Determination of composite meshing errors and its influence on the vibration of gear system

The tooth deformation is separated into linear global term and nonlinear local contact term, and a modified loaded tooth contact model is built. The nonlinear contact problem is transformed into solving a set of linear algebraic equations by considering two iterative loops. According to the deformation relationship of contact points, the mesh stiffness and composite meshing errors can be obtained when the error distribution on tooth surface has been known. By introducing the stiffness exciting force, the time-variant differential equations of motion are transformed into the time-invariant ones of which the steady-state solution can be calculated using Fourier series method. Taken a helical gear pair as an example, the influence of gear errors is studied under different torque levels and input speeds. The results show that the mesh stiffness will decrease for lightly loaded gears as the effect of gear errors, which will cause the system resonance speed decreased. As the impact of contact ratio and tooth deformation, the amplitude of composite meshing errors is much smaller than the original amplitude of manufacturing errors on tooth surface. The method can be used to analyze the influences of different types of manufacturing errors and different error distributions on system vibration, which provides an effective means to establish the control principles for gear errors.