Tooth Contact Analysis of Spur and Helical Gears in Case of Shafts Deflections

Abstract The paper presents semi-analytical methods (SAMs) for determination of pressures distributions on the flank surfaces of spur and helical gears with both pinion and gear shafts deformed. In case of spur gear pair, a nonstandard gear pair was chosen. It is well known that the curvature of the tooth profile decreases when a negative correction of the gears is made, this thing leading to higher contact pressures and a decrease of durability. The SAMs starts from Hartnett’s approach based on Boussinesq equation from half-space theory of linear elasticity, which means implicitly an infinite width of gear’s flank. To simulate the more realistic quarter-space conditions, a correction based on virtual mirror pressures is introduced in the computational algorithm. For spur gears, the elements of the matrix of separations are obtained using analytical equations derived from involute properties while a methodology dedicated to helical gears was developed. The pressures distributions obtained with worked up SAMs have been validated by comparisons with results obtained by neutral research by using FEM or a dedicated SAM. The present paper took into consideration both deflections of pinion and gear’s shaft, so that a more realistic pressures distribution is obtained. The contact surfaces are considered smooth surfaces and the contact between mating surfaces is considered as dry contact.