中文摘要：

利用微分几何与啮合理论建立变齿厚内齿轮包络鼓形蜗杆齿面数学模型。基于有限元法分析了齿面接触应力在不同工况下的载荷分布情况,探讨了内齿轮沿齿宽方向齿面倾角δ对鼓形蜗杆副的影响。通过齿面应力分布与齿间载荷分配的分析,比较了有限元法与经验强度公式法的结果,验证了有限元法的可行性。结果表明：变齿厚内齿轮齿面应力主要分布于内齿轮中间平面一侧,最大应力出现在内齿轮齿顶处;第一、二个啮合齿载荷分配较高,另外两个啮合齿载荷分配较小;在额定载荷工况下,齿间载荷分配相对均匀。

英文摘要：

By using the differential geometry and meshing theory, the mathematical model of the tooth surface of drum-type worm gear enveloped by internal variable-tooth-thickness gear is established. Through finite element method,the load distribution under different conditions is analyzed, and the effect of the inclination angle δ along tooth width direction on the worm gear pair is discussed. The stress distribution along tooth surface and the load distribution among teeth are analyzed, and the finite element method is compared with the empirical strength formula method. The results show that the tooth surface stress is mainly distributed in the middle plane of the internal gear,and the maximum stress appears at the top of the internal gear teeth. The loads of the first two meshing teeth are higher than the rest two meshing teeth. In the rated load condition, the tooth load distribution is relatively uniform.