Determination of an optimum geometrical arrangement of workpiece in the ultrasonic elliptic-vibration shoe centerless grinding

This paper clarifies the influence of the geometrical arrangement of the workpiece on workpiece roundness in the ultrasonic elliptic-vibration shoe centerless grinding, and determines an optimum geometrical arrangement for minimizing the roundness error of the workpiece. The influence of the geometrical arrangements (alpha, beta, phi) of the workpiece on workpiece roundness were investigated by computer simulation involving a cylindrical workpiece of 5 mm in diameter with an initial roundness error of 25 mu m. The results indicated that the final roundness error of the workpiece after grinding reaches a minimum at alpha+beta=7 degrees for various values of phi. It was found that the smaller the blade angle 0, the more precise the workpiece in terms of final roundness. Practical grinding operations involving pin shaped workpieces, such as SKH51, 5 mm in diameter and 15 mm in length, were carried out on the experimental apparatus previously developed. The experimental results agreed closely with those obtained by the simulation, showing that the optimum geometrical arrangement of the workpiece can be determined at alpha+beta=7 degrees and phi=60 degrees, in which the workpiece roundness was improved from an initial roundness error of 25 mu m to the final one of approximately 0.6 mu m.