THE TORQUE AND THRUST FORCE IN TWIST DRILLING .1. THEORY

Previously derived expressions for the torque and the thrust force generated by spade drills are examined with a view to determining their applicability to twist drilling. This leads to the question whether, to every twist drill, there exists an equivalent spade drill. In turn, this demands the resolution of the problem that, in general, the rake angle varies much more with twist drills than with spade drills as the lip is traversed from the chisel edge to the margin. This latter phenomenon is shown to present no impediment since the parameters of interest are the average rake (and obliquity) angles as seen by the drill and, except with very small diameter drills, the average rake and obliquity angles are much the same for twist and spade drills. Accordingly it is concluded that to every twist drill an equivalent spade drill can be found, the condition of equivalence being that the chip deflection and the chip thickness ratio produced by the spade drill are the same as those produced by the twist drill. From this it follows that expressions for the torque and the thrust which are applicable to spade drills are equally applicable to twist drills. These expressions have been derived for the condition that the removal process is quasi-orthogonal, and this is satisfied if the drill diameter is sufficiently large in relation to the chisel edge length. The condition that the coefficients appearing in these expressions are constant is that the equivalent spade drills be geometrically similar. Hence, if the torque and the thrust generated by a set of twist drills are to be represented by expressions with constant coefficients, it is necessary that the equivalent spade drills and therefore, the set of twist drills be geometrically similar.