Thus the edges available for the metals commonly treated in the lathe find their maximum at 90° and minimum at 60°. The maximum requires no explanation, as when any edge is larger it ceases to be an acute edge.
With regard to the minimum of 60°, Babbage has pointed out that this is dependent not only on the strength necessary to resist the strain of the cut, but further and chiefly on the temper which must be preserved in the edge; and if this be less than 60° the mass of metal composing the extreme edge will be too small to carry off the heat generated by the cut, consequently the extreme edge would soon lose temper and become useless.
But these different edges are formed in very different ways according to the purpose for which the tool is intended; and this will be best understood by comparing the action of a hand-turning chisel with that of a pointed slide-rest tool. In the first case the edge is applied at an oblique tangent to the surface, and removes the shaving by passing under its whole width, much after the manner in which an apple is pared, or a ribbon unwound from a stick, when the lower edge of one turn just overlaps the top edge of the turn below it, and so on. In this case the shaving can be cleanly detached by one straight edge. But the position and motion of the slide-rest tool being perpendicular to the axis of the work, its action becomes that of uncoiling rather than paring; and as a cord or wire wound round a stick touches the face of the stick in one direction, and the coil next to itself in another, so in this case the width and thickness of the shaving lie in opposite directions, as illustrated by the dark band in [Fig. 10]. Consequently, unless the shaving be cut simultaneously in these two directions—viz., from the face of the work on one side, and from the matter under removal on the other, it is obvious that it must be torn from the work in one direction, thus increasing the labour and spoiling the appearance of the work if the tearing should be from its face. Now, in practice, at any rate in the rough cut, it is usual to take the width of the shaving from the superfluous matter; and if the tool be placed, as in [Fig. 11], it can only cut on one edge; thus the edge of the shaving will be torn from the face of the work, while the point of the tool will trace a fine thread in its progress along it, leaving the face with a rough unfinished appearance.
But if the edges be formed so that they can be placed as in Figs. [10 and 12], then both can cut simultaneously, and the screw-like trace of the point may be obliterated. This method of using the tool will leave the work with a good face from the first rough cut, leaving very little for the finishing cut to do; in addition to which the labour will be reduced to a minimum, thereby permitting a much heavier cut from the same amount of force. In turning any plane surface the corner of the edge should be sufficiently relieved from it to avoid the danger of catching; but, in turning cylindrical surfaces, if the tool be carefully made and placed, the slope of the upper surface will carry the corner out of cut. Experiment must decide the exact adjustment; but the great aim should be to keep the face of the tool next the work as nearly parallel with it as possible, because it is only that face which leaves any trace of the tool's action on the face of the work—the action of the other edge being lost with the shaving.
Illustration No. 4.(10, 11, 12)
Thus tools may be broadly divided into two classes—viz., single-edged and double-edged—remembering always that this distinction refers to the manner in which they should act, and not to the number of edges which it may be convenient to form on the same tool. In single-edged tools, whether there be one or many edges, each edge acts independently in removing its own shaving, and may therefore be formed separately. In this case a longitudinal section, showing the angle of the point, will give a true idea of that of the cutting edge. But, in the case of double-edged tools, as the two edges should co-operate in the removal of the same shaving, they must also be formed so that, while each lower face can occupy its proper position with regard to that surface of the work opposed to it, both edges shall possess the same degree of acuteness. In this case the two edges are formed by three planes—viz., two side faces and one upper surface common to both; and the angle of the point is now not only not that of the cutting edges, but has not even any fixed relation to them, for the cutting edges may vary some 25° or more on the very same longitudinal section of the point.
Prof. Willis has pointed out that in these tools the angles of the cutting edges depend on the section and plan angles of the point conjointly ([Fig. 8] is a section view; [Figs. 10, 11 and 12] are plan views). From this it follows that cutting edges of exactly the same angle may be obtained by a great variety of combinations in the plan and section angles; and in note A, U, of Holtzapffel's work, vol. ii. p. 994, Prof. Willis has given a table, showing some of the different combinations by which cutting edges of certain angles may be produced with accuracy and simplicity. The following short table is arranged from this source and though much abbreviated will be found sufficient for all ordinary purposes.