An examination of the nature of the force required to separate any shaving will show the importance of close attention to the above rule. Babbage has pointed out that this process involves two forces, which, though simultaneous in their action, are distinct in the nature of their operation. The first is that necessary to divide the material atom from atom, and depends on the kind of edge employed. The second force is that required to wedge back the shaving, so as to make way for the further progress of the edge, and depends on the manner in which it is applied to the work. Now in fibrous and cohesive materials, the amount of force required to wedge back the shaving is usually greater than that required to effect the initial penetration, and must always depend on the angle which the upper surface of the edge makes with the face of the work; while it is obvious that, whatever the acuteness of the particular edge employed may be, this angle will be reduced to the minimum obtainable with such an edge, by keeping its lower face as close as possible to the surface from which the shaving is being wedged off.[25] A comparison of Figs. 4 [4 and 5] will illustrate this. Both edges are supposed to be of the same acuteness, viz., 60°, and in [Fig. 4], where the angle of relief is only 3°, the edge of 60° will wedge off the shaving at the smallest available angle, viz., 63°, while the position of the same edge in [Fig. 5] increases this angle to 90°.
[25] In adopting Mr. Babbage's arguments I have varied their form. Mr. Babbage takes the square of 90° and divides it into three parts, viz.:
|
Angle of relief 3° Angle of edge 60° Angle of escape 27° | 90° |
The angle of escape is thus estimated from the horizontal line perpendicular to a base line presented by the surface of the work or by a tangent to it. But as the value of this angle depends directly on its relation to the base line, and has only a complementary relation to the horizontal line, I have thought it better to confine the illustration to the same base as being more directly connected with the wedge-like action of the edge.
Thus, as far as regards the force required to bend back the shaving, the edge of [Fig. 5] might just as well be nearly square, or 87°, taking off 3° for the angle of relief. Indeed, this less acute edge would work better than one more acute but badly placed, as in [Fig. 5]; for the lower face here points too much into the work, creating the tendency to dig explained above. The same arguments and illustrations apply with equal force to drills and boring tools, and [Fig. 5] may be looked at as representing one edge of a common drill, in which the acuteness is obtained by bevelling the under sides only, leaving the upper face of each edge perpendicular to the surface acted upon. Nasmyth has pointed out that the less acute drills of this class are made the better and more smoothly they will cut; for, so long as the upper faces are left square to the surface of the work, increasing the bevel of the lower faces can only increase the tendency to dig and chatter. Thus, whenever acuteness is desired in any cutting edge, it should always be obtained from the upper face; and the dotted lines in [Fig. 4], suggesting a tool for metal in one case, and a common wood-turning chisel in the other, are added to illustrate this, by showing that the line of the lower face is common to both. No tools afford a better illustration of this principle in boring tools than the American twist drills, which owe the ease and beauty of their action to the spiral flutes being placed so as to give the necessary acuteness from the upper face of each edge, thus allowing the lower faces to be kept as close as possible to the surface of the work. There is yet one more important practical advantage to be gained from adopting the smallest possible angle of relief. The arrow in Figs. [4 and 5] shows the direction in which the strain of the cut will fall on the edges respectively. It has been shown that the position of [Fig. 5] increases the amount of strain on the edge, and yet it is apparent that it is less able to bear this increased strain; for while this falls on Fig. 4 in its strongest direction—viz., almost down the length of one face—it falls on [Fig. 5] across the end of the edge, thus rendering it far more liable to wear and fracture.
It is therefore evident that, in treating plane surfaces, the cutting action of any acute edge is most favoured when its lower face is placed nearly parallel with the surface acted on; and in treating cylindrical surfaces, when the same face occupies the same position with regard to some tangent of the circumference; or, in other words, when the lower face is almost at right angles to some radius of the circle, as in [Fig. 4]: and it follows that the tendency to penetrate will be most effectually counteracted when a line at right angles to the surface, or a radius of the circle, as in [Fig. 6], bisects the edge, making each face equidistant from the surface which moves across it. Thus, [Fig. 6] represents the scraping position; and it is obvious that all bow-drills or other tools, which are said to cut both ways, must really act on the scraping principle.
Practical illustrations in support of the universal application of these principles might be multiplied indefinitely; but two very common operations will suffice to prove that the position of the edge determines the nature of its action. If a penknife be not held with its blade perpendicular to the paper, when used for scratching out, it will be sure to hang and chatter; and the flatter a razor is held to the skin in shaving the more free will the chin be from uncomfortable digs and chatters afterwards.
The conditions which next demand notice in the case of turning-tools are those which must be observed to preserve the proper position of the edge under the strain put upon it. These relate to the form of the tool, and, in the case of cylindrical work with fixed tools, to the part of the surface at which the edge of the tool should be applied. Drills and boring tools require little notice in this respect, for, as the strain is round their axis, it is only necessary that their shafts should be strong enough not to twist or bend. It must, however, be remembered that when common drills are required to be very acute, the edges should be thrown up a little or hollowed out so as to give the acuteness on the upper face as explained above.[26]
[26] The common form of drill is rendered far more efficient with wrought iron and materials that require cutting, by twisting the flat shaft when hot, so as to reverse the position of each edge after the manner of a screw-auger. The lower faces can then be kept as close as possible to the face of the work while the twist will give a moderate degree of acuteness on the upper face.
Hand-turning is simply a matter of manual dexterity, and as any part of the same plane or the same circumference presents the same surface to the edge of the tool, the correct relation between the edge and the surface can be obtained in many places, and therefore the particular point at which the edge should be applied is simply a matter of personal convenience, and may vary with the height of the lathe or that of the workman, or the shape and nature of the tool employed. The use of the graver affords a good illustration of this; and it may be remarked, in connection with this tool, that none is more simple in construction, more perfect in principle, or more convenient in application. When its use is once thoroughly mastered it will do anything from smoothing a pin to roughing out a cylinder four or five inches in diameter. The graver is simply a square bar of steel ground off obliquely at the end; and by varying the obliquity of this slope the act of grinding one plane face will give two cutting edges of any desired acuteness, and three heels from which to use these edges at choice. In hand-turning only one edge of the graver is used at a time, and the lozenge-shaped face is made the lower face common to each edge. Now, when the graver is used for roughing, the point is generally buried in the clean metal below the central line of the work, and the lower face is placed against, and takes the shaving from, the little shoulder which it forms on the cylinder. When the graver is used for smoothing, the lower face is placed nearly flat against the face of the work, and the edge is generally made to bite on, or a little above, the central line. But for very light finishing cuts the graver may be used from the heel at the bottom of its lozenge face, and in this position its point is over the top of the work, bringing the biting part of the edge still more above the central line. Thus, the only three points to consider in placing the tool in hand-turning are—first, that the lower face of the edge should occupy the proper position with regard to the surface; secondly, that the handle of the tool should come up conveniently to the hands of the operator; and thirdly, that while these two conditions are observed, the heel of the tool should be able to take a firm bearing on the rest.