- 2 0 1 8 - - 2 0 1 8 - XXVI INTERNATIONAL SCIENTIFIC CONFERENCE ON TRANSPORT, ROAD-BUILDING, AGRICULTURAL, HOISTING & HAULING AND MILITARY TECHNICS AND TECHNOLOGIES PROCEEDINGS V O L U M E 1 ISSN 1313-5031 (Print) ISSN 2535-0307 (Online) TRANSPORT TECHNIQUES. INVESTIGATION OF ELEMENTS. VEHICLE ENGINES. SCIENTIFIC-TECHNICAL UNION OF MECHANICAL ENGINEERING - INDUSTRY 4.0 BULGARIA
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- 2 0 1 8 -- 2 0 1 8 -
XXVI INTERNATIONAL SCIENTIFIC CONFERENCEON TRANSPORT, ROAD-BUILDING, AGRICULTURAL,
HOISTING & HAULINGAND MILITARY TECHNICS AND TECHNOLOGIES
PROCEEDINGSV O L U M E 1 ISSN 1313-5031 (Print) ISSN 2535-0307 (Online)
TRANSPORT TECHNIQUES. INVESTIGATION OF ELEMENTS. VEHICLE ENGINES.
SCIENTIFIC-TECHNICAL UNION OF MECHANICAL ENGINEERING - INDUSTRY 4.0
TRANSPORT TECHNIQUES. INVESTIGATION OF ELEMENTS. VEHICLE ENGINES
CALIBRATION OF AN ARTICULATED VEHICLE MODEL
Prof. dr hab. n.t. Adamiec-Wójcik I., Prof. dr hab. n.t. Wojciech S. .................................................................................................................. .. 4
ДИНАМИЧЕСКАЯ НАГРУЖЕННОСТЬ ЭНЕРГОСИЛОВОГО БЛОКА ПРИ ПУСКЕ ДВИГАТЕЛЯ ВНУТРЕННЕГО
СГОРАНИЯ, ОСНАЩЕННОГО СИСТЕМОЙ
Prof. Dsc. Taratorkin I., Prof. Dsc. Derzhanskii V., PhD Taratorkin A. , postgraduate Volkov A., Corresponding author - Taratorkin I. ........ 8
AN ALTERNATIVE DESIGN OF TESTING BENCH FOR DYNAMIC WHEEL CORNERING FATIGUE TESTS
THE METHOD OF NUMERICAL MODELING OF HYDRODYNAMICS AND HEAT EXCHANGE IN A CHANNEL WITH
DISCRETE ROUGHNESS Dr.sc.ing. Sidenko N., Dr. sc.ing. hab. prof. Dzelzitis E. ............................................................................................... .................................... 21
DEVELOPMENT AND RESEARCH OF TEMPERATURE CONTROL SYSTEM OF A HIGH-VOLTAGE BATTERY OF A
PERSPECTIVE ELECTRIC VEHICLE
Ph.D., Ass. Prof. Kurmaev R.Kh., Umnitsyn A.A., Struchkov V.S., Ph.D., Ass. Prof. Karpukhin K.E., Liubimov I.A. ................................. 25
MODELING AND SIMULATION OF VEHICLE AIRBAG BEHAVIOUR IN CRASH
Associate Prof. J. Marzbanrad, PhD student - V. Rastegar ......................................................................................................................... ....... 29
ПОВЫШЕНИЕ СКОРОСТНЫХ КАЧЕСТВ ТРАНСПОРТНОЙ ГУСЕНИЧНОЙ МАШИНЫ СОВЕРШЕНСТВОВАНИЕМ
ДИНАМИЧЕСКИХ СВОЙСТВ СИСТЕМЫ УПРАВЛЕНИЯ ПОВОРОТОМ
PhD Gizatullin U. Prof. Dsc. Taratorkin I., Prof. Dsc. Derzhanskii V., PhD Taratorkin A. , postgraduate Volkov A.,
Corresponding author - Gizatullin U. ............................................................................................................. .................................................... 33
MATHEMATICAL MODELING AND SIMULATION OF POWER UNIT WORKING ON MOTOR FUELS DERIVED FROM
NATURAL GAS IN TOTAL LIFE CYCLE
Eng. Mirenkova E., Assoc. Prof. D.Sc. Kozlov A., Assoc. Prof. Ph.D. Terenchenko A. .................................................................................. 37
A RESEARCH ON THE STATIC STABILITY OF THE MAVS USING VIRTUAL TUNNELS
M.Sc. Kambushev M. PhD., M.Sc. Biliderov S. PhD. .............................................................................................................................. ......... 41
ANALYTICAL AND FINITE ELEMENT IN-PLANE VIBRATION ANALYSIS OF A GANTRY CRANE
M.Sc. Şahin T., M.Sc. Candaş A., Prof. İmrak C.E. PhD. ................................................................................................................................. 45
MECHANICAL DESIGN AND FINITE ELEMENT ANALYSIS OF A 3 UNIT CUBESAT STRUCTURE
BsC. Güvenç, C. C., BsC. Topcu B., and Ph.D. Tola C. .......................................................................................................................... .......... 48
EFFECTS OF PROPELLANT PROPERTIES ON INTERNAL BALLISTIC PERFORMANCE RESULTS OF SOLID ROCKET
THREE-DIMENSIONAL SIMULATION OF THERMAL STRESSES IN DISCS DURING AN AUTOMOTIVE BRAKING
CYCLE
M.Sc. Rouhi Moghanlou M., Assist. Prof. Saeidi Googarchin H. PhD. .................................................................................................... ........ 56
NATURALLY ASPIRATED GASOLINE ENGINE UPGRADE WITH TURBOCHARGER - NUMERICAL INVESTIGATION OF
THE ANALYTICAL RESEARCH OF THE DYNAMIC LOADING EFFECT ON THE ROAD-HOLDING ABILITY
CHARACTERISTIC SIGNS OF EARTH-MOVING MACHINE
Cand. Eng. Sc., Associate Professor Shevchenko V., Post-graduate student Chaplygina A., Cand. Eng. Sc., Krasnokutsky V.,
Associate Professor Logvinov E. .............................................................................................................................................. .......................... 68
РЕГИСТРАЦИЯ И КОНТРОЛ НА ИНФРАЧЕРВЕНОТО ИЗЛЪЧВАНЕ ЕМИТИРАНО ОТ АВИАЦИОННИТЕ
ДВИГАТЕЛИ
Инженер-физик Ташев В. Л, Главен асистент Манев А. П. ............................................................................................................... .......... 73
VEHICLES FOR THE FUTURE – DILLEMAS AND PERSPECTIVES
Prof. Dr Nataša Tomić-Petrović ....................................................................................................................................... .................................. 76
COMPARATIVE ANALYSIS OF LITHIUM-ION BATTERIES FOR EV/HEV APPLICATIONS
M.Sc. Velev B. PhD. .................................................................................................................................... ...................................................... 79
CONSTRUCTIVE DESIGN OF A BELT CONVEYOR FOR A COAL MINE
M.Sc. Solak A., M.Sc. Kalay E., Prof. Dr. Imrak E. ....................................................................................... ................................................... 83
ВАКУУМНЫЕ ПОКРЫТИЯ ДЛЯ АЭРОКОСМИЧЕСКОЙ И АВИАЦИОННОЙ ТЕХНИКИ
МЕТОД ЗА ОРАЗМЕРЯВАНЕ И ИЗБОР НА ЕЛАСТИЧЕН СЪЕДИНИТЕЛ
Assoc. Prof. M.Sc. Pandev G. PhD. ............................................................................. ...................................................................................... 91
EXPERIMENTAL SIMULATION OF COMMON RAIL ELECTROMAGNETIC INJECTORS WEARING
Dipl. eng. Yordanov N., Assoc. Prof. Kiril Hadjiev, PhD ,Assoc. Prof. Emiliyan Stankov, PhD ..................................................................... 95
CALIBRATION OF AN ARTICULATED VEHICLE MODEL
Prof. dr hab. n.t. Adamiec-Wójcik I. 1, Prof. dr hab. n.t. Wojciech S. 1 Faculty of Management and Transport – University of Bielsko-Biala, Poland 1
Abstract: A model of an articulated vehicle (tractor with a trailer and/or semitrailer) formulated using joint coordinates and homogenous transformations is presented. Experimental measurements of yawing velocities of the vehicle units have been carried out for a sharp turn manoeuvre. These results are used to calibrate the mathematical models. Using optimisation methods the parameters of tires for the Dugoff-Uffelman model are chosen in such a way that the results of calculations and measurements are compatible.
Keywords: ARTICULATED VEHICLE, MULTIBODY MODEL, MODEL CALIBRATION, OPTIMISATION
1. Introduction
Articulated vehicles are vehicles which consist of two or more units, the first one of which is a tractor and the others are trailers connected by pivot joints, which enable the vehicle to perform a sharp turn. Due to the trends in the world economy the use of articulated vehicles plays a significant role in transport systems. Development of unmanned and automotive transportation systems requires much research in control and analysis of dynamics of articulated vehicles.
Safety is one of the main issues in analysis of behavior of the articulated vehicles especially in respect of stability of motion. There is a considerable amount of research devoted to the analysis of rollover and jack-knifing problems [1-4]. Control strategies are usually proposed on the basis of simplified dynamic models [5,6]. On the other hand the dynamic model has to take into account as many parameters as possible in order to reflect real motion but numerical efficiency is also a very important factor.
In this paper the dynamic model of an articulated vehicle is derived using multibody methods [7]. Joint coordinates are used to describe kinematics of the vehicle which makes the model to be derived with the smallest number of generalized coordinates. In order to define the geometry of the system we use homogenous transformations which are very popular in robotics [8].
Tire models play an important role in every model of a vehicle. The most popular models are Pacejka’s magic formula [9] and the Dugoff-Uffelman model [10]. Both of them depend on parameters which have to be determined experimentally and the results of numerical simulations strongly depend on the values chosen. In this paper the Dugoff-Uffelman model is used and in order to choose the parameters of the model calibration procedure based on solution of an optimization problem is proposed. The optimization problem is defined so that the parameters of the tire are chosen in such a way that the results of experimental measurements are compatible with those from numerical simulations.
2. Mathematical model of an articulated vehicle
Mathematical models of vehicles are derived with a different level of detail depending on the purpose of the model. Very often the equations of motion are formulated analytically. Multibody methods are useful especially in the description of articulated vehicles consisting of 𝑛 vehicle units, where each unit is treated as a separate rigid body connected with others in the kinematic chain by means of rotary joints. When joint coordinates and homogenous transformations developed in robotics are applied, the motion of each link (unit) in the chain is described with respect to the preceding link. The main difference, as far as vehicles are concerned, is that the additive units (suspension, wheels, steering system) are coupled to the link (vehicle unit) and thus a tree shape of the whole system is obtained (Fig.1).
Fig. 1 System of vehicle units (links) in the tree like shape.
The procedure of generating the equations of motion is general and a single vehicle can be considered (𝑛 = 1) as a special case. In order to describe kinematics of the articulated vehicle, the coordinate systems are assigned to each vehicle unit. If the first link (tractor or a single vehicle) is considered, the respective coordinate system is placed in the center of mass of the unit and its motion is described by six coordinates which are three displacements 𝑥( ), 𝑦( ), 𝑧( ) and three ZYX Euler angles 𝜓( ), 𝜃( ), 𝜑( ). The motion of vehicle unit 𝑝 (𝑝 = 1, … , 𝑛) is described with respect to preceding unit 𝑝-1 in the kinematic chain by means of one to three rotary degrees of freedom depending on the kind of the coupling between those units.
For the purpose of the paper let us consider a truck with a trailer (Fig.2).
Fig. 2 Truck with a trailer.
In this case the whole vehicle is treated as a system of four vehicle units: a truck, a drawbar, a dolly and a trailer. Some of the units have wheels and thus the generalized coordinates describing the motion of the unit consist of the main unit generalized coordinates and rotation angles of wheels. A simplified model of suspension which reduces its flexibility to the contact point between the tire and the road is considered. Thus the model of the truck with a trailer shown in Fig.2 is described by the following generalized coordinates:
1) tractor with four wheels:
(1.1) 𝐪(𝟏) = 𝐪(𝟏) = 𝐪𝐛(𝟏)𝐓
𝐪𝐬(𝟏)𝐓 𝐓
where 𝐪( )= 𝑥( ) 𝑦( ) 𝑧( ) 𝜓( ) 𝜃( ) 𝜑( ) ,
𝐪( )
= 𝜑( )
𝜑( )
𝜑( )
𝜑( )
X
YZ
X1
Y1
Z1
θ( )1
ψ( )1
1
φ( )1x ,y ,z1 1 1
X2
Y2
Z2
θ( )2ψ( )2
2
φ( )2
X3
Y3
Z3
θ( )3
3
X4
Y4
Z4
ψ( )4
4
4
2) drawbar:
(1.2) 𝐪( ) = 𝐪( )
𝐪( ) = 𝐪
( ) 𝜓( ) 𝜃( ) 𝜑( )
3) dolly with two wheels:
(1.3) 𝐪( ) = 𝐪( )
𝐪( ) = 𝐪
( )𝐪
( )𝐪
( )
where 𝐪( )= 𝜃( ) , 𝐪( )
= 𝜑( )
𝜑( )
4) trailer with two wheels:
(1.4) 𝐪( ) = 𝐪( )
𝐪( ) = 𝐪
( )𝐪
( )𝐪
( ) 𝐓
where 𝐪( )= 𝜓( ) , 𝐪( )
= 𝜑( )
𝜑( )
The equations of motion of the whole vehicle can be formulated in the partitioned form as follows:
(2) 𝐀 = 𝐟
where 𝐀 =
⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎡
𝐀 ,( )
+ 𝐀 ,( )
+ 𝐀 ,( )
+ 𝐀 ,( )
𝐀 ,( )
+ 𝐀 ,( )
+ 𝐀 ,( )
𝐀 ,( )
+ 𝐀 ,( )
+ 𝐀 ,( )
𝐀 ,( )
+ 𝐀 ,( )
+ 𝐀 ,( )
𝐀 ,( )
+ 𝐀 ,( )
𝐀 ,( )
𝐀 ,( )
+ 𝐀 ,( )
𝐀 ,( )
𝐀 ,( )
𝐀 ,( )
𝐀 ,( )
𝟎 𝟎 𝟎
𝐀 ,( )
+ 𝐀 ,( )
𝐀 ,( )
+ 𝐀 ,( )
𝐀 ,( )
𝐀 ,( )
𝐀 ,( )
+ 𝐀 ,( )
𝐀 ,( )
𝐀 ,( )
𝐀 ,( )
𝟎 𝟎 𝐀 ,( )
𝟎 𝟎 𝐀 ,( )
𝐀 ,( )
𝟎
𝐀 ,( )
𝟎
𝐀 ,( )
𝟎
𝟎 𝟎
𝟎 𝟎
𝐀 ,( )
𝐀 ,( )
𝐀 ,( )
𝟎 𝟎
𝟎 𝐀 ,( )
𝟎
𝟎 𝐀 ,( )
⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎤
𝐪 =
⎣⎢⎢⎢⎢⎢⎢⎢⎢⎡𝐪
( )
𝐪( )
𝐪( )
𝐪( )
𝐪( )
𝐪( )
𝐪( )
⎦⎥⎥⎥⎥⎥⎥⎥⎥⎤
, 𝐟 =
⎣⎢⎢⎢⎢⎢⎢⎢⎢⎡𝐟
( )+ 𝐟
( )+ 𝐟
( )+ 𝐟
( )
𝐟( )
+ 𝐟( )
+ 𝐟( )
𝐟( )
+ 𝐟( )
𝐟( )
𝐟( )
𝐟( )
𝐟( )
⎦⎥⎥⎥⎥⎥⎥⎥⎥⎤
.
The number of degrees of freedom of the tractor with a trailer is:
(3) 𝑛 = 𝑛
( )+ 𝑛
( )+ 𝑛
( )+ 𝑛
( )+ 𝑛
( )+ 𝑛
( )+ 𝑛
( )
= 6 + 4 + 3 + 1 + 2 + 1 + 2 = 19
The above is just an example of generating the equations of motion of an articulated vehicle. Using this procedure the model can be easily extended with more bodies such as other trailers. In the formulae presented the general notation is assumed in which sign ~ above a coordinate means that the coordinate is defined in the local coordinate system while a coordinate without this sign is defined in global coordinate system.
3. Tire model
In order to consider forces acting between the tire and the road we use the Dugoff-Uffelman tire model. It is simpler and requires smaller number of coefficients than the most popular model called ’Pacejka magic formula’. The forces and moments acting at wheel 𝑘 of unit 𝑝 shown in Fig.3 can be calculated as functions of
normal force 𝐹 ,( ) according to the formulae:
Fig. 3 Forces acting on wheel j of unit p.
(4.1) 𝐹 ,( )
= 𝜒 , ,( )
𝐹 ,( )
(4.2) 𝐹 ,( )
= 𝜒 , ,( )
𝐹 ,( )
(4.3) 𝑀 ,( )
= 𝑀 ,( )
𝐹 ,( )
where 𝑘 = 1, … , 𝑛( )is the number of a wheel in unit𝑝 𝜒 ,
( ), 𝜒 ,
( ) are coefficients.
Coefficients 𝜒 ,( )
, 𝜒 ,( ) and function 𝑀 ,
( ) depend on tire and road parameters (stiffness, material characteristics, geometry) and vehicle motion. One of those parameters is basic lateral stiffness coefficient
𝐿 ,( ), which will be used in the optimization problem described in the
next section. Formulae for calculation of coefficients 𝜒 ,( )
, 𝜒 ,( ) and
moment 𝑀 ,( ) are presented in [11].
4. Optimisation problem
Validation is an important stage of development of a model. In order to validate the model presented in section 2 experimental measurements have been carried out for a truck with a trailer shown in Fig.4.
5
Fig. 4 Articulated vehicle used in experiments.
