泵用直谷转子的参数化造型与尺寸优选

Formulation of Parameter Model and Size Optimization of Rotor Profiles with Linear Valley of Roots Vacuum Pump

为实现罗茨泵直谷转子型线的造型参数化与尺寸最优化。基于直谷型线与峰型线的共轭关系,通过法线法的旋转和平移的矩阵变换,构建出实际型线最简洁的全参数化的坐标方程与3D模型;其次,以节圆半径为设计变量,转子副所占方体空间的最小体积为目标函数,构建单变量优化模型和实例分析。结果表明:直谷转子的最大谷部尺寸以容积利用率最小化为代价,多适用于有粗轴需求的特定场合。转子叶数对泵体积的影响很大,3叶是2叶的1. 84倍; 4叶是2叶的3. 04倍;直谷型多适用2叶转子。参数化转子副的实例造型和节圆半径的优选结果,说明型线方程正确,优选结果可靠。为泵用其它型线的转子,提供一种全参数的造型和设计方法。

The rotor profiles with linear valley for roots pump were analytically modeled first with the theoretical profiles for size optimization. Next,the parametric,concise coordinate equation and 3-D model of the realistic profiles and the size optimization equation were derived by mathematical manipulation and approximation with proper assumptions. And finally,the validity of the parameter model and size optimization equation was proved with a specific example. The results show that the valley size can be maximized by minimizing the volume utilization,and only roots pump with a thick shaft requires the maximum valley size. The lobe number strongly affects the pump volume. For example,the volume of roots pump with 3（ 4） lobes is 1. 84（ 3. 04）times larger than that of the pump with 2 lobes,indicating that 2 lobes are suitable for the rotor profiles with linear valley.