Load distribution in spline coupling teeth with parallel offset misalignment

In spline couplings, torque is theoretically transmitted by all teeth, supporting the same loading level. In practice, due to manufacturing and mounting errors, not all teeth transmit the same amount of torque and as a result an overloading condition may occur. In traditional design practice, this uneven load sharing between teeth is often neglected or taken into account by means of a simplified approach. In this article, a theoretical method, non-finite element method based, is developed in order to determine both exact number of engaging teeth and shared forces in involute spline couplings with parallel offset errors. The described process consists of an iterative procedure, in which algorithm is divided into three main modules: the first one aims to calculate geometrical parameters, the second one analytically determines both deformation and stiffness of teeth and the third one calculates the actual number of engaging teeth and the shared load. The algorithm has been benchmarked against finite element method results, showing a very good agreement.