Comparison of Result of Analytical and Modeling Software for Critical Section Thickness, Tip Thickness of Asymmetric Spur Involute Gear Tooth

Comparison of Result of Analytical and Modeling Software for Critical Section Thickness, Tip Thickness of Asymmetric Spur Involute Gear Tooth

Dr J M Prajapati1, P A Vaghela2 1Department of Mechanical Engineering,

Faculty of Technology & Engineering, Baroda, Gujarat, India

2Department of Mechanical Engineering, Government Polytechnic, Vadnagar, Gujarat, India

Abstract

The main objective of this paper is to compare result obtain from analytical calculation and modeling software for critical section thickness and tip thickness of asymmetric spur involute gear tooth. Equations are developed for analytical calculation for critical section thickness & tip thickness of asymmetric spur involute gear tooth and estimate the critical section thickness and tip thickness. And validate the result with help of graph by comparing analytical calculation and modeling software for critical section thickness and tip thickness of asymmetric spur involute gear tooth.

Keywords: Critical section thickness, tip thickness, Asymmetric spur gear

1. Introduction

   There has been a lot of research activity on spur gears with asymmetric teeth. New gear designs are needed because of the increasing performance requirements, such as high load capacity, high endurance, low cost, long life, and high speed. In some applications gears experience only unidirectional loading. In this instance, the geometry of the drive side does not have to be symmetric to the coast side. This allows for the design of gears with asymmetric teeth. These gears provide flexibility to designers due to their non-standard design. If they are correctly designed, they can make important contributions to the improvement of designs of gears.

   In a standard symmetric gear, both left and right sides of a gear tooth profile have same bending and contact strength. However, in most practical cases, both the forward and backward rotations are not always used for power transmission. Therefore, two sides of the gear toot hare functionally different for most gears. Even if one side (drive side) is significantly loaded for longer periods, the

   opposite side (coast side) is unloaded or slightly loaded for short duration only. Thus Asymmetric tooth are well suited for cases where the torque is transmitted mainly, in one direction.

   As the pressure angle on drive side increases, the bending stress reduces at critical section of asymmetric spur gear and Decision on maximum magnitude of drive side pressure angle is constraint by the safe contact ratio and tooth peaking effect (tip thickness). Its value is should be greater than equal to 0.2 times the module for the hardened gears. Bellow this value, tip thickness decreases and tip becomes too sharp, more and more pointed. This reduction in bending stress can translated into Increased Load Capacity (15-30%), Size and Weight Reduction (10- 20%), Longer Life, Cost Reduction, Increased Reliability, Noise and Vibration reduction, Increased Gear Efficiency and Maintenance Cost Reduction.

   Thickness of the critical section increases with increase in pressure angle, the bending stress reduces at critical section of asymmetric spur gear as critical section thickness increases. The gear becomes bigger and having more resistance to the load as critical section thickness increases. This way critical section thickness parameter is very important for bending stress.

2. Analytical solution of critical section thickness and tip thickness

   Equations are developed for analytical calculation for critical section thickness & tip thickness of asymmetric spur involute gear tooth to estimate the critical section thickness and tip thickness.

   Thickness of tooth at any radius r thickness of tooth is calculated by following equations.

   Sr Srd Src

   Where, Srd r. Src r.

   With help of above equation obtained the tip thickness and critical section thickness of asymmetric spur gear tooth which are listed in bellow table.

   2.z

   • inv invr

   r

   r

   cos1 rp

   r

   .cos

   Fig. 1 Representation of angle at tip radius

   For this analysis solutions following gear tooth parameters are used. Gears are used to transmit a power of 18KW at 1600 rpm.

   Gear tooth parameter

   Sr. No.	Description	Value
   1	Pressure angle, Coast side	200 fixed
   2	Pressure angle, Drive side	200 400 increment by 20
   3	Number of teeth	25 and 47
   4	Module	4 mm

   Table 1 Gear tooth parameter

   Sr.No .	Asymmetri c gear of different pressure angle of drive side profile	Tip thickness of spur gear in mm	Critical thickness in mm
   1	20	2.662812431	7.770234788
   2	22	2.530329326	7.953000430
   3	24	2.390176814	8.115205444
   4	26	2.242216251	8.271424667
   5	28	2.086155863	8.426176879
   6	30	1.921555886	8.581968613
   7	32	1.747827740	8.740556189
   8	34	1.564227332	8.903373338
   9	36	1.369842319	9.071725278
   10	38	1.163572744	9.246897198
   11	40	0.944104088	9.430227550

   Sr.No .	Asymmetri c gear of different pressure angle of drive side profile	Tip thickness of spur gear in mm	Critical thickness in mm
   1	20	2.662812431	7.770234788
   2	22	2.530329326	7.953000430
   3	24	2.390176814	8.115205444
   4	26	2.242216251	8.271424667
   5	28	2.086155863	8.426176879
   6	30	1.921555886	8.581968613
   7	32	1.747827740	8.740556189
   8	34	1.564227332	8.903373338
   9	36	1.369842319	9.071725278
   10	38	1.163572744	9.246897198
   11	40	0.944104088	9.430227550

   Table 2. Critical section thickness and tip thickness obtained from analytical calculation

3. Modeling software solution of critical section thickess and tip thickness

   In pro-e software different model of spur gear with different pressure angle on drive side profile are generated. From these models obtained the tip thickness and critical section thickness of spur gear tooth which are listed in bellow table.

