Engineering estimates of strain and strain rate in helical rolling of balls

The subject of the research is the process of helical rolling of balls with a diameter of 15 to 125 mm for grinding mills. Analytical estimates of the equivalent strain and the rate of equivalent strain averaged within the volume of the metal were obtained. A simple formal model of equivalent strain distribution within the ball in the direction of the rolling axis is also proposed. The proposed solutions predict that in the working ranges of the rolling parameters the value of the volume-averaged strain can vary from about 0.6 to 5, meanwhile in the jumper area the equivalent strain is two orders of magnitude higher than in the axial zone. It is shown that the principal influence on the magnitude of strain is caused by ovalization of the workpiece during rolling, which leads to multiple repeated deformation of the same volumes of metal when the workpiece rotates. As an example, the use of obtained estimates to calculate the strain, strain rate, flow stress, force and rolling torque under the conditions of the real experiment performed by other authors is shown. The proposed models allow solving engineering problems of certain classes (for example, calculation of energy-force parameters) without using FEM software packages and are recommended for optimization and real-time control of the helical rolling of balls.