An analytical approach for predicting the fillet and contact stresses in symmetric and asymmetric spur gears under frictional mesh assumptions

Abstract

A precise estimation of the bending and contact stresses, as well as the true friction value during the gear mesh, are critical aspects of a cost-effective and safe gear design. Previous studies have usually neglected friction by assuming a frictionless contact. Additionally, the impact of friction on the bending stress of spur gears has rarely been addressed. Moreover, to the authors' best knowledge, the impact of friction on the weakest section, stress concentration factor, and Lewis form factor remain unexplored for both symmetric and asymmetric gears. This study presents an analytical model incorporating friction at different contact locations to calculate the variables related to the tooth's weakest section. This model facilitates the evaluation of the stress concentration factor, Lewis form factor, and maximum tensile stress for symmetric and asymmetric gears. The proposed model is especially beneficial for assessing the load-carrying capacity of spur gears operating in challenging conditions. The results showed that the asymmetric spur gear is superior to its equivalent symmetric counterpart in terms of tooth form factor; however, this superiority decreases as the coefficient of friction increases. In addition, friction has been found to have a greater effect on fillet stress than contact stress. For μ = 0.2, at the HPSTC, the contact load and tooth form factor decreased by 7 % and 12 %, respectively, and the fillet stress worsened by 13 % compared to the frictionless assumption. Meanwhile, at the LPSTC, the stress concentration factor and contact stress increased by 9 % and 3 %, respectively.

Keywords

• Asymmetric gear
• Friction
• Weakest section
• Lewis form factor
• Fillet stress
• Photoelasticity