Measurements were taken during the motion of the vehicle with constant speed v =60 km/h which was performed for a sharp turn of the steering wheel. Both the steering angle of the steering wheel and yawing velocity of the tractor (value ( )) and the trailer ( ( ) +
( ) + ( )) were measured. When parameters for the tire were assumed equal to those given in literature the results of numerical simulations for yawing velocities differed from experimental measurements. Thus a dynamic optimization problem has been formulated as minimization of the functional:
(5)
𝛺 = 𝛺(𝑝 , … , 𝑝 ) = 𝑐1
𝑇
( )−
( )𝑑𝑡
+ 𝑐1
𝑇
( )−
( )𝑑𝑡
where: 𝑐 , 𝑐 are assumed constants, 𝑇 is the simulation time,
( )
, ( ) are measured yawing velocity of the tractor and trailer
respectively and ( )
, ( ) are calculated yawing velocity of the
tractor and the trailer respectively. The parameters 𝑝 , … , 𝑝 of the minimized functional represent values of basic lateral stiffness
coefficient 𝐿 ,( ) for all the tires. It is assumed that these stiffness
coefficients are the same for the right and left wheels and thus the following is assumed:
(6)
𝑝 = 𝐿 ,( )
= 𝐿 ,( )
for front wheels of the tractor,
𝑝 = 𝐿 ,( )
= 𝐿 ,( ) for rear wheels of the tractor,
𝑝 = 𝐿 ,( )
= 𝐿 ,( ) for the wheels of the dolly,
𝑝 = 𝐿 ,( )
= 𝐿 ,( ) for the trailer wheels.
It has to be noted that when solving this task in order to calculate the value of Ω for a given combination of parameters 𝑝 , … , 𝑝 , it is necessary to integrate the equations of motion (3), which now depend not only on the generalized coordinates but also on parameters 𝑝 , … , 𝑝 over the interval < 0, 𝑇 >; this means that the equations of motion (3) have to be integrated at each optimization step. The boundary conditions for the task are formulated in the form:
(7) 𝑝 , ≤ 𝑝 ≤ 𝑝 , 𝑓𝑜𝑟 𝑖 = 1, … ,4
where 𝑝 , , 𝑝 , are minimum and maximum admissible values of parameter 𝑝 .
The nonlinear optimization task (5), (7) was solved using the
downhill simplex method. Table 1 presents the values of 𝐿 ,( )
= 𝐿 ,( )
obtained as a solution of this task.
Table 1: Initial (before optimization) and calculated (after optimization) values of parameters 𝑝 , … , 𝑝 ..
Before
optimization After
optimization 𝑝 15 20.96
𝑝 15 16.29
𝑝 13 14.39
𝑝 13 14.97
These values are obtained when it is assumed that there is viscous friction in the connection between the dolly and the trailer and the friction coefficient equals 0.04. Figures 5 and 6 present yawing velocity of the tractor and trailer respectively.
Fig. 5 Yawing velocity of the tractor
Fig. 6 Yawing velocity of the trailer
It can be seen that the courses of yawing velocities obtained for values of the lateral stiffness coefficient taken from literature (broken line) differ from those from the experiment although the form of the course is similar. When tire parameters are calculated as a result of optimization procedure the results of experimental measurements and numerical simulations are compatible.
5. Final remarks
This paper presents a procedure which enables us to improve the accuracy of the articulated vehicle model elaborated. The tire parameters obtained on the test stands should be adjusted by comparing of the results of the real tests of truck behavior with the results of the calculations. The application of dynamic optimization enables the modified tire parameters to be quickly determined. The method of modelling by means of joint coordinates and homogenous transformations seems very advantageous for mathematical modeling of a truck combination.
Finally, it can be concluded that calibration of a dynamic model of a truck combination ensures that we achieve good qualitative and
6
quantitative compatibility between the results of the real test and results of calculations.
References
1. Bouteldja M., V.Cerezo. Jackknifing warning for articulated vehicles based on a detection and prediction system, in Proceedings of the 3rd International Conference on Road Safety and Simulation, Indianapolis, 2011.
2. Fencher P.S., Winkler C., Ervin R., Zhang H., Using braking to control the lateral motion of full trailers Supplement to Vehicle System Dynamics 29, 462-468, 1998
3. Hussain K., Stein W., Day A. J. Modelling commercial vehicle handling and rolling stability Proc. IMechE Part K: J. Multi-body Dynamics 219, pp. 357-369, 2005.
4. Kaneko T., Kageyama I., A study on the braking stability of articulated heavy vehicles, JSAE Review 24, 157-164, 2003.
5. Bolzern P., DeSantis R.M., Locatelli A. An input-output linearization approach to the control of an n-body articulated vehicle. Journal of Dynamic Systems, Measurement, and Control. 123, 309-316, 2001.
6. Yang X., Song J., Gao J., Fuzzy Logic Based Control of the Lateral Stability of Tractor Semitrailer, Mathematical Problems in Engineering Volume 2015, Article ID 692912
7. Adamiec-Wójcik I., Awrejcewicz J., Grzegożek W., Wojciech S., Dynamics of articulated vehicles by means of multibody methods, in J. Awrejcewicz, M. Kaźmierczak, J. Mrozowski, P. Olejnik editors: Dynamical systems: mathematical and numerical approaches, Łódź, 2015.
8. Craig J.J. Introduction to robotics, Massachusetts, Addison-Wesley 1988.
9. Pacejka H.B., Bakker E.,The Magic Formula Tyre Model. Suppl. to Vehicle System Dynamics, vol.21, pp.1-18, 1993.
10. Dugoff H., Fancher P.S., Segel L., An Analysis of Tire Traction Properties and Their Influence on Vehicle Dynamics Performance. SAE Technical Paper 700377, 1970.
11. Grzegożek W., Adamiec-Wójcik I., Wojciech S., Komputerowe modelowanie dynamiki pojazdów samochodowych (Computer modelling of vehicle dynamics) Kraków: Cracow University of Technology Press, 2003.
7
ДИНАМИЧЕСКАЯ НАГРУЖЕННОСТЬ ЭНЕРГОСИЛОВОГО БЛОКА ПРИ ПУСКЕ
ДВИГАТЕЛЯ ВНУТРЕННЕГО СГОРАНИЯ, ОСНАЩЕННОГО СИСТЕМОЙ
COMMON RAIL
DYNAMIC LOADING OF THE ENERGY-SILIC BLOCK AT THE START OF THE INTERNAL
COMBUSTION ENGINE, EQUIPPED WITH THE COMMON RAIL SYSTEM
Prof. Dsc. Taratorkin I.1, Prof. Dsc. Derzhanskii V.1, PhD Taratorkin A.1 , postgraduate Volkov A.1 – Institute of Engineering Science of the
Ural Branch of the Russian Academy of Sciences (IES UB RAS), Russia
Abstract: The possibility of obtaining the reduced friction coefficient in the turning pair with cylindrical working surfaces is considered in the article. Theoretical dependences are obtained to determine the value of the reduced friction coefficient, realized in conjugation of run-in cylindrical surfaces for different laws of distribution of pressure: cosine, parabolic and elliptical. It is shown that the smallest discrepancy between the theoretical and experimental values of the reduced friction coefficients is observed for the cosine law of pressure distribution over cylindrical surfaces. It was experimentally confirmed that that the value of the reduced friction coefficient in the proposed type of turning pair increases by 2.5...5.0 times in comparison with the actual sliding friction coefficient.
1. Введение Передачи нагрузки силами трения широко применяется в
различных механических устройствах: ременных передачах [1–7]; механизмах свободного хода [2, 8–11]; фрикционных тормозах [12–16] и др. Нагрузочная способность таких устройств определяется величиной силы трения, возникающей в контакте их рабочих поверхностей.
Для увеличения силы трения можно придавать контактирующим поверхностям специальную форму. Например, выполнять желоб клиновой (рис. 1,а) или цилиндрической формы (рис. 1,б). В этом случае, за счет клинового сопряжения рабочих поверхностей, будет реализовываться приведенный коэффициент трения, который определяется соответственно по формулам [1, 2, 17, 18]
α=∗
sinff , (1)
ffπ
=∗ 4 , (2)
где f – действительный коэффициент трения; α – половина угла при вершине призмы.
Однако в ряде случаев, например, в механизмах свободного
хода, такое конструктивное решение усложняет технологию изготовления и монтажа, а также увеличивает потери на трение в период свободного хода, из-за постоянного контакта их рабочих поверхностей.
Предлагается получить эффект клинового сопряжения более простым и технологическим способом во вращательной кинематической паре, элементы которой контактируют по гладким цилиндрическим поверхностям.
В этом случае использование формул (1) или (2) будет некорректно. Получим формулу для определения приведенного коэффициента трения в предлагаемой кинематической паре.
2. Расчетная схема и математическая модель Рассмотрим вращательную кинематическую пару (рис. 2),
образованную внешним кольцом 1 с внутренней цилиндрической поверхностью и внутренним кольцом 2, выполненным с дуговыми выступами 3 и 4 на внешней цилиндрической поверхности, расположенными под углом α . Тогда контактирование в такой кинематической паре происходит по поверхностям дуговых выступов.
Рис. 2. Расчетная схема кинематической пары.
В общем случае на внутреннее кольцо действует нагрузки в
виде силы прижатия RF и давления )(ϕp . Под действием этих нагрузок кольцо находится в равновесии.
Выделим элементарную площадку на поверхности контакта внешней обоймы и кольца
ϕ= lrdds , (3)
где l – длина поверхности контакта; r – радиус поверхности контакта.
Элементарная сила нормального давления на элементе ds , с учетом выражения (3) определяется как
ϕϕ=ϕ= dlrpdspdFN )()( , (4)
где )(ϕp – функция, характеризующая закон распределения давления на поверхности контакта.
Элементарная сила трения на элементе ds , с учетом выражения (3), определяется как
ϕϕ== dflrpfdFdF NT )( . (5)
18
Выражение для определения результирующей силы нормального давления можно найти из условия равновесия кольца
∫
π
α−π
ϕϕϕ==2
2
cos)(2 dplrFF RN . (6)
Выражение для определения результирующей силы трения можно записать как
∫
π
α−π
ϕϕ=2
2
)(2 dpflrFT . (7)
Тогда приведенный коэффициент трения в такой кинематической паре можно определить как
N
T
FFf =∗ . (8)
Из выражений (6) и (7) видно, что функция )(ϕp оказывает существенное влияние на величину приведенного коэффициента трения.
С достаточной для практических расчетов точностью характер распределения давления для приработавшихся цилиндрических поверхностей можно аппроксимировать несколькими типами зависимостей: косинусоидальной; параболической; эллиптической [1, 2, 16–18]. Получены формулы для определения приведенного коэффициента трения для этих законов распределения давления (табл. 1).
Таблица 1: Зависимости для определения приведенного коэффициента трения.
Закон распределения давления Формула
Косинусоидальный ϕ=ϕ cos)( maxpp α−α
α−=∗
2sin2)cos1(4 ff (9)
Параболический
ϕ=ϕ 2max cos)( pp α+α⋅−
α−α=∗
3coscos32)2sin2(75.0 ff (10)
Эллиптический
2
2
max41)(πϕ
−=ϕ pp 234.149.1061.0
)2(
α+α+
α+π=∗ f
f (11)
Корректность выбора характера распределения давления
Проведено экспериментальное исследование приведенных коэффициентов трения в предлагаемой кинематической паре для получения их опытных величин и проверки достоверности полученных формул (9)–(11).
Исследования приведенных коэффициентов трения скольжения проводили на специально разработанной экспериментальной установке.
Экспериментальная установка (рис. 3) состоит из электродвигателя 1, соединенного клиноременной передачей 2 с валом 3. На валу 3 установлена испытательная головка 4, в которой при помощи кинематической пары, состоящей из цилиндрической втулки 5 и полукольца 6, выполненного с радиальными дуговыми выступами, расположенными под углом α , создается эффект клинового сопряжения.
Испытательная головка 4 установлена на шарикоподшипниках и может свободно поворачиваться относительно вала 3.
Нагружение полукольца радиальной силой RF осуществляется с помощью винта 7. При этом возникающий в кинематической паре втулка-полукольцо момент сил трения
TT поворачивает корпус испытательной головки, и закрепленная на нем штанга 8 действует на тензорезисторный силоизмеритель 9. Величина радиальной силы RF измеряется тензорезисторным силоизмерителем 10.
помощью тензорезисторных силоизмерителей был выбран как наиболее удобный.
Тензорезисторные силоизмерители предварительно тарировали при помощи динамометрического кольца и индикатора часового типа (цена деления 0.002 мм) для получения зависимости выходного сигнала от величины действующей силы.
Для регистрации сигнала тензорезисторных силоизмерителей применяли регистрирующую аппаратуру – тензометрический усилитель и измерительный блок с микроамперметром.
При проведении эксперимента была использована втулка, одно полукольцо с гладкой цилиндрической поверхностью α =90º и полукольца с углами α = 15º, 25º и 35º. Радиус сопряжения поверхностей втулки и полукольца r =28 мм, длина сопряжения l =10 мм. Экспериментальные образцы втулки и полуколец были изготовлены из материала сталь 14NiCr10 с последующей термообработкой до 58...62 HRC..
Эксперименты проводились в условии смазки маслом SAE30, при установившемся тепловом режиме с температурой масла t = (55±5) oC и скорости скольжения v = 2 м/с.
В качестве исследуемого фактора принимали приведенный коэффициент трения скольжения ∗f , в качестве независимого
фактора – среднее контактное давление mp . Перед проведением экспериментальных измерений все
образцы проходили приработку под нагрузкой mp = 0.5 МПа в течение 15 часов.
В процессе эксперимента применяли метод ступенчатого нагружения полукольца давлением от mp =0.5 до 5.5 МПа
через 1 МПа и измеряли момент сил трения TT в паре сопряжения. Нагружение проводили до критической величины давления, при которой появлялись признаки заедания.
Экспериментальные значения приведенных коэффициентов трения находили по формуле
19
R
T
rFTf =∗ . (12)
4. Экспериментальные результаты
На рис. 4 показаны графики зависимости приведенного коэффициента трения ∗f от контурного давления mp и углов α для приработавшихся поверхностей при эллиптическом, косинусоидальном и параболическом законах распределения давления по дуговым выступам.
Сплошные и пунктирные линии соответствуют теоретическим значениям, полученным на основании формул (9)–(11), где f принимался по результатам опытов полукольца с гладкой цилиндрической поверхностью.
Рис. 4. Зависимость приведенного коэффициента трения от контактного давления для α =15º ( ), α =25º( ∆ ) и α =35º ( О )
Анализ полученных результатов показывает достаточно
хорошее качественное и количественное совпадение экспериментальных и теоретических значений приведенного коэффициента трения.
Количественная оценка величин экспериментальных и теоретических значений приведенного коэффициента трения, проводилась с применение метода наименьших квадратов и их относительной погрешности
На основании результатов количественной оценки можно сделать вывод, что наименьшее расхождение теоретических и экспериментальных значений ∗f наблюдается при косинусоидальном и параболическом законах распределения давления по дуговым выступам, для которых относительная погрешность соответственно находится в диапазоне 1.1...15 % и 0.5...17.7 %.
5. Выводы Теоретически обоснована и экспериментально
подтверждена возможность получения эффект клинового сопряжения простым и технологическим способом – в контакте гладких цилиндрических поверхностей.
На основании анализа теоретических и экспериментальных значений приведенных коэффициентов трения определено, что их наименьшее расхождение наблюдается при косинусоидальном и параболическом законах распределения давления по дуговым выступам. Окончательно выбираем косинусоидальный закон распределения давления, т.к. в этом случае ни для одной точки относительная погрешность не превышает 15%, и, кроме того, он описывает распределение давления в простой аналитической форме.
Показано, что использование такого эффекта для пары трения «сталь-сталь» с действительным коэффициентом трения f =0.04…0.05 [1, 2, 17, 18] величина приведенного коэффициента трения увеличивается в 2.5…5.0 раз и может составлять ∗f =0.10…0.25.
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[18] Мышкин Н.К., Петроковец М.И. Трение, смазка, износ. Физические основы и технические приложения трибологии. Москва: Физматлит, 2007. 367 с.
20
THE METHOD OF NUMERICAL MODELING OF HYDRODYNAMICS AND HEAT
EXCHANGE IN A CHANNEL WITH DISCRETE ROUGHNESS
МЕТОДИКА ЧИСЛЕННОГО МОДЕЛИРОВАНИЯ ГИДРОДИНАМИКИ И ТЕПЛООБМЕНА В КАНАЛЕ
С ДИСКРЕТНОЙ ШЕРОХОВАТОСТЬЮ
Dr.sc.ing. Sidenko N., Dr. sc.ing. hab. prof. Dzelzitis E.
Riga Technical University, Faculty of Civil Engineering, Institute of Heat, Gas and Water Technology.
Москва, Издательство МГТУ им.Н.Э. Баумана, 2002, 383 стр.
[8] Chang P. Separation of Flow //New York, Pergamon Press,
1971.
[9] Алямовский А.А. и др. SolidWorks 2007/2008.
Компьютерное моделирование в инженерной практике.// БХВ–
Петербург, Санкт – Петербург, 2008.
[10] Гомелуари В.И. Влияние искуственной шероховатости на
конвективный теплообмен. «Труды Института физики АН
ГССР», Тбилиси, 1963, т.9,с 111-145.
[11] Михеев М.А. Михеева И.М. Основы теплопередачи. – М.:
Энергия.1977. 344с.
This work has been supported by the European Regional
Development Fund within the Activity 1.1.1.2 “Post-doctoral
Research Aid” of the Specific Aid Objective 1.1.1 “To increase the
research and innovative capacity of scientific institutions of Latvia
and the ability to attract external financing, investing in human
resources and infrastructure” of the Operational Programme
“Growth and Employment” (No Nr.1.1.1.2./VIAA/1/16/093).
24
DEVELOPMENT AND RESEARCH OF TEMPERATURE CONTROL SYSTEM OF A HIGH-VOLTAGE BATTERY OF A PERSPECTIVE ELECTRIC VEHICLE
РАЗРАБОТКА И ИССЛЕДОВАНИЕ СИСТЕМЫ ТЕРМОСТАТИРОВАНИЯ
ВЫСОКОВОЛЬТНОЙ АККУМУЛЯТОРНОЙ БАТАРЕИ ПЕРСПЕКТИВНОГО ЭЛЕКТРИЧЕСКОГО ТРАНСПОРТНОГО СРЕДСТВА
Ph.D., Ass. Prof. Kurmaev R.Kh.1, Umnitsyn A.A. 2, Struchkov V.S. 3, Ph.D., Ass. Prof. Karpukhin K.E. 4, Liubimov I.A. 5
Head of Department 1,4, Head of sector 3, Design Engineer 2,5 – Federal State Unitary Enterprise “Central Scientific Research Automobile and Automotive Engines Institute” (FSUE “NAMI”), the Russian Federation
Abstract: The development of temperature control system of high-voltage batteries is an actual and important task in the development of modern electric and hybrid vehicles. There are a large number of designs and types of temperature control systems. In this article, we propose to consider a temperature control system based on a liquid cooling system and designed for both cooling and heating the battery in a wide range of ambient temperatures. In the development process of temperature control system for high-voltage batteries were carried calculations, 3D modelling of the design and tests.
