The true bending stress in spur gears.

Introduction In today’s gear industry, designers typically utilize rating methods of gear load capacity based on standards or the customary design rules. In these methods, nominal quantities are calculated in order to characterize the stress field in the gear. These nominal quantities are compared with limit values derived from tests using gears as specimens. In the case of tooth bending strength, a cantilever-beam model is generally used to compute the bending stress. With this approach, Lewis in 1892 first calculated the tooth root stress of spur gear teeth (W. Lewis, “Investigation of the Strength of Gear Teeth,” Proceedings of Engineers Club, Philadelphia). This model is still the basis for standard calculation methods successfully used in gear design. However, the local stress state—the “true” stress—in the tooth root fillet may be different from the nominal values obtained by this method. In truth, the calculation of the maximum tensile stress at the tooth root is a three-dimensional problem: The plane strain or plane stress model can be used without approximations only in the case of infinite, or infinitesimal, face width. In Reference 1, starting from the analytical solution of Jaramillo (Ref. 2), Wellauer and Seireg introduced a study of the bending stress of gear teeth based on a cantilever-plate model. This method shows clearly that a threedimensional model must be used to evaluate the variation of the tooth root stress along the face width. Current numerical methods, FEM and BEM, for example, are available for the solution of the elasticity problem for complex domains. Thus it is possible to calculate accurately the local strain and stress state in the tooth root, taking into account the real geometry of both gear THE “TRUE” BENDING STRESS in SPUR GEARS