Involute spline couplings are used to transmit torque from ashaft to a gear hub or other rotating component. External gearteeth on the shaft engage an equal number of internal teeth in thehub. Because multiple teeth engage simultaneously, they cantransmit much larger torques than a simple key and keyway assembly.However, due to manufacturing variations, the clearance betweeneach pair of mating teeth varies, resulting in only partialengagement. A new model for tooth engagement, based on statistics,predicts that the teeth engage in a sequence, determined by theindividual clearances. As the shaft load is applied, the tooth pairwith the smallest clearance engages first, then deflects as theload increases, until the second pair engage. Thus, only a subsetof teeth carry the load. In addition, the load is non-uniformlydistributed, with the first tooth carrying the biggest share. As aconsequence, the load capacity of spline couplings is greatlyreduced, though still greater than a single keyway. This paperdiscusses the results of a statistical model which predicts theaverage number of teeth which will engage for a specified load,plus or minus the expected variation. The model quantitativelypredicts the load and stress in each engaged pair. Critical factorsin the model are the stiffness and deflection of a single toothpair and the characterization of the clearance. Detailed finiteelement analyses were conducted to verify the tooth deflections andengagement sequence. The closed form statistical results wereverified with intensive Monte Carlo simulations.
- Edition:
- 09
- Published:
- 09/01/2009
- Number of Pages:
- 14
- File Size:
- 1 file , 580 KB
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