Variation Analysis of Tooth Engagement and Loads in Involute Splines

Involute spline couplings are used to transmit torque from a shaft to a hub or other rotating component. In theory, all teeth of the spline share the load equally. In practice, due to manufacturing variations, the teeth are unequally loaded. A new model for tooth engagement, based on statistics, predicts that the teeth engage in a sequence, determined by the individual clearances. As the shaft load is applied, the tooth pair with the smallest clearance engages first, then deflects as the load increases, until the second pair engage. The two engaged pairs deflect together until the third pair engage, and so on, until the full load is reached. The statistical model predicts the average number of teeth which will engage for a specified load, plus or minus the expected variation. It also quantitatively predicts the load and stress in each engaged pair. Critical factors in the model are the stiffness and deflection of a single tooth pair and the characterization of the clearance. Detailed finite element analyses were conducted to verify the tooth deflections and engagement sequence. This model has led to a simple closed-form solution that has been implemented in a spreadsheet to allow designers to predict the load in spline teeth based upon the characteristics of the spline.