Performance assessment of solution methods for load distribution problem of gear teeth

In this paper three different procedures to solve load distribution problems of gear teeth for static transmission error (TE) calculation of gear pairs are presented. Performance assessment was carried out with the three procedures in static TE calculation of a helical gear pair under load with global tooth contact analysis. The procedures were compared in terms of computational effort to solve the load distribution problem and the accuracy of the solution. An incremental procedure with gradual and iterative load application was assessed for solving the full load distribution problem and calculating TE. Then the full load distribution problem was replaced by a reduced, but equivalent, problem through a method called pseudo-interference. The reduced problem was solved using the other two proposed procedures, a linear programming solution based on an interior-point algorithm and a direct matrix solver based on Cholesky factorisation. This latter procedure showed to be highly efficient in solving load distribution problems of gear teeth.