Effects of Tooth Indexing Errors on Load Distribution and Tooth Load Sharing of Splines Under Combined Loading Conditions

In this paper, influences of tooth indexing errors on load distribution and tooth load sharing of spline joints are investigated by modifying an existing semi-analytical load distribution model for side-fit involute splines. Two commonly observed loading conditions, namely (i) combined torsion and radial loads representative of a spline joint of a spur gear with shaft and (ii) combined torsion, radial loads, and tilting moment representative of a spline joint of a helical gear with shaft are considered in this study. Numerical results of an example spline having (i) no tooth indexing error, (ii) a single tooth with indexing error, and (iii) a random sequence of tooth indexing errors under these two loading conditions are presented to demonstrate the effects of tooth indexing errors. In addition, a practical study of the robustness to manufacturing tolerances is also presented where probability distributions of load sharing factor of the critical tooth of an example spline designed to certain manufacturing tolerance classes are obtained with a large number of randomly generated indexing error sequences.