基于向量方法的通用涡旋型线生成研究

Generation of General Scroll Profiles Based on Vector Method

以向量计算作为研究工具,针对单一型线设计不利于实际多性能需求的柔性化设计,利用Taylor级数思想和微分几何理论推导出基于泛函的通用涡旋型线方程。通过平面曲线啮合理论和泛函通用型线方程,得出型线向量在其啮合点处的法线和切线方向分解后的向量大小的关系,并证明其沿啮合点法线方向分解的向量大小可以用泛函通用型线方程表示。这种向量表示方法在型线生成时省去求积分的繁琐,有助于系数变化时生成的型线特性的研究。用向量计算的方式推导出涡旋型线啮合条件,便于在MATLAB上生成涡旋型线及共轭型线,因为向量矩阵的表示在运算中更符合MATLAB的计算规则,加快了运算速度,有助于通用涡旋型线的研究设计。

Using vector method as a research tool,aiming at the restriction of single profile,we gave the general scroll profiles equations based on functional expression with Taylor series and differential geometry theories.Through planar curve meshing theory and general scroll profiles equations,we proved the department vector size relationship between normal and tangent direction of scroll profile at its meshing point,also its normal vector size can be expressed by general scroll profiles equation. In creating of scroll profiles,this vector expression saves hassle of quadrature by coefficient changes. Derive the conjugation meshing condition with vector method is easy to create scroll profiles and conjugated profiles based on the MATLAB,since vector method is in line with the calculation ruled of MATLAB,which can speed up the calculations,contribute to research on the designing of profiles of the scroll compressors.