Effect of Backlash on Dynamics of Spur Gear Pair System with Friction and Time-varying Stiffness

The chief objective is to study the effect of backlash on nonlinear dynamic response of spur gear pair system with consideration of friction and time-varying stiffness.Three different kinds of backlash, i.e.constant backlash, time-varying backlash and stochastic backlash, are established.The dynamic responses are studied over a wide frequency range by using numerical integration, Runge-Kutta method, to check the nonlinear behavior and jump phenomena in the frequency response.The results indicate that:① At low speed, with the increase of friction coefficient, the root-mean-square value xr ms and mean value xm of system response increase, and the system enters into chaotic motion state after three times of jump.② The increase of amplitude of time-varying backlash causes the system to early enter into chaotic state, and with the increase of time-varying amplitude, the jump frequency decreases gradually.When the frequency of time-varying backlash is small, the influence of backlash on the system is small.When the frequency of time-varying backlash is great, the system produces obvious resonance response at ω=0.2 and ω=0.3.The frequency responses are mainly 4ω, 5ω and 6ω.③ With consideration of stochastic backlash, the value of xr ms has less change, but xm has obvious fluctuation.