A New Mathematical Model Of Nonlinear Gear Vibration Modeling And Analysis Solution Study

This paper is mainly concerned with the non-linear dynamic characteristic of gear pairs system on the basis of combining friction, gear mesh stiffness and backlash by use of qualitative and quantitative methods. The whole work consists of five parts:(1).This paper regards involute spur gear as the target, and set up a improved nonlinear dynamics model of the system, which consider the frictional force of meshing teeth. In order to study the effect of friction and time-varying stiffness on system dynamic characteristics, a new period-enlargement method is put forward to set up friction force and gear meshing stiffness model respectively. The non-linear dynamic model is a non-autonomous system. Comparing with the former models, in this model the damping coefficient and stiff coefficient set up by period enlargement method is a periodic function with the same period. Thus it becomes advantageous for applying EM(energy method) or other methods to calculate approximate analytical solves of the gear transmission dynamic equations combined with time-varying damping and stiff.(2).Frequency response function of the non-linear dynamic model is obtained by using harmonic balance method.(3). An improved energy iterative method which is used to solve strong nonlinear system including time varying damping and stiffness coefficient is developed. The improved energy iterative method is used to analyse the harmonic resonance frequency factors existing in the system. The frequency-response equation of steady vibriation of the primary resonance, 1/3 sub-harmoic vibration and 1/5 sub-harmoic vibration under the action of internal excitation in the system is deduced. The results which are obtained by the energy iterative method are compared with those by computer numerical simulation. The results show that the energy iterative method is correct in qualitative analysis and also can meet the demands in engineering application.(4).The influence of the frictional forces, excitation frequency and stiffness ratio upon the chaos and bifurcation are investigated by means of phase plots, Poincare maps, FFT spectra and bifurcation diagrams based on the single degree of freedom system. The result shows that periodic attractor educes discrete spectra while chaos educes continuous spectra. With the coupling of friction and time-varying stiffness influences the system, Friction makes the system come into the periodic state in advance and chaotic area decrease.(5). The same analysis method used in the multiple-degree-of-freedom system can also obtained the parameter resonance and two different route, period doubling bifurcation and quasi-periodic bifurcation, to get into chaos. Explosive bifurcation was first detected in nonlinear gear pairs system.