Helical Gear Design

INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 1, No1, 2010

© Copyright 2010 All rights reserved Integrated Publishing Association

RESEARCH ARTICLE ISSN 09764259

103

Design, Modelling and Manufacturing of Helical Gear B.Venkatesh 1 V.Kamala 2 A.M.K.Prasad 3

1 Assoc.Prof, MED, Vardhaman College of Engg, Hyderabad, India 2 Professor, MED, MJCET, Hyderabad; DGM (Retd), BHEL R&D, Hyderabad, India

3 Professor, & Head, MED, Osmania college of Engg, Osmania University, Hyderabad, India [email protected]

ABSTRACT Marine engines are among heavyduty machineries, which need to be taken care of in the best way during prototype development stages. These engines are operated at very high speeds which induce large stresses and deflections in the gears as well as in other rotating components. For the safe functioning of the engine, these stresses and deflections have to be minimized. In this work, structural analysis on a high speed helical gear used in marine engines, have been carried out. The dimensions of the model have been arrived at by theoretical methods. The stresses generated and the deflections of the tooth have been analyzed for different materials. Finally the results obtained by theoretical analysis and Finite Element Analysis are compared to check the correctness. A conclusion has been arrived on the material which is best suited for the marine engines based on the results. Basically the project involves the design, modelling and manufacturing of helical gears in marine applications. It is proposed to focus on reduction of weight and producing high accuracy gears.

Key words: Gear design, Computer aided analysis, Gear hobbing, Gear shaving, Structural analysis

1. Introduction A gear is a rotating machine part having cut teeth, which mesh with another toothed part in order to transmit torque. Two or more gears working in tandem are called a transmission and can produce a mechanical advantage through a gear ratio and thus may be considered a simple machine. Geared devices can change the speed, magnitude, and direction of a power source. The most common situation is for a gear to mesh with another gear however a gear can also mesh with a nonrotating toothed part, called a rack, thereby producing translation instead of rotation. The gears in a transmission are analogous to the wheels in a pulley. An advantage of gears is that the teeth of a gear prevent slipping. When two gears of unequal number of teeth are combined, a mechanical advantage is produced, with both the rotational speeds and the torques of the two gears differing in a simple relationship. In transmissions which offer multiple gear ratios, such as bicycles and cars, the term gear, as in first gear, refers to a gear ratio rather than an actual physical gear. The term is used to describe similar devices even when gear ratio is continuous rather than discrete, or when the device does not actually contain any gears, as in a continuously variable transmission.

2. Design Methodology In order to design a helical gear system the following procedure should be followed; the input conditions are power, speed, helix angle, gear ratio.




104

Step: 1 Gear design starts with material selection. Proper material selection is very important; aluminium has been selected as a material. If the material for gear and pinion is same then the design should be based since it is weak.

Step: 2 Find out the minimum central distance based on the surface compression stress is

a≥ (i+1)3√ (0.7/σc) 2 E (Mt) iψ……. [Design data]

Here Mt=torque transmitted by the pinion=97420(KW/N)*Kd*K

Where Kd*K=1.3 , ψ=b/a………..[Design data]

Step: 3Minimum normal modules may e determined as mn≥1.15Cosβ Mt/Yv σb ψm Z1 ^1/3..[design data] Assume Z1=18, ψm=b/mn=10 from ..[design data] Virtual number of teeth Zv=Z1/cos3β , Lewis form factor Yv=0.1540.192/Zv ….[ Design data] Number of teeth on pinion Z1=2acosβ/mn*(i+1) , Number of teeth on gear Z2=iZ1 Diameter of pinion D1=mn*Z1/cosβ , Diameter of gear D2=mn*Z2/cosβ Centre distance a=D1+D2/2 , Face width b= ψa

Step: 4 checking the calculations: a): based on the compressive stress, σc=0.7(i+1)/a*√(i+1/ib)*E[mt] b): based on the bending stress, σb=0.7(i+1) (Mt)/a.b.mn.Yv

Here the bending and compressive stress values obtained are less than the material property values, then the design is safe

2.1 Theoretical design calculation

The theoretical design calculations are performed using the input parameters such as power for marine high speed engine, pinion speed, gear ratio, helix angle, pressure angle etc. i.e Power P = 9000 KW, Speed of Pinion N = 3500 rpm, Gear Ratio i = 7, Helix Angle, β = 25oMinimum centre distance based on surface compression strength is given by

