Transmission error modeling and analysis of herringbone gear drive based on the measured manufacturing errors

Transmission error (TE) is an important index affecting the positioning accuracy and dynamic performance of gear drive. An original discrete slice model for TE analysis of herringbone gear drive based on the measured manufacturing errors (ME) is proposed, involving tooth surface error, cumulative pitch error and alignment error of double helical surfaces. In the model, herringbone gears are discretized into a series of slices in order to deal with the 3D contact problem. The measured cumulative pitch error and alignment error are described as the position error of slices, while the measured tooth surface error is constructed as the real surface shape by B-spline method. Thus, the measured ME are converted into the contact gaps of slices. The compatibility and equilibrium equations under error and load conditions are derived from the kinematic geometry and elastic mechanics. Based on the discrete slice model, the relationship between measured ME and TE are established explicitly. The ME of herringbone gear drive is measured, the effects of measured ME on TE under no-load and load conditions were analyzed, and TE test of herringbone gears was carried out. The test results are consistent with the properties and values of simulations, which verifies the proposed model.