Dynamics modeling and analyzing of spur gear pair with pitch deviation considering time-varying contact ratio under multi-state meshing

The pitch deviation caused by machining error affects the transmission stationarity of the spur gear pair. It results in time-variation of the contact ratio for the system by corner contact. Meshing characteristics of the spur gear pair with the pitch deviation are studied in order to analyze the time-varying contact ratio and motion characteristics of the system. The mathematical model of time-varying contact ratio is established to explore its time-varying characteristics. Dynamics model of the spur gear pair with the pitch deviation considering time-varying contact ratio under multi-state meshing is proposed. The transmission stationarity of the spur gear pair are explored by dynamic meshing forces. The influence of system parameters and operating parameters on dynamics characteristics of the spur gear pair with the pitch deviation considering time-varying contact ratio is studied by bifurcation diagrams, phase portraits and Poincare maps. Results show that the pitch deviation as a short-period error in the spur gear pair leads to complex periodic motions. The possibility of the tooth disengagement, back-side teeth contacting and chaotic motion for the spur gear pair increases with the increase of complexity of pitch deviation values. The transmission accuracy and stationarity for the spur gear pair decrease when pitch deviation values are complex. This study provides a theoretical basis for dynamics modeling and stationarity analysis of the spur gear transmission system and other gear transmission systems.