Influence of system-inherent phase in spur gear multi-state mesh based on nonlinear dynamics

Owing to backlash, the drive- and back-side meshing points have an asymmetric relationship relative to the initial positions of the respective line of meshing. This study investigates the geometric phase difference of a spur gear multi-state mesh system corresponding to two-side impact. The affected time-varying parameters include meshing stiffness, load sharing ratio and friction torque. A time-varying asymmetric parameter system was built and employed in the nonlinear dynamic model considering teeth disengagement and back-side impact to simulate the effect of the system-inherent phase by backlash. Furthermore, to judge whether the dynamic system will have back-side collision, a three-dimensional map with two-parameter variables was introduced to describe the back-side impact frequency per meshing cycle. This was achieved by defining a particular Poincaré mapping, in which phase portraits, time history, bifurcation and top Lyapunov exponent diagrams were comprehensively used. The results indicate that the asymmetry phenomenon in different meshing states significantly affects the nonlinear characteristics of the back-side impact system, especially in the parameter interval of transition from the chaotic to the periodic state. This study provides an improved dynamic model of the spur meshing system, and is helpful in the selection of conditions to avoid a stable high-frequency impact. • System-inherent phase relationship between two-sides of tooth profile during meshing process is analyzed. • Mathematical model of asymmetric multi-state mesh of spur gear pair is established. • A method of judging high frequency impact interval in two-parameter condition is given. • Nonlinear dynamic characteristics of spur gear pair with asymmetric meshing impact is explored.