Analytical formulas for gear body-induced tooth deflections of spur gears considering structure coupling effect

A Detailed Investigation of Gear Body-Induced Tooth Deflections and Development of an Improved Analytical Solution

“…To address this shortcoming, Xie et al [23] introduced a correction factor to consider the load dependence in the double-tooth-pair meshing duration and to account for the errors of using Equation (1) in the double-tooth-pair meshing duration. Meanwhile, Xie et al [24] derived new formulas for gear body induced deflections considering cubic and parabolic stress distribution around the tooth root and also load dependence between teeth. Chen et al [25] extended the formula reported in Ref.…”

“…[1] while cubic and parabolic stress distributions were assumed in Ref. [24]. Based on our finite element analysis, these assumptions are far from real situations.…”

“…In [1,24], finite element models were developed for gears with the assumption of the elastic body and rigid teeth to evaluate gear body-induced deflections. In these models, a contact force F was applied along the action line and the tooth deflection δ was considered as the deflection caused by gear body along the action line.…”

“…[11] is modified to test the performance of our two methods and the method used in Refs. [1,24]. The gears are modeled using the element type SOLID185 and the element shape of mapped hexahedral.…”

“…Gear parameters are given in Table 3 and Figure 3 shows the finite element model (a two-dimensional plane strain model) developed in Ansys. Figure 4 gives a comparison of three methods: the method reported in [1,24] and our methods 1 and 2. A constant force F (contact force per unit of tooth width F/b = 10 N/m) is applied on a single gear tooth from the tooth tip to the tooth root.…”