Method for calculating the tooth root stress of plastic spur gears meshing with steel gears under consideration of deflection-induced load sharing

The operational behavior and, in particular, the bending strength of thermoplastic gears are substantially influenced by the significant increase in contact ratio under load. According to current analytic calculation standards and guidelines, this effect is neglected when tooth root stress is calculated. Using numerical methods, such as the finite element method (FEM), a consideration of deflections is possible but the usage is complex and extensive in engineering practice compared to recomputing guidelines or standards like VDI 2736 or ISO 6336. In this work, a method is presented for calculating the nominal tooth root stress based on existing analytic guidelines, taking the actual contact ratio into account. Based on the example of three test gear geometries, the results are compared to existing guidelines, as well as numerical computations, showing that the presented method correlates well with the latter.