Investigation of Time-Varying Backlash of Spur Gears in Thermoelastic Coupling Conditions

In gearing systems with frequent forward and reverse rotation, improper backlash settings will produce serious vibration and impact. This study obtains the precise time-varying backlash of a spur gear pair in thermoelastic coupling conditions. Based on the principle of gear meshing, the phase difference between the meshing and backlash points in the gear transmission process was determined. A new gear backlash model (the segmented backlash model) is proposed. The model considers the influences of the thermoelastic deformation of the meshing point, thermal contact deformation, and oil film thickness on the backlash in thermoelastic coupling conditions. Thermal expansion of the backlash point was directly considered, and a calculation method for each backlash component was presented. The distribution curves of the backlash along the Drive-Side Line of Action (DLoA) and the Back-Side Line of Action (BLoA), as well as the time-varying backlash curve, were obtained. The results show that, compared to the influences of thermoelastic deformation, thermal contact deformation, and thermal expansion on the backlash, the influence of the oil film thickness can be neglected when initially estimating the gear backlash. Mutations in the time-varying backlash emerge at the alternating points of the single- and double-tooth meshing regions and within the double-teeth meshing region. These research findings can be directly applied to the dynamic analysis of gear systems.