Involute spline couplings are used to transmit torque from a shaft to a gear hub or other rotating component.
External gear teeth on the shaft engage an equal number of internal teeth in the hub. Because multiple teeth
engage simultaneously, they can transmit much larger torques than a simple key and keyway assembly.
However, due to manufacturing variations, the clearance between each pair of mating teethvaries, resulting in
only partial engagement.
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. Thus, only a subset of teeth carry
the load. In addition, the load is non-uniformly distributed, with the first tooth carrying the biggest share. As a
consequence, the load capacity of spline couplings is greatly reduced, though still greater than a single
keyway.

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