As the core component of screw compressors, the rotor profile projected by a screw rotor on the rotor's end face is one of the most important parts of twin-screw compressors to study. The performance of the designed rotor profile directly affects the efficiency, accuracy, and service life of twin-screw compressors. The key to design and machine the rotors is to efficiently and highly accurately overcome problems in the mutual solution of male and female rotors. As for the design of the rotor profile, according to the principle of gear meshing, the meshing of any graph conforms to the Willis principle,¹ that is, at any moment during the transmission, the common normal at the contact point must pass through the instantaneous center point of this moment. Litvin² applied the principle of gear meshing to calculate the profiles of meshing components such as the screw rotor and gear. Since the screw rotor can be regarded as a special helical gear, the principle of gear meshing discussed by Litvin² became part of the basic theory of the design of the rotor profile. In the nearly half century since the screw compressor was invented, there have been many excellent patents regarding the rotor profile. According to Chen,³ Robert,⁴ and Yoshimura,⁵ these successful patents were all generated by the classic envelope method. Stosic et al.⁶ proposed a method to generate the rotor profile using the meshing line equation of male and female rotors of the twin-screw compressor based on the conjugate principle. According to the conjugate principle, this method determined the corresponding rotor profile based on the distance between the rotor axes, the number of teeth, and the given meshing line equation. Stosic,⁷ Zaytsev and Ferreira,⁸ and Fong et al.⁹ designed the male and female rotor profiles through the defined rack profile and a meshing line equation that can be optimally controlled.^10–13

中文翻译：

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基于Alpha Shape算法的边缘检测方法求解螺杆压缩机转子的共轭齿形

作为螺杆式压缩机的核心部件，螺杆转子投射到转子端面上的转子轮廓是双螺杆压缩机最重要的部分之一。设计的转子轮廓的性能直接影响双螺杆压缩机的效率，准确性和使用寿命。设计和加工转子的关键是要高效，高精度地克服公，母转子相互解决的问题。至于转子轮廓的设计，根据齿轮啮合的原理，任何图形符合威利斯原理，的啮合¹即，在任何时刻在发送期间，在接触点处的共同法线必须穿过此刻的瞬时中心点。Litvin ²运用齿轮啮合原理来计算啮合部件的轮廓，例如螺杆转子和齿轮。由于螺杆转子可以看作是一种特殊的斜齿轮，Litvin ²讨论的齿轮啮合原理成为转子轮廓设计基本理论的一部分。自发明螺杆压缩机以来的近半个世纪中，已经有许多关于转子轮廓的优秀专利。根据Chen，³ Robert，⁴和Yoshimura的说法，这些成功的专利都是通过经典的包络法生成的，其中⁵项是成功的。Stosic等。⁶提出了一种基于共轭原理的双螺杆压缩机公，母转子啮合线方程生成转子轮廓的方法。根据共轭原理，此方法根据转子轴之间的距离，齿数和给定的啮合线方程式确定相应的转子轮廓。Stosic，⁷ Zaytsev和Ferreira，⁸和Fong等。⁹通过定义的齿条轮廓和可以最佳控制的啮合线方程式设计了公转子轮廓和母转子轮廓。^{10 –13}