A Contribution to the Design of Robust Profile Modifications in Spur and Helical Gears by Combining Analytical Results and Numerical Simulations

This paper addresses the definition of robust profile modifications in spur and helical gears. An original methodology is introduced which relies on closed-form analytical results on transmission errors combined with a gradient descent algorithm and a Gauss quadrature (GQ) based full factorial method. The results compare very well with those delivered by using classic Monte Carlo simulations with a considerable gain in computational time. The influence of the probability distribution law for the design parameters (depth and extent of modification) is analyzed along with the contribution of gear quality grade and load variation. Some optimum robust linear relief is presented which minimizes transmission error fluctuations over a broad range of loads even in the presence of significant geometrical tolerances.