Keywords: VEHICLE, ELECTRIC VEHICLE, TEMPERATURE CONTROL SYSTEM, COOLING SYSTEM, HIGH-VOLTAGE BATTERY
1. Introduction The development of electric transport in the European Union
has become one of the three priority areas of the European economy, and in Russia energy efficiency is declared the main direction of the country's development in the coming years. According to the forecasts of the Subcommittee on Strategic Innovations in the Automotive Industry of the Chamber of Commerce and Industry of the Russian Federation, by 2025 at least 50% of the world's produced vehicles will be on electric traction [1, 4]. Already, all major automobile plants are developing or producing such vehicles. Developments in the field of electromobile transport are engaged in the largest universities, scientific organizations, and enterprises of the Russian Federation. However, in our country now, electric vehicles is not very popular. This is due not only to the underdeveloped infrastructure, but also to climatic conditions. In the greater territory of the Russian Federation is prevailed the cold climate [3, 4, 5 and 6]. Studies show that the mileage of electric vehicles depends strongly on the temperature conditions of the high-voltage battery, which is one of the main elements of the functioning of such vehicles. At low temperatures, the mileage of electric vehicles falls sharply (to 30…40%), and at high temperatures, the high voltage battery can overheat, which can lead to degradation of battery cells. Thus, the task of thermostating high-voltage battery is very important for our country.
Consider the design of high-voltage batteries with thermostating systems of commercially produced vehicles on electric traction.
The Chevrolet Volt T-shaped lithium-ion high-voltage battery, shown in Figure 1, is installed under the car and passes through the central tunnel and under the rear seats.
Fig. 1 T-shaped lithium-ion high-voltage car battery Chevrolet Volt with aluminum cooling plate.
Through the quick-release couplings, the coolant enters into the of the high-voltage battery. Inside the housing of battery, there are thermal channels that allow the coolant to flow through the cooling plates between the flat cells of the lithium-ion batteries. These channels allow cooling or heating of the cells depending on operational requirements. If the temperature of the battery is lower
than the operating temperature, the heating element located on the input channel of the cell is activated directly from the 360 V of lithium-ion battery.
The high-voltage battery of the hybrid Toyota Prius, shown in Figure 2, is located in the trunk above the rear axle of the car. Battery in the car has an air cooling. This type of cooling has a disadvantage, since in this case the air must be cleaned. Therefore, the battery is located inside the car and the air intake comes from the cabin.
Fig. 2 High-voltage car battery Toyota Prius.
The high-voltage battery of the Audi A3 e-tron PHEV-20, shown in Figure 3, has a complex liquid cooling system in which four cooling plates regulate the temperature of the eight modules. Cooling is carried out using a separate controlled low-temperature circuit. To warm up the battery using a thermoelectric heating element and gasoline preheater.
Fig. 3 High-voltage car battery Audi A3 e-tron PHEV-20.
The high-voltage battery of the Tesla Model S, shown in Figure 4, is arranged under the bottom of the car and consists of 16 battery modules with liquid cooling system. As a coolant in the cooling system, a solution of glycol is used. The battery module consists of a flat curved tube with battery cells, as shown in the figure, which evenly distribute the coolant between the cells. Further heat is diverted to the cooling circuit and is used by the climate system to heat the car's cabin.
25
Fig. 4 High-voltage car battery Tesla Model S.
Based on the analysis of the thermostating systems for high-voltage batteries produced vehicles, we can conclude that the liquid cooling system is mainly used. In addition, the thermostating system is influenced by the type and design of the battery cells used in the car.
2. Solution of the examined problem Now, FSUE NAMI conducts research on the topic «Creation of
new technologies and systems in the field of increasing the level of use of alternative energy sources for vehicles, based on the introduction of new scientific and technical solutions aimed at the use of electric and renewable (solar) energy for the movement of vehicles». As a model of an electric vehicle, the Russian electric vehicle LADA Ellada was used. This car uses the air-cooling system of the high-voltage battery (Figure 5) (the incoming airflow to the battery housing is supplied through the front bumper and radiator). On this vehicle, there is no battery heating system.
Fig. 5 High-voltage car battery LADA Ellada.
One of the main tasks of the project was the development of a high-voltage battery with thermostating system, which allows increasing the temperature range of vehicle operation and maintaining the temperature of the high-voltage battery in the operating range. The operating range of the battery cell without a significant decrease in its life 0 ... 50 ºС. Such a temperature range is most suitable for the careful operation of the battery [2, 5, 7 and 8]. With the existing form of battery cells and the limited layout space, an air-water thermostating system for a high-voltage battery was developed. In addition, it was required to rework the concept of a system for the thermostating of a car. The result is shown in Figure 6.
Fig. 6 Schematic diagram of the thermostating car LADA Ellada.
A schematic diagram of the car thermostating system comprises an electric pump 16 for supplying coolant from the radiator 18 along the pressure main to the housing of the high-voltage battery 10. To regulate the flow of the pump 16, the system has valves 4, 7, 8, 15, 17 with an electromechanical drive, which are controlled respectively by temperature sensors 1, 5, 11 and 13. The thermostating system has a cooler 12 and an electric heater 14, from where, depending on the operating mode (cooling or heating), the coolant flows through the check valve 9 to the battery housing 10 and then through the drain line 3 to the radiator 18. Also in the thermostating system there is a heater 6 and an expansion tank 2.
3. Results and discussion The main stages in the development of a high-voltage battery
with a thermostating system were:
- 3D modeling;
- calculation of heat and mass transfer.
Based on the car's engine compartment (Figure 7), and technical requirements for the high-voltage battery, it was decided to use 26 cells Winston WB-LYP90AHA as the battery cells.
Fig. 7 The layout of a high-voltage battery in the car's engine compartment.
The high-voltage battery is a closed box with a thermal insulation layer, which significantly reduces the temperature effects of the environment. The housing of high-voltage battery has two sections. In the upper section, where the battery cells are located, there is a system of air circulation inside the closed volume (Figure 8). The movement of air inside the volume of the high-voltage battery is organized as follows. In the upper cavity of the closed volume, a depression is created, and in the lower cavity, a zone of increased pressure is obtained. These cavities are connected by channels formed by the shape of battery cells. The pressure difference is explained by the use of the fan SPAL VA32-A101-62S. The position of the high-voltage battery cells and the characteristics of the fan have been optimized to ensure sufficient air circulation inside the volume of the high-voltage battery.
In the lower section, there is a heat exchanger, which is a curved tube with many copper plates.
Fig. 8 3D-model of high-voltage battery.
26
The calculation of the efficiency of the system of thermostating of a high-voltage battery was carried out in two modes:
1) Loaded battery operation mode. The ambient temperature is + 40 ° C.
2) The battery is inactive. The ambient temperature is -25 ° С.
The main task of the calculations was to determine the flow rate and temperature of the coolant through the heat exchanger, to provide the target temperature values of the battery cells (0…50°C).
Figures 9-10 show the results of calculations for the first mode.
Fig. 9 Distribution of airflow and temperature in the battery.
Fig. 10 Section through a radiator.
Figures 11-12 show the results of calculations for the second mode.
Fig. 11 Distribution of airflow and temperature in the battery.
Fig. 12 Section through a radiator.
According to the figures, it can be seen that the developed thermostating system has optimal characteristics and allows maintaining the temperature inside the high-voltage battery within operating limits. This design of thermostating system of the high-voltage battery requires a small flow of coolant through the heat exchanger 3 l / min. The coolant temperature measured at the inlet to the heat exchanger + 10 ° C is constant both during cooling and heating. This shows a good level of thermal insulation of the battery volume from the environment.
After the manufacture of a high-voltage battery with a thermostating system, tests were carried out in the temperature test chamber of FSUE NAMI. Tests showed that in a loaded high-voltage battery at a temperature of + 40°C inside n the temperature test chamber and a coolant temperature of + 10°C, which is supplied to the heat exchanger of the battery housing with a flow rate of 3 l/min, a temperature of + 49°C is maintained.
In turn, at a temperature of -25°C inside the temperature test chamber and a coolant temperature of + 10 ° C, which is supplied to the heat exchanger of the battery housing with a flow rate of 3 l / min, the cells of the high-voltage battery warm up above 5°C. This is enough for quickly heat the internal volume of cells of battery, safely activate the car and charge the battery when the car is parked.
A sufficient accuracy of the calculated results with the results of laboratory studies is obtained.
4. Conclusion Currently, the car with a developed high-voltage battery with a
thermostating system is preparing for road tests, which must confirm the effectiveness of the developed design.
This paper is made within the applied research under Agreement No. 14.624.21.0047 dd. 26 October 2017 for the following: “Creation of new technologies and systems in the field of increasing the level of use of alternative energy sources for vehicles, based on the introduction of new scientific and technical solutions aimed at the use of electric and renewable (solar) energy for the movement of vehicles” (unique project identifier RFMEFI62417X0047), made with the Ministry of Education and Science of the Russian Federation.
5. References 1. Rodrigo Garcia-Valle, João A. Peças Lopes. Electric Vehicle
Integration into Modern Power Networks. Springer Science & Business Media, 2012, pp. 1-6.
2. Angelo Greco, Dongpu Cao, Xi Jiang, Hong Yang, A theoretical and computational study of lithium-ion battery thermal management for electric vehicles using heat pipes, Journal of Power Sources, Volume 257, 2014, pp. 344-355
3. Terenchenko A., Karpukhin K., Kurmaev R. Features of operation of electromobile transport in the conditions of Russia. Paper of EVS 28 International Electric Vehicle Symposium and Exibition, KINTEX, Korea, 2015.
27
4. Kurmaev R.H., Terenchenko A.S., Karpukhin K.E., Struchkov V.S., Zinov’ev E.V. Maintaining the required temperature of high-voltage batteries in electric cars and hybrid vehicles. Russian engineering research, 2015, vol. 35, No. 9, pp. 666-669.
5. Karpukhin K.E., Kurmaev R.Kh., Terenchenko A.S., Struchkov V.S., Tsimbaluk M.A. Aspects of construction of combined thermo-statics system for electric vehicle. ARPN Journal of Engineering and Applied Sciences, 2016. Т. 11. 23. pp. 13674-13680.
6. Karpukhin K. E., Shorin A. A., Terenchenko A. S., Umnitsyn A. A., Kondrashov V. N. Research of effectiveness of accumulator systems of hybrid motorcars and electromobiles in conditions of negative temperatures, Russian Engineering Research, 2016, 8 pp. 26-29. (In Russian).
7. Guodong Xia, Lei Cao, Guanglong Bi. A review on battery thermal management in electric vehicle application. Journal of Power Sources, Vol. 367, 11 November 2017, pp. 90-105.
8. Maan Al-Zareer, Ibrahim Dincer, Marc A.Rosen. Novel thermal management system using boiling cooling for high-powered lithium-ion battery packs for hybrid electric vehicles. Journal of Power Sources, Vol. 363, 11 September 2017, pp. 291-303.
28
MODELING AND SIMULATION OF VEHICLE AIRBAG BEHAVIOUR IN CRASH Associate Prof. J. Marzbanrad1, PhD student - V. Rastegar2
School of Automotive Engineering, Iran University of Science and Technology
Abstract: Since safe transportation is one of the biggest concerns of vehicle manufactures, occupant safety in vehicle accidents becomes a great challenge.
The severity of the crash reflects the energy absorption of the car's structure during the accident and also has a close relationship with the amount of energy absorbed by the restraint system. Among components involved in restraint system, airbags are the most complex ones. The simulation and modelling of this system due to the nonlinear behaviour of the passenger and the vehicle add more complexity to its design and fabrication. Airbag system, which is a subsystem of the restraint system, is very important due to the nature of its multi-physical problem and the direct connection with passenger safety.
Therefore, in this paper, different approaches to develop airbag dynamics equations has been reviewed. Further a fast design and simulation method for airbag parameters in the concept design phase by an impact problem has been investigated to contribute to a comprehension of the relation between occupants and airbags.
1. IntroductionOccupant safety is one of the principal objectives in the design
of vehicles. Numerous innovations have appeared aimed at increasing safety in vehicles [1–3]. As is known, airbags, like safety belts are now devices designed to provide protection to the users of vehicles during crash events, minimizing the loads necessary to adapt their movement to the movement of the car [4, 5]. The airbag acts to cushion any impact with vehicle structure and has positive internal pressure, which can exert distributed restraining forces over the head and face. Furthermore, the airbag can act on a wider body area including the chest and head, thus minimizing the body articulations, which cause injury [6]. These safety elements can so reduce the death rates on the roads, and its protection effects have been widely approved [7, 8]. Thus, new types of airbag products are being developed to handle different collision scenarios.
Airbags have been in construction since the late 1940s, when they had first been manufactured and investigated by automobile engineers. The first airbag to be installed in a vehicle appeared in 1971, in the 831 Mercury models that were manufactured by Ford [9], followed by General Mo- tors offering frontal airbags as an optional extra between 1974 and 1976 [10]. In the 1980s, airbags were being mass- produced and by the 1990s they were accepted as an effec- tive supplemental restraining system, along with seatbelts.
Airbag is a primary component of the occupant restraint system, and its protection is widely accepted and analyzed [11]. NHTSA pointed out in a recent data report of traffic accidents that barrier/sled-certified airbags reduce about 20% fatality risk in frontal crashes of cars [12]. Braver et al [13], used Poisson marginal structural model to calculate standardized mortality rate ratios (MRRs), and found that advanced airbag features appeared protective for some occupants, but further study is needed.
While a vehicle is crashing heavily in the front, the forward movement of the front passengers can be perceived as an acceleration process towards the instrument panel starting with a zero speed in a reference coordinate system on a moving vehicle. During this process, airbags are inflated to tolerate parts of the initial kinetic energies of occupants, and compressed to absorb these energies [14]. Meanwhile, the gas in airbags discharges from vents due to the high pressure of airbag chamber compared with the atmosphere pressure, and this drastic venting process releases the energies absorbed by airbags. Based on the above overview, the mechanics relationship between occupants and airbags can be regarded as a simplified model, in which an impactor impacts an airbag with vents on at a given speed.
As an elementary module test method to investigate the performance of airbags, the drop tower test has been widely used in the product development phase of airbags [15–16]. Generally,
before suitable airbags matches a certain vehicle, many times of drop tower test could be conducted by suppliers. This process can not only test the reliability of an airbag’s deployment process, but also verify the correctness of preliminary defined parameters.
Traditionally, airbags have been simulated using the control volume (CV) approach. In the CV model, the pressure inside the airbag is calcu- lated using the mass flow and temperature curves obtained from a tank test. This pressure is assumed to be uniform inside the airbag, and thus a uniform force is applied on all the surfaces of the airbag, including those surfaces which are yet not unfolded. CV approach is hence analogous to a lumped parameter model in which the flow of inflating gases inside the airbag is not discretized. The effect of the gas jet from the inflator is not taken into account in these models. To overcome this shortcoming, jetting is added to CV models to add a momentum to the airbag in the direction of the jet from the inflator [17-18].
In this paper, first the the governing equation on airbag dynamics has been investigated, after that a specified airbag has beed simulated under development and drop test by using LS-dyna.
2. Modelling2.1. System equation
Different approaches in modeling of an airbag can be used. In adrop tower test, the basic mechanics relationship between the impactor and the airbag is expressed as follows [19]:
𝑀𝑀𝑀𝑀 − (𝑃𝑃 − 𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎 )𝐴𝐴𝑒𝑒 = 𝑀𝑀𝑎𝑎 (1)
Another model has been used for an external airbag. As shown in Fig. 1, in this model airbag will work like a static air spring and so there is a necessity to know the spring coefficient and the damping coefficient for the external airbag.
Fig. 1 Air spring – damper/spring model. 𝐹𝐹𝑥𝑥 = 𝑃𝑃.𝐴𝐴𝑒𝑒 (2)
29
𝐾𝐾 =𝑑𝑑𝑃𝑃𝑑𝑑𝑥𝑥 .𝐴𝐴𝑒𝑒 + 𝑃𝑃.
𝑑𝑑𝐴𝐴𝑒𝑒𝑑𝑑𝑥𝑥
(3)
𝐾𝐾𝑥𝑥1 =𝑑𝑑𝑃𝑃𝑑𝑑𝑥𝑥 .
𝐴𝐴𝑒𝑒𝑥
(4)
𝐾𝐾𝑥𝑥2 = 𝑃𝑃.𝑑𝑑𝐴𝐴𝑒𝑒𝑑𝑑𝑥𝑥
(5)
By assuming an inviscid flow, the damping coefficient can be found as follows:
𝐶𝐶 =𝐹𝐹𝑥 =
𝜌𝜌.𝑀𝑀 𝑣𝑣𝐵𝐵2 + 𝑣𝑣𝐴𝐴2
2𝑀𝑀 + 32𝜇𝜇𝜇𝜇𝑣𝑣𝐵𝐵𝜌𝜌𝑀𝑀𝑑𝑑2 .𝐴𝐴𝑒𝑒
𝑥
(6)
Based on the original dynamics model used to develop the airbag system for the Mars Pathfinder, another governing equation can be developed as follows:
𝑀𝑀𝑥 + (𝑃𝑃 − 𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎 )𝐴𝐴𝐹𝐹𝑃𝑃 = 𝑀𝑀𝑀𝑀 (7)
In this model the airbags hit the ground and AFP shows the area of the airbags which is in contact with surface.
2.2. Geometry
There is a tendency to assume a two-dimensional design to analysis the airbag behavior. In Fig. 2 a schematic of an airbag system is shown.
Fig. 2 Airbag schematics
In this paper, a three-dimensional analysis in regards to volumetric changes in airbag has been studied. A predefined airbag geometry is shown in Fig 3. Relations of volume changes are divided in two sections, V1 shows the volume of the cylindrical volume in the middle and V2 is related to torus around the cylinder.
