Part 24

Principle may be looked upon as the essence of practice, and in connection with this particular subject, the reduction of practice to principle is of comparatively modern growth. This will account for the fragmentary character and occasional difference of opinion, which marks the treatises of the above-named eminent authorities when compared with each other. As a step towards some more concise and perfect code of principle, I have endeavoured to collate and arrange in consecutive order, all those laws which govern the action of acute edged turning tools.

The object of this paper is not to supply patterns of tools, as the best form will be no better than the worst unless properly applied; but to set forth those general principles, which may enable the workman to distinguish between forms which are accidental and those which are essential, and thus to make the shape of any tool his servant rather than his guide.

Whatever the shape or purpose of any acute-edged tool may be, its action will always depend on the manner in which the extreme edge is applied to the surface acted upon; and as the same laws govern the action of every acute edge, whether formed on a razor or a tool for cast iron, it will assist a clear comprehension of this subject to consider first the action of edges generally, without reference to any particular tool.

The same edge may be made to act in four different ways, viz.: to cut, dig, chatter or scrape. Digging and chattering are intermediate stages between cutting and scraping, and are fatal to good work. Thus _cutting_ and _scraping_ remain the two standard principles, on one of which every tool should be made to act; and while cutting depends on the penetration of the edge, scraping results from using an edge so that it cannot penetrate. Consequently, the conditions most favourable to cutting will give the key to both principles of action.

Every cutting edge is simply a wedge, keen enough to guide its own path without depending on the grain or other accidental line of separation in the material on which it is employed; and when such a wedge is forced into any substance, it will show a constant tendency to penetrate in a line with that face which receives most opposition. The comparative amount of opposition which each face receives, will be determined either by one having more of its surface in contact with the material than the other as in Fig. 2, or by the material giving way on one side, as in Figs. 1 and 3. These last two figures illustrate the action of all _paring_ tools, to which class cutting lathe tools belong. The dotted lines are added in Fig. 2, to show that the action of the edge is the same, whether it be formed by one or two bevels.

Thus in all cases,--except when an edge