Effects of Gyroscopic Moment on the Dynamics and Vibrations of a High- Speed Double- Helical Gear Pair

علوم کاربردی و محاسباتی در مکانیک

Article 3, Volume 29, Issue 1 - Serial Number 17, May 2017, Pages 31-48   

Document Type: Original Article

DOI: 10.22067/fum-mech.v29i1.54911

Authors

mohammad karimi khoozani¹; Mehrdad Poursina^{* 2}; ali pourkamali anaraki¹

¹Shahid Rajaee Teacher Training University

²Isfahan University

Abstract

In this research a linear time- invariant lumped mass model, LTI, in three-dimensional space for a double- helical gear pair is developed and effects of gyroscopic moment on the dynamics and vibrations are studied. In this model, each member has six degrees of freedom and both of the mesh stiffness and bearing stiffness are undertaken. The dynamic response due to transmission errors excitations is calculated by using the modal summation technique. The results of this research show that, by taking the gyroscopic effects in double- helical gear pair, most of the natural frequencies are reduced. In addition, the gyroscopic moment have an important role on the dynamic response of a high- speed double- helical gear pair. In order to verify the equations and solution methodology, the obtained dynamic response from a pair of double- helical gear pair is compared with the empirical results of other researches.

Keywords

Double- helical gear; Gyroscopic moment; High- speed; Dynamic model; Vibration

References

1. Kahraman, A. and Singh, R., "Non-linear dynamics of a spur gear pair", Journal of sound and Vibration, Vol. 142, No. 1, pp. 49-75, (1990):

2. Kahraman, A. and Blankenship, G.W., "Interactions between commensurate parametric and forcing excitations in a system with clearance", Journal of Sound and Vibration, Vol. 194, No. 3, pp.

317-336, (1996).

3. Blankenship, G.W. and Kahraman, A., "Steady state forced response of a mechanical oscillator with combined parametric excitation and clearance type non-linearity", Journal of Sound and Vibration, Vol. 185, No.5, pp. 743-765, (1995).

4. Kahraman, A. and Blankenship, G.W., "Experiments on nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters", Journal of Applied Mechanics, Vol. 64, No.1, pp. 217-226, (1997).

5. Kahraman, A. and Blankenship., G.W., "Effect of involute tip relief on dynamic response of spur gear pairs", Journal of Mechanical Design, Vol. 121, No. 2, pp. 313-315, (1999).

6. Kahraman, A. and Blankenship, G.W., "Effect of involute contact ratio on spur gear dynamics", Journal of Mechanical Design, Vol. 121, No. 1, pp. 112-118, (1999).

7. Neriya, S.V., Bhat, R.B. and Sankar., T.S., "On the dynamic response of a helical geared system subjected to a static transmission error in the form of deterministic and filtered white noise inputs", Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 110, No. 4, pp. 501-506, (1988).

8. Kahraman, A., "Effect of axial vibrations on the dynamics of a helical gear pair", Journal of Vibration and Acoustics, Vol. 115, No. 1, pp. 33-39, (1993).

9. Kahraman, A., "Dynamic analysis of a multi-mesh helical gear train", Journal of Mechanical Design, Vol. 116, No. 3, pp. 706-712, (1994).

10. Kahraman, A. "Planetary gear train dynamics", Journal of Mechanical design ,Vol. 116, No. 3, pp. 713-720, (1994).

11. Umezawa, K., Houjoh, H., Matsumura, S., Wang, S. and Ohshima, S., "‘Experimental Investigation on Modal Behavior of Helical Gear Units with Various Ratio", Proc. 7th ASME Int. Power Trans. and Gearing Conference, San Diego, pp. 509-518, 6- 9 October, (1996).

12. Kubur, M., Kahraman, A., Zini, D.M. and Kienzle, K., "Dynamic analysis of a multi-shaft helical gear transmission by finite elements: model and experiment", Journal of vibration and acoustics, Vol. 126, No. 3, pp. 398-406, (2004).

13. Kang, M.R. and Kahraman, A., "An experimental and theoretical study of the dynamic behavior of double-helical gear sets", Journal of Sound and Vibration, Vol. 350, pp. 11-29, (2015).

14. Prashant, S. and Kahraman, A. "A dynamic model of a double-helical planetary gear set", Mechanism and Machine Theory, Vol. 70, pp. 157-174, (2013).

15. Thomas, J., "A procedure for predicting the load distribution and transmission error characteristics of double helical gears", MSc Thesis, The Ohio State University, (1991).

16. Clapper, M. and Houser, D.R., "Prediction of fully reversed stresses at the base of the root in spur and double helical gears in a split torque helicopter transmission", Proceedings of American Helicopter Society Rotor Wing Specialists Meeting, Williamsburg, VA, pp. 26-28, (1993).

17. Zhang, T., "Noise optimization of a double helical parallel shaft gearbox", Proceedings of the Int. Gearing Conf., University of Newcastle upon Tyne, pp. 93-98, (1994).

18. Wang, Ch. and Hai-tao, J., "Investigation of a design modification for double helical gears reducing vibration and noise", Journal of Marine Science and Application, Vol. 9, No. 1, pp. 81-86, (2010).

19. Wang, S., Zhang C. and Wang, F., "The analysis of dynamic load coefficients of double- helical planetary gear sets", International gear conference, France, pp. 888- 895, 26- 28 August, (2014).

20. Sheng, Zh., "Modal Analysis of Double-Helical Planetary Gears With Numerical and Analytical Approach", Journal of Dynamic Systems, Measurement, and Control, Vol. 137, No. 4, pp. 1-17, (2015).

21. Seager, D.L. "Conditions for the Neutralization of Excitation by the Teeth in Epicyclic Gearing", Journal of Mechanical Engineering Science, Vol. 17, No. 5, pp. 293-299, (1975).

22. Kubur, M., "Dynamic analysis of a multi-shaft helical gear transmission by finite elements: model and experiment", Journal of vibration and acoustics, Vol. 126, No. 3, pp. 398-406, (2004).

23. Kang, M.,R., and Kahraman, A., "Measurement of vibratory motions of gears supported by compliant shafts", Mechanical Systems and Signal Processing, Vol. 29, pp. 391-403, (2012).

24. Ajmi, M. and Velex, P., "A model for simulating the quasi-static and dynamic behaviour of solid wide-faced spur and helical gears", Mechanism and Machine Theory, Vol. 40, No. 2, pp. 173-190, (2005).

25. LDP Gear Load Distribution Program, Gear and Power Transmission Research Laboratory, the Ohio State University, USA, (2011).

26. Meirovitch, L., "Fundamentals of vibrations", International Edition, McGraw-Hill, pp. 280-365, (2001).