3

2 ] [ 7 . 0 ) 1 7 (

ψ σ i M E x a t

c

+ ≥

[Table 8 PSG] 2.2 Material Selection

Let the material for Pinion & Gear is Aluminum Alloy ; Its design compressive stress & bending stresses are [σc = 25000 kgf/cm 2 ], [σb = 3500 kgf/cm 2 ] [12]

2.2 Material Selection

Let the material for Pinion & Gear is Aluminum Alloy ;




105

Its design compressive stress & bending stresses are [σc = 25000 kgf/cm2], [σb = 3500 kgf/cm2] [15]

2.2.1 Properties for Aluminum Alloy

Density of Aluminum Alloy (ρ) = 3900 kg/m 3 Young’s Modulus = 340 x 10 3 N/mm2 Poisson’s Ratio (v) = 0.220

i = 7 , ψ =b/a ,ψ = 0.3 , [MT] = MT kd k ,MT = 97420 KW/N, kd k = 1.3 [15] [MT] = MT kD k = (97420x9000x1.3)/3500 = 325661.14 kgfcm

Now, minimum centre distance based on the surface compressive strength is given by

) (

] [ c

0.7 1)x (i 3

ψ σ i

M xE a

t

+

≥

a > 27.66 cm = 28 cm

Minimum module based on beam strength:

Mn > 1.15cosβx3√ 1

] [ Z Y

M m b v

t

ψ σ [Table 8, PSG]

Let Z1 = 18, ψm = 10, Virtual number of teeth Zv = Z1 / cos 2 β = 18/0.744 = 25 from [Table 11, PSG design data book]

Lewis form factor Yv (for Zv = 25) = 0.4205

mn > 1.15cos25x3√ 18 10 3500 4205 . 0 ] 14 . 325661 [ x x x

mn > 1.11 cm , mn > 11.16 mm , But for mn = 1116 mm, σc and σb are > [σc] & [σb] also FS < FD which makes design unsafe.

So mn = 18 mm = 1.8 cm

No. of teeth of pinion, Z1 = 5 . 3

) 1 ( cos 2

= + i m

a

n

β

But in order to avoid interference, Zt is taken as 18, No. of teeth on gear, Z2 = iZ1 = 126

Diameter of the pinion (d1) = cm x xZ

m n 74 . 35 18 25 cos 8 . 1

cos 1 = = β

Diameter of the gear (d2) = 1 id = 7 x 35.74 =250.2 cm

Centre distance (a) = cm d d

99 . 142 2

2 1 = +

Face width b = ψ.a = 0.3 x142.99=42.899 cm




106

Checking Calculations:

σc = 0.7x ] [ ] [ 1 1

c t M xE ib i

a i σ ≤

+ +

σb= 0.7x ] [ ] [ 1 c t

v n

M Y abM

i σ ≤ +

Based on the Compressive Stresses

σc= 0.7x ] [ ) ( ] [ ) 1 ( 1

c

T

ib M xEx i

a i

σ ≤ + +

σb= 0.7x ] [

) ( ] [ ) 1 (

b T

abxmxnxYv M x i σ ≤

+

Based on the compressive stress

σc = 2 / 303 . 150

4205 . 0 * 8 . 1 * 43 * 143 14 . 325661 8 7 . 0 mm N x x

=

Based on bending stress σb = 220.35 N/mm 2 From the calculations, σc and σb are > [σc] & [σb] values of given material, i.e., Aluminum alloy [98%Al2O3, 0.40.7%Mn, 0.40.7&Mg].Therefore our design is safe. Addendum, mn = 18 mm, Dedendum = 1.25 x mn = 22.5 mm, Tip circle diameter of the pinion=d1+ (2 x addendum) =357.4 + 36 = 393.4 mm Tip circle diameter of gear = d2 + (2 x addendum) = 2502.4+ 36 = 2538.46 mm Root circle diameter of pinion = d1 (2 x addendum) = 357.4 – 36 = 321.4 mm Root circle diameter of gear = d2 (2 x addendum) = 2502.4– 36 = 2466.4 mm When the gear transmits the power P, the tangential force produced due to the power is given by

v Pxk F s

t = ,

s m x x x

x xN xD

V p p / 51 . 65 1000 60

3500 4 . 357 1000 60

= = = π π

N x x F t 26 . 274749 51 . 65

2 10 9000 3

= =

Lewis derived the equation for beam strength assuming the load to be static when the gear is running at high speeds; the gears may be subjected to dynamic effect. To account for the dynamic effect, a factor Cv known as Velocity factor or dynamic factor is considered.

