4 1 -1 -1 0,17 3,72

5 1 +1 0 0,16 3,74

6 1 -1 0 0,16 5,31

7 1 0 +1 0,14 3,86

8 1 0 -1 0,14 3,93

9 1 0 0 0,16 3,73

After treatment the results with the software product "Statistika" -10 for regression equations is obtained:

Y1 = 0,151 + 0. x1 − 0,0067. x2 − 0. x1. x2 + 0,013. x1

2

− 0,0067. x22

Y2 = 4,489− 0,937. x1 + 0,043. x2 − 0,193. x1. x2 − 0,343. x12 −

0,973. x22

(2) With so received by the program coefficients for the model Y1 is inadequate and that for Y2 is considered adequate. This is confirmed by those in Table 3 and Table 4 data. The model for the regression parameterY1 shows that none of the controllable factors, it does not affect the depth of the furrow. This is confirmed by the value of the coefficient of determination (R2) which model is equal to 0.7 from which it is clear that only 70% of climate parameters was due to controllable factors. Therefore, the size of the furrow is not determined by the selection of technological factors, by appropriate design parameters of the working bodies which they formed.

Ta b le 3 .Reg ress ion a na l y s i s f o r 𝑌𝑌1

Ta b le 4 .Reg ress ion a na l y s i s f o r 𝑌𝑌2

Figure. 4. Lines with equal level for Y2

However, the depth of the groove formed in the experiments is close to the desired, indicating that the structure of the tools is suitable. In terms of quantity imported VSM speed impact, as 85% R2 = 0.85) of Y2 change is due to it. The linear nature of this change can be seen when at a fixed level of insignificant factor x2 with increasing speed, reducing the amount of imported materials. This is mainly due to the fact that with increasing speed deteriorates the filling of the grooves in the wheels of the metering devices. In this series of experiments desired rate of VSM is 35 m3 ha⁄ with tolerances of ± 10%. In the test machine, these requirements are covered in the range of coded speed levels of 0.7 to 0.8, which correspond to 7,7 km/h and 7,8 km/h in natural values . Maintaining these levels ensures optimum operation of the machine, both in terms of the parameter Y2, and the machine as a whole. The test results reject the need to seek aggregate function of desirability, which indicate the optimum in the experiment.

Conclusion The justification of technological parameters of the machine for introducing VSM is made from two aspects: the degree of loosening the soil and depositing the required amount of material at a certain depth in the soil. For this purpose are established appropriate regression models show that the selected control factors do not affect the terms of the depth of the furrow, but in terms of the quantity imported VSM influenced only the speed of the machine.

Regression Summary for Dependent Variable: Y1 (пла R= ,83405766 R?= ,69565217 Adjusted R?= ,1884058F(5,3)=1,3714 p<,42278 Std.Error of estimate: ,01018

N=9b* Std.Err.

of b*b Std.Err.

of bt(3)

Interceptx1x2x12x11x22

0,151111 0,007590 19,908360,000000 0,318511 0,000000 0,004157 0,00000

-0,510754 0,318511 -0,006667 0,004157 -1,60357-0,000000 0,318511 -0,000000 0,005092 -0,000000,589768 0,318511 0,013333 0,007201 1,85164

-0,294884 0,318511 -0,006667 0,007201 -0,92582

Regression Summary for Dependent Variable: Y2 (пла R= ,91936420 R?= ,84523053 Adjusted R?= ,5872814F(5,3)=3,2767 p<,17875 Std.Error of estimate: ,67902

N=9b* Std.Err.

of b*b Std.Err.

of bt(3)

Interceptx1x2x12x11x22

4,488889 0,506114 8,86932-0,767464 0,227134 -0,936667 0,277210 -3,378900,035505 0,227134 0,043333 0,277210 0,15632

-0,128783 0,227134 -0,192500 0,339512 -0,56699-0,162416 0,227134 -0,343333 0,480142 -0,71507-0,460441 0,227134 -0,973333 0,480142 -2,02718

y y y y

4,6 4,1 3,6 3,1 2,6 2,1

-1,0 -0,8 -0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0x1

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

x2

71

At a speed of 7,7 km/h to 7,8 km/h ensures optimum operation of the machine in terms of the parameter Y2.

Sources: 1. Alexandrov, V. et all, 1967. Manual for design of

Agricultural Machines, Machinostroenie, Moskow, v.2

2. Daskalov, Dj., J. Demirev, Hr. Beloev, 1995. Manual for Agricultutal Machines, part I.

3. Demirev, J., Kr. Bratoev, 2012. Agricultural Machines, I., Ruse,

4. Dimitrov, P., A. Lazarov, D.Dimitrov, Hr. Beloev, P. Radulov, S. Valchinkov.2008. Antierosion technique for maize growing on slopy fields. Agricultural Academy, Ruse Press, p.59

5. Georgiev, I.,1973. Fundamentals of similarity and modeling of agricultural equipment. Zemizdat, Sofia,

6. 7. Vagin, A. et all. 1977. Mechanization and protection

of soil from water erosion I not chernozem area, Kolos, Leningrad, 1977.

