A model and method for load-bearing contact analysis of herringbone gears

In the light of the meshing characteristics of herringbone gears, established was a model for load-bearing contact analysis of such gears. First, a finite element method was used to calculate and obtain flexibility coefficients at various grid nodes on the working tooth surface and also the flexibility coefficients through an interpolation at all the long-axis discrete points on the transient contact ellipse during the gear engagement period. On the basis of the gear engagement at various contact locations, a normal flexibility matrix was constituted at the contact points on the tooth surface. Moreover, through a super-imposition, a tooth surface normal flexibility matrix of the gear pair was obtained. By taking account of the influence of shaft deformation on the tooth surface flexibility matrix, the additional matrix produced by the shaft deformation was added to the tooth surface normal flexibility matrix to obtain a flexibility matrix of the gear system. Then, based on the gear tooth deformation and displacement coordination equation, the force equilibrium conditions and non-insertion conditions were introduced to establish a mathematical programming model for the contact problem of herringbone gears. Finally, with a pair of herringbone gears under test serving as an example, through a comparison of load-bearing transmission errors (the measured amplitude and theoretical one are 0.451669 and 0.439 radial second respectively, the difference between the two is very small), the correctness of the established model was verified.