Analysis and formulation of spur gear stresses with different tip modifications

Abstract

Spur gears are widely used in the power transmission mechanism of several machines. Due to the transmitted torque, spur gears experience high stresses which could cause gear tooth failure by surface pitting or root fracture. Tip relief and other gear profile modification have been considered for reducing the induced stresses in the gear tooth. In this work, the influence of tip relief on stresses on a pair of identical spur gear was analyzed using commercial FEA software ANSYS, and formulae for estimating contact and bending stresses were derived. Three cases of gear sets were analyzed; a non-modified pair and another two sets with linear and parabolic tip relief profiles. The non-modified gear set frictionless contact stress was validated against the calculated AGMA pitting resistance, Hertzian contact stress and a reported contact stress value in the literature. The four methods agreed well with each other. Similarly, bending stress was also compared with the AGMA bending strength and Lewis bending stress for validation. Then, friction coefficient was varied from 0.0 to 0.3 with increment of 0.1. The gear contact stress increased up to 11% relative to the frictionless case, whereas bending stress decreased by 6%. Linear tip relief modification was carried out for increasing normalised tip relief values of 0.25 to 1.0 with increment of 0.25. The gear frictionless contact and bending stresses decreased by a maximum of 4% and 2%, respectively. Frictional contact stress increased by up to 7.1% and the bending stress is almost identical with the frictionless case. Parabolic tip relief was also carried out with similar normalised tip relief values. Frictionless contact stress decreased by 5% while frictional contact stress increased by up to 11.5% and the bending stress is also almost identical with the frictionless case. Finally, four formulae were introduced for estimating the contact and bending stresses for a tip modified spur gear.