Transmission Error Analysis of Helical Gears in Consideration of Shaft and Bearing Deformation

축과 베어링 변형을 고려한 헬리컬 기어의 전달오차 해석

  • 박찬일 (강릉대학교 정밀기계공학과) ;
  • 조도현 (강릉대학교 대학원 정밀기계공학과)
  • Published : 2002.10.01


Transmission error is highly related to gear noise. In order to predict the helical gear noise, transmission error analysis is needed. Up to now, the studies for the transmission error were conducted by the modeling of helical gears only. However, since helical gears are supported by the shaft and bearing, transmission error has the effects of the elements. In this study, the procedure to consider the shaft deformation with bearing stiffness for the transmission error analysis is proposed. To do so, the relationship between gear error and shaft deformation is analytically derived. Shaft deformation with bearing stiffness is analyzed by FEM. It is measured in the experimental test rig by the non-contact displacement sensors. Using the tooth error from tooth modification and the shaft deformation, the effects of shaft on the loaded transmission error are investigated.


Transmission Error;Helical Gear;Shaft;Bearing;Deformation


  1. Park, C.I. and Lee, J.M., 2001, 'The Experimental Study of Helical Gear Noise on the Effect of Lead Errors,' Transactions of the Korean Society of Mechanical Engineers, Vol. 25, No.9, pp. 1475-1482
  2. Brandlein, Johannes et al., 1999, Ball and Roller Bearings Theory, Design and Application, 3rd ed. John Wiley & Sons, NY
  3. National Instruments, 2000, Lab VIEW Basic I Hands-On Course
  4. National Instruments, 2000, Lab VIEW Data Acquisition Hands-On Course
  5. Park, C.I. and Kim, D.S., 2001, 'Transmission Error Analysis of the Helical Gear for the Elevator,' Proceedings of the KSME 2001 Spring Annual Meeting C, pp. 470-475
  6. Park, C.I. and Lee, J.M., 1995, 'Analysis of Load Transmission Characteristics for Automobile Helical Gear,' Journal of Korea Society of Automotive Engineers, Vol. 5, NO.3, pp. 1-9
  7. Park, C.I., and Cho, D.H., 2001, 'Transmission Error Analysis of Helical Gears in Consideration of Shaft and Bearing Deformation,' Proceeding of the KSAE 2001 Autumn Conference, pp. 1119-1124
  8. Joo, S.H., Roh, O.H., Chung, D.H., Bae, M.H., Park, N.G., 1998, 'Modeling of Transmission Error of A Gear Pair with Modified Teeth,' Journal of KSNVE, Vol. 8, NO.5, pp. 841-848
  9. Saiki, K., and Watanabe, T., 2000, 'Transmission Error Analysis of Helical Gear for Any Load Condition,' Proceedings of DETC2000/ PTG-14421, pp. 1-7
  10. Conry, T.F., and Seireg, A., 1973, 'A Mathematical Programming Technique for the Evaluation of Load Distribution and Optimal Modifications for Gear Systems,' ASME Journal of Engineering for Industry, Nov., pp. 1115-1122
  11. Houser, D.R., 'Load Distribution Program User's Manual LDP8.3,' The Ohio State University
  12. Weber, C., 1949, 'The Deformations of Loaded Gears and the Effects on Their Load-Carrying Capacity,' Sponsored research(Germany), British Dept. of Scientific and Industrial Research, Report No.3
  13. Velex, P., and Maatar, M., 1996, 'A Mathematical Model for Analyzing the Influence of Shape Deviations and Mounting Errors on Gear Dynamic Behavior,' Journal of Sound and Vibration, 191(5), pp. 629-660
  14. Gargiulo, E.P., 1980, JR., 'A Simple Way to Estimate Bearing Stiflhess,' Machine design, July 24, pp. 107-110
  15. Umezawa, K., 1974, 'The Meshing Test on Helical Gears under Load Transmission(3rd Report, the Static Behaviors of Driven gear),' Bulletin of the JSME, Vol. 17, No. 112, pp. 1348-1355
  16. Barnett, D. W., and Yildirim, N. 1994, 'Loaded Transmission Error Prediction using a Computer Model and its Verification,' Proceedings of the 1994 International Gearing Conference, pp. 57-61
  17. Umeyama, M., Kato, M., Inoue, K., 1998, 'Effects of Gear Dimensions and Tooth Surface Modifications on the Loaded Transmission Error of a Helical Gear Pair,' Trans. of the ASME, Journal of Mechanical Design, Vol. 20, pp. 119-125
  18. Park, C.I. and Lee, J.M., 1993, 'The Load Transmission and Vibration Characteristics of Automobile Gear,' SAE Paper 932917