   Sr.No.	Asymmetric gear of different pressure angle of drive side profile	Tip thickness of spur gear in mm	Critical thickness in mm
   1	20	2.66	7.48
   2	22	2.53	7.62
   3	24	2.40	7.75
   4	26	2.25	7.90
   5	28	2.10	8.04
   6	30	1.92	8.17
   7	32	1.74	8.33
   8	34	1.61	8.48
   9	36	1.32	8.63
   10	38	1.11	8.79
   11	40	0.86	8.97

   Sr.No.	Asymmetric gear of different pressure angle of drive side profile	Tip thickness of spur gear in mm	Critical thickness in mm
   1	20	2.66	7.48
   2	22	2.53	7.62
   3	24	2.40	7.75
   4	26	2.25	7.90
   5	28	2.10	8.04
   6	30	1.92	8.17
   7	32	1.74	8.33
   8	34	1.61	8.48
   9	36	1.32	8.63
   10	38	1.11	8.79
   11	40	0.86	8.97

   Data obtained from analytical calculation and software data are same which validate analytical solution. As the pressure angle on drive side increases, tip thickness reduces. Tip thickness decreases and tip becomes too sharp, more and more pointed.

   From above data critical section thickness Vs pressure angle on drive side of asymmetric spur gear graph is developed to compare data obtained from analytical calculation and software data.

   Table 3. Critical section thickness and tip thickness obtained from modeling software.

4. Results & Discussions

   From above data tip thickness Vs pressure angle on drive side of asymmetric spur gear graph is developed to compare data obtained from analytical calculation and software data

   Fig. 2 Graph tip thickness Vs pressure angle on drive side gear tooth.

   Fig. 3 Graph critical section thickness Vs pressure angle on drive side gear tooth.

   Data obtained from analytical calculation and software data are same which validate analytical solution. Thickness of the critical section increases with increase in pressure angle, the bending stress reduces at critical section of asymmetric spur gear as critical section thickness increases. The gear becomes bigger and having more resistance to the load as critical section thickness increases.

5. Conclusion

   Graphs are generate to compare result obtain from analytical calculation and modeling software for critical section thickness and tip thickness of asymmetric spur involute gear tooth. Data obtained from analytical calculation and software data are same which validate analytical solution for critical section thickness and tip thickness of asymmetric spur involute gear tooth.

   Reference PAPERS

   1. Alexander Kapelevich Geometry and design of involute spur gears with asymmetric teeth Mechanism and Machine Theory 35 (2000) 117 to

      130

   2. Faydor L. Litvin , Qiming Lian , Alexander L. Kapelevich Asymmetric modified spur gear drives: reduction of noise, localization of contact, simulation of meshing and stress analysis Computer Methods Applied Mechanics and Engineering. 188 (2000) 363 to 390

   3. Alexander L. Kapelevich and Thomas M. McNamara Direct Gear Design for Optimal Gear Performance SME's Gear Processing and Manufacturing Clinic, October 6, 2003 held in conjunction with AGMA's GEAR EXPO '03 in Columbus, OH

[4]V. Senthil Kumar, D.V. Muni, G. Muthuveerappan Optimization of asymmetric spur gear drives to improve the bending load capacity Mechanism and Machine Theory 43 (2008) 829858

1. Singh Vedang and Senthilvelan S., Computer Aided Design of Asymmetric Gear, 13th National Conference on Mechanisms and Machines (NaCoMM07),IISc, Bangalore, India,

   December 12-13, 2007

2. Th. Costopoulos, V. Spitas Reduction of gear fillet stresses by using one-sided involute asymmetric teeth, Mechanism and Machine Theory 44 (2009) 15241534

3. Niels L. Pedersen Improving bending stress in spur gears using asymmetric gears and

   Shape optimization Mechanism and Machine Theory 45 (2010) 17071720

4. Moya J.L., A.S. Machado, J.A.Velásquez, R. Goytisolo, A.E.Hernández, J.E. ernández, and

   J.M. Sierra a study in asymmetric plastic spur gears, 2010

5. G. Mallesh, Dr. Math V B, Venkatesh, Shankarmurthy H J , Prasad Shiva P, Aravinda K Parametric analysis of Asymmetric Spur Gear Tooth 14th National Conference on Machines and Mechanisms (NaCoMM09),NIT, Durgapur,

   India, December 17-18, 2009

6. Vaghela P A, Patel D A Improvement of Load Carrying Capacity of Spur Gear by Asymmetric Teeth the 5th International Conference on Advances In Mechanical Engineering-2011 (ICAME2011) at Sardar Vallabhbhai National Institute of Technology, Surat during 6-8th June, 2011

7. Vaghela P A, Patel D A Effect of rim thickness on asymmetric spur gear tooth bending stress at National Conference on Recent Advances in Mechanical Engineering(NCRAME-2011) at R V R & J C College of Engineering, Chowdavaram, Guntur, Andhra Pradesh, India during 7- 8th July 2011.

8. Vaghela P A, Patel D A Optimize base on load carrying capacity and reduction in weight without compromising a bending stress at critical section of asymmetric spur gear at International Conference on Design And Advances In Mechanical Engineering(ICDAAIME-2011) at S K P Collage of engineering ,Thiruvannamalai, Tamilnadu, India -606 611 during 16-17th December 2011.

9. J M Prajapati,P A Vaghela factor affecting the bending stress at critical section of asymmetric spur gear at International Journal Of Mechanical Engineering And Technology (IJMET), Volume 4, Issue 4, July – August (2013), pp. 266-273, ISSN 0976 6340 (Print) ISSN 0976 6359 (Online)

   THESIS

10. Vaghela P A, Patel D A Effect of rim thickness on asymmetric spur gear tooth bending stress Gujarat Technological

University,Gujarat,India,2011