Abstract: With the developing trend toward high-speed, heavy load and light mass, especially with the demand to decrease vibration and noise, the issues relating to non-linear gear drive dynamics have brought a great concern to scholars world-wide. The time-varying mesh stiffness, transmission error, and backlash existing in gear drives lead to the inclusion of time-varying parameters and piecewise linearity functions in vibration differential equations, which gives rise to difficulties in solution.The dynamic model employs four torsional degrees of freedom. These degrees of freedom represent the input (motor), the two gears, and the output (load). In the proposed model, time-varying meshing stiffness, transmission error and backlash are considered. Considering the rotational periodicity of gear structure, a technique is proposed of using the parameter on one meshing tooth pair to represent that of other meshing pairs. Therefore, one can get the formula for meshing force under multiple-teeth meshing. An efficient method to solve nonlinear vibration equations is proposed. That is locally parameterized continuation scheme based on the shooting method, which has a unique effect on solving nonlinear problems with singularity. Finally, a numerical example is given by the proposed methods. The complete dynamic response is obtained. The data demonstrate several nonlinear phenomena, such as transition, period-doubling bifurcation.

Key words: gear, t ransm ission erro r, clearance, non2linearity, vibrat ion