Fast unconditionally stable 2-D analysis of non-conjugate gear contacts using an explicit formulation of the meshing equations

Computerised analysis of the contact of gear teeth is currently dependent on numerical solution techniques involving implicit multi-equation systems. These present inherent convergence problems when the initial values are not close enough to the real solution and require significant computational effort. Here a comprehensive new solution is presented using a modified form for the fundamental gear meshing equations in two dimensions. This formulation allows the analytical reduction of the system of meshing equations to a single scalar equation, which is solved using a fast unconditionally stable numerical method. The need for careful determination of initial values for the numerical solution is eliminated and test runs on real gear geometries verify solution accuracy, stability and speed. Application of the algorithm to profile-modified involute gears and Geneva-type mechanisms and related results are shown.