8. Galushka, I., I. Ovchinnikov. 1967. Device for local injection of fertilizers in orchards. Mechanization and Electrification of the Agriculture, Urogaj, Kiev, 8:,

9. Markov, N., 1986. Study on chisel working bodies of machines for deep loosening of soil waterlogged surface. Abstract, Sofia, 1986

10. Mitev, G.V., A. Pavlikianova, Kr. Bratoew, St. Manushkov, 2011. Study of soil mixes for water holding materials. Proceedings of Scientific Publications, Ruse University “Angel Kanchev”, p. 231-234.

11. Mitkov, A., 2011. Theory of the experiments, Dunav Press, Ruse.

12. Panov, I., V. Vetrohin, 2008. Physical fundamentals of the soil mechanics, Kiev.

13. Fishstenko, G., 1967. Mechanization of irrigation the underplough soil layers. Mechanization and Electrification of the Agriculture, Jrojai, 8:23-25

14. 15. Srivastava ,A. K et al. 1993. Engineering principles of

agricultural machines. American Society of agricultural engineers

.

72

FUZZY PROPORTIONAL DERIVATIVE APPROACH FOR VIBRATION CONTROL OF VEHICLES

Asst. Prof. Taskin Y. PhD.1

Department of Mechanical Engineering, Faculty of Engineering, Istanbul University, Turkey1

[email protected]

Abstract: In this paper a fuzzy logic proportional derivative controller is proposed for suppressing vertical vibrations of vehicles. Initially quarter vehicle model is presented. Afterwards fuzzy proportional derivative approach is described in order to minimize vertical displacement of vehicle body. The proposed controller is applied to quarter vehicle model to demonstrate and evaluate performance of the controller. Time responses of vehicle body displacement, acceleration and suspension deflection are compared between controlled and uncontrolled cases. The proposed controller exhibits promising behavior.

Keywords: FUZZY LOGIC, PROPORTIONAL, DERIVATIVE, VIBRATION CONTROL, QUARTER VEHICLE

1. Introduction Traditionally vehicle vibrations are controlled by passive

suspension systems. A passive suspension system is composed of spring and damper elements. The control objectives cannot be achieved in broadband frequencies with these systems. Therefore, there occurs tradeoffs between ride comfort and road holding in passive suspensions [1-2]. The desired suspension system has to suppress the vehicle body displacement and acceleration together while providing adequate suspension deflection to maintain road holding. Active suspension systems have great potential to achieve these achievement goals. [3-5].

In this study, a new fuzzy logic approach is proposed in order to provide the suppression of vehicle body bounce and acceleration using active suspension system. The controller is applied on a quarter vehicle model in order to indicate the performance of the proposed controller comparing with passive case.

2. Quarter Vehicle Model Vertical dynamics of a vehicle can be analyzed by quarter

vehicle model shown in Figure 1 [6-7]. The model has two degrees of freedom which are the wheel-axle and body bounces. 1m and 2m are the wheel-axle and body masses, respectively. Wheel and suspension spring stiffnesses are denoted as 1k and 2k , respectively. 2b is damping coefficient of viscous damper and u corresponds to the control force that is produced by the actuator. 0y is the road profile changing by time which is to wheel. 1y and 2y are the absolute displacements of the unsprung and sprung masses respectively.

Fig. 1 Quarter vehicle model.

Equations of motion for the quarter car model are given below:

1 1 2 1 2 2 1 2 1 1 0( ) ( ) ( )m y b y y k y y k y y u+ − + − + − = − (1)

2 2 2 2 1 2 2 1( ) ( )m y b y y k y y u+ − + − = (2)

In this study, the quarter car model is subjected to the road input

as shown in Figure 2 and vehicle model vibrates as it passes over the road profile with the constant velocity V at first second of its travel. For the given numerical parameters in Table 1, both uncontrolled and controlled cases are computed.

Fig. 2 Road profile. Table 1: Numerical parameters of the quarter vehicle model.

Parameter Value SI Unit

1m 36 kg

2m 240 kg

2b 980 Ns/m

1k 160000 N/m

2k 16000 N/m V 72 Km/h h 0.035 m

3. Fuzzy Proportional Derivative Controller Fuzzy logic theory was first presented by Zadeh [8]. Fuzzy

logic control provides ability to use the experience of vehicle suspension system experts. In proposed fuzzy proportional derivative controller, the gains are varied by time while classical proportional derivative controller includes constant gains. Each controller gain is calculated by a fuzzy logic unit. In figure 3 representative unit is shown with a single input - single output relation.

Fig. 3 Fuzzy logic input-output representation.

