罗茨转子共轭轮廓曲线的存在与极限条件式

Existence and Ceiling-Limit Formula of Conjugate Profile Curves of Roots Rotor

为共轭轮廓曲线的类型创新或现有类型的性能评估,基于转子与配对转子轮廓间的共轭原理,依序建立出以法向长度和传动角为构造参数的共轭轮廓方程,构建出其能作为共轭轮廓曲线的存在关系式和不发生共轭轮廓曲线几何干涉的极限关系式。结果表明:量纲一化法向长度对转角的一阶导数等于传动角的正弦函数为共轭轮廓曲线的存在条件;某一转角下存在传动角对转角的一阶导数等于0、+1分别为非直线、外直线轮廓转子取得上限形状系数的极限条件;传动角对转角的一阶导数恒等于-1,为内直线转子定值形状系数的独有特性。

Focusing on innovating new conjugate profile curves or performance evaluation of existing conjugate profile curves,from conjugate principle between a rotor profile and its matched rotor profile,the coordinate equations of conjugate profile curves with normal length and driving angle as structural parameters was established,the existence conditions and ceiling-limit conditions without geometric interference of the conjugate profile curves were derived successively.The results show that the first derivative of dimensionless normal length with rotation angle equals to sine function of driving angle is the existence condition of conjugate profile curves;at a certain rotation angle,the first derivative of dimensionless normal length with rotation angle equals to 0 or 1 is separately ceiling-limit conditions of non-linear or outer linear rotor with maximum shape factor;first derivative of dimensionless normal length with rotation angle identically equals to-1 is the unique characteristic of the inner linear rotor with fixed shape factor.