Multi-tooth contact behavior of helical gear applying modified meshing equation

In tooth contact analysis, the numerical process of searching for true contact lines or points is always a daunting task. The true contact lines for ideal helical gear transmission can be easily obtained through the helical gear meshing theory; however, in practice, this approach does not work well due to effect of tooth elasticity that shifts the contact lines from their ideal position. To address this problem, an approximate method to seek the true contact positions is proposed applying a modified meshing equation for a pair of helical gear with error free and no shaft deformation. First, the helical gear tooth deformation is calculated with the combination of contact mechanics and finite element method. Second, the deformed tooth flanks are fitted with Chebyshev polynomials. Third, the modified meshing equation is formulated by accounting for the influence of not only gear rigid body movement but also the gear deformation on the meshing process. Finally, the true contact points are determined by solving the correlated tooth flank equations, meshing equations, and force balance equations. The deformations of the gear and pinion teeth within the meshing plane are analyzed, and the contact load distributions along with the Von Mises stresses over a mesh cycle are examined. The study indicates that the proposed numerical method can yield true contact lines quickly while avoiding costly computational time in the traditional true contact line searching process that searches iteratively in the whole meshed tooth flank.