An analytical method for calculating the tooth surface contact stress of spur gears with tip relief. (February 2019) - Wen, Qi; Du, Qungui; Zhai, Xiaochen
Highlights: A new more accurate analytical model for calculating the tooth surface contact stress of tip-relieved gears is established based on the accurate tooth profile equations represented by the parameter equations, which can be used to calculate both the standard gear and tip-relieved gear. The solutions of equation with implicit function and singular integral are studied. The influence of the tip relief on the tooth surface contact stress of gears is measured and compared with the results of the finite element method and Hertzian contact model. Abstract: Spur gears with tip relief can effectively improve transmission performance, and accurate determination of their tooth surface contact stress (TSCS) can provide guidance for structure optimization and performance evaluation. However, since the tip-relieved gear profile has not been accurately approximated with a quadratic parabola, the TSCS cannot be calculated using the cylindrical contact model of the Hertzian contact theory (Hertz model). Therefore, a new more accurate analytical model for calculating the non-Hertzian TSCS of tip-relieved gears is proposed in this paper. This model is established based on the accurate tooth profile equations represented by the parameter equations (new model). The solution of the model with an implicit function and a singular integral is also studied. Finally, the TSCS of two gear pairs with and without tip relief are compared for different parameters under different loads according to the new model, the finite element method (FEM model) and Hertz model. The results show that the tip relief will affect the maximum TSCS, location and size of the contact area, whereas the Hertz model cannot quantify these effects. However, the new model, which is validated using the FEM model, can provide accurate and reliable results. Graphical abstract: