Novel Parabolic Rotor of Roots Pump: A Theoretical Study
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摘要: 为降低共轭泄漏和缓解转子的动不平衡,提出一款新的抛物线转子。基于抛物线的成形原理,从几何关系、理论型线、实际型线、取值上限、坐标方程和参数化模型等6个方面展开研究;其次,以节圆半径和形状系数为设计变量,转子副所占方体空间的最小体积为目标函数,构建优化模型和实例分析。结果表明:抛物线转子因更大的综合曲率半径和较小的顶部几何特征,既能降低共轭泄漏,又能缓解转子动不平衡,最大形状系数为2叶的1.4871,3叶的1.3865,4叶的1.3159;非1.3865最大形状系数的1.367最优值,说明转子尺寸须优化。Abstract: A novel parabolic rotor of Roots pump was developed.The mathematical study of parabolic rotor included:the formulation of geometric relationship,parameterization of 3 D model,derivation of ideal and realistic shape-profiles,upper-limits of shape-factor and coordinate equation.The upper-limits of shape-factor for 2-,3-and 4-lobes were 1.4871,1.3865 and 1.3159,respectively.The influence of the pitch-circle radius and shape-factor on Roots pump's volume,approximated by a wrapping cubic volume of rotor-pair,was investigated for design optimization.The optimized parabolic rotor with 3-lobes was simulated.The results show that the new parabolic rotor is capable of reducing the conjugate leakage and easing the dynamic imbalance because of larger integrated curvature radius and simpler geometric feature at the top.However,its optimal shape-factor was 1.367,instead of 1.3865,suggesting a further design optimization of rotor geometry.
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