Dynamic analysis of tooth profile modification to herringbone gears based on analytical solutions

Based on the structure of a single-stage herringbone gear transmission,a nonlinear lateral-torsional-axial coupling dynamic model and corresponding dynamic equations considering the time-varying mesh stiffness,tooth profile modification and tooth backlash were proposed,for which the tooth profile modification was considered as a time-varying tooth backlash.The numerical solutions were analyzed and the results show that the total tooth separation can be suppressed with rational tooth profile modification.Then,according to the method of multiple scales,perturbation analysis of the dynamic equations finds that appropriate analytical frequency response solutions for the case cause no total tooth separation at primary resonance.Compared to the numerical method,the analytical method is more efficient.At last,the influence of the modification parameters on the amplitude of the dynamic load factor was analyzed on the basis of the analytical solutions.The analysis results present that the magnitude of tip relief decreases as the helical angle increases to reduce the dynamic load factor,while the length of modification increases in this case.In addition,the optimal solution domain of the minimum dynamic load factor is a meniscoid zone,it increases firstly as the support stiffness of the driving gear increases to a value,after that value,it decreases when the support stiffness of the driving gear continues to increase;the optimal solution domain decreases as the support stiffness of the driven gear continuously increases.