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本文应用南开大学齿轮啮合理论研究组提出的“齿轮啮合的数学理论”,系统地研究了蜗杆轴截面为圆弧齿廓的圆柱蜗杆传动啮合原理。用矢量解析法推导出了这种蜗杆传动啮合原理的下列计算公式:1)、蜗杆齿面方程式;2)、啮合方程式;3)、接触线方程式,4)、啮合区方程式;5)、一类界限曲线方程式;6)、二类界限曲线方程式;7)、诱导法曲率计算公式;8)、接触线方向与相对速度方向夹角的计算公式。这些公式可用于分析蜗杆轴截面为圆弧齿廓的圆柱蜗杆传动的啮合质量。
In this paper, the mathematical theory of gear meshing proposed by the research group of gear meshing theory of Nankai University was used to systematically study the meshing principle of cylindrical worm gear with worm tooth profile in circular arc profile. The following calculation formula of the meshing principle of worm drive is deduced by the vector analytic method: 1) the worm tooth surface equation; 2) the meshing equation; 3) the contact line equation; 4) the meshing area equation; Class boundary curve equation; 6), the second type of limit curve equation; 7), induction method curvature formula; 8), contact line direction and relative speed direction angle formula. These formulas can be used to analyze the meshing mass of a cylindrical worm drive with an arcuate tooth profile on the worm shaft.