Abstract

The study derives the kinetics equation of the system and analyzes vibration performance considering the nonlinear factors like time-varying mesh stiffness, gear back lash, mesh error. With the time-varying mesh stiffness of the gear increasing, the vibration of the gear system is more intense. The gear backlash has little effect on the aperiodic behaviour. However, with the clearance increasing, the system response quickly converts to chaos response from single frequency response with the increase of gap and the mesh impact is more serious. The excitation frequency is close to the resonance frequency of system, the system appears chaotic response and the vibration amplitude increases. When the frequency is far from the natural frequency, the response of the system tends to be steady. So it is easy to predict the dynamic performance in the design and make the system avoid the resonance frequency. In the following profile modification of gear, it also provides the data sources.

Keywords:

Gear system, nonlinear vibration, time-varying mesh stiffness,

References

1. Al-Shyyab, A. and A. Kahraman, 2005. Non-linear dynamic analysis of a multi-mesh gear train using multi-term harmonic balance method: period-one motions. J. Sound Vib., 279: 417-451.
   CrossRef    
2. Ambarisha, V.K. and R.G. Parker, 2007. Nonlinear dynamics of planetary gears using analytical and finite element models. J. Sound Vib., 302: 577-595.
   CrossRef    
3. Dubowsky, S. and F. Freudenstein, 1971. Dynamic analysis of mechanical systems with clearances, part 1: formulation of dynamic model. J. Manuf. Sci. Eng., 93(1): 305-309.
   CrossRef    
4. He, S., T. Rook and R. Singh, 2008. Construction of semianalytical solutions to spur gear dynamics given periodic mesh stiffness and sliding friction functions. J. Mech. Design, 130(12): 1-9.
   CrossRef    
5. Li, R.F. and W.J. Jun, 1997. Gear System Dynamics. Beijing Science Press, Beijing.
   
6. Munro, R.G., 1992. Review of the theory and measurement of gear transmission error. Proceeding of the Inst. of Mechanical Engineers, First International Conference on Gearbox Noise and Vibration, Cambridge.
   
7. Raclot, J.P. and P. Velex, 1999. Simulation of the dynamic behavior of single and multi-stage gear systems with shape deviations and mounting errors by using a spectral method. J. Sound Vib., 220 (5): 861-903.
   CrossRef    
8. Shaw, S.W., 1985. The dynamics of a harmonically excited system having rigid amplitude constraints. J. Appl. Mech., 52(2): 459-464.
   CrossRef    
9. Smith, C.E. and P. Liu, 1992. Coefficients of resultation. ASME Appl. Mech, 59: 663-669.
   
10. Tamminana, V.K., A. Kahraman and S. Vijayakar, 2006. A study of the relationship between the dynamic factor and the dynamic transmission error of spur gear pairs. J. Mech. Des., 129(1): 75-84.
    CrossRef    
11. Theodossiades, S. and S. Natsiavas, 2000. Nonlinear dynamics of gear-pair systems with periodic stiffness and backlash. J. Sound Vib., 229(2): 287-310.
    CrossRef    
12. Veluswami, M.A. and F.R.E. Crossley, 1975. Multiple-impact of a ball between two plates, Parts 2: Mathematical modeling. J. Eng. Ind., 97: 828-835.
    CrossRef    
13. Wang, J. and I. Howard, 2005. Finite element analysis of high contact ratio spur gears in mesh. ASME J. Tribol., 127(7): 469-483.
    CrossRef    
14. Wang, Y.X. and Y. Liu, 2003. Dynamic load analysis of spur gear pairs with backlash. J. Mech. Strength, 25(4): 373-377.
    

Competing interests

The authors have no competing interests.

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