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.