An improved model for time-varying mesh stiffness of super-high-contact-ratio helical gear pair considering contact disparities on differently sliced fractal surfaces

Comprehensive studies that fully explore the impact of tooth surface morphology on the time-varying mesh stiffness (TVMS) of helical gear pairs are limited. The slicing method in helical gears leads to significant differences in fractal contact stiffness compared to spur gears, affecting stiffness calculations. Consequently, this research focuses on super-high-contact-ratio (SHCR) helical gears, commonly used in electric vehicles. The fractal contact model for the SHCR helical gear pair is developed based on fractal theory. The tooth contact coefficients in the conventional contact model have been improved. The new model considers distinctions in the tooth surface contact coefficients for different slices simultaneously in the helical gear pair. Furthermore, considering the axial force components, an improved model for the TVMS of the SHCR helical gear pair is developed. The investigation examines the effects of fractal and gear parameters on TVMS. The findings reveal that the TVMS escalates with an increase in fractal dimension and a decrease in the characteristic scale coefficient. Moreover, it is observed that the TVMS of the SHCR helical gear exhibits a relatively lower sensitivity compared to spur gears to changes in fractal parameters. Additionally, the contact ratio emerges as a crucial factor affecting TVMS. Notably, when the contact ratio approximates an integer value, the peak-to-peak value of TVMS diminishes. Conversely, in instances where the contact ratio is large, the average value tends to increase.