摘要
以高阶椭圆齿轮为研究对象,根据非圆齿轮啮合的基本原理,建立起非圆齿轮节曲线的数学模型。应用MATLAB的数值计算方法,对椭圆齿轮节曲线的凹凸性进行判断,并对其弧长进行精确的计算。运用三次样条插值法进行拟合,绘制出椭圆齿轮副的节曲线,从而使椭圆齿轮节曲线的设计更加精确快速。另外,还以Pro/E为建模平台,以其提供的关系特征为基础,建立了渐开线齿形与椭圆齿轮基本参数的对应关系,并成功地实现了一对椭圆齿轮的参数化造型设计,为渐开线椭圆齿轮的原形制作和数控加工提供了方便。
Abstract
We established mathematical model of pitch curve of non-circular gear according to the meshing theory of non-circular gears. We studied the convex-concave and arc length of the pitch curves of higher-order elliptic gears using MATLAB. We used cubic spline interpolation method to fit and draw out the gear pair of pitch curve graph in order to make non-circular pitch curve of gear more quickly and accurately. A corresponding relationship was built up among the models of the involute tooth profiles and the basic parameters of elliptic gears by Pro/E. Parametric modeling of a pair of involute elliptic gears was achieved. The convenience for NC machining and prototype＇s manufacturing was provided.
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