The design tangential force along with dynamic effect is given by V xCv Pxk xCv F F s

t D = =

The velocity factor Cv is developed by Barth. It depends on the pitch line velocity and the workmanship in the manufacture and is given by

5 . 5 5 . 5 V C v

+ =




107

For V > 20 m/s , Where FT = 274749.26 N, Ks = 2, V = 65.5m/s

47 . 2 5 . 5

51 . 65 5 . 5 =

+ = v C

FD = 274749.26x 2.4 = 679084.7315 N ,

According to Lewis equation, the beam strength of helical gear tooth is given by FS = [σb].b.π.mn.yv and FS = (3500) x 42.8 x П x 18 x 0.4205 =3570318.5 N Since, FS > FD, Our design is safe.

When the power is transmitted through gears, apart from static (steady) load produced by the power, some dynamic loads are also applied on the gear tooth due to reasons like inaccuracies of tooth profiles and deflections of tooth under load. Considering the above conditions Buckingham derived equation to find out the maximum load acting on the gear tooth and is given by FD = Ft + Fi, Where Fd = Maximum dynamic load, Ft = Static load produced by the power, Fi = Incremental load due to dynamic action, Incremental load depends on the pitch line velocity, face width, of a gear tooth, gear materials, accuracy of cut and the tangential load and is given by

t m

m i

F cb V Cos Ft cb V F

+ +

+ =

β

β β 2

2

cos 485 . 1 164 . 0 ) cos ( 164 . 0

where, Vm = Pitch line velocity in m/s,b = Face width of the gear tooth in mm C = Dynamic factor (or) Deformation factor in N/mm. Deformation factor “C”, [15] Here, C = 11860 x e, C = 11860 x 0.026, = 308.36 N/mm

Ft = 137572.60 N, m = 65.51 x 103 mm/sec ,b = 428.9 mm ,β = 25 0 Fd = Ft + Fi

t m

t m t d

F cb V

Cos F cb V F F + +

+ + =

β

β β 2

2

cos 485 . 1 164 . 0

) cos ( 164 . 0

N F d 19 . 273754 76937 . 11315

1540999543 26 . 274749 = + =

Since Fs > Fd, our design is safe.

One of the most predominant gear failures is the failure of gear tooth due to pitting. This pitting failure occurs when the contact stresses between the two meshing teeth exceed the surface endurance strength of the material. In order to avoid this type of failure the proportions of gear tooth and the surface properties such as surface hardness should be selected in such a way that the wear strength of the gear tooth is more than the effective load between the meshing teeth.

Based on Hertz theory of contact stresses, Buckingham derived an equation for wear strength of gear tooth which is given by

Fw = β 2 1

cos .b.Q.Kw d

where; Fw = Max or limiting load for wear in Newton’s




108

d1 = pitch circle diameter of pinion in mm, b = Face width of the pinion in mm, Q = Ratio factor = 75 . 1

) 1 ( 2i

= + i

Kw = 2.553 N/mm2 [Table 25.37 JDB] d1 = 357.4mm, b = 428.9 mm

Fw = β 2 1

cos .b.Q.Kw d

= N 62 . 834168

25 cos 8 685180.942

2 =

Fd = 273754.19 N since Fw > Fd our design in safe.

3. Modelling

A model is generated using CATIA software and then it is retrieved into ANSYS using IGES files. Helical Gear teeth as shown in fig:1

Figure 1: Image showing the model prepared in CATIA

A complete helical gear is obtained as shown in figure 2




109

Figure 2 : Image showing the designed helical gear

3.1 Analysis

Significant Development in analysis of strength properties of gear transmission follows the achievements in computation design, simulation of meshing and tooth contact analysis made by Lewiki,Handschuh.They carried out 2D analyses using finite element method, boundary element methods & Compared the results to experimental ones validated crack simulation based on calculated stress intensity factors and mixed mode crack angle prediction. In practice, simplified formulas are usually used in gear transmission design. They enables estimation of stresses at tooth root with accuracy acceptable for engineering design. In every case, strength properties of gear transmissions are strongly influenced by gear geometry, applied manufacturing processes, and dimensional accuracy of manufactured gears.

