A mathematical model for manufacturing ball-end cutters using a two-axis NC machine

The paper presents a mathematical model for producing a ball-end cutter by first defining the helical angle as the angle between the cutting edge and the centre-line axis. The velocities of the cutter in the radial and axial directions are then derived based on a given rotating speed The radial feed speed of the grinding wheel is calculated according to the groove cross-se ction passing through the centre of the ball-end cutter. A ball-end cutter of constant helical angle is designed and produced by using a two-axis NC m achine. To enhance the dimensional accuracy of the mathematical model, a co mpensatory grinding operation is also proposed and applied to the ball-end cutter. A ball-end milling cutter is selected for design and manufacture to illustrate the effectiveness of the proposed design and numerically contro lled (NC) manufacturing procedure. The result of data verification indicate s that the proposed procedure is systematic, straightforward and reliable. The ball-end cutter that is designed, refined and produced bq using a simpl e two-axis NC machine is accurate enough to meet the specified tolerance.