In this paper, an analytical method is used to investigate the distortions of involute spline teeth. The following hypotheses are adopted: teeth geometry is in conformity with standardization, dimensions are nominal (no defect), there is no friction and the load is a pure torsional torque. Teeth distortions due to bending, shear, compression, and foundation rotation are analysed. As the load is distributed along the tooth height, the displacement calculation differs from the conventional approach used for gear teeth. Sliding over the contact surfaces is also considered as it emerged during the study that this phenomenon, that has not hitherto been taken into account, plays a significant role. A punch model is used to describe the radial distribution of the contact pressure. Ascribing an arbitrary value to the tilted angle between the two contacting flanks enables the pressure profile to be evaluated, from which calculation of teeth distortions can be arrived at so as finally to obtain a new estimation of the tilted angle. Thus, displacements and the contact load can be determined together by iterating the calculation procedure until convergence. Torsional stiffness, which is one of the main parameters required to predict the torque distribution along the spline coupling, is evaluated from the various displacement components. The results derived from the proposed analytical method are compared with finite-element results and show good correlation.
Analysis of the algorithm for determining the meshing forces in a spline coupling with misalignment