73

Time varied gains of fuzzy PD are obtained from two fuzzy logic units that are for proportional and derivative gains. The input is the related variable and the output is the related variable gain of the proposed controller. SF is the related scaling factor. In Table 2, the input-output relations are given for the related terms of proposed fuzzy PD controller. Actuator control force computed from the proposed fuzzy PD controller is the sum of these terms and is obtained by equation (3). Error is also defined in equation (4).

FP FDdeu K e Kdt

= + (3)

0 2e y y= − (4)

Table 2: Fuzzy logic input-output relation. Input Scaling Factor (SF) Output

e PSF FPK

de dt DSF FDK

For each fuzzy logic unit of the proposed controller, Mandani type fuzzy inference with triangular membership functions is utilized and centroid method is used for defuzzification. Fuzzy rule base is very simple and given in Table 3. It involves the same rules for each fuzzy logic unit.

Table 3: Fuzzy logic input-output relation.

Input Output e de dt FPK FDK

S SG M MG B BG

- If input is small (S) then output gain is small (SG)

- If input is medium (M) then output gain is medium (MG)

- If input is big (B) then output gain is big (BG)

4. Simulation Results Passive and active suspension system comparisons are

computed as it is mentioned in section 2. Both cases are evaluated by time responses of body bounce, acceleration, suspension deflection and control force.

0 1 2 3 4 50

0.01

0.02

0.03

0.04

0.05

0.06

t (s)

y 2 (m)

Road profile

No Control

Fuzzy PD

Fig. 4 Comparison of body bounce responses.

In Figure 4, the vehicle body overshoots the height of the road profile after it reaches over the obstacle in passive suspension case that is denoted as no control in the figure legend. If the active suspension case is considered for the proposed controller; Fuzzy

PD, the vehicle body settles on its steady state value very smoothly as seen in the same figure.

0 1 2 3 4 5-5

0

5

10

t (s)

d2 y 2/ dt2 (m

/s2 )

No Control

Fuzzy PD

Fig. 5 Comparison of body acceleration responses.

The body acceleration is also decreased by the proposed control strategy and acceleration oscillations have declined rapidly as seen in Figure 5.

0 1 2 3 4 5-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

t (s)

y 2-y1 (m

)

No Control

Fuzzy PD

Fig. 6 Comparison of suspension deflection responses.

There isn’t any permanent deflection in suspension for proposed controller case in figure 6. It is seen that the suspension system gets back to its original position after reaching to the top of the obstacle. Therefore, in both cases, the suspension deflection reaches to zero as the vehicle body settles seen in Figure 4.

0 1 2 3 4 5-600

-400

-200

0

200

400

600

t (s)

u (N

)

Fuzzy PD

Fig. 7 Time response of control force.

74

Control force given in Figure 7 acts on both vehicle body and wheel-axle masses simultaneously. Actuator force is saturated at 500 N during computations. This situation is seen as the truncation of force value at ±500 N in control force diagram. Actuator force is also reaches to zero as the vehicle body settles seen in Figure 4.

5. Conclusion Proportional and derivative gains varied by two single input-

single output fuzzy logic controller is proposed in this study in order to reach to the suspension system objectives that aim providing ride comfort without any suspension working space degeneration. Time responses demonstrate that the vehicle body settles smoothly with decreasing body acceleration and preserving suspension working space. The results indicate that the proposed controller exhibits promising behavior.

References 1. Cherry, A. S., Jones, R. P. (1995) Fuzzy logic control of an

automotive suspension system, IEE Proc.-Control Theory Appl., Vol. 142, No. 2, March 1995, 149-160.

2. Hrovat, D. (1997) Survey of advanced suspension developments and related optimal control applications. Automatica, Vol. 33, Issue 10, 1781–1817.

3. Snamina J., Kowal J., Orkisz P. (2013) Active suspension based on low dynamic stiffness. Acta Phys. Pol. A 123: 1118–1122.

4. Yagiz N., Hacioglu Y. (2008) Backstepping control of a vehicle with active suspensions. Control Engineering Practice 16: 1457–1467.

5. Taskin, Y., Hacioglu, Y., Yagiz N. (2016) Experimental evaluation of a fuzzy logic controller on a quarter car test rig. J Braz. Soc. Mech. Sci. Eng. doi:10.1007/s40430-016-0637-0.

6. Onat C., Kucukdemiral I.B., Sivrioglu S., Yuksek I., Cansever G. (2009) LPV gain-scheduling controller design for a non-linear quarter-vehicle active suspension system. Transactions of the Institute of Measurement and Control 31: 71–95.

7. Soliman H.M., Bajabaa N.S. (2013) Robust guaranteed-cost control with regional pole placement of active suspensions. Journal of Vibration and Control 19: 1170–1186.

8. Zadeh L.A. (1965) Fuzzy sets. Information and Control 8: 338–353.

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MACHINES, TECHNOLOGIES, MATERIALS · 2018. 10. 10. · Prof. Anatoliy Kostin RU ... Doctor of Sciences, Professor of Machine Tools and Systems Department of the National Technical

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