3.2 Gear Manufacturing

Gears are manufactured by various processes. These are, casting, stamping, rolling, extruding, and machining. Gears can also be produced by powder metallurgy. Among the above said process, machining process in most commonly used. It is an accurate method. Basically gears are produced by machining by a) Forming method. b) Generating method.

3.2.1 Forming Method In this method a form cutter is used. The formed cutter may be single point cutting tool or a multipoint milling cutter. The cutting edges formed cutter has been finished to the shape between the gear teeth being cut. Forming method is used for producing very small number of gears. Gears produced by forming are less accurate. Forming process is simple and cheaper. This method is takes more time.

3.2.2 Gear Generating Process




110

This method of gear manufacturing is based on the fact that any two involute gears of the same module will mesh together. Here one of the meshing gears is made as the cutter. The other gear rotates and also reciprocates along the width of the gear blank. Because of the relative rolling motion between cutter and the blank, gear teeth are generated on the gear blank. The gear may be generated by rack cutter, pinion cutter or a hob. Using the generated method, profile of the gear teeth can be very accurately produced. The following generating methods used for gear production are Gear shaping, Gear planning, Gear hobbing.

3.2.3 Gear Hobbing It is a process of generating a gear by means of a rotating cutter called hob. The hob has helical threads. Grooves are cut in the threads parallel to the axis. This will provide the edges. Proper rake and clearance angle are ground on these cutting edges. The rotating hob acts like a continuously moving rack as it cuts. The blank is mounted on a vertical arbour. The hob is mounted in a rotating arbour. The hob axis is tilted the hob lead angle so that its teeth are parallel to the axis of the gear blank.

Then = (90º1).Where 1 = helix angle of the hob thread. NOTE: (hob lead angle = 90º hob helix angle) The hob is rotated at suitable cutting speed. It is fed across the blank face. The hob and blank are made to rotate in correct relationship to each other; they rotate like a worm and worm gear in mesh. For one relation of the hob, the blank rotates by one tooth. (In case of single start hob). For helical gears, the axis of the hob is inclined to horizontally. Where α= θ + (90º1). (If the helix of the hob and the helix of the gear to be cut are different. One is right and another is left handed.) α= θ (90º1) (if the helix of the hob and the helix of the gear to be cut are both right handed or both is left handed.) Where, α = helix angle of the helical gear to be cut.,1 = helix angle of the hob. The gear hobbing technique is used for generating spur, helical and worm gears. Gear hobbing is used in automobiles, machine tools, various components, instruments, clocks and other equipment. In the present the helical gears were produced by gear hobbing technique and finished by gear shaving operation. The gear teeth generating process by milling machine is shown in fig 3




111

Figure 3: Image showing milling machine

The gear teeth generating process by hobbing process is shown figure 4

Figure 4: Image showing the hobbing process

The gear finishing process is shown in the figure 5

Figure 5: Image showing the gear finishing process




112

3.2.4 Finishing Process

Gears manufactured by different machining processes will have rough surfaces. The machined gears may have errors in tooth profiles, concentricity and helix angles. For quiet and smooth running of gears, these errors and rough surfaces should be removed. Gear finishing operations are done for this purpose. The various gear finishing processes like gear burnishing, gear shaving etc.

3.2.5 Gear Burnishing Is a method of finishing of gear teeth which are not hardened. This is a cold working process. This method is used to improve the surface finish of the gear teeth. This also increases the hardness at the teeth surface. The teeth of burnishing gears are very hard, smooth and accurate. They are arranged at 120º position around the work gear. The gears are rotated in one direction for some period. Then they are rotated in the reverse direction for the some period. The pressure is applied by the harder burnishing teeth on the work gear.

