中文摘要：

假设在已知多头螺杆泵断面具体型线方程的条件下，即不讨论多头螺杆泵的断面的具体型线方程，沿多头螺杆泵的轴向给出了螺杆泵的定、转子型面表述矩阵方程式。在确定了螺杆泵转子断面的具体型线方程后，就可以很方便地进行螺杆泵的定、转子空间型面的数学建模，为其数控加工程序的编制和型面精度测量提供理论依据。

英文摘要：

Nowadays ,multi-lobe progressing cavity pump is widely applied in oil industry. Based on the assumption that the geometric shape of end-section of multi-lobe progressing cavity pump is known, the modeling method of the complex curve surface is discussed and the matrix express equation of the rotor along axial direction is given. With such coordinate transformation equation,as soon as the geometric shape is predetermined,the spatial curve of the rotor and stator of the multi-lobe progressing cavity pump can be approached conveniently. This result provides the theoretical facts for the programming of NC machining and measurement of rotor and stator.