Analysis of the Transmission Error and Mesh Stiffness of Load-Induced High Contact Ratio External Spur Gears

The tooth deflections caused by the transmitted load in spur gears results in a sooner start of contact (and a delayed end of contact) and parabolic loading and unloading processes along the additional contact intervals. For spur gears with contact ratio close to 2 and heavy load, the increase on the length of contact may lead to an effective contact ratio above 2. In this case, the interval of single tooth contact is eliminated and intervals of three pair tooth contact arise inside the additional contact intervals. The load sharing, meshing stiffness and loaded transmission error are therefore influenced, and not adequately described by the dynamic behavior models for high contact ratio spur gears. This paper presents an analytic model for the time-varying mesh stiffness and quasi-static transmission error of spur gears with contact ratio greater than 2 under loading conditions.