Load distribution analysis of clearance-fit spline joints using finite elements

Splines are widely used in mechanical drive systems to transfer rotary motion from an input to an output. Despite their wide application in rotating machinery, very little is known about their contact behavior and load distribution characteristics. In this study, a combined finite element and surface integral contact analysis model is employed in order to investigate load distribution along the spline interfaces. Three loading cases are considered: (i) purely torsional loading representing power transfer through two concentric shafts, (ii) combined torsional and radial loading representing a spur gear-shaft interface, and (iii) combined torsional, radial, and moment loading representing a helical gear-shaft interface. The effect of spline misalignment is investigated along with intentional lead crowning of the contacting surfaces. In addition to spur spline teeth, helical spline teeth are investigated. Influence of intentional mismatch of splines through a slight helix angle applied to the external spline is also investigated within a range of torque transmitted. Finally, the effects of manufacturing tooth indexing error on spline load distributions are quantified using the proposed model.