Fig. 3 Airbag geometry
𝑉𝑉2 = 4𝜋𝜋𝑥𝑥𝑋𝑋2
2− 𝑥𝑥 −
𝑙𝑙2
2𝑙𝑙+𝑋𝑋2
𝑙𝑙2
𝑑𝑑𝑥𝑥 (8)
𝑉𝑉1 = 𝜋𝜋 𝑙𝑙2
2
𝑋𝑋 (9)
𝑉𝑉 = 𝑉𝑉1 + 𝑉𝑉2 (10)
According to Wang and Nefske, the relationship between the pressure (P2) and the volume (V2) of the airbag will be expressed as:
𝑉𝑉2 = 𝑉𝑉20(1 + 𝑐𝑐𝛽𝛽(𝑃𝑃2 − 𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎 )) (11)
𝑐𝑐𝛽𝛽 is bag stretch factor and P2 and V2 are pressure and volume of airbag [20]
2.3. Ventilation
For the leakage or venting in the airbag, the Bernoulli equation can be used. It is assumed that the flow between location inside the airbag and location outside the airbag is inviscid, incompressible, free from heat transfer, and steady. Thus the Bernoulli equation between these two locations is derived according to head loss from inside and outside of the airbag after traveling through the vents:
𝐻𝐻 =32𝜇𝜇𝜇𝜇𝑣𝑣𝐵𝐵𝜌𝜌𝑀𝑀𝑑𝑑2
(12)
Also standard gas dynamics equations can be used to determine the conditions required for the airbag venting mechanism by using a standard nozzle flow equation to relate the flow velocity through the vent:
𝑑𝑑𝑑𝑑𝑑𝑑𝑎𝑎
= 𝐶𝐶𝐷𝐷𝐴𝐴𝑎𝑎ℎ𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎 1𝑅𝑅𝑅𝑅
1
2
[2𝛾𝛾𝛾𝛾 − 1
𝑃𝑃
𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎𝛾𝛾−1
𝛾𝛾
]12 [
𝑃𝑃𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎
𝛾𝛾−1
𝛾𝛾
− 1]12
(13)
Another approche is to assume a vent on an airbag is a circular hollowed-out region, which acts as a channel for the gas in the airbag chamber exhausts from the inside to the outside. Thus, the vent area directly affects the exhausted gas mass of an airbag. Based on the momentum theorem, mass of the exiting gas can be found as follows:
ℎ = 𝑃𝑃 − 𝑃𝑃𝑎𝑎𝑎𝑎𝑎𝑎
𝜌𝜌
(14)
𝑎𝑎 = 𝑎𝑎(𝑎𝑎) − 2 𝜌𝜌𝐴𝐴ℎ𝑑𝑑𝑎𝑎𝑎𝑎
0
(15)
2.4. Solution algorithm
A time stepping scheme is employed where at each time increment, the change in airbag geometry is calculated based on the position of the supported mass as shown in the Fig. 4. This is then
30
used to obtain the pressure, volume, and mass of the operating medium, which is in turn used to determine conditions for venting of the airbag.
Fig 4. Overview of iterative process
3. Simulation
In the area of numerical simulations involving the use of airbags to absorb impact energy, passively or actively, accurate definitions of airbag leakage parameters play a crucial role in predicting the response of impacting objects. LS-DYNA is a software package for dynamic analysis and study of fluid structure interactions can widely be investigated.
Base on the geometry of a common driver airbag, the basic test conditions are described as follows: the diameter of the airbag is 610 mm, two vents on the airbag with the same diameter of about 30 mm, two straps in the airbag have the same length of 200 mm, the volume of the airbag chamber is about 45 L when the inflator has just finished its inflating process, the mass of the impactor is 4.8 kg with initial velocity of 14 m/s2.
The impact problem has been imported in LS-dyna solver and the graphical view is shown in Fig. 5.
Fig. 5 Graphical view of main LS-dyna simulation window
Inflator mass flow pressure rate is dependent on the inflator function, but a common inflator is selected [19] and imported in software as Fig. 6:
Fig. 6 Mass flow pressure
4. Result and Discussions
The airbag system is part of the passenger car restraint system. Therefore, the exact design of the airbag is very important. In this
article it has been tried to review on different mathematical modelling and Ls-dyna simulation.
As of that, the results generated by coding in Matlab and Ls-dyna has been shown in Fig. 7 and Fig. 8.
From analytical approach, Fig 7. shows the acceleration changes of the impactor after dropping with initial acceleration (g) and contacting the airbag surface.
Acc
eler
atio
n (g
)
Time s
Fig. 7 Impactor acceleration
The same drop test has been simulated in Ls-dyan and acceleration changes of impactor is shown in Fig. 8.
Fig. 8 Impactor acc. (Ls-dyna)
5. Conclusion
Since in the crashworthiness studies the head acceleration is one of the important parameters to determine the occupant injury, in this paper investigation of the acceleration of the impactor has been chosen as an important factor.
By comparing the results developed for the impactor acceleration from analytical and simulation, it was cleared that the results showed a similar trend almost same extreme points.
It should be noted that the proposed theoretical model cannot solve the situation in which the impactor contacts the airbag before it is fully inflated.
Since ventilation has a great impact on the airbag behavior, on the premise of reasonable simplifications and assumptions, the momentum theorem (which was proposed by formula 14 and 15) did not reflect a good relation between different design parameters and the impactor response. On the other hand, Bernoulli and dynamic gas equations showed better results.
In this paper three different approaches to analytically solve an impact problem has been studied. In all of them an impactor has been dropped on a fully developed airbag and the acceleration of the impactor has been investigated. After that in order to compare the accuracy of the results, a simulation with the same scenario has been developed in Ls-dyna.
01-0841, SAE World Congress, 8–11 March 2004, Detroit,Michigan, 8–11 March (2004)
2. Soongu, H., A study on the modeling technique of airbag cushionfabric. In: SAE 2003-01-0512, SAE World Congress, 3–6March 2003, Detroit, Michigan, 3–6 March (2003)
3. Canaple, B., Impact model development for the reconstruction ofcurrent motorcycle accidents. Int. J. Crash 7, pp. 307–320(2002)
4. Freesmeier, J.J., Butler, P.B., Analysis of a hybrid dual-combustion-chamber solid propellant gas generator. J. Propuls.Power 15, 552–561 (1999)
5. Schmitt, R.G., Butler, P., Freesmeier, J., Performance and COproduction of a non-azide airbag propellant in a pre-pressurizedgas generator. Combust. Sci. Technol. 122, pp. 305–350 (1997)
6. Gabauer, D.J., Gabler, H.C., The effects of airbags and seatbeltson occupant injury in longitudinal barrier crashes. J. Saf. Res.41, pp. 9–15 (2010)
7. Crandall, C.S., Olson, L., Sklar, D.P., Mortality reduction withair bag and seat belt use in head-on passenger car collisions.Am. J. Epidemiol. 153, pp. 219–224 (2001)
8. Teru, I., Ishikawa, T., The effect of occupant protection bycontrolling airbag and seatbelt. In: Proceedings of the 18thInternational Technical Conference on the Enhanced Safety ofVehicles. NHTSA, Nagoya, Japan (2003)
9. Thompson, K.M., Segui-Gomez, M. and Graham, J.D.,Validating analytical judgements: the case of airbag’s lifesavingeffectiveness, Reliability Eng. System Safety 66, pp. 57–68.(1999)
10. Chan, C.-Y., Crash Sensing in Automotive Airbag Systems,Warrendale, Society of Automotive Engineers (2000)
11. Greenwell, N K. Evaluation of the certified-advanced airbags[R]. Washington, DC: National Highway Traffic SafetyAdministration, Report No. DOT HS 811 834.
12. Kahane, C J., Injury vulnerability and effectiveness of occupantprotection technologies for older occupants and women.Washington, DC: National Highway Traffic SafetyAdministration, Report No. DOT HS 811 766.
13. Braver, E. R., Shardell, M., Teoh E. R., How have changes inair bag designs affected frontal crash mortality. Annals ofEpidemiology, 20(7): pp. 499–510 (2010)
14. Shi, L., Cao, L., Weixiong, Y., Test and simulation study on theperformance improvement of SUV airbag. Chinese Journal ofAutomotive Engineering, 2(5): pp. 334–340 (2012)
15. Keun, L., Hyun, L., Hyung, L., Validation methodology onairbag deployment process of driver side airbag, 21th EnhancedSafety of Vehicles (ES) Conference, Stuttgart, Gernany, June15–18, Paper No. 09-0363 (2009)
16. Bok, L., Gu, H., Parametric study on mid-mounted passengerairbag cushion using design of experiments[R]. SAE TechnicalPaper, (2003).
17. Cirak, F., Radovitzky, R., ‘A new Lagrangian Eulerian shellfluid coupling algorithm based on level sets’, Proceedings of the44th AIAA/ASCE/ASME/AHS Structures, StructuralDynamics, and Materials Conference, Norfolk, Virginia, USA,(2003).
18. Marklund, P., Nilsson, L., ‘Simulation of airbag deploymentusing a coupled fluid structure approach’, 7th International LS-DYNA Users Conference, Detroit, MI, USA, (2002).
19. Zhang, J., Jin, Y., Xie, L., and Chen, C., Establishment andValidation for the Theoretical Model of the Vehicle Airbag,Chinese Journal Of Mechanical Engineering, Vol. 28,No. 3,(2015)
20. Wang, J.T., Nefske, D.J., A New CAL3D Airbag InflationModel, SAE Technical Paper Number 880654, (1972)
32
ПОВЫШЕНИЕ СКОРОСТНЫХ КАЧЕСТВ ТРАНСПОРТНОЙ ГУСЕНИЧНОЙ
МАШИНЫ СОВЕРШЕНСТВОВАНИЕМ ДИНАМИЧЕСКИХ СВОЙСТВ СИСТЕМЫ
УПРАВЛЕНИЯ ПОВОРОТОМ
INCREASE OF HIGH-SPEED QUALITY OF A TRANSPORT CRAWLER MACHINE BY IMPROVING THE
DYNAMIC PROPERTIES OF THE CONTROL SYSTEM OF A TURN
PhD Gizatullin U.1 Prof. Dsc. Taratorkin I.1, Prof. Dsc. Derzhanskii V.1, PhD Taratorkin A.1 , postgraduate Volkov A.1 – Institute of
Engineering Science of the Ural Branch of the Russian Academy of Sciences (IES UB RAS), Russia
Abstract: Every object in nature has an infinite number of vibration frequency and amplitude as called “Natural Vibration Frequency”.
Developing computer capacities allow calculating of natural frequencies and shapes of complex structures more accurate and
understandable. In this study, a dual-trolley (2x400 tons) heavy-duty overhead gantry crane that can carry loads up to 800 tons was
analysed by mathematical and finite element methods. The mathematical method is based on Euler-Bernoulli transverse vibration approach.
On the other hand, finite element method is one of the most common numerical methods that can solve many engineering problems in a
range from solid mechanics to acoustic. The generated solid model was analysed by the finite element method with the help of ANSYS
Workbench 14.5 which is a commonly used analysis program. The obtained values of natural frequencies at mathematical calculations and
finite element analysis were compared and presented.
Keywords: GANTRY CRANE, EULER-BERNOULLI TRANSVERSE VIBRATION, VIBRATION ANALYSIS, FINITE ELEMENT
ANALYSIS
1. Introduction
The cause of environmental impact and other reasons, vibration
is a problem in gantry crane constructions. Vibrations can lead to
serious consequences, sometimes leading up to the collapse of a
crane. Concepts of “Natural Frequency” and “Resonance” should be
examined firstly when determination of mentioned vibrations. The
calculation of “Natural Vibration Frequencies” and to know the
amplitudes of them are essential in solving of the vibration-induced
engineering problems. Natural frequency is a frequency which
depends on mass and flexibility of a structure and if it is induced at
that frequency, it will vibrate continuously at high amplitude. If an
object is excited by a frequency coincides with the natural
frequency of that object, a resonance occurs and it vibrates structure
excessively. Different methods can be used to avoid the resonance
problem during the design of structures. Analytical approaches for
non-complex system makes it easy such as verifying by numerical
methods for detecting errors in the calculations and preventing the
problems that may be encountered. Although analytical calculations
can be made, for calculating of complex shapes numerical methods
should be applied, such as finite element method [1].
In this study a dual-trolley, 2×400 tons, heavy duty overhead
gantry crane (Fig. 1) that can carry loads up to 800 tons was
analyzed by mathematical and finite element methods.
Fig. 1Vibration model of the crane
In this figure, dimensions and other parameters are L = 103.85
m; H = h =74.27 m; A1 = 1.04 m2; I1 = 2.078 m4; ρ = 7850 kg/m3;
E=210 GPa and the relation of this parameters with unknown
parameters for α=0,332; β=75,643; 𝜉=0,8846; η=1,1663 are;
𝑠 =𝐻
𝐿 , 𝑝 =
ℎ
𝐿 , 𝛼 =
𝐼1
𝐼2 , 𝛽 =
𝐼1
𝐼3, 𝜉 = 𝛼
𝐴2
𝐴1
4 , 𝜂 = 𝛽
𝐴3
𝐴1
4
The more precise dynamical analysis of engineering structure is
based on the assumption that a structure has distributed masses. In
this case, the structure has infinite number degrees of freedom and
mathematical model is presented with a partial differential equation.
Additional assumptions allow construction of the different
mathematical models of transversal vibration of the beam. The
simplest mathematical models consider a plane vibration of a
uniform beam with, taking into account only, bending moments;
shear and inertia of rotation of the cross sections are neglected. The
beam upon these assumptions is called as Bernoulli-Euler beam.
2. Mathematical Modelling
The mathematical method is based on Euler-Bernoulli
transverse vibration approach [2]. Early researchers recognized that
that the bending effect is the single most important factor in a
transversely vibrating beam. The Euler Bernoulli model includes
the strain energy due to the bending and the kinetic energy due to
the lateral displacement. The Euler-Bernoulli model dates back to
the 18th century. Jacob Bernoulli (1654-1705) first discovered that
the curvature of an elastic beam at any point is proportional to the
bending moment at that point. Daniel Bernoulli (1700-1782),
nephew of Jacob Bernoulli formulated the differential equation of
motion of a vibrating beam. Later, Jacob Bernoulli's theory was
accepted by Leonhard Euler (1707-1783) in his investigation of the
shape of elastic beams under various loading conditions. Many
advances on the elastic curves were made by Euler. The Euler-
Bernoulli beam theory, sometimes called the classical beam theory,
Euler beam theory, Bernoulli beam theory, or Bernoulli-Euler beam
theory, is the most commonly used because it is simple and
provides reasonable engineering approximations for many
problems. The differential equation of a uniform beam [2]:
𝐸𝐼𝑑4𝑦
𝑑𝑥4 = 𝑞
The elastic modulus is E; the moment of inertia is I, the
transverse load that applied on a unit length of the beam is q. The
load that applied on a unit length in case of free vibration:
𝑞 = −𝜌𝐴𝑑2𝑦
𝑑𝑡2
Here, ρ is density of the material and A is the sectional area. The
mathematical model of plane vibration of Euler-Bernoulli Beam
when the beam is under a force f(x,t).
𝐸𝐼𝑑4𝑦
𝑑𝑥4 + 𝜌𝐴𝑑2𝑦
𝑑𝑡2 = 𝑓(𝑥, 𝑡)
Here, y(x,t) is the lateral displacement and x and t are x-axis and
time respectively. The initial and boundary conditions are:
𝑦 𝑥, 0 = 𝑢 𝑥 ; 𝑑𝑦
𝑑𝑥 𝑥, 0 = 𝑣(𝑥)
The lateral displacement of the beam when t = 0 is u(x) and the
first derivative of the displacement is v(x). However, the Euler
Bernoulli model tends to slightly overestimate the natural
frequencies. The procedure of determining Eigen frequencies at
complex systems (systems with large number of the freedom
45
degrees) is the most crucial phase of dynamic analysis. Accurate
determination of Eigen frequencies was limited to the simple
supporting structure (simple beam and console). Finding out
solutions of frequent equation for complex elastic bodies is very
difficult, because it contained the trigonometric and hyperbolic
functions. Mathematica software enables routine solving of
frequency equations for complex elastic bodies oscillation.
3. Finite Element Analysis
By Finite Element Method (FEM), structural analyzes can be
made rapidly, reliably and nondestructively. Its popularity comes
from his realistic results which were taken from the comparisons
between FEM and analytical approaches. A variety of
specializations such as mechanical, aeronautical, biomechanical
engineering commonly use integrated finite element method in
design and development of their products. As finite element method
software, ANSYS helps tremendously in visualization of stiffness
and strength and also in minimizing weight, materials, and costs. In
this study, ANSYS is used to determine the natural frequencies with
modal analysis. In analysis, 260991 meshed elements and 666104
nodes were used. Finite element method allows entire designs to be
constructed, refined, and optimized before the design is
manufactured.
4. Results
The maximum displacements in different mods are shown in
Figure 2. The natural frequencies and relative error between
mathematical and finite element analysis are shown in Table 2. The
maximum difference is 7.02%. In modal analysis of a crane, the
reliable results can be obtained by using of finite element analysis.
It can be used in the design stage of a crane to avoid the resonance
situations.
Fig. 2 Maximum Displacements in Different Mods: a, b) Front and Top View in Mod 1; c, d) Front and Top View in Mod 2; e, f) Front and Top View in Mod 3; g, h) Front and Top View in Mod 4.
46
Table 1: Comparison of Mathematical and Finite Element Analysis Natural Frequencies [Hz]
Mod Natural Frequency [Hz]
Mathematical Analysis
Natural Frequency [Hz]
Finite Element Analysis
% Relative
Error
1 0.1908 0.2052 7.02
2 1.4526 1.5758 7.81
3 2.3861 2.4432 2.33
4 3.3048 3.3249 0.60
5. Conclusion
In the first chapter, historical development of cranes and crane
types are introduced primarily. Then, according to Euler-Bernoulli
transverse vibration approach, the applied method for the creation
of the mathematical model of the in-plane vibration of a gantry
crane is introduced. For the mathematical model, the differential
equations are prepared by using Fourier and Krylov-Duncan
Methods. By the methods Fourier and Krylov-Duncan, the
differential equation of the transverse vibration of the uniform
Bernoulli-Euler beam changed to uncoupled ordinary differential
equations with respect to unknown functions which are depend on
coordinate and time. Eigen functions and eigenvalues, the natural
frequencies of this crane was obtained. In the same section, the
modal analysis of the crane made by using finite element method
and natural frequencies are obtained. Before running the program,
the general settings of modal analysis were prepared. Most
important parts of the settings are, entering the engineering data,
sizing and the tolerance value. After the settings, meshing was
generated.
