面齿轮副小轮拓扑修形设计及啮合性能分析

Design of topological shape modification of auxiliary pinion of face gears and analysis of meshing performance

为改善面齿轮啮合性能,设计了小轮齿廓、齿向修形曲线,将3次B样条拟合的修形曲面与小轮理论齿面叠加构造精确的拓扑修形齿面,建立了小轮拓扑修形面齿轮副TCA、LTCA计算模型,并试验验证了理论分析的正确性。算例分析表明:小轮拓扑修形能获得开口向下2阶抛物线几何传动误差,接触路径与齿根倾斜,较传统面齿轮副,有效重合度提高了约10%,容差能力提高了400%;各载荷下承载传动误差波动幅值均减小,齿面载荷分布变化均匀,轮齿进入和退出啮合时承受载荷变小。

To improve the meshing performance of face gears,in this study,we designed a tooth profile and a direction modification curve on a pinion. A topologically modified tooth surface was represented accurately by the sum of two vector functions that determined the theoretical tooth surface and the deviation surface,and the latter was fitting three B-splines on the tooth surface grid. We then established computational models for the tooth contact analysis（ TCA） and loaded tooth contact analysis（ LTCA） of face gear pairs with the topologically modified pinion. To verify our theoretical analysis results,we then conducted an experiment. The results show that the proposed design enables the transmission error to form a second-order parabolic function by opening downward and tilting the tooth contact path. Compared with traditional face gear pairs,the effective overlap ratio increas by about 10% and tolerance ability increases by 400%. Under different degrees of torque,the fluctuation amplitudes of the loaded transmission errors all decrease significantly. The load distribution changes gently on the flank of the tooth,and the load is reduced when gear tooth enters and withdraws.