Dynamic Modeling and Analysis of Involute Spur Gear Transmission System Considering Friction and Multi-State Meshing Conditions

A dynamic model for an involute spur gear system involving multi-state mesh and friction is formulated to analyze the dynamic response and meshing state property under different lubrication conditions, such as an elastohydrodynamic and mixed lubrications as well as dry friction. The dynamic equations of the system under teeth separation, drive-side and back-side tooth meshes are derived respectively based on the meshing principle of the gear transmission and the force analysis acting on teeth. The effects of the different lubrication schemes on the dynamic meshing force and motion orbit of the system are studied. Results show that the lubrication scheme greatly affects the amplitude of dynamic meshing force. However, the influence of the lubrication scheme on the motion orbit depends mainly on the meshing state. It means that the system motion orbit is largely affected by the lubrication scheme without drive-side and back-side tooth impacts, while the orbit is slightly affected by the lubrication scheme when drive-side and back-side impacts occur. Additionally, the dynamic response and meshing property are investigated with the decrease in load by defining three different Poincaré mappings. The system performs a drive-side meshing state as the load is large. The teeth separation is observed periodically with the decrease in load. While, both teeth separation and back-side mesh are observed under small load, which strengthens the impact vibration between the meshing teeth.