Two-Sided Contact Mesh Stiffness and Transmission Error for a Type of Backlash-Compensated Conical Involute Gear Pair

Abstract

Both the drive- and back-side contact mesh stiffnesses (two-sided contact mesh stiffness) for a new type of conical involute gear (NTCIG) is developed analytically. Instead of the conventional spring preload anti-backlash method, an active control strategy to eliminate the time-varying backlash is presented by adjusting the axial displacement of the driven gear. The dynamic transmission error (DTE) of the gear pair is calculated under different load excitations to analyze the differences between the drive- and back-side meshes under a time-varying backlash with anti-backlash conditions based on the NTCIG model with an eccentricity error. Considering the additional rotational angle caused by the anti-backlash and the differences from the two-sided contact, the theory of no-load transmission error for the NTCIG is modified by agreeing considerably well with the low component of the DTE. Moreover, the DTE curve under varying load excitations showed that the dynamics of the NTCIG improved considerably after backlash compensation. The drive- and back-side tooth meshes were analyzed according to the DTE of NTCIG with backlash control under various external excitations at different speeds and variable initial phases, frequencies, and amplitudes of the sinusoidal load.