Innovative method for optimising flank modification on toothings

Any significant improvement of running behaviour and load capacity of gears by means of flank modification is only possible by properly considering deflections and geometrical deviations in the full tolerance range. The presented method diminishes uncertainties of how to specify size and shape of the right flank modification. It is based on the geometry in the meshing area and on the tolerance range of the geometrical deviations. A system of equations with deviations, influence-coefficients of deflection and initially unknown modifications at node points of a flank grid Is set up. It is used for optimising the modification of the whole flank, I. e. finding the minimum of the maximum stress for the permissible range of geometrical deviations. For the optimisation a FSQP algorithm is used (Feasible Sequential Quadratic Programming). The required gradients of the objective function are calculated with the method of Automatic Differentiation using the ADOL-C package. For determining the flank distances along the contact line the optimisation code is interlinked with the proven FVA bevel gear software BECAL. On a bevel gear pair the method is demonstrated and first results are shown.