On the profile design of transmission splines and keys

Splines and keys are machinery components placed at the interface between shafts and hubs of power-transmitting elements. A spline (or key) is usually machined (or attached) onto the shaft of a power-transmitting pair, and the corresponding groove is cut into the hub. The influence of spline profiles on the performance of power transmission is investigated in this paper. The optimal design of spline profiles for three different design criteria is presented. The method of calculus of variation is used to determine profile functions for maximum value. Analytical results are successfully obtained. They show that the splines with involute profiles lead to uniform deformation on the hub, in addition they can carry the maximum transmission load capacity. On the other hand, radial straight profiles result in optimum transmission efficiency. We think that these findings are worthy reporting and also believe that this approach could be used for the spline design with other performance criteria imposed.