Multi-State Meshing-Collision Dynamics Modeling and Analysis of High-Contact-Ratio Spur Gear System Considering Tooth Breakage

Tooth breakage is a common issue in geared systems. The high-contact-ratio spur gear system (HCRSG) maintains continuous transmission despite tooth breakage, but experiences increased impact vibration. In aviation, even if the gear teeth break, the gear's transmission cannot be stopped immediately. Therefore, studying gear system dynamics with tooth breakage is crucial for assessing the reliability of mechanical equipment. This study treats the tooth-back contact induced by backlash as the tooth-back collision and presents the multi-state meshing-collision pattern of HCRSG with one tooth breakage (OTB), including triple-tooth, double-tooth, single-tooth meshes, disengagement, and tooth-back collision. Time-varying meshing stiffness and load distribution coefficients of HCRSG with OTB are calculated. Then a multi-state meshing-collision nonlinear dynamic model of HCRSG with OTB is established. The meshing forces of HCRSG with OTB and without OTB are calculated and compared to examine the effect of tooth breakage. The multi-state meshing-collision nonlinear dynamics of HCRSG with OTB are studied via bifurcation diagram, phase portraits, and Poincaré maps by changing the transmission error amplitude. The results show that 3-2-3-2-3 meshing pattern of HCRSG is shifted to 2-1-2-1-2 meshing pattern due to tooth breakage. The effect of tooth breakage on the meshing force and dynamic behavior significantly depends on teeth disengagement or tooth-back collision. Tooth breakage greatly affects the bifurcation and chaos characteristics of multistate meshing-collision behavior of HCRSG. This study creates a framework to predict and assess the dynamics of gear transmission systems with tooth breakage in extreme aviation and aerospace environments.