Dynamic characteristics of a straight bevel gear drive system considering multi-state meshing and time-varying parameters

In order to investigate the dynamic characteristics of the straight bevel gear drive system, its torsional-bending-axial dynamics model considered the multi-state meshing characteristics is established. The time-varying load distribution ratio and meshing stiffness of the system are calculated by micro element method according to the performance of the straight bevel gear. Three different Poincaré sections are defined to study the dynamic characteristics of the system. The mechanism of tooth disengagement and back-side contacting is studied according to the time history diagram of the total normal force. The nonlinear dynamics equation of the system is solved by the variable step fourth-order Runge-Kutta method when the bevel gear drive system in automobile reducer is taken as the research object. The transition process of system dynamic characteristics and the influences of the meshing frequency, load coefficient and the comprehensive transmission error are studied by using the time history diagram of the total normal force, phase portraits, Poincaré maps, bifurcation diagrams and the corresponded top Lyapunov exponent (TLE). The chaotic motion found in the research is unfavorable from a practical point of view which can be avoided by adjusting the value of parameters or the initial value of state variables in engineering. The research can provide a theoretical basis for the parameter design and dynamic characteristic control of straight bevel gear drive system.