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The objective of this work is to present a mathematical model which studies helical gears made of a material with a small modulus of elasticity, when one or more pairs of teeth mesh prematurely during engagement. This phenomenon may lead to the modification of the load distribution on the teeth which are initially in contact and to a kind of interference causing additional tooth wear of the gear. In this case, the calculation of the contact ratio must account for the real number of pairs of teeth in contact. This is especially important when large deformations occur as is confirmed in the results presented to confirm the validity of the proposed method.

This paper presents a method for the calculation of the stresses around three non-intersecting identical circular holes in a row, in a thin and infinite isotropic plate subjected to in-plane longitudinal, transverse or biaxial tension at infinity. The calculation of the stresses around any of the three holes is obtained in terms of the stresses that would exist around and at the center of the contour of a third would-be hole in the plate, initially, containing two holes. The results from the present method are compared to finite element as well as to published results in the literature. It is seen that the method yields satisfactory results at key points around the contour of the holes.