Journal of Mechanical Science and Technology

  • 제20권12호
  • /
  • Pages.2105-2114
  • /
  • 2006
  • /
  • 1738-494X(pISSN)
  • /
  • 1976-3824(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
권호 표지

Vibration from a Shaft-Bearing-Plate System Due to an Axial Excitation of Helical Gears

  • Park, Chan-Il (Department of Precision Mechanical Engineering, Kangnung National University)
  • 발행 : 2006.12.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, a simplified model is studied to predict analytically the vibration from the helical gear system due to an axial excitation of helical gears. The simplified model describes gear, shaft, bearing, and housing. In order to obtain the axial force of helical gears, the mesh stiffness is calculated in the load deflection relation. The axial force is obtained from the solution of the equation of motion, using the mesh stiffness. It is used as a longitudinal excitation of the shaft, which in turn drives the gear housing through the bearing. In this study, the shaft is modeled as a rod, while the bearing is modeled as a parallel spring and damper only supporting longitudinal forces. The gear housing is modeled as a clamped circular plate with viscous damping. For the modeling of this system, transfer matrices for the rod and bearing are used, using a spectral method with four pole parameters. The model is validated by finite element analysis. Using the model, parameter studies are carried out. As a result, the linearized dynamic shaft force due to the gear excitation in the frequency domain was proposed. Out-of-plan displacement from the forced vibrating circular plate and the renewed mode normalization constant of the circular plate were also proposed. In order to control the axial vibration of the helical gear system, the plate was more important than the shaft and the bearing. Finally, the effect of the dominant design parameters for the gear system can be investigated by this model.

키워드

참고문헌

  1. ？Bishop, R. E. D. and Johnson, D. C., 1960, The Mechanics of Vibration, Cambridge University Press, London
  2. Cai, Y. and Hayashi, T., 1994, 'The Linear Approximated Equation of Vibration of a Pair of Spur Gears (Theory and Experiment),' Journal of Mechanical Design, Vol. 116, pp. 558-564 https://doi.org/10.1115/1.2919414
  3. Doyle, J. F., 1997, Wave Propagation in Struc？tures, 2ed., Springer, NY
  4. Gargiulo, E. P. JR., 1980, 'A Simple Way to Estimate Bearing Stiffness,' Machine Design, July, pp. 107-110
  5. Graff, K. F., 1991, Wave Motion in Elastic Solids, Dover, NY
  6. Jacobson, M. F., Singh, R. and Oswald, F. B., 1996, 'Acoustic Radiation Efficiency Models of a Simple Gear box,' NASA TM-107226
  7. Kraus, J. et aI., 1987, 'In Situ Determination of Rolling Bearing Stiffness and Damping by Modal Analysis,' Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 109, pp. 235-240 https://doi.org/10.1115/1.3269426
  8. Lim, T. C. and Singh, R., 1991, 'Statistical Energy Analysis of a Gearbox With Emphasis on the Bearing Path,' Noise Control Engineering Journal, Vol. 37, No.2, pp.63-69 https://doi.org/10.3397/1.2827795
  9. McLachlan, N. W., 1955, Bessel Functions for Engineers, 2nd ed., Oxford University, London
  10. Misun, V. and Prikryl, K., 1995, 'Acoustic Response Modeling of the Mechanical Gearbox,' Gearbox Noise, Vibration, and Diagnostics, MEP, pp. 153-162
  11. Morse, P. M. and Ingard, K. U., 1968, Theoretical Acoustics, McGraw-Hill, NY
  12. Ozguven, H. N. and Houser, D. R., 1998, 'Mathematical Models Used in Gear Dynamics-A Review,' Journal of Sound and Vibration, 121 (3), pp. 383-411 https://doi.org/10.1016/S0022-460X(88)80365-1
  13. Park, C. I. and Lee, J. M., 1993, 'Load Transmission and Vibration Characteristics of Automobile Gear,' SAE Paper 932917
  14. Park, C. I. and Grosh, Karl, 1998, 'Radiated Noise From a Clamped Circular Plate-Shaft System,' ASME International Mechanical Engineering Congress, Recent Advances in Solids and Struc？tures, Anaheim, CA, USA, pp. 199-204
  15. Park, C. I. and Kim, D. S., 2002, 'Transmission Error Analysis of the Helical Gears for the Elevator,' Trans. of KSME, A, Vol. 26, No. 12, pp.2695-2702 https://doi.org/10.3795/KSME-A.2002.26.12.2695
  16. Park, C. I., 2000, 'Analytical Procedure for Prediction of Radiated Noise From a Gear-ShaftPlate System,' Proceedings of DETC'00, DETC 2000/PTG-14444, USA
  17. Park, C. I., 2005, 'Noise and Vibration From a Shaft-bearing-plate system due to an Excitation of Helical Gears,' Proceedings of Twelfth International Congress on Sound and Vibration, Lisbon, Portugal
  18. Rautert, J. and Kollmann, F. G., 1989, 'Computer Simulation of Dynamic Forces in Helical and Bevel Gear,' Proceedings of 1989 International Power Transmission and Gearing Conference, USA, Vol. 1, pp.435-446
  19. Sabot, J., Perret- Liaudet, J., 1994, 'Computation of the Noise Radiated by a Simplified Gearbox,' Proceedings of 1994 International Gearing Conference, UK, pp. 63-68
  20. Snowdon, J. C., 1971, ' Mechanical Four-pole Parameter and Their Application,' Journal of Sound and Vibration, Vol. 15, No.3, pp.307-323 https://doi.org/10.1016/0022-460X(71)90427-5
  21. Snowdon, J. C., 1970, 'Forced Vibration ofIntern ally Damped Circular Plates with Supported and Free Boundaries,' The Journal of the Acoustical Society of America, Vol. 47, No.3, pp. 882-891 https://doi.org/10.1121/1.1911974
  22. Soedel, W., 1993, Vibrations of Shells and Plates, 2nd ed. Marcel Dekker, NY
  23. Zaveri, K. (ed), 1994, B & K Technical Review, No.2, B & K, Denmark