A New Statistical Model for Predicting Tooth Engagement and Load Sharing in Involute Splines

Load-sharing among the teeth of involute splines is little understood. Designers typically assume only a fraction of the teeth are engaged and distribute the load uniformly over the assumed number of engaged teeth. This procedure can widely overor underestimate tooth loads. A new statistical model for involute spline tooth engagement has been developed and presented earlier, which takes into account the random variation of gear manufacturing processes. It predicts the number of teeth engaged and percent of load carried by each tooth pair. Tooth-to-tooth variations cause the clearance between each pair of mating teeth to vary randomly, resulting in a sequential, rather than simultaneous tooth engagement. The sequence begins with the tooth pair with the smallest clearance and proceeds to pick up additional teeth as the load is increased to the maximum applied load. The new model can predict the number of teeth in contact and the load share for each at any load increment. This report presents an extension of the new sequential engagement model, which more completely predicts the variations in the engagement sequence for a set of spline assemblies. A statistical distribution is derived for each tooth in the sequence, along with its mean, standard deviation and skewness. Innovative techniques for determining the resulting statistical distributions are described. The results of an in-depth study are also presented, which verify the new statistical model. Monte Carlo Simulation of spline assemblies with random errors was performed and the results compared to the closed-form solution. Extremely close agreement was found. The new approach shows promise for providing keener insights into the performance of spline couplings and will serve as an effective tool in the design of power transmission systems.