In the next section, the finite element method and the modal
analysis has described. In order to apply this method to the problem,
firstly, all parts creating the crane were 3-D modeled by using the
SOLIDWORKS drawing program.3-D modeled parts were
assembled by using the same drawing program. All 3-D models
were created with the help of the draft drawings which were formed
by mechanical calculations and the selection of the structural
elements. The generated solid model was analyzed by the finite
element method with the help of ANSYS Workbench 14.5. Mesh
quality is the most important factor that affects the finite element
results. Increasing mesh quality increases the accuracy of the finite
element method. Although minimizing size of the meshes can be an
effective method to increase mesh quality, the solving capacity of
the computers limit us. Then, the boundary conditions were applied.
It was applied by fix support and displacement commands.
In the last section, the obtained values of natural frequencies at
previous section are compared and the results of comparison are
presented.
5. References
[1] Akgün G. (2013) Design and analysis with numerical method of
2x400 ton gantry crane, MSc Thesis, ITU Graduate School of
Science, Engineering and Technology, Istanbul Technical
University, Turkey.
[2] Karnovsky İ.A. ve Lebed O. (2009) Advance Method of
Structural Analysis, Springer, New York, USA.
47
MECHANICAL DESIGN AND FINITE ELEMENT ANALYSIS OF A 3 UNIT CUBESAT
STRUCTURE
BsC. Güvenç, C. C., BsC. Topcu B., and Ph.D. Tola C.
Faculty of Aeronautics and Astronautics – University of Turkish Aeronautical Association, Turkey
analysis, heat transfer analysis and thermal stress analyses are
performed and evaluation methodology of the results are
explained.
According to the results, cubesat’s modal frequency values
are sufficiently higher than the excitation frequency values of the
launch vehicle (PSLV) and factor of safety value of the cubesat
structure governing from launching process is approximately 1.1
that is acceptable. According to the heat transfer analysis results
that are determined considering the worst case scenario, the
highest temperature value on the cubesat frame will be at most
approximately 329 oC. The temperature distribution values may
change and probably decrease according to the orbital position
and also according to the axial rotation motion of the satellite
itself. On the other hand, the structural factor of safety value of
the cubesat is calculated as 2.91 according to the thermal stress
analysis results that are conducted using the temperature
distribution results of the heat transfer analysis. Under these
circrumstances it can be stated that analysis results of the
preliminary design of the 3U cubesat structure is satisfactory and
detail design process can be initiated.
As a future work, it is planned to add further details such as
card structures, connection parts and other kinds of subsystem
elements to the finite element model to perform a detailed
analysis for both quasi-static launch and heat transfer analysis. It
will be better to use an orbital simation software to increase the
accuracy of the heat transfer and thermal stress analysis for the
future work.
9. References
[1] M. Cihan, A. Çetin, A., M. O. Kaya, and Inalhan, G., “Design and analysis of an innovative modular cubesat structure for ITU-pSAT II,” 5th International Conference on Recent Advances in Space Technologies, Istanbul, Turkey, 2011.
[2] H. Oh, S. Jeon, and S. Kwon, “Structural Design and Analysis of 1U Standardized STEP Cube Lab for On-Orbit Vertification of Fundamental Space Technologies,” International Journal of Materials, Mechanisms and Manufacturing, vol. 2, no. 3, pp. 239-244, 2014.
[3] K. Sekerere, and T. Mushiri, “Finite element analysis of a cubesat,” International Symposium on Industrial Engineering and Operations Management, Bristol, UK, 2017.
[4] Matweb Material Property Data, retrieved from: http://www.matweb.com/search/DataSheet.aspx?MatGUID=4f19a42be94546b686bbf43f79c51b7d on 05.03.2018.
[5] N. Khalifa, and T. E. Sharaf-Eldin, “Earth Albedo perturbations on Low Earth Orbit Cubesats,” International Journal of Aeronautical and Space Sciences, vol. 14, no. 2, pp. 193-199, 2013.
[6] M. Süer, E. Yakut, C. Oran, and A. R. Aslan, “NART – Nano Küp Uydular için Boyutlandırılabilir Modüler Uydu Yapısı Alt Sistemi,” V. Ulusal Havacılık ve Uzay Konferansı, Kayseri, Turkey.
[7] S. Raviprasad and N. S. Nayak, “Dynamic Analysis and Verification of Structurally Optimized Nano-Satellite Systems,” Journal of Aerospace Science and Technology, , vol. 1, no. 2, pp. 78-90, 2015.
[8] A. Lahrichi, “Heat Transfer Modeling and Simulation of MASAT1”, M.Sc. Thesis, Al Akhawayn University, 2017.
51
EFFECTS OF PROPELLANT PROPERTIES ON INTERNAL BALLISTIC
PERFORMANCE RESULTS OF SOLID ROCKET MOTORS
Ceyhun Tola, Ph.D.
Faculty of Aerospace Engineering – University of Turkish Aeronautical Association, Turkey
During the design phase of a solid rocket motor (SRM),
determination of the internal ballistic performance of the system has
a special importance since this process enables to check whether the
system requirements are satisfied or not. In order to analyze the
performance of the system and to meet these requirements in a
fastest manner, different researches on SRM design have been
conducted so far. Açık, developed a tool to optimize thrust – time
profile of a SRM by changing sectional parameters of the propellant
coupled with nozzle dimensions [1]. Celegern developed a code to
select best parameters providing desired internal ballistic
performance with lowest possible mass [2]. In addition to geometric
optimization studies which are conducted to find out the best
propellant or SRM geometry, solid propellant selection process has
also be taken into account meticulously. Therefore, effects of
propellant properties on pressure – thrust curve and performance
results based on this curve are examined for a constant SRM
geometry using the response surface method. Internal ballistic
performance analyses required to construct response surfaces are
conducted using a zero dimensional (0D) internal ballistic solver
which is developed in Matlab environment. Graphical results
summarizing the effects of combustion temperature, propellant
density, characteristic velocity, reference burning rate and burning
rate pressure exponent on maximum combustion pressure, burning
time, specific impulse, total impulse provide useful information that
can be used during the design phase of the SRMs.
2. Solid Rocket Motors
SRMs are consist of motor case, insulation, igniter, nozzle and
solid propellant. Sectional geometry of the propellant determines
the burning behavior of it and so, shape of the propellant is selected
in accordance with mission type of the system. Fig. 1 shows thrust –
time profiles belonging to different propellant sections.
Fig. 1 Variation of thrust profiles according to propellant section [3].
Propellant type also affects the combustion pressure and thrust
history of the system. Therefore, during preliminary design phase,
propellant have to be selected so that its burning characteristics will
satisfy the performance requirements of the mission without
compromising from structural integrity of the propellant. It is
significant to examine the effects of propellant properties on
internal ballistic performance results to make better selections.
3. Internal Ballistic Performance Analysis
Development of Zero Dimensional Internal Ballistic Solver
Performance of a SRM can be analyzed using a zero
dimensional (0D) internal ballistic solver. Thus, it is possible to
determine pressure – time and thrust – time histories coupled with
total impulse and specific impulse in the fastest manner. These
kinds of practical solvers are widely used for optimization processes
and they can also be used to provide results required to construct
response surfaces.
In this work, a 0D internal ballistic solver is developed under
the following assumptions. Combustion gasses are assumed as ideal
gasses. Properties of combustion gases are not varying throughout
the motor. Effects of erosive burning is neglected since aspect ratio
of the analyzed propellant geometry is less than 5. Inertia of the
combustion gasses is neglected. The flow through the nozzle is
assumed as one dimensional, steady and isentropic. It is also
assumed that burning rate (rb) is varying in accordance with Saint
Robert’s burn rate law shown in equation (1) [4].
(1) n
b cr a P
Where, Pc is chamber pressure, a is burn rate coefficient and n is burn rate exponent. For a certain type of solid propellant, a and n are constant.
The 0D internal ballistic solver is based on the conservation of
mass principle. Application of the principle constructs equation (2).
(2)
dt
dVP
c
APPaATR
Vdt
dP ic
tcn
cbpc
i
c
*
1
Where dVi/dt = Ab.rb = Ab.a.Pcn. Additionally, Tc is chamber
temperature, R is universal gas constant, ρp is density of the
propellant, Ab is burning surface of the propellant, At is throat area
of the nozzle, c* is characteristic velocity of the propellant and Vi is
port volume. Since Ab and Vi are varying with time, these
parameters are calculated performing burn-back analysis.
Solution of the equation (2) provides chamber pressure – time
history of the SRM. In order to calculate thrust – time history,
nozzle exit pressure (Pe) is calculated from equation (3) using
nozzle dimensions and thrust coefficient (CF) is calculated from
equation (4) [4].
52
(3)
11
1
1
11
1
2
1
c
e
c
e
e
t
P
P
P
P
A
A
(4)
c
ambe
c
eF
P
PP
P
PC
1
1
12
11
2
1
2
Where, 𝛾 represents the ratio of specific heats, Pamb denotes
ambient pressure, and ε represents the ratio of nozzle exit area to
nozzle throat area (Ae/At). Finally, thrust (F), total impulse (Itotal)
and specific impulse (Isp) are calculated using equations (5), (6) and
(7) respectively [4].
(5) tcF APCF
(6)
t
total dtFI0
(7)
0
*
g
CcI Fsp
Where, g0 denotes gravitational constant.
Area under the thrust – time curve corresponds the total impulse
which designates range of the system. On the other hand, the
specific impulse is measurement of efficiency of the SRM.
Therefore, during the design phase, it is crucial to satisfy the total
impulse requirements with a motor having higher specific impulse.
Grain Burn-back Analysis
This study only investigates the effects of propellant properties
on internal ballistic performance results. To do this, it is required to
perform analyzes on a constant SRM geometry by changing
propellant data. Fig. 2. represents the propellant geometry having
slotted cross section and Table 1 contains geometrical dimensions
of the propellant and the nozzle that are analyzed in this work.
Fig. 2 Geometry of the analyzed slotted grain.
Grain burn-back analysis are required to determine the variation
of Ab and Vi values with time. This information is required to solve
the equation (2). Analytical, numerical and drafting techniques can
be used to solve burn-back process. Since analytical method is the
best method to calculate exact solution in the fastest manner for
simple and some of the complex geometries, usage of analytical
techniques are preferred during the burn-back solutions within the
content of this work. Therefore, analytical burn-back equations are
derived for the slotted grain geometry making geometrical
calculations. Then, a solver working in Matlab environment is
developed and validated with drafting techniques using a CAD
software. Since derivation and validation of the burn-back solutions
are beyond the scope of this work, further details are not presented
in this research.
Table 1: Dimensions of the propellant and nozzle.
Symbol Definition Value Unit
N Number of slots 4 -
L Propellant length 500 mm
Rport Port radius 65 mm
Rout Outer radius 100 mm
Rtip-center Slot length 80 mm
Rtip Tip radius of slot 5 mm
Ae/At Ratio of nozzle exit area
to nozzle throat area 4 -
At Nozzle throat area 2800 mm2
Validation of 0D Internal Ballistic Solver
Validation of the developed 0D internal ballistic solver is accomplished using both experimental and analytical results presented in Shekhar’s work [5]. Same geometry is solved applying the same propellant data and geometry with Shekhar and results of the 0D internal ballistic solver is compared with Shekhar’s analytical and experimental results (see Fig. 3).
0
1
2
3
4
5
6
7
8
9
10
0 0.5 1 1.5 2 2.5 3 3.5
Pre
ssu
re [
MP
a]
Time [s]
Comparison of Internal Ballistic Performance Analysis Results
Shekhar's Analytical Results Experimental Results
0D Internal Ballistic Solver Results
Fig. 3 Validation of 0D internal ballistic solver [5].
As it can be seen from the comparison that 0D internal ballistic
solver results are same with Shekhar’s analytical solutions which
are quite good agreement with experimental results [5].
According to Sheikholeslam’s work, if the aspect ratio (L/D) of
a SRM is equal to 5 or lower than this value, neglection of erosive
burning does not affect the accuracy of the solution [6]. Therefore,
the aspect ratio of the design is set as approximately 3.85.
4. Response Surface Analysis
Response surface is a method used to determine detailed
information about variation of a response variable with design
variables. Response surface results has a special importance during
preliminary design phase since they illustrate summarized
information about which of the design variables have great
importance on the response variable and how they are varying it.
The aim of the study is to examine the effects of propellant
properties on internal ballistic performance results; so, combustion
burning rate and burning rate pressure exponent are defined as
design variables and maximum pressure value during the burning
process, burning time, total impulse and specific impulse are
defined as response variables. Table 2 summarizes the boundaries
of the design variables.
53
Table 2: Boundaries of the design variables.
Symbol Definition Lower
Boundary
Upper
Boundary Unit
Tc Combustion temperature 2000 4000 K
ρp Propellant density 1500 2000 kg/m3
c* Characteristic velocity 1300 1700 m/s
n Burning rate pressure
exponent 0.3 0.4 -
rb-ref Reference burning rate at
7 MPa combustion
pressure
10 20 mm/s
Four different response surface analyses are performed. Each of
them are constructed preparing full composite models consisting of
52 cases.
Response Surface of Maximum Pressure Value
Maximum pressure value (max. Pc) has a special importance on
the SRM design since this parameter both designates thickness of
the motor case and stress level on the propellant. Fig. 4 shows the
percentage effects of propellant properties and interactions of them
on maximum pressure value.
Fig. 4 Percentage effects of propellant properties on max. Pc.
According to the figure, rb-ref has the greatest effect on
maximum pressure value. Density of the propellant and c* has also
considerable amount of effect on it. Fig. 5 illustrates how these
critical design parameters affect the magnitude of maximum
pressure value.
Fig. 5 Response surface results of max. Pc parameter.
According to the results, increment of reference burning rate,
propellant density and characteristic velocity leads to increment of
the maximum pressure value.
Response Surface of Burning Time
Duration of the thrust generation is another important issue, so,
burning time of the propellant is a significant parameter. Fig. 6
shows the percentage effects of propellant properties and
interactions of them on burning time.
Fig. 6 Percentage effects of propellant properties on burning time.
According to the results, rb-ref has the greatest effect on
maximum pressure value. Additionally, burning rate pressure
exponent (n) has also minor effects on the burning time. Fig. 7
illustrates the relationship among rb-ref, n, and burning time.
Fig. 7 Response surface results of burning time.
Results indicates that, increment of burning rate exponent
increases the duration of the burning process. On the other hand,
increment of reference burning rate leads to decrement of the
burning time as expected.
Response Surface of Specific Impulse (Isp)
Specific impulse is main performance parameter that determines
efficiency of a SRM. Therefore, this parameter is also quite
significant. Fig. 8 illustrates the percentage effects of propellant
properties and interactions of them on specific impulse.
Fig. 8 Percentage effects of propellant properties on Isp.
According to the results, characteristic velocity (c*) has the
greatest effect on the specific impulse. Additionally, reference
burning rate (rb-ref) has also considerable amount of effect on it.
Finally, density of the propellant has minor effect on Isp. Fig. 9
illustrates how these critical design parameters affect the magnitude
of the specific impulse.
54
Fig. 9 Response surface results of Isp.
According to the results, increment of c*, rb-ref and propellant
density leads to more efficient designs by increasing the specific
impulse of the system.
Response Surface of Total Impulse (Itotal)
Total impulse corresponds to area under the thrust – time curve.
This parameter is quite important since there is a strong relation
between the range of the rocket motor and itself. Fig. 10 illustrates
the percentage effects of propellant properties and interactions of
them on total impulse.
Fig. 10 Percentage effects of propellant properties on Itotal.
According to the graph, propellant density and characteristic
velocity (c*) dominates the magnitude of the total impulse coupled
with reference burning rate (rb-ref) value. Fig. 11 shows how these
critical design parameters affect the magnitude of the specific
impulse.
Fig. 11 Response surface results of Itotal.
According to the results, increment of the propellant density, c*
and rb-ref increases the total impulse value.
5. Conclusion
Within the content of this research, effects of propellant
properties on internal ballistic performance results are examined
performing response surface analysis. Performance analysis are
accomplished using a zero dimensional internal ballistic
performance solver that uses analytical burn-back equations.
According to the response surface results, reference burning rate
(rb-ref) has a great significance on burning time and maximum
encountered combustion pressure value. Specific impulse that
designates the effectivity of the propellant is strongly depend on
characteristic velocity. On the other hand, total impulse of the
system is dominated by propellant density and characteristic
velocity of the propellant (c*).
In addition to the main results, this work showed that usage of
zero dimensional internal ballistic solver coupled with analytical
burn-back solutions provides accurate results with very short
amount of time that enables to accomplish many analyses required
for construction of response surfaces. Finally, this study also
revealed that designers could have detailed information about the
behavior of design variables on response variables and it is possible
to gain time during the preliminary design phase constructing
response surfaces.
6. References
[1] S. Açık, “Internal ballistic design optimization of a solid rocket motor,” M.Sc. Dissertation, Mechanical Engineering Department, Middle East Technical University, Ankara, 2010.
[2] J.B. Clegern, “Solid rocket motor conceptual design – The development of a design optimization expert system with a hypertext user interface,” 29th Joint Propulsion Conference and Exhibit, Monterey, CA, USA, 1993.
[3] T. Ward, Aerospace Propulsion Systems. John Wiley & Sons (Asia) Pte. Ltd., Singapore, 2010.
[4] G.P. Sutton and O. Biblarz, Rocket Propulsion Elements, 7th Ed., John Wiley & Sons, New York, 2001.
[5] H. Shekhar, “Effects of burning rate index on the pressure time profile of progressive burning tubular rocket propellant configurations,” Central European Journal of Energetic Materials, vol. 12, no. 2, pp. 347-357, 2015.
[6] M.R. Sheikholeslam Z., D. Kazemi, and H. Amiri, “Exprerimental analysis of the influence of length to diameter ratio on erosive burning in a solid tubular propellant grain,” Applied Mechanics and Materials, Trans Tech Publications, Switzerland, vol. 110-116, pp. 3394-3399, 2012.
