Efficient nonlinear spur gear analysis using an interpolated analytical model

Abstract This work presents an efficient analytical method for spur gear modelling based on the interpolation of precomputed power-law parameters to calculate contact forces. The motivation arises from the fact that, when a nonlinear contact expression is combined with the linear deformations of the tooth body, the resulting force must be obtained through an iterative procedure to ensure deformation compatibility, which increases computational cost. To overcome this, a preprocessing stage is introduced together with the assumption that, for a meshing situation, the force-penetration relation can be represented by a power-law combining the linear stiffnesses of the tooth bodies with the nonlinear contribution of local contact. In this stage, a database is generated by fitting the power-law parameters for all combinations of contacting points between the teeth. Then, during simulation, the position and rotation of the gears directly provide the penetration and active contact points, from which the corresponding parameters are interpolated within the database, and the force is evaluated through the power-law. This strategy eliminates the iterative compatibility procedure required in the traditional approach when nonlinear contacts are included, inherently reducing the computational time while preserving accuracy.