The surface geometry of rollers with skew rolling of steel balls

The ball shaping process is considered from a geometric viewpoint as a meshing pair of conjugate surfaces at the precise rolling stage. This viewpoint offers a simple method and procedure for determining the groove design of each forming roll in the skew rolling process of steel balls. Based on the envelope theory, a shape design of the forming roll is a composite of two helical grooves with constant pitch and variable pitch. Through this method, the mathematical model of the forming rolls for skew rolling, which can be used to design and manufacture a skew roller for manufacturing steel balls, can be derived and simulated. Finally, the required cutter path is provided for a spherical-end cutter in the manufacturing process. The size of the spherical-end cutter may be identical with or smaller than that of the steel ball.