S型齿廓少齿数齿轮的几何建模与强度分析
Geometric Modeling and Strength Analysis of Gear with S-Shaped Tooth Profile and Small Number of Teeth

针对渐开线少齿数齿轮副因齿面接触应力大导致承载能力低而难以广泛应用的问题，提出了一种能够实现 凹凸弧齿廓啮合的基于正弦曲线齿条刀具加工的S 型齿廓．给出了齿条刀具正弦函数的曲线方程，推导了S 型齿廓 数学模型，建立了S 型齿廓少齿数齿轮的几何模型，分析了S 型齿廓的诱导法曲率的计算方法，开展了齿轮副接触 应力的有限元仿真分析，并与渐开线少齿数齿轮作了对比分析．结果表明，相互共轭啮合的S 型齿廓齿轮副具有相 同的齿廓方程形式，能够用一把齿条刀具或滚刀加工，且能较大幅度地提高少齿数齿轮副的承载能力．
The large contact stress of involute gear pair with small number of teeth causes a low load-carrying capacity and failure in wide application．To solve this problem，an S-shaped tooth profile was proposed that could achieve concave-convex profile meshing based on sinusoidal rack tool．A curvilinear equation of sinusoidal rack tool was introduced， a mathematical model of S-shaped tooth profile was deduced，and a geometry model of S-shaped tooth profile with small number of teeth was established．Then，the calculation method of induced normal curvature of Sshaped tooth profile was analyzed，simulation analysis on the contact stress of gear pair was conducted by FEM，and finally a comparative analysis on S-shaped tooth profile gear and involute gear with small number of teeth was made．The results show that the S-shaped tooth profile gear pair with mutual conjugate meshing shares the same equation， and one common rack tool or hob can be used to machine them，improving greatly the load-carrying capacity of the gear pair with small number of teeth