泵用圆弧转子造型与尺寸的参数化与最优化研究

Research of Parameterization and Optimization of Shaped-profile and Size of Circular Arc Rotor Pair for Roots Pump

为实现泵用圆弧转子的造型参数化与尺寸最优化,由共轭关系构建峰圆弧与谷圆弧两类情况下的全参数型线方程与三维模型。其次,以节圆半径和形状系数为设计变量,圆弧转子副所占方体的空间体积为目标函数,形状系数上限值、中心距取整和宽径比为约束函数,构建优化模型和实例分析。结果表明,峰圆弧与谷圆弧转子的两类型线,经三维模型验证,均能实现零件与装配件的全参数化;容积利用系数的拟合精度高,3阶的多项式拟合足能满足设计要求;实例参数下103 mm节圆半径和1. 394 4形状系数的优化结果,说明转子尺寸存在优选的必要性。为泵用其它型线的转子提供了一种全参数的优化设计方法。

In order to achieve integration of shaped-profiles parameterization and size optimization of rotor pair for roots pump.From the common circular arc rotor as a example and the conjugate rotation relationship of two identical rotors,full parameter coordinate equation and its corresponding3D model are derived in both cases of circular arc as peak profile or circular arc as valley profile.Then,from pitch circle radius and shape coefficient as two design variables,the minimum wrapping cube space volume of rotor pair as an objective function,the upper limit of the shape coefficient and rounded-value of center distance and the diameter ratio of the rotor and other as constraint functions.The size optimization model is derived,then an instance is operated and its results are analyzed.All results show that the two sets of coordinate equations described for rotor shaped-profiles with circular arc as peak profile or circular arc as valley profile is verified absolutely correct by its corresponding3D parameter model of single part and assembly rotor parts.Only by the three-order polynomial fitting,the fitting accuracy of the volume utilization coefficient is higher to be met the design requirements.The optimization selecting of rotor size is necessity emphasized by the optimal pitch circular radius of103mm and the optimal shape coefficient of1.3944,etc.It is concluded that the full parameter optimization design method can be used for other shape rotor of roots pump.