55
THREE-DIMENSIONAL SIMULATION OF THERMAL STRESSES
IN DISCS DURING AN AUTOMOTIVE BRAKING CYCLE
M.Sc. Rouhi Moghanlou M., Assist. Prof. Saeidi Googarchin H. PhD.
School of Automotive Engineering – Iran University of Science and Technology, Iran
Abstract: Numerical investigation of naturally aspirated gasoline engine main operating parameters and engine upgrade with a turbocharger is presented in this paper. Analysis is performed by using numerical 0D (zero-dimensional) simulation model. Turbocharging process with a selected turbocharger increases engine maximum torque for 62.58 % and also increases maximum engine effective power for 58.82 %. One of the main reasons of turbocharging process usage is reduction of engine brake specific fuel consumption. The highest decrease in brake specific fuel consumption for a turbocharged engine, in comparison with naturally aspirated one, is obtained at 4000 rpm and amounts 8.83 g/kWh (from 239.01 g/kWh for naturally aspirated engine to 230.18 g/kWh for a turbocharged engine). Turbocharging process brings several useful benefits to the analyzed gasoline engine, which is also a valid conclusion for internal combustion engines in general. KEYWORDS: GASOLINE ENGINE, TURBOCHARGER, NUMERICAL SIMULATION, ENGINE UPGRADE 1. Introduction
Internal combustion gasoline engines with spark ignition were developed as a counterweight to diesel engines in which fuel and air mixture combust due to high in-cylinder pressures and temperatures. Both internal combustion engine types have many advantages and disadvantages [1] which are dependable on several elements and characteristics. Researchers are currently investigating various phenomena related to gasoline engines. Kilicarslan and Qatu [2] performed an exhaust gas analysis of gasoline engine based on engine speed, while Elsemary et al. [3] investigated spark timing influence on performance of a gasoline engine fueled with a mixture of hydrogen-gasoline. Effect of spark timing on the performance of a hydrogen-gasoline rotary engine (Wankel engine) was also investigated by Su et al. [4]. Alternative fuels for gasoline engines, or gasoline mixtures with an alternative fuel and its influences on engine performance and characteristics are analyzed by many authors. Alptekin and Canakci [5] analyzed performance and emission characteristics of solketal-gasoline fuel blends in a vehicle with gasoline engine. Optimized ethanol-gasoline blends for turbocharged engines were investigated by Zhang and Sarathy [6]. Turbocharging process which uses the energy of engine exhaust gases is one of the best methods for improving naturally aspirated engine operating parameters and characteristics, as well as to reduce engine brake specific fuel consumption [7]. Turbocharging system diagnosis for a large power engine presented and analyzed Barelli et al. [8]. Investigation of the influences of turbocharging process on the gasoline engine exhaust emission levels performed Mahmoudi et al. [9]. Modeling and control of the air system of a turbocharged gasoline engine investigated Moulin and Chauvin [10]. In this paper were firstly investigated main operating parameters of naturally aspirated gasoline engine for automotive usage. Investigations were performed by numerical analysis with 0D (zero-dimensional) simulation model. After obtaining the results of numerical simulation for a naturally aspirated engine, the same engine was upgraded with a turbocharger. During the engine upgrade, engine main operating and geometrical characteristics remain unchanged. Turbocharging process increases engine torque and engine effective power in each engine rotational speed, but the increases in those two parameters are significant for higher engine rotational speeds. Turbocharging increases maximum cylinder pressure, but maximum cylinder pressure limits were not reached in any observed engine operating point. Engine with turbocharger has significant lower brake specific fuel consumption in comparison with naturally aspirated. Turbocharging process increases pressures and temperatures at intake and exhaust manifolds, what is significantly noticeable at higher engine rotational speeds where the turbocharger reaches its optimal operating parameters.
2. Basic equations of 0D numerical model for internal combustion engine simulations
Numerical model used for simulation in this study is 0D (zero-dimensional) model presented by prof. Medica in [11]. Numerical model is basically developed for simulation of diesel engines and a few years later is upgraded on QD (quasi-dimensional) numerical model presented in [12] and [13]. To be able to simulate the operating parameters of a gasoline engine with the mentioned 0D model, the model is modified in necessary elements which present main differences in operating characteristics between gasoline and diesel engines. Modified 0D model is tested on a few gasoline engines which measurements were obtained from the manufacturers. For all analyzed gasoline engines and its operating parameters were obtained deviations between measurements and numerical model results in the range of ± 3 %. The basic 0D model equations are related to the temperature and pressure change for each engine control volume (engine cylinder, intake and exhaust manifolds, turbine and compressor - if turbocharger applied, air cooler - if applied, etc.). Equation for temperature change in each engine control volume is:
ii
i
i
i
i
iii
ii
ii
iii
i
dd
dd
dd
dd1
dd
∂∂
+
∂∂
−
∂∂
−
−
−
=
pu
Tp
BA
Tu
CummuVpQmT ϕ
λλϕϕϕ
ϕ
(1)
where the coefficients Ai, Bi and Ci are defined as:
ii
ii 1
∂∂
+=TR
RTA (1a)
ii
ii 1
∂∂
−=pR
RpB (1b)
∂∂
+
−
∂∂
=iiiiiiiii
ii d
d1dd1
dd1
ϕλ
λϕϕR
RV
Vm
mpu
BpC
(1c)
Pressure change in each engine control volume is calculated by using ideal gas state equation:
i
iiii V
TRmp = (2)
In the equations (1), (1a), (1b), (1c) and (2), used symbols are: T = operating medium temperature, φ = engine crankshaft angle, m = operating medium mass, Q = heat amount, p = operating medium pressure, V = operating area volume,
60
u = operating medium specific internal energy, λ = excess air ratio, R = operating medium gas constant, i = index for any engine control volume.
Calorific gas properties (u, ∂u/∂λ, ∂u/∂T, ∂u/∂p, ∂R/∂λ, ∂R/∂T, ∂R/∂p) are modeled from the analytical expressions relating the temperature and gas composition [14]. To make the simulation as fast as possible, it is assumed that in each engine cylinder happens the same change of pressure and temperature (phase-shifted). Because of the simplicity of the numerical model, this assumption presents the inability of such numerical model to investigate the processes within each engine cylinder individually.
3. Engine and turbocharger characteristics
Investigated engine is a four stroke, high speed gasoline engine with direct fuel injection. The engine is designed for application in passenger road vehicles. The first version of the analyzed engine was designed without any upgrades known from automotive industry (turbocharging, air cooling after turbocharging, usage of west-gate valve or usage of EGR - Exhaust Gas Recirculation valve). Main operating parameters and specifications of the basic, naturally aspirated engine are presented in Table 1. In Table 1 are also presented used cylinder materials and fuel specifications in order to provide a proper calculation of heat exchange for the in-cylinder process.
Table 1. Main operating parameters of investigated naturally aspirated engine
Fuel Gasoline Fuel lower calorific value 43 MJ/kg Fuel density 0.75 kg/l Cylinder bore 84 mm Stroke 86 mm Number of cylinders 4 Cylinder clearance volume 0.0477 l Connecting rod length 129.8 mm Compression ratio 11 Ignition order 1-3-4-2 Intake manifold volume 2.0 l Exhaust manifold volume 2.5 l Engine cooling With water Materials: Cylinder head Aluminum Piston Aluminum Cylinder liner Cast Iron
After obtaining the results of numerical simulation for a naturally aspirated engine, the same engine, which main operating parameters are presented in Table 1, is upgraded with a turbocharger. Usually, during the upgrade of naturally aspirated gasoline engine numerical model with a turbocharger, it is usual to change some engine geometric and operating parameters such as intake and exhaust manifold volumes or valves opening/closing periods. During the engine upgrade with turbocharger presented in this paper, engine main operating and geometrical characteristics remain unchanged. One of the author’s intentions was to investigate the possibility and quality of engine operation with selected turbocharger, without any engine modifications. The main geometrical characteristics of selected turbocharger KKK 30.60/13.21 are presented in Table 2 and in Fig. 1:
Table 2. Main geometrical parameters of selected turbocharger KKK 30.60/13.21 [15]
Description Variable Dimension Charger intake diameter d 0.0457 m Charger outlet diameter D 0.0762 m
Intake turbine flowing surface A 0.0013 m2
Fig. 1. Geometrical characteristics of charger and turbine [15]
Much more information’s and features for similar turbochargers, used in automotive engines such as engine analyzed in this paper, can be found in [16].
4. Numerical model results and discussion
Change in engine torque for the analyzed engine with and without turbocharger, at different engine rotational speeds is presented in Fig. 2. At each engine rotational speed engine torque obtained with turbocharger is higher. At a rotational speed of 1000 rpm, engine torque obtained with turbocharger is slightly higher in comparison with a naturally aspirated engine. During the increase in the engine rotational speed, the difference in engine torque between turbocharged and naturally aspirated engine increases. The highest difference in engine torque was obtained at engine rotational speed of 5000 rpm where turbocharged engine obtains torque of 307.45 Nm, while at the same engine rotational speed naturally aspirated engine obtained torque of 189.11 Nm. A decrease in engine torque can be seen only in the rotational speeds from 5000 rpm to 6000 rpm. At the highest engine rotational speeds, there is no need for high torque, so it decreases. The introduction of turbocharging on the analyzed gasoline naturally aspirated engine can increase engine torque up to 62.58 % (obtained at 5000 rpm).
Fig. 2. Change in engine torque for the analyzed engine with and without turbocharger
Increase in engine torque of turbocharged engine when compared to naturally aspirate in any observed rotational speed, resulted also with an increase in engine power. During the increase in the engine rotational speed, engine power continuously increases for both naturally aspirated and turbocharged engine, Fig. 3. In Fig. 3 can also be seen that increase in engine power of a turbocharged engine is low at lower rotational speeds (at 1000 rpm and 2000 rpm). As the engine rotational speed increase, engine power of turbocharged engine when compared to naturally aspirate significantly increases. At the highest engine rotational speed (6000 rpm) naturally aspirated engine develops output power of 111.44 kW, while at the same rotational speed turbocharged engine develops power of 176.99 kW, what is the highest difference in engine power for the entire field of engine rotational speeds. The engine effective power is obtained by multiplication of engine torque and angular velocity. On Fig. 2 can be seen that between rotational speeds 5000 rpm and 6000 rpm engine torque
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decrease for each observed engine. Simultaneously, engine power between the same rotational speed increases. It can be concluded that engine power is more influenced with an increase in the engine rotational speed from 5000 rpm to 6000 rpm than with decrease in engine torque at the highest rotational speeds.
Fig. 3. Change in engine power for the analyzed engine with and without turbocharger
Upgrade of naturally aspirated gasoline engine with turbocharger resulted in a significant increase in maximum cylinder pressure, as presented in Fig. 4. Maximum cylinder pressure for both observed engines was obtained at the 5000 rpm and amounts 72.38 bars for a naturally aspirated engine and 121.7 bars for turbocharged engine. Turbocharger usage is usually limited with maximum cylinder pressure. For similar automotive gasoline engines with turbocharger, it is common to set a maximum cylinder pressure limit between 150 bars and 170 bars in order to avoid any damage which can occur at very high maximum pressures. The selected turbocharging process of the analyzed engine did not reach common maximum cylinder pressure limits in any observed operating point.
Fig. 4. Change in cylinder maximum pressure for the analyzed engine with and without turbocharger
One of the essential reasons for turbocharging process usage is reduction of engine brake specific fuel consumption (injected fuel mass per unit of produced power). As presented in Fig. 5, the analyzed gasoline engine with turbocharger has significant lower brake specific fuel consumption in comparison with a naturally aspirated engine, for the most engine rotational speeds. Only at the lowest and the highest engine rotational speeds (1000 rpm and 6000 rpm) brake specific fuel consumption of an engine with turbocharger is lower in comparison with naturally aspirated one, but not significantly. The highest differences in brake specific fuel consumption between two analyzed engines can be seen at engine rotational speeds of 3000 rpm, 4000 rpm and 5000 rpm. Turbocharged engine, in comparison with naturally aspirated one, saves 5.10 g/kWh of fuel at 3000 rpm, 8.83 g/kWh of fuel at 4000 rpm and 6.95 g/kWh of fuel at 5000 rpm. Engine volumetric efficiency is defined as a ratio of air mass brought to engine cylinders and air mass which can be brought to engine cylinders at the environment state. For naturally aspirated gasoline engine, volumetric efficiency is always lower than 100 % because of air pressure losses and temperature increase during the air supply to the cylinders, Fig. 6.
Turbocharging process resulted with volumetric efficiency significantly higher than 100 % at the higher engine rotational speeds, because in the engine cylinder, air charger compresses the higher air mass than those which can be brought at the environment state, Fig. 6. At lower engine rotational speeds (lower than 3000 rpm) volumetric efficiency of a turbocharged engine is lower than 100 % because at that engine rotational speeds turbocharger is unable to develop optimal operating parameters. The highest volumetric efficiency of a turbocharged engine is obtained at 5000 rpm and amounts 154.2 %.
Fig. 5. Brake specific fuel consumption change for the analyzed engine with and without turbocharger
Fig. 6. Change in volumetric efficiency for the analyzed engine with and without turbocharger
At the lower engine rotational speeds of the naturally aspirated engine (1000 rpm and 2000 rpm) air pressure in the intake manifold is slightly lower than ambient pressure (ambient pressure is 1.01 bars), Fig. 7. As naturally aspirated engine rotational speed increases, intake manifold pressure decreases to ensure smooth flow of air from the atmosphere to the engine cylinders. Decrease in air pressure is as higher as the rotational speed increases and lowest intake manifold pressure of 0.96 bar is obtained at 6000 rpm. Intake manifold pressure of turbocharged gasoline engine is higher than ambient pressure and it continuously increases during the increase in the engine rotational speed, Fig. 7. The highest increase in intake manifold pressure of turbocharged engine can be seen at rotational speeds higher than 4000 rpm. The highest intake manifold pressure of turbocharged engine amounts 1.23 bars and is obtained at 6000 rpm.
Fig. 7. Change in intake manifold pressure for the analyzed engine with and without turbocharger
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Exhaust manifold pressure of naturally aspirated engine increases very slightly during the increase in the engine rotational speed, Fig. 8. The exhaust manifold pressure of turbocharged engine increases notably during the increase in the engine rotational speed. The highest increase in exhaust manifold pressure of turbocharged engine can be seen at rotational speeds higher than 4000 rpm, where the turbocharger reaches its satisfactory operating conditions. The highest exhaust manifold pressure of turbocharged engine amounts 3.14 bars and is reached at the highest engine rotational speed of 6000 rpm.
Fig. 8. Change in exhaust manifold pressure for the analyzed engine with and without turbocharger
Exhaust manifold temperature continuously increases during the increase in the engine rotational speed for both naturally aspirated and turbocharged engine, Fig. 9. From the lowest to the highest engine rotational speed, exhaust manifold temperature increases from 761.2 °C to 951.9 °C for a naturally aspirated engine and from 801.8 °C to 1051.1 °C for turbocharged engine. At any observed rotational speed, turbocharged engine has a higher exhaust manifold temperature in comparison with a naturally aspirated engine. When compared analyzed two engines, the highest differences in exhaust manifold temperatures can be seen at rotational speeds of 5000 rpm and 6000 rpm and amounts 98.3 °C and 99.2 °C.
Fig. 9. Change in exhaust manifold temperature for the analyzed engine with and without turbocharger
5. Conclusions
The paper presents an investigation of main operating parameters of naturally aspirated gasoline engine for automotive usage and its upgrade with a turbocharger. Analysis is performed by numerical 0D (zero-dimensional) simulation model. During the engine upgrade, engine main operating and geometrical characteristics remain unchanged. Selected turbocharger inclusion into the gasoline engine operation resulted with an increase in engine maximum torque for 62.58 % (from 189.11 Nm to 307.45 Nm) and with an increase in engine maximum effective power for 58.82 % (from 111.44 kW to 176.99 kW). Turbocharging process also resulted with an increase in maximum cylinder pressure, but the limits were not reached with a usage of selected turbocharger. One of the main reasons of turbocharging process usage is reduction of engine brake specific fuel consumption. The highest decrease in brake specific fuel consumption for a turbocharged engine, in comparison with naturally aspirated one, is obtained at
4000 rpm and amounts 8.83 g/kWh (from 239.01 g/kWh for naturally aspirated engine to 230.18 g/kWh for a turbocharged engine). Pressures and temperatures in intake and exhaust engine manifolds also increase when the turbocharger is used. Therefore, it would be advisable for the intake and exhaust manifolds to be dimensioned more robustly with better thermal insulation, in order to be able to withstand the introduction of turbocharger on the naturally aspirated engine without any modifications.
6. Acknowledgment
A retired professor Vladimir Medica, Faculty of Engineering, University of Rijeka is gratefully acknowledged for the ceded numerical model as well as for helpful suggestions and discussions.
7. References
[1] Stone, R.: Introduction to Internal Combustion Engines, Fourth edition, Palgrave Macmillan, 2012. [2] Kilicarslan, A., Qatu, M.: Exhaust gas analysis of an eight cylinder gasoline engine based on engine speed, Energy Procedia 110, p. 459 – 464, 2017. (doi: 10.1016/j.egypro.2017.03.169) [3] Elsemary, I. M. M., Attia, A. A. A., Elnagar, K. H., Elsaleh, M. S.: Spark timing effect on performance of gasoline engine fueled with mixture of hydrogen-gasoline, International Journal of Hydrogen Energy, In Press, 2017. (doi: 10.1016/j.ijhydene.2017.10.125) [4] Su, T., Ji, C., Wang, S., Shi, L., Yang, J., Cong, X.: Effect of spark timing on performance of a hydrogen-gasoline rotary engine, Energy Conversion and Management 148, p. 120–127, 2017. (doi: 10.1016/j.enconman.2017.05.064) [5] Alptekin, E., Canakci, M.: Performance and emission characteristics of solketal-gasoline fuel blend in a vehicle with spark ignition engine, Applied Thermal Engineering 124, p. 504-509, 2017. (doi: 10.1016/j.applthermaleng.2017.06.064) [6] Zhang, B., Sarathy, M.: Lifecycle optimized ethanol-gasoline blends for turbocharged engines, Applied Energy 181, p. 38- 53, 2016. (doi: 10.1016/j.apenergy.2016.08.052) [7] Garrett, T. K., Newton, K., Steeds, W.: The Motor Vehicle, Thirteenth edition, Butterworth-Heinemann, 2001. [8] Barelli, L., Bidini, G., Bonucci, F.: Diagnosis of a turbocharging system of 1 MW internal combustion engine, Energy Conversion and Management 68, p. 28–39, 2013. (doi: 10.1016/j.enconman.2012.12.013) [9] Mahmoudi, A. R., Khazaee, I., Ghazikhani, M.: Simulating the effects of turbocharging on the emission levels of a gasoline engine, Alexandria Engineering Journal, In Press, 2017. (doi: 10.1016/j.aej.2017.03.005) [10]Moulin, P., Chauvin, J.: Modeling and control of the air system of a turbocharged gasoline engine, Control Engineering Practice 19, p. 287–297, 2011. (doi: 10.1016/j.conengprac.2009.11.006) [11]Medica, V.: Simulation of turbocharged diesel engine driving
electrical generator under dynamic working conditions, Doctoral Thesis, University of Rijeka, Rijeka, 1988.
