中文摘要：

在单螺杆泵转子和定子是刚性接触的假设前提下,以短幅内摆线线型理论为基础,建立多元变量多目标函数的双头单螺杆泵短幅内摆线线型优化的数学模型。利用数值积分法对目标函数的复杂积分进行处理,求出变幅系数k在不同取值范围内的复杂积分拟合方程,确定约束条件,简化了线型优化的数学模型。采用复合形法对该数学模型进行优化,可计算出优化范围内各点的几何参数。结果显示,当变幅系数k=0.5、等距线半径趋于无穷大时线型结果最好。将优化结果应用在双头单螺杆泵的线型设计中,计算出线型各点绕中心做螺旋运动时空间位置坐标,利用OpenGL技术建立双头单螺杆泵短幅内摆线线型的参数化运动仿真模型,实现优化设计与运动仿真相结合,为多头单螺杆泵线型理论的深入研究提供一个可视化的操作平台。

英文摘要：

Based on the assumption that the rotor should contact with the stator liner rigidly, the mathematical model of linear optimization with multi-variable and multi-objective for double helix single progressing cavity is set up with the linear theory of short-amplitude cycloid. The complex integrated forms of objective function are processed with numerical integration method. The fitting equations of the objective functions are obtained according to the scope of the variation-coefficient k. Then, the constraints of mathematical model of linear optimization are determined. Moreover, this study simplifies the mathematical models of linear optimization. The geometric parameters within the range of optimization are calculated with the complex method to optimize the simplified mathematical model. The results show that the linear type is optimal when the coefficient of variation k is equal to 0.5 and equidistant line radius tends to infinity. The optimized results are applied to the linear design of double helix single progressing cavity pump. The coordinates of points in the spiral movement are calculated. OpenGL technology is used to set up the parameterized simulation model of short-amplitude cycloid for double helix single progressing cavity. The simulation contributes to the integration of optimal design and motion simulation, and provides a visual operating platform for in-depth study of linear theory with multi-helix single progressing cavity.