Formation of nonsmoothness lines in optimization of screw pairs in screw pumps

Computer modeling of screw pairs in screw pumps reveals the formation of nonsmoothness lines on the screw surface (with the growth of the height of the helical tooth) conjugate to the smooth helical surface. The mathematical explanation of the appearance of such lines represents considerable interest for the theory and practice of pumps manufacturing. In this paper we show that one can explain the mentioned phenomenon by studying a wider problem, namely, the bifurcation of regressive points on a plane contour conjugate to the smooth one.