Effects of Natural Frequency and Rotational Speed on Dynamic Stress in Spur Gear

Natural frequencies and dynamic response of a spur gear sector are investigated using a two dimensional finite element model that offers significant advantages for dynamic gear analyses. The gear teeth are analyzed for different operating speeds. A primary feature of this modeling is determination of mesh forces using a detailed contact analysis for each time step as the gears roll through the mesh. Transient mode super position method has been used to find horizontal and vertical components of displacement and dynamic stress. The finite element analysis software ANSYS has been used on the proposed model to find the natural frequencies by Block Lanczos technique and displacements and dynamic stresses by transient mode super position method. A comparison of theoretical (natural frequency and static stress) results with the finite element analysis results has also been done. The effect of rotational speed of the gears on the dynamic response of gear tooth has been studied and design limits have been discussed.

Authors:

• Ali Raad Hassan
• G. Thanigaiyarasu
• V. Ramamurti

Keywords:

• Natural frequency
• Modal and transientanalysis
• Spur gear
• Dynamic stress.

References:

[1] Fundamental Rating Factors and Calculation Methods for Involute Spur
and Helical Gear Teeth," ANSI/AGMA 2001-B88, American Gear
Manufacturers Association, Arlington, VA, 1988.
[2] V. Ramamurti, K. R. K. Reddy, Dynamic analysis of spur gear tooth.
The Institution of Engineering (India) Journal 82 (April 2001) 33-40.
[3] L. Wilcox, W. Coleman, Application of finite elements to the analysis of
gear tooth stresses. Journal of Engineering for Industry 95 (4) (Dec.
1973) 1139-1148.
[4] V. Ramamurti, L. S. Gupta, Dynamic stress analysis on spur gear teeth.
ASME Conference 38, 1979 DET.
[5] S. Oda, K. Nagamura, K. Aoki, Stress analysis by thin rim spur gears by
finite element method. Bulletin of the Japanese Society of Mechanical
Engineers 24 (193) (1981) 1273-1280.
[6] H. Von Eiff, K.H. Hirschmann, G. Lechner, Influence of gear tooth
geometry on tooth stress of external and internal gears, ASME Journal of
Mechanical Design 112 (4) (1990) 575-583.
[7] V. Ramamurti, Nayak H. Vijayendra , C. Sujatha, Static and dynamic
analysis of spur and bevel gears using fem, Mechanism and Machine
Theory 33 (8) (1998) 1177-1193.
[8] B. Hefeng, M. Savage, R.J. Knott, Computer modeling of rack generated
spur gears. Mechanism and Machine Theory 20 (4) (1985) 351-360.
[9] R.S. Khurmi, J.K. Gupta, A Textbook of Machine Design, Eurasia
Publishing House (PVT.) LTD., New Delhi, pp 1035-1038, 2006.
[10] V. Ramamurti, Mechanical Vibration Practice with Basic Theory,
Narosa Publishing House, New Delhi, 2002.
[11] V. Ramamurti, Computer Aided Design in Mechanical Engineering,
McGraw Hill Publishing Co., New York, 1998.
[12] D. Mohammad, N U Khan, V. Ramamurti, On the role of Rayleigh
damping. Journal of Sound and Vibration 185 (2) (1995) 207.
[13] Singiresu S. Rao (2004), ÔÇÿMechanical Vibrations-, 4th Edition, Pearson
Education (Singapore) Pte. Ltd., India Branch, Delhi.
[14] Shigley J.E. and Charles R.M. (2003), ÔÇÿMechanical Engineering
Design-, Tata McGaraw-Hill, New Delhi, 6th edition.