A model for the study of meshing stiffness in spur gear transmissions

This work describes an advanced model for the analysis of contact forces and deformations in spur gear transmissions. The deformation at each gear contact point is formulated as a combination of a global and a local term. The former is obtained by means of a finite element model and the latter is described by an analytical approach which is derived from Hertzian contact theory. Then the compatibility and complementary conditions are imposed, leading to a nonlinear system of equations subjected to inequality restrictions that should be solved once the position of each gear centre is known. A numerical example is presented where the quasi-static behaviour of a single stage spur gear transmission is discussed, showing the capabilities of the methodology to obtain the Loaded Transmission Error under several load levels as well as some other related measures such as load ratio or meshing stiffness.