Abstract: 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 and mean value 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 =0.2 and =0.3.The frequency responses are mainly 4, 5 and 6. ③ With consideration of stochastic backlash, the value of has less change, but has obvious fluctuation.

Key words: Backlash, Dynamic response, Friction, Gear, Time-varying stiffness