Direct analytical solution of the inverse gear tooth contact analysis problem

Despite the advances in gear tooth contact analysis and the existence of many competent theories, the fundamental inverse problem of determining the gear profile form that produces a desired kinematical response, or function of transmission errors, remains to be solved. This is because the usually employed form of the equations governing tooth contact is so complex and implicit, that it is impossible to solve inversely. To bypass this handicap, current design methodologies have to rely on indirect calculations, often requiring substantial computational effort. Here, a new more versatile formulation of the fundamental surface contact equations is proposed, leading to a set of meshing equations that allows the direct analytical solution of the inverse problem. The solution itself is in elegant vector-matrix form and it is explicit and fast. Applications of the proposed solution are discussed.