Influence of profile modification on the transmission error of spur gears under surface wear

The load distribution, transmission error, and time-varying meshing stiffness of spur gears are all influenced by the teeth dimensions and profiles shape. Any modification on the teeth geometry, as a profile relief frequently used to avoid the mesh-in impact, will affect all these parameters and the entire dynamic behavior of the gearset. In addition, due to the friction between contacting surfaces, wear arises at the teeth flanks. This causes the shape of the meshing profiles to change, which will affect the load distribution and the transmission error for the subsequent meshing cycles. And this new load distribution causes a surfaces wear different form that of the previous meshing cycle. Consequently, the wear depth increase is different at any contact point -because the load and sliding velocity are different- and at any meshing cycle as well -because the load distribution changes with the accumulated wear-. And all the above is also influenced by the profile modification the teeth were manufactured with. In this paper, a simple, analytic model of meshing stiffness, load sharing, and transmission error for spur gears with profile modifications including the influence of surfaces wear is presented. The evolution of the transmission error with the number of wear cycles is studied, and the optimal profile modification for minimizing the dynamic load induced by the transmission error is investigated.