Generation mechanism and evolution of five-state meshing behavior of a spur gear system considering gear-tooth time-varying contact characteristics

Abstract

Teeth disengaging or back-side teeth meshing induced by backlash reduces the transmission quality and dynamic performance of gear systems, and accurate interpretation of multi-state meshing behavior can provide guidance for structural optimization and performance evaluation. Therefore, the multi-state meshing behavior of the gear system is elaborated. A new nonlinear dynamic model of a spur gear system with five-state meshing behavior is proposed based on time-varying backlash and contact ratio. The time-varying meshing stiffness and time-varying backlash considering the elastic contact of gear teeth, gear temperature rise and lubrication are included in the model. The five-state meshing behavior is clearly characterized by constructing five Poincaré maps, and its generation mechanism is studied using dynamic meshing force time history, teeth relative displacement time history and phase portrait. The bifurcation and evolution of five-state meshing behavior are analyzed under the effects of load factor, meshing frequency and error coefficient. The results show that the mutation in the direction of dynamic meshing force leads to teeth disengaging and back-side single or double teeth contact, forming multi-state meshing behavior. Bifurcation caused by parameter changes greatly affects the evolution of five-state meshing behavior, particularly grazing bifurcation can decrease the number of teeth disengagement. Chaotic behavior or trajectory expansion inspires multi-state meshing vibration of the system. Previous gear system models could not reveal these phenomena due to ignoring the multi-state meshing behavior.

An efficient analytical approach to assess root cause of nonlinear electric vehicle gear whine

“…This study focuses on the effects of lubricant-surface interactions in predicting TVMS and the overall nonlinear dynamics response of the gear system. Therefore, the analytical formulation for the fillet-foundation stiffness in [31] is used based on the research carried out in [25,27,[32][33][34]. The more comprehensive approach in [38] can be adapted in future to account for the gear body compliance coupling with its neighbouring teeth.…”

“…The pseudo-Hertz contact stiffness is k ph ¼ pEL= ð4 1 À m 2 ð ÞÞ. This model has been largely adapted in the energy-based TVMS [25][26][27][28]32]. In this model, E is the Young's modulus of elasticity.…”

“…Sainsot et al [31] evaluated the tooth fillet-foundation deflection using a simple empirical formula to account for the tooth deflections induced by the gear body compliance. Other researchers adapted this model to determine the fillet-foundation stiffness [25,27,[32][33][34]. A few studies combined the bending, axial, shear, and tooth fillet compliances in the prediction of the total TVMS [25,27,33].…”

“…Lubricant damping varies with contact load, speed, lubricant's rheological properties, film thickness and squeeze film effect. Analytical models use formulations based on either constant damping ratio or simplified solutions of Reynolds equation [6,11,[32][33][34][35][41][42][43][44][45]. Chen et al [21] combined the analytical TVMS model with a damping coefficient which varied with the compressive deformations of the contacting teeth.…”

Dynamic modelling and analysis of cracked gear system with tip relief based on proposed variable-angle deformation energy integration method

“…The gear system is an important part of mechanical equipment, which is widely used as the key component of power and motion transmission in aerospace, energy development, industrial production and other modern mechanical equipment [1][2][3]. As one of the important basic components of the gear system, gear often produces crack failures in the operation of the system due to excessive load, improper assembly or fatigue caused by long-term operation [4][5].…”