泵CAT出厂试验中椭圆包络线的确定方法

Determination of ellipse envelopes in ex factory test of pump CAT

在水泵性能计算机辅助测试系统中 ,进行出厂试验的测试结果判别需要分别以标准性能曲线上的小流量点、设计点、大流量点为中心作三个椭圆 ,并作这三个椭圆的包络线。本文通过对椭圆、包络线、切点相互关系的分析 ,建立了确定包络线数学模型的非线性方程组 ,同时 ,提出了一种在Newton -Raphson迭代法基础上加以改进的包络线多项式系数数值求解方法 ,该方法适用于计算机求解。

During ex factory test of pump CAT, it's necessary to draw three ellipses at minor discharge point, designed point and large discharge point, and then, to draw the envelopes of these ellipses. Based on the analysis to ellipses, envelopes, tangent points and their relationship, this paper establishes non-linear equations which is used to determine the mathematical model of envelopes. At the same time, an imprived Newton-Raphson numerical solution algorithm is presented. The algorithm is suitable for computer solving.