Geometry of Radial Displacement (Screw) Rolling on Plane with Inverse Problem Solution

This article suggests a geometrical model of radial displacement rolling on the plane. Finite formulae of calculating the spatial position parameters of the rollers and the workpiece are presented as a solution for rectangular triangles drawn in a plane perpendicular to the rolling axis. The properties of process gorge using the angles of expanding and feeding the workpiece relative to the roller axis are used to solve the inverse problem of determining the deformation region radius at a known roller radius. As shown by evaluating the solution for accuracy, its maximal error in the workspace of SDR does not exceed 0.5%.