Innovative approach and method of conjugate-contour construction for Roots rotor

ObjectiveThe conjugate-contour of Roots rotor has attracted much attention because of its characteristics that directly determine the product performance; whereas some common curves used in its structure often fail to meet the specific performance requirements of products. Therefore, an innovative approach and method are proposed which is suitable not only for common known but also for current unknown conjugate-contour curves.MethodsThe concepts of engagement-distance as length and engagement-angle as direction of conjugate-vector from the pitch-point to the engagement-point was proposed, the intrinsic logic relation of engagement-distance and engagement-angle was summarized, and then the innovative approaches and methods of conjugate-contour construction were proposed.ResultsThe results show that different conjugate-vector functions uniquely determine different conjugate-contour shapes; different conjugate-contour shapes directly determine different output performance; the innovation of output performance is equivalent to the innovation of conjugate-contour; the engagement-angle is equal to the arc cosine function of the first derivative of engagement-distance to the rotation-angle of pitch-circle; the innovation of the conjugate-contour is equivalent to the innovation of the engagement-distance function. Different innovation-combinations of orders and coefficients of engagement-distance polynomial-function can innovate more current unknown types of the conjugate-contour curve, etc. The innovative approaches and methods have the application-value for any conjugate-contour construction of the convex cylindrical-gear and cylindrical-rotor, so as to provide some reference and point out the direction for subsequent expand research.