Novel kinematic and geometric views for improving tooth contact analysis of spatial gears

Tooth contact analysis (TCA) has been widely applied to evaluate the working performance of gear pairs. TCA is often formulated with five unknowns and five independent scalar equations. The solution process involves a global optimization problem with strong nonlinearity and numerical instability, especially for spatial gears with complicated tooth geometries. This study proposes novel kinematic and geometric views of gearing that reveal insights into the meshing process of spatial gears. One unknown can be removed from the position and normal equations of the TCA formulation. To solve the remaining four unknowns, a simplified optimization model with two unknowns is proposed, and the other two unknowns are obtained by using geometric iterative methods or directly from explicit expressions in some cases. A general algorithm was developed to solve the simplified TCA. The test results of both the spiral bevel and face gear drives validate the effectiveness of the proposed method.