[12]Mrzljak, V., Medica, V., Bukovac, O.: Volume agglomeration process in quasi-dimensional direct injection diesel engine numerical model, Energy 115, p. 658-667, 2016. (doi: 10.1016/j.energy.2016.09.055) [13]Mrzljak, V., Medica, V., Bukovac, O.: Simulation of a Two Stroke Slow Speed Diesel Engine Using a Quasi-Dimensional Model, Transactions of Famena, 2, p. 35-44, 2016. (doi: 10.21278/TOF.40203) [14]Jankov, R.: Mathematical modeling of flow, thermodynamic processes and engine operation characteristics, Naučna knjiga, Beograd, Part 1 and Part 2, 1984. [15]Škifić, N.: Influence analysis of engine equipment parameters on diesel engine characteristics, Doctoral Thesis, Rijeka, University of Rijeka, 2003. [16] http://www.aet-turbos.co.uk (accessed: 14.12.2017.)
Abstract: The influences of liquid fuel temperature, pressure and injection rate on fuel contraction coefficient and Reynolds number during a fuel injection were investigated in this paper. Nozzle geometry parameters remained constant during the whole numerical analysis. Calculations were performed with a standard diesel fuel D2. Increase in liquid fuel temperature cause increase in fuel contraction coefficient. Fuel temperature increase resulted in a slight increase in contraction coefficient at low fuel pressures, while at high fuel pressures increase in fuel temperature causes significant increase in fuel contraction coefficient. Increase of fuel pressure resulted in a decrease in liquid fuel contraction coefficient, for every fuel injection rate and for every fuel temperature. Reynolds number increases with an increase in fuel temperature and also with an increase in fuel injection rate. The main goal of presented analysis is to be usable not only for one fuel injector and its nozzles, but for a large number of the fuel injectors and for many liquid fuels. KEYWORDS: LIQUID FUEL, FUEL INJECTOR NOZZLE, CONTRACTION COEFFICIENT, REYNOLDS NUMBER 1. Introduction
In internal combustion engine fuel temperature, pressure and injection rate as well as the injector nozzle geometry strongly affect the fuel atomization process. A liquid fuel atomization process has a strong influence on the engine combustion process and on exhaust emissions. However, due to the small length and time scales during the fuel injection process, it is still a challenge to capture and explain the physics and influences behind those processes. Internal nozzle flow influence on spray atomization along with fuel properties and injection rates was investigated by several authors in the past [1], [2]. Newer investigations about this topic is presented by Madero and Axelbaum [3] which was investigated fuel spray breakup and structure of spray flames for low-volatility wet fuels. Greenberg [4] investigated the impact of the initial droplet size distribution on the behavior of an edge flame. Nozzle configuration effects on internal flow and primary spray breakup for flash boiling fuel sprays was analyzed by Wu et al. [5] while Abianeh et al. [6] investigated the nozzle flow influence and characteristics on multi-component fuel spray evaporation process. Experimental study on fuel spray characteristics under atmospheric and pressurized cross-flow conditions presented Guo et al. [7]. The impact of the injector nozzle geometry and fuel properties on fuel injection, fuel atomization and evaporation processes must be involved in any detail internal combustion engine simulation, as the one presented in [8] for a high speed direct injection turbocharged diesel engine. The same impact is inevitable in simulations of large marine two-stroke slow speed diesel engines [9].
2. Liquid fuel contraction coefficient
Liquid fuel contraction is liquid stream constriction which occurs because the fluid streamlines cannot abruptly change direction. For the fuel injector nozzle, the fluid streamlines are unable to closely follow the sharp angle in the nozzle wall. Maximum contraction is the place in a liquid fuel stream where the diameter of the stream is the lowest. The maximum contraction takes place slightly downstream of the fuel injector nozzle, Fig. 1.
According to Fig. 1, the liquid fuel contraction coefficient for the fuel injector nozzle is defined as a ratio of liquid fuel stream diameter at maximum contraction point and the nozzle diameter:
ddC MC
d (1)
where: Cd = liquid fuel contraction coefficient, dMC = liquid fuel stream diameter at maximum contraction point, d = nozzle diameter.
Liquid fuel contraction coefficient value is always lower than 1 and depends on the fuel stream parameters (pressure, temperature and injection rate) as well as on nozzle geometry.
3. Injector nozzle geometry parameters
The main goal of presented mathematical model in this analysis is to be usable not only for one fuel injector and its nozzles, but for a large number of the fuel injectors and for many liquid fuels. As analysis baseline is used fuel injector DLLA 775 from [10]. Three fuel injector nozzle geometry parameters which influenced liquid fuel contraction and Reynolds number are nozzle diameter (d), nozzle length (l) and nozzle inlet radius (r). The nozzle inlet radius value is usually shown as a ratio of nozzle diameter (r/d), what was also adopted in presented analysis. In analysis were selected nozzle geometry parameters similar to ones for fuel injector DLLA 775 [10], which are the most used in practice. Selected nozzle geometry parameters remain unchanged throughout the analysis. The variables which strongly influenced fuel contraction coefficient and Reynolds number are fuel pressure, fuel temperature and fuel injection rate. Those variables were varied.
4. Liquid diesel fuel used in the analysis
In analysis was used diesel fuel D2, which main characteristics and specifications are presented in Table 1. Although the analysis is made with diesel fuel D2, the mathematical description of the liquid fuel contraction coefficient and the Reynolds number allows the usage of any standard or alternative liquid fuel.
Table 1. Main specifications of diesel fuel D2 [11] Liquid diesel fuel D2 property Value Sulfur content 0.3 percentage of mass Molecular mass 198 kg/kmol Density at 15.5 °C 0.842 g/cm3 Kinematic viscosity at 38 °C 2.84 · 10-6 m2/s Critical pressure 20.9 bar Critical temperature 453 °C Boiling point 266 °C Flash point 75 °C Aniline point 71.7 °C
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5. Liquid diesel fuel D2 thermodynamics properties necessary for analysis
5.1. Density of liquid diesel fuel D2
Liquid diesel fuel D2 density dependence on the fuel pressure and temperature is given by the following equation [11]:
At
Ep10 (2)
where: = liquid fuel current density (g/cm3), 0 = 0.845 g/cm3 (liquid fuel density on the environmental pressure = 1 bar and temperature = 25 °C), p = liquid fuel current pressure (Pa), 8106.19 E Pa (liquid fuel elasticity module), t = liquid fuel temperature above the environment temperature, A = 1350 °C (reciprocal value of the liquid fuel thermal expansion coefficient).
5.2. Dynamic viscosity of liquid diesel fuel D2
Liquid diesel fuel D2 dynamic viscosity change can be calculated by a second degree polynomial [11]:
221 )()()( ptBptBtA (3)
77.7745789.17exp0036761.0
98351.1345789.17exp0030803.01092723.5)( 5
t
ttA (4)
312
210761
1030035.1
1082129.31017256.11002964.8)(
t
tttB
(5)
453.5120exp1085318.5
126829.920exp1021756.2)(
9
82
t
ttB (6)
where: p = liquid fuel current pressure (bar), t = liquid fuel current temperature (°C), = liquid fuel current dynamic viscosity (kg/m·s).
6. Liquid fuel Reynolds number and contraction coefficient
The Reynolds number for the fuel injector nozzle is defined by the expression:
3
i 10Re
dv (7)
where: = liquid fuel density (kg/m3), vi = liquid fuel injection rate (m/s), d = nozzle diameter (mm), = liquid fuel dynamic viscosity (kg/m·s).
Reynolds number coefficient f used in the contraction coefficient equation was calculated by the equation:
)Re64,Re316.0(Max 25.0f (8)
Contraction loss coefficient Kin is a function of nozzle inlet radius r and nozzle diameter d ratio. According to [12] contraction loss coefficient Kin can be defined by the following polynomial:
drdr
drdrK
/·/·
/·/·162.52076 in (9)
where: Kin = contraction loss coefficient (-), r = nozzle inlet radius (mm), d = nozzle diameter (mm).
Flow in the fuel injector nozzle is turbulent with the possibility of cavitation occurrence. Taking into account the turbulent flow in the fuel injector nozzle without the occurrence of cavitation [12], the liquid fuel contraction coefficient can be defined as:
1
1
in
d
dlfK
C (10)
where: Cd = liquid fuel contraction coefficient (-), Kin = contraction loss coefficient (-), f = Reynolds number coefficient (-), l = nozzle length (mm), d = nozzle diameter (mm).
7. Mathematical model results and discussion
Change in liquid fuel contraction coefficient for different fuel injection rates and temperatures, at fuel pressure of 800 bars, was presented in Fig. 2. This figure, as all the other figures through this paper, was obtained by using nozzle geometry and fuel characteristics presented in boldface legend in the figure. From Fig. 2 can be seen that contraction coefficient increases with the increase in fuel temperature. During the injection rate increase, at any fuel temperature, increase in contraction coefficient is significant for low injection rates (from 10 m/s to 100 m/s). Further increase in the fuel injection rate (above 100 m/s) causes low, almost negligible increase in contraction coefficient, for any fuel temperature.
Fig. 2. Change in liquid fuel contraction coefficient for different fuel injection rates and temperatures (p = 800 bars)
For the same fuel injector nozzle operating parameters and fuel pressure as in Fig. 2, change in Reynolds number which is calculated according to equation (7) is presented in Fig. 3. For any fuel injection rate, Reynolds number increases with an increase in fuel temperature. Increase in fuel injection rate also increases Reynolds number, for every fuel temperature. During the increase in injection rate, the increase in Reynolds number is as higher as the fuel temperature increase, so the highest Reynolds numbers were obtained for the highest observed fuel temperature and injection rate. Dispersion of Reynolds numbers for a various fuel temperatures became as higher as fuel injection rate increases.
Fig. 3. Change in Reynolds number for different fuel injection rates and temperatures (p = 800 bars)
Change in liquid fuel contraction coefficient for different fuel injection rates and temperatures, for the same fuel injector nozzle operating parameters as in Fig. 2, but with increased fuel pressure (from 800 bars to 2000 bar) is presented in Fig. 4.
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For any fuel pressure is valid a fact that the increase in fuel temperature causes an increase in contraction coefficient, for any fuel injection rate. Increase in fuel injection rate causes a different change of contraction coefficient for low fuel pressures (Fig. 2) in comparison with high fuel pressures (Fig. 4). At high fuel pressures, increases in the fuel injection rate (from 10 m/s to 500 m/s) causes a continuous and significant increase in contraction coefficient, when the fuel is on environmental temperature (25 °C). For higher fuel temperatures, an increase in contraction coefficient during the increase in injection rate is significant only for lower injection rates (from 10 m/s to 250 m/s).
Fig. 4. Change in liquid fuel contraction coefficient for different fuel injection rates and temperatures (p = 2000 bar)
Change in Reynolds number for different fuel injection rates and temperatures at fuel pressure of 2000 bar is presented in Fig. 5. When compared Fig. 5 (fuel pressure 2000 bar) and Fig. 3 (fuel pressure 800 bar) it can be concluded that a change in Reynolds number during the change in the fuel injection rate and fuel temperature has the same trend for every fuel pressure. The only significant influence of fuel pressure on Reynolds number can be seen in the Reynolds number value. Increase in fuel pressure causes decrease in Reynolds number, for the same fuel injector nozzle operating parameters. At fuel pressure of 2000 bar, Fig. 5, maximum Reynolds number does not exceed Re = 7500, while at fuel pressure of 800 bars, Fig. 3, maximum Reynolds number reaches almost Re = 21000. Again, for both fuel pressures, the maximum Reynolds number was obtained at the highest fuel temperature and at the highest injection rate.
Fig. 5. Change in Reynolds number for different fuel injection rates and temperatures (p = 2000 bar)
Change in liquid fuel contraction coefficient for different fuel pressures and injection rates at a fuel temperature of 25 °C, is presented in Fig. 6. Increase in fuel pressure resulted with a decrease in liquid fuel contraction coefficient, for every fuel injection rate, but the decrease trends are not the same at each injection rate. For the lowest observed injection rate (100 m/s) decrease in contraction coefficient, during the increase in fuel pressure is the sharpest. Increase in fuel injection rate causes that decrease in contraction coefficient, during the fuel pressure increase, becomes less and less sharp. For low fuel pressures, dispersion of contraction coefficients for every observed injection rate is low, while it becomes bigger and bigger as fuel pressure increases.
Fig. 6. Change in liquid fuel contraction coefficient for different fuel pressures and injection rates (t = 25 °C)
Change in liquid fuel contraction coefficient for different fuel pressures and injection rates, for the same fuel injector nozzle operating parameters, but for increased fuel temperatures was presented in Fig. 7 for fuel temperature of 40 °C and in Fig. 8 for fuel temperature of 70 °C. As in Fig. 6, increase of fuel pressure resulted in a decrease in liquid fuel contraction coefficient, for every fuel injection rate, and the decrease is the highest for the lowest observed fuel injection rate (100 m/s). When compared Fig. 6 and Fig. 7, it can be noted that the increase in fuel temperature from 25 °C to 40 °C resulted in a slight increase in contraction coefficient at low fuel pressures, while at high fuel pressures increase in fuel temperature causes significant increase in fuel contraction coefficient, for any injection rate. This conclusion and comparison with lower fuel temperature is also valid when fuel temperature is the highest observed (70 °C, Fig. 8).
Fig. 7. Change in liquid fuel contraction coefficient for different fuel pressures and injection rates (t = 40 °C)
Fig. 8. Change in liquid fuel contraction coefficient for different fuel pressures and injection rates (t = 70 °C)
Change in Reynolds number for different fuel pressures and injection rates is presented in Fig. 9 and Fig. 10. Injector nozzle geometry parameters remains the same in all figures, while the fuel temperature was varied and amounts 25 °C - Fig. 9 and 70 °C - Fig. 10. The most of the conclusions for Reynolds number change are the same at each fuel temperature. Increase in fuel pressure causes decrease in Reynolds number for every fuel temperature and injection rate. The decrease in Reynolds number during the fuel pressure increase is the highest for the highest fuel injection rates, at
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any fuel temperature. Dispersion of Reynolds numbers for different fuel injection rates are the highest at the lowest fuel pressures while the same dispersion is the lowest for the highest observed fuel pressures, what is a valid conclusion for every fuel temperature. Change in fuel temperature influences only the Reynolds number value. For every fuel temperature, the highest Reynolds numbers were obtained at the lowest fuel pressure and at the highest fuel injection rate. Increase in fuel temperature resulted in an increase in Reynolds number.
Fig. 9. Change in Reynolds number for different fuel pressures and injection rates (t = 25 °C)
Fig. 10. Change in Reynolds number for different fuel pressures and injection rates (t = 70 °C)
8. Conclusion
In this paper were investigated influences of liquid fuel temperature, pressure and injection rate on fuel contraction coefficient and Reynolds number during fuel injection. Nozzle geometry parameters remained constant during the whole numerical analysis. As expected, fuel temperature, pressure and injection rate are very influential parameters which can significantly change the fuel contraction coefficient and Reynolds number. Calculations were performed with a standard diesel fuel D2. Increase in liquid fuel temperature cause increase in fuel contraction coefficient. Fuel temperature increase resulted in a slight increase in contraction coefficient at low fuel pressures, while at high fuel pressures increase in fuel temperature causes significant increase in fuel contraction coefficient. To obtain contraction coefficient as high as possible, for low fuel pressures is advisable to increase the fuel injection rate, but not much higher than 100 m/s. At high fuel pressures, increases in the fuel injection rate causes a continuous and significant increase in contraction coefficient when the fuel is on environmental temperature (25 °C), while for higher fuel temperatures increase in contraction coefficient during the increase in injection rate is significant only for lower injection rates. Increase of fuel pressure resulted in a decrease in liquid fuel contraction coefficient, for every fuel injection rate and for every fuel temperature. Reynolds number increases with an increase in fuel temperature and also with an increase in fuel injection rate. During the increase in injection rate, the increase in Reynolds number is as high as the fuel temperature increase, so the highest Reynolds numbers were obtained for the highest observed fuel temperature and injection rate. Change in Reynolds number during the change in the fuel injection rate and fuel temperature has the same trend for every fuel
pressure. For every fuel temperature, the highest Reynolds numbers were obtained at the lowest fuel pressure and at the highest fuel injection rate. Increase in fuel pressure causes decrease in Reynolds number for every fuel temperature and injection rate. The main goal of presented analysis is to be usable not only for one fuel injector and its nozzles, but for a large number of the fuel injectors and for many liquid fuels. Future research will be based on investigations of the same fuel and fuel injector operating parameters for alternative fuels and its comparison with presented ones for a standard diesel fuel.
9. Acknowledgment
This work was supported by the University of Rijeka (contract no. 13.09.1.1.05) and Croatian Science Foundation-project 8722.
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Model of a Diesel Fuel Injector nozzle, SAE Paper 922308, 1992. (doi:10.4271/922308)
[2] Chaves, H., Knapp, M., Kubitzek, A., Obermeier, F., Schneider, T.: Experimental Study of Cavitation in the Nozzle Hole of Diesel Injectors Using Transparent nozzles, SAE Technical paper 950290, 1995.
