Research on the dynamic transmission error of a spur gear pair with eccentricities by finite element method

The existing lumped parameter model was commonly used to analyze the non-linear dynamics of gear systems, in which stiffness excitation and error excitation due to eccentricity were major considerations, while time-varying backlash caused by gear eccentricity and varying load were rarely concerned. In this paper, theoretical formulas of no load transmission error (NLTE) and time-varying backlash are presented, which are suitable for the double gear eccentricities system whose contact ratio is random. The finite element model is developed and confirmed by the results of dynamic transmission error (DTE) without gear eccentricity, furthermore, the DTE can be predicted by this model in consideration of gear eccentricities and varying load. Under three different cases (no backlash, constant backlash and time-varying backlash), the influence of backlash on DTE is investigated with the gear pairs suffering from sinusoidal varying loads. It turns out that the DTE curve jumps as the load direction changes, and the discontinuity value is just equal to the backlash size at that time. What is more, if the frequency of load change is high enough (here, mesh frequency is chosen), the DTE curve distributes in a certain region, whose lower outline is approximately (transmission error caused by tooth deformations is taken into account as well) consistent with the NLTE curve and the upper outline is approximately consistent with the curve of NLTE plus backlash.