On the contact stress analysis of spur gears using variational inequalities

This paper is concerned with the development and implementation of a new mathematically consistent method for the analysis of contact stresses in spur gears. The method depends on solving the variational inequality representing the general contact problem which takes into account the effect of interfacial friction. A two-step algorithm, which employs Quadratic Programming and Lagrange's multipliers, is used to solve the variational inequality and to provide the contact and root stresses of gearing problems. The proposed method, which is verified by solving special cases of contact problems for which analytical solutions exist, is applied to the case of a rack-pinion assembly to determine the resulting contact and root stresses. The proposed approach overcomes most of the difficulties and approximations evident in current analysis techniques of contact stresses in spur gears.

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