(doi:10.4271/950290) [3] Madero, J. E., Axelbaum, R. L.: Spray breakup and
structure of spray flames for low-volatility wet fuels, Combustion and Flame, 180, p. 102–109, 2017. (doi:10.1016/j.combustflame.2017.02.029)
[4] Greenberg, J. B.: Droplet size distribution effects in an edge flame with a fuel spray, Combustion and Flame, 179, p. 228–237, 2017. (doi:10.1016/j.combustflame.2017.02.002)
[5] Wu, S., Xu, M., Hung, D. L. S., Pan, H.: Effects of nozzle configuration on internal flow and primary jet breakup of flash boiling fuel sprays, International Journal of Heat and Mass Transfer, 110, p. 730–738, 2017.
(doi:10.1016/j.ijheatmasstransfer.2017.03.073) [6] Abianeh, O. S., Chen, C. P., Mahalingam, S.: Numerical
modeling of multi-component fuel spray evaporation process, International Journal of Heat and Mass Transfer, 69, p. 44–53, 2014.
(doi:10.1016/j.ijheatmasstransfer.2013.10.007) [7] Guo, M., Nishida, K., Ogata, Y., Wu, C., Fan, Q.:
Experimental study on fuel spray characteristics under atmospheric and pressurized cross-flow conditions, second report: Spray distortion, spray area, and spray volume, Fuel, 206, p. 401–408, 2017. (doi:10.1016/j.fuel.2017.05.088)
[8] Mrzljak, V., Medica, V., Bukovac, O.: Volume agglomeration process in quasi-dimensional direct injection diesel engine numerical model, Energy, 115, p. 658-667, 2016. (doi:10.1016/j.energy.2016.09.055)
[9] Mrzljak, V., Medica, V., Bukovac, O.: Simulation of a Two-Stroke Slow Speed Diesel Engine Using a Quasi-Dimensional Model, Transactions of Famena, 2, p. 35-44, 2016. (doi:10.21278/TOF.40203)
[10] Škifić, N.: Influence analysis of engine equipment parameters on diesel engine characteristics, Doctoral Thesis, Rijeka, University of Rijeka, 2003.
[11] Cvetić, M.: Combustion modeling in direct injection diesel engine based on fuel injection rate, Doctoral thesis, University of Belgrade, Belgrade, 2000.
[12] Von Kuensberg Sarre, C., Song-Charng, K., D. Reitz, R.: Modeling the effects of injector nozzle geometry on diesel sprays, SAE paper 1999-01-0912, 1999. (doi:10.4271/1999-01-0912)
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THE ANALYTICAL RESEARCH OF THE DYNAMIC LOADING EFFECT ON THE
ROAD-HOLDING ABILITY CHARACTERISTIC SIGNS OF EARTH-MOVING
MACHINE
Cand. Eng. Sc., Associate Professor Shevchenko V. 1, Post-graduate student Chaplygina A. 1, Cand. Eng. Sc., Krasnokutsky V2,
Associate Professor Logvinov E. 3
Faculty of Mechanical – Kharkiv National Automobile and Highway University, Ukraine 1
Educational and Scientific Institute of Mechanical Engineering and Transport – National Technical University "Kharkiv Polytechnic
University", Ukraine 2
Faculty of International Education – National Technical University "Kharkiv Polytechnic University", Ukraine 3
Abstract: The homeland of the first modern electrical car is Greece. Legendary Enfild 8000 is one of the first electrical cars in the world, and that small two-seater was also extremely economical. It originated from the Greek island of Syros, where it is exhibited today at the Industrial Museum in Hermoupolis.It is believed that electrical cars are the real small revolution, because we replaced one type of engine with the other, while the autonomous vehicles resistant to human errors will represent the first real big transport revolution of the 21st century. Experts believe that new models of cars will have the best test in Norway1, where during the last year drivers mostly (52%) voted for electric cars and hybrids. Electrified icons: Ford Mustang and Ford F-150 hybrids are coming by 2020. Porsche plans to sell 20,000 cars E mission per year. Also the French are planning to present 8 new electric cars (record holder is the model "zoe"2, and soon the EV version of the "Quid", a small SUV that is sold on developing markets should join) before year 2022. In Serbia there is a plan to set up more charging stations for electrical vehicles. It will be initially only 3 stations within the project "Green Balkanica", while it is cited that in China there are even 5 million of these stations.
Would you be in a car that is driving instead of you? Many car manufacturers and other companies that are not part of the auto industry, have been working on the development of autonomous vehicles for years. So far they have mainly been focused on solving the problems that may occur when these cars find themselves in real traffic conditions and did not think too much about the future customers and their attitudes towards self-driving vehicles.
Real struggle is led in the world for new technologies between China and the United States, i.e. the race to develop the first "egzaskejl“1 computer, as previously Russia and the United States fought for the development of space technology. The biggest problem in its development will be to ensure sufficient electricity, because its work requires the capacity of a small nuclear power plant. We should mention the supercomputer 'Sunway TaihuLight" and computer "The Summit". Building the "Summit" America could for the first time after year 2013 again take over the primacy in the development of supercomputers. China then launched the computer "Tianhe-2" and took over the primacy in the development of the fastest computers in the world. In this race participate also Japan and the European Union (EU) and promote the development of various scientific disciplines, industrial technology, defense.
According to the data of "France Press" the European Automobile Manufacturers Association (ACEA) announced that in March 2007 in EU the number of registered passenger cars increased by a significant 11.2%. Today, the European car market is growing2 and returns to the level before the economic crisis of 2008.
The question is "if your vehicle is fully autonomous (there is no steering wheel or steering commands) do you need auto insurance? Do you need a driver's license? Are you responsible in the event of a collision, or the manufacturer? Should a car manufacturer or its owner have insurance in the case of an accident? Should the liability coverage be included in the purchase price of the car? These are important legal issues that need to be answered.3
1 China has announced that this computer will be completed by 2020. 2 Better results were observed in all 5 major markets, so that in March in Italy, the
number of newly registered cars increased for 18.2%, in Spain for 12.6%, in Germany for 11.4%, in the UK for 8, 4% and in France for 7%. /Tanjug/
3 Poitras Colin, The rise of self-driving cars, March 2017. https://phys.org/news/2017-03-self-driving-cars.html
Greece is the home of the first modern electric car. Enfield 8000 was one of the first electric cars in the world, and a small two-seater was also extremely economical. It is interesting that it just originated at the Greek island of Syros (Syra island archipelago), where it is exibited today at the Museum of Industry in Hermoupolis. The owner of the British company Enfield Automotive, Mr. Janis Goulandris in early seventies, contacted Mr. Jorgos Mikhail who was dealing with the construction of space shuttles for NASA. Specifically, he wanted that the first electric car is produced just in Greece, but its further production will take the company Enfield in the UK. For the Greeks themselves was of the great importance to continue the relationship with the company of Gulardis in Britain since it is precisely the one that produced vehicles used for the struggle against the Germans in the Second World War.
A small car was great and the most convenient discovery for the time when it was manufactured as evidenced by the interest in it from the whole world. A small two-seater battery was more popular beyond the borders of Greece, especially in London, where its 123 copies were sold, a few hundred were also sold in Sweden, where it was used as the primary mean of transport in the mines. Automobile worked on eight batteries and after seven hours of charging it was able to hold out the next 24 hours. It reached speed of 80 kilometers per hour and it was perfect car for the city in which it ran about 70 kilometers daily.
2. Serbia and World Experience
"Superchargers" connections that fill in "Tesla" vehicles in six countries of South-Eastern Europe by the end of 2017 have been set in our country at three locations: - near Belgrade, - Požega and - the city of Niš. The founder of the "Tesla" expects that fully autonomous "Tesla" will be ready in 2018, but it is clear that legal approval will take another one to three years more. Meanwhile the first electrocharger started to work on Corridor 10, and in Serbia the first device for charging electric cars began to work at the toll station of Preševo, on the border with Macedonia. Testing has shown that it works excellent and that it is possible to simultaneously charge three cars.
The production of the new “Fiat 500 L“ has started on 25th of May 2017 year, and it is the best-selling model in its category in Europe. About 40% of built in parts are new. On one chassis can be made at least four models, and Italian partners are trying to keep the Serbian car factory from Kragujevac under its auspices mostly because of cheap labor. Unfortunately, the wages of workers in
factory based in Kragujevac and today are 3-4 times lower than than those of "Fiat"’s workers in Italy, Turkey and in Brasil. The term contract of Italian-American group "Fiat-Chrysler" with Serbia for 10 years expires at the end of year 2018. It is believed that the car factory in Kragujevac can not survive if we do not produce a totaly new car soon.
For the first time in March 2015, the autonomous car drove from San Francisco to New York. Mining company “Rio Tinto“ already operates a fleet of self-driving garbage trucks in the mine in Western Australia.
During the spring 2015, the Federal Department of Environment, Transport, Energy and Communications
in Switzerland has given permission to the company "Swisscom" to test "Volkswagen Passat" without a driver on the streets of Zurich. But still "Volkswagen" remained the largest European manufacturer with regard to the new registrations of its "BMW", "Audi", "Porsche", "Seat" and "Scoda," there is an increase of 6.5%, so that this manufacturer dominates on the market with a share of 21.3%.
Since the summer in 2015 the French Government allowed to "Peugeot Citroen" to perform testing under real conditions in the area of Paris. These experiments were extended to other French cities such as Bordeaux and Strasbourg in 2016, and the first demonstration of autonomous vehicles on the open road in France was performed in Bordeaux in October 2015. Also, the French are planning to present 8 new electric cars till 2022-year. (Record holder is model "Zoe" and very soon the EV version of "Quid", an small SUV, that is sold in developing markets should join.) In mid-October 2017, the French car company "Renault" published that half of its models will be hybrid or electric till 2022. These "robotic" vehicles will have an elevated degree of autonomy and "Renault" will offer 8 fully electric and 12 hybrid vehicles before year 2022 and strategic plans anticipate the doubling of vehicle sales in the markets of Russia and China.
At the end of October 2017 it was announced that it was a successful first testing of vehicles in Bavaria, i.e. smart bus without the driver was the first pickup truck without driver4 presented by the German railway "Deutsche ban". And related to railroad, probably that is why once is said that where there are no trains - there is no life. The testing was conducted in the spa Bad Birnbach, in Bavaria on the south of Germany, and this electric mini bus can carry 12 passengers and represents a new era of public transport. So the first public transport line with autonomous vehicles was opened. Since 2018, "Deutsche ban" who founded the branch "Joki" dedicated to electric mobility and transport of the future, intends to test his pickup truck in several German cities, including Hamburg. Paris, Lyon, Las Vegas and Dubai already have such vehicles, but in smaller proportions. The new German law also contains a special provision that allows for self-driving cars in certain limited areas, such as parking areas in shopping malls.5
Company "NuTonomy" is planning to place commercially self-driving taxis in Singapore during 2018, with the intention to be operational with the fleet of self-driving taxis in 10 world cities till
4 This pickup truck was projected by the French start-up company „Easy mail“.
5 See: Hetzner C, “German industry welcomes self-driving vehicles law”, Automotive News Europe, May 15, 2017, http://europe.autonews.com/article/20170515/ANE/170519866/german-industry-welcomes-self-driving-vehicles-law, 22.09.2017.
2020. Electrified icons: Ford Mustang and Ford F-150 Hybrids are coming by 2020 and Porsche plans to sell 20.000 mission E cars a year.
"BMW" has already announced that by 2025 it is planning to put on the market 12 electric models and 13 versions of hybrid cars. The first "BMW" electric car "mini" will come off the production line in year 2019, according to the report of the British public Service BBC. "General Motors" is testing 50 self-driving vehicles "Chevrolet Bolt Sedan“ in several states including California and Michigan.
During January 2018 in town Jeddah (Saudi Arabia) was opened the first Car Show dedicated to women – customers. Also manufacturers have prepared many novelties for Geneva Motor Show, the most influential automotive event in Europe on the 8th of March 2018. Thus, in "Merecedes" A class now new trunk will be larger, of 370 liters and aerodynamics and performance have been improved. While the "Opel" will not show up at this event in 2018, "Škoda" has prepared redesigned "Fabia" which is improved and with a screen of 6.5 inches impresses at first glance. Sales of this model should begin in mid-March this year. It was expected that the "Hyndai" in Geneva exposes the fourth generation of the car "Santa Fe" with more modern design. 6
Romanian brand "Dacia" continues to develop under the control of "Renault". This reliable and safe car, "Duster" got all it could from the "Renault" and "Nissan". But also the leaders in the "Maserati", who were planning that SUV "Levante" becomes a pillar of financial stability of this Italian brand, have failed, during the 2017 production has been stopped for several days due to the weaker demand. "Fiat-Chrysler cars" will reduce working hours until June 2018 and the factory "Mirafiori" will produce less 'Levante“. Yet the contracts of solidarity for workers were introduced, so workers will not receive temporary layoffs, but they will be earning less. Thus, a little more than 2000 jobs have been rescued.
3. Importance of Safety Issues
Industry of self-driving cars has experienced that regulators prevented innovations that could improve public safety. In the USA, 30 000 people die every year on the roads, and over a million are injured. 94% of these accidents are caused by human factor.7 Self-driving cars could eliminate human error as the cause of 90% of collisions and they could make people more mobile, may be reduce emissions and set in motion economy.
These days in Serbia new stricter regulations on traffic safety were adopted. Harsher penalties are provided for speeding and also the mandatory installation of video surveillance during the inspection, which will be associated with the Ministry of Internal Affairs by a special program, is predicted.
During July 2017 year more than 5.3 million vehicles passed along highways in Serbia. (statement of the Public Enterprise "Roads of Serbia"). Unfortunately, there are also thefts8 of traffic
6 Koreans have changed the interior and set a high central touchscreen. 7 Draxler B, Who’s Responsible When A Self-Driving Car Crashes ? June 2015,
Bryant Walker Smith talks shop, https://www.popsci.com/whos-responsible-when-self-driving-car-crashes
8 About 120 million dinars or around one million euros.
signs and other traffic signalization and equipment along our roads, and that directly reduces security and directly endangers the lives of participants in traffic.
At the same time the authorities in France have decided to tighten laws on road safety, all in order to help reduction of the number of fatalities on the roads and improve safety. So in the future the drivers will not be able to stand on the side in order to check the phone9; even though the engine is shut down. If drivers are caught by the authorities with a mobile phone in their hands, for that they will pay a fine of 135 euros. The law now provides for an obligation for the driver to park the vehicle in the parking place, turn off the engine and then check the mobile device.
And in China at every more significant crossroads in Beijing, the teams of emergency services are stationed and ready to react in the case of traffic accidents. Traffic violations are charged for immediately after the execution, on-site, and police has devices in which data of the offender are entered and issues the proof of payment of such penalty.
Researchers from the Serbian Institute of Nuclear Energy "Vinča" in cooperation with colleagues from the Croatian Institute "Ruđer Bosković" and the Swiss Federal Institute EMPA already for two years are working on the project of hydrogen energetics with the title "New materials for saving energy." It is about development of methods for storing hydrogen that would be applied as fuel and energy source. The authors develop complex hybrids (which contain large quantities of hydrogen) capable of releasing or receiving hydrogen according to our need.
In the final version of the Climate Action Plan, the Government in Germany lowered the aims on reducing emissions of carbon-dioxide for industrial sector, however, the industrial sector calls for reducing carbon dioxide emissions for only 20% by year 2030, comparing to year 2014.
It is stated that "Audi" is buying the technology for cars using hydrogen. "Numbers are the language to confirm the truth." From the company "Folkswagen“ we are notified that Germany should reduce subsidies for diesel cars and ban vehicles that are big polluters. It is also pointed out that the gradual tax relief should be directed towards the promotion of environmentally friendly technologies. The scandal that broke out in 2015 indicated that the diesel cars of this manufacturer are to blame for the problems of air pollution in Germany and abroad. Calls for a ban on diesel cars already have full support in some major German cities.
The wider European project Central European Green Corridors (CEGC) included Slovakia, Germany, Austria, Croatia and Slovenia where the dense network of 115 modern fast chargers for electric cars was placed.
9 The only exception is in the case of a traffic accident or some similar situation when the use of a mobile phone is allowed, in order to realize an urgent call.
4. Conclusion
The first modern electrical car was great and the most practical discovery for the time in which it was produced what testifies the interest in it from the whole world. It is believed that electric cars are the real small revolution, because we replaced one type of the engine with another, while the autonomous vehicles resistant to human errors will represent the first real big transport revolution of the 21st century. Be ready for any surprise - it is a sign of culture, wrote the Indian philosopher and poet Rabindranath Tagore.
Having in mind that electric cars have become our future, on this path Serbia is still lagging behind, but on the way of electrification the most advanced is Scandinavia, especially Norway. The primary objectives are of economic - environmental nature with regard to electrical vehicles which produce significantly less carbon dioxide and in Serbia the setting up charging stations for electric vehicles is planned. As it was mentioned the first electrical charger on the Corridor 10 started to work, i.e. in Serbia the first device for charging electrical cars began to work at the toll station of Presevo, on the border with Macedonia. It will be initially only 3 stations within the project "Green Balkanika", while the cited data show that China has even 5 millions of these stations.
Expecting news from the area of self-driving cars this paper represents my contribution to the vehicles for the future for the generations to come.
References
1. Draxler Breanna, Who’s Responsible When A Self-Driving Car Crashes? June 2015, Bryant Walker Smith talks shop, https://www.popsci.com/whos-responsible-when-self-driving-car-crashes
2. Hetzner Christiaan., “German industry welcomes self-driving vehicles law”, Automotive News Europe, May 15, 2017, http://europe.autonews.com/article/20170515/ANE/170519866/german-industry-welcomes-self-driving-vehicles-law, 22.09.2017.
3. Poitras Colin, The rise of self-driving cars, March 2017,
Abstract: At the time of exploitation, the geometrical position of the control valve changes as a result of wearing, which leads to a change of residual
electromagnetic gap stroke and force of control valve spring. The following study measures the hydraulic characteristic changes, based only
on common rail injector increased stroke of control valve and residual electromagnetic gap. The results show that the increasing of control
valve stroke and residual electromagnetic gap increase the fuel flow rate and return fuel flow. Increased fuel flow rate and return fuel flow
are presented with short injector signal time and lower levels of working pressure. The increasing is lower with longer injector signal time
and high level of working pressure. The follow-up results are practically significant by common rail electromagnetic injector diagnosing and