Theoretical analysis of profile shift effects and design parameter interactions on herringbone gear mesh stiffness

Precise profile shift design enables targeted optimization of herringbone gear pairs through load distribution control. Time-varying meshing stiffness (TVMS) emerges as a significant dynamic excitation that can affect the operational performance of herringbone gear pairs. This study develops an analytical framework for stiffness simulation in profile-shifted herringbone gears and systematically quantifies mesh stiffness variability under individual shift and compound shift configurations. The research further elucidates the synergistic effects of profile shift coefficients and key design variables—tooth width, helix angle, and normal module—on mesh stiffness evolution through parametric coupling analysis. The research results show that the positive shift decreases the mesh stiffness of gear pairs, with a 0.1 increment in the profile shift coefficient reducing the mean mesh stiffness by approximately 2.0%, while the negative shift increases it by approximately 1.9% per 0.1 decrement. For compound equal shift, mean stiffness decreases 0.9%–1.0% per 0.1 increment in the absolute value of the profile shift coefficient. For gear design parameters, quantitative analysis reveals substantial sensitivity differences: Negative shift gears exhibit 5.5%, 13.6%, and 8.9% higher mean stiffness sensitivity to tooth width, helix angle, and normal module variations, respectively, compared to standard gears. Conversely, positive shift configurations demonstrate stabilized stiffness sensitivity with 6.2%, 15.1%, and 9.9% reductions in parametric sensitivity for these respective variables. Moreover, the variation in mesh stiffness variance of the profile-shifted and standard gears caused by modifying the tooth width demonstrates monotonic trends, whereas alterations in helix angle and normal module induce non-monotonic relationships. These findings enable the precision design of herringbone gears with tailored stiffness characteristics, which is particularly beneficial for high-speed, heavy-load transmission applications.