STRESS ANALYSIS OF SPUR GEARS, WITH TIP RELIEF

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. In this work, stress analysis of a pair of spur gears was conducted using ANSYS software with the aim of analysing the influence of tip relief on gear stresses, and to propose mathematical formulae for estimating bending and contact stresses in a tip modified spur gear. The project scope was limited to finite element modelling of spur gear stresses with pre-defined frictional coefficients. Three cases of gear-sets were analysed; a non-modified pair, and another two sets with linear and parabolic tip relief profiles. The non-modified gear-set frictionless contact stress deviated by 32.1%, 4.6%, and 1% with respect to the AGMA pitting resistance, Hertzian contact stress and a reported contact stress value in the literature. Bending stress also differed with the AGMA bending strength and Lewis bending stress by 82.7% and 48%. Friction coefficient was varied from 0.0 to 0.3 with increment of 0.1. The gear contact stress increased by 2 to 11 % relative to the frictionless case. Frictional bending stress first decreased by 5 and 6 % for friction values of 0.1 and 0.2 and increased again by 1% for friction value of 0.3. Linear tip profile 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 stress decreased by 1 to 4 %, and the bending stress decreased by 1 to 2 % except for tip relief value of 1.0 which matched the non-modified case. Frictional contact stress increased by 4.5 to 8.1 % for frictional values of 0.1 to 0.3 and the bending stress matched the frictionless case. Parabolic tip relief was also carried out with similar normalised tip relief values. Frictionless contact stress decreased by 3 to 5 %. With friction values of 0.1 to 0.3, contact stress increased by 2.9 to 6.3 %. Whereas bending stress matched the linear case. Four equations were proposed for estimating bending and contact stresses of a tip modified spur gear. It is hoped that this work contributes towards the knowledge of spur gear stress analysis and mitigation via application of tip relief.