3.2.6 Gear Shaving

This is the most common method of gear finishing. In this method a very hard gear shaving cutter is used to remove fine chips from the gear teeth. The shaving cutter may be in the form of a rack or a pinion. The rotary method using pinion cutter is used on all types of gears. The rotating cutter will have helical teeth of about 15º helix angle. The cutter has a number of serrations on its periphery. These act as cutting edges. In the rotary type of gear shaving the work gear is held between centres and is free to rotate. The shaving cutter meshes with the work gear. The axis of the cutter is inclined to the gear at an angle equal to the helix angle of the cutter (θ) when the cutter rotate, the cutter reciprocates in a direction parallel to the gear axis. The cutting edges of the shaving cutter remove burrs, nicks and high points on the surface of the work gear. It can remove from the teeth flank, chips up to 0.1mm thick.

4. Results and discussions

Theoretical design is carried out using standard design formulae as per AGMA procedure and

carried out analyses by ANSYS and analysis carried out using ANSYS .The following table.1

shows the comparison the theoretical design values with ANSYS values.

Table1. Comparison of theoretical and ANSYS design values

S.No Parameter Design values Ansys values

1 Bending stress 220.35N/mm 2 205.576N/mm 2

2 Compressive stress

150.303N/mm 2 139.076/mm 2

3 Vonmisses stress

2000N/mm 2 260.92N/mm 2




113

4 Deflection 0.058752 mm

From the table.1, it is observed that the bending stress, compressive stress, vonmisses stresses of ANSYS values are less than the design values. Hence the design is safe. Then the gears are manufactured using gear hobbing technique and finished by gear shaving operation.

5. Conclusions

1. Bending, compressive, Vonmisses stresses were obtained by theoretical and Ansys software for Aluminum alloy. The obtained stresses by ANSYS are less than that of the theoretical calculations.

2. From the results, it is observed that the bending and compressive stresses of aluminum alloy (ceramics) are less than that of the other material like steel.

3. Aluminum alloy reduces the weight up to 5567% compares to the other materials

4. Aluminum is having unique property (i.e. corrosive resistance), good surface finishing, hence it permits excellent silent operation.

5. Weight reduction is a very important criterion, in order to minimize the UN balanced forces setup in the marine gear system, there by improves the system performance.

6. Hence aluminum alloy is best suited for marine gear in the highspeed applications.

7. The designed gear set have been manufactured using gear hobbing technique and finished by gear shaving operation and tested for the strength of the gear teeth.

Acknowledgements

First author is grateful to Dr.T.Srinivasulu, Principal VCE shamshabad and Dr.G.V.Rao Head Mechanical Engineering Department for their valuable support. He is also thankful to the management of the institute for the encouragement, support, and cooperation during the entire work. 6. References

1. Emmanuel RIGAUD, Ecole Centrale de Lyon., 1999,”Modelling and analysis of Static Transmission Erroreffect of wheel body deformation and interactions between adjacent loaded teeth,” hal – 00121847, Version 122 Dec 2006.

2. Zeping Wei., 2004”Stresses and Deformations in Involute spur gears by Finite Element method,” M.S, Thesis, College of Graduate Studies and research, University of Saskatchewan, Saskatchewan.




114

3. PSG,2008, “Design data,” Kalaikathir Achchagam publishers, Coimbatore India

4. Joseph E.Shigley.charles R.Mischike, 2003, Mechanical Engineering design, Tata McGraw Hill.

5. Andrzej kawalec, Jerzy Wiktor., 2006, “Comparative analysis of tooth root strength Using ISO and AGMA

6. Standards in spur and helical gears with FEM based verification,” ASME Journal of Mechanical Design,Vol 128/114

7. Lazar Chalik, DE, 1996, “Preloaded Gearing for high speed application” Vol 88, ASME Power transmission &Gearing conference

8. P.N.Rao, 2003, “Manufacturing Technology,” 2 nd Edition, Tata Mc Grew Hill 9. Metals Handbook, 1990, “ Properties and Selection: Nonferrous Alloys and Special Purpose Materials,” ASM International Vol.2, 10th Ed.

10. R.E. Sanders, Technology Innovation in aluminum Products, The Journal of the Minerals, 53(2):21–25, 2001

11. Stephen F. Pollard, Boatbuilding with Aluminum, International marine/Ragged Mountain Press; 1 edition, 1993

Helical Gear Design

Documents

2materialselection letthematerialforpinion

gear hobbing technique

high speeds

gear ratio

gear tooth

dindigul volume1

2010 copyright2010allrightsreservedintegratedpublishingassociation researcharticleissn09764259

rough surfaces