Spline couplings are used in applications involving high torque; however, due to variations in teeth clearances, all teeth in spline couplings do not engage simultaneously, causing some of the teeth to carry a disproportionately large portion of the total load. Variations in tooth-to-tooth clearances mean the first pair of teeth to engage will carry more load and fail sooner. This has lead to an industry practice of designing splines around the criteria that only 25-50% of the teeth on a spline coupling will engage and carry the load, and the load is generally assumed to be uniformly distributed. This research on tooth engagement is part of an ongoing study sponsored by an industrial partner with the intent to more accurately describe and improve tooth engagement in spline couplings. Tooth engagement in involute spline couplings is difficult to predict due to the complex geometry and even more complex manufacturing processes. Although manufacturing is closely controlled, with precision tooling, engagement problems persist. Presented herein is a detailed study of an involute spline coupling and its associated errors. Mating internal and external involute splines have been analyzed in order to identify variation and error patterns associated with spline coupling assemblies. These error patterns aid in understanding the manufacturing processes and ways in which we can better understand and predict tooth engagement. Spline manufacturing processes were studied in an attempt to relate tooling and processing errors to the resultant error patterns observed in production couplings. Some correlation with tooth engagement measurements have been found, but significant differences remain unexplained. Tooth engagement measurements exhibited anomalous behavior, which raised questions about test apparatus and procedures. The main contributions of this work are: A process for analytically creating torque-deflection curves in any configuration using measurement data, confirmation of the analytical tooth engagement sequence model from measured variation data, a better understanding of the experimental results, how to design future experimental tests, and the importance of early quasi-simultaneous tooth engagement. Several valuable insights have resulted in a better understanding of the mechanics of tooth engagement and load-sharing among spline teeth. The progress made should encourage further study, which may lead to processes which are better understood and controlled, and to designs which are more robust to variation, with more predictable performance and improved load-carrying capacity.

The purpose of this thesis is to provide an in-depth understanding of tooth engagement in splined couplings based on variations in clearances between mating teeth. It is standard practice to assume that 25-50% of the total spline teeth in a coupling are engaged due to variations from manufacture. Based on the assumed number of teeth engaged, the load capability of a splined coupling is determined. However, due to the variations in tooth geometry from manufacuture, the number of teeth actually engaged is dependent on the applied load and the tooth errors. The variations result in sequential tooth engagement with increasing load. To date, little work has been done to model tooth engagement and the stresses resulting from unequal load sharing among engaged teeth. A Statistical Tooth Engagement Model (STEM) has been developed which allows designers to estimate tooth engagement and resulting stress based on a statistical representation of the tooth errors. STEM is validated with finite element models as well as some preliminary experimental tests. Parametric studies are performed to determine the effect and sensitivities of variations in tooth parameters and tooth errors.