Numerical calculation and experimental measurement for gear mesh force of planetary gear transmissions

In this paper, we propose a numerical method to calculate the dynamic mesh forces of planetary gear transmissions (PGTs). In this model, the effects of addendum modification are included in the time-varying mesh stiffness (TVMS) and then the influence of TVMS and relative mesh phase on the dynamic mesh forces are considered in the proposed model. To verify the proposed model, an experimental method is proposed to measure the dynamic ring-planet mesh forces by using gear tooth root-fillet strain signals. Static mesh experiments and dynamic mesh experiments are carried out to obtain the strain signals. To measure the dynamic mesh force, the loaded tooth contact analysis (LTCA) method and quasi-static experiments are carried to determine the coefficient matrix which is used to descript the relationship between the mesh force and tooth root-fillet strain. Finally, calculated mesh forces and measured forces are compared and discussed. Results indicate that the proposed experimental method can effectively measure the dynamic ring-planet mesh forces, and the numerical mesh forces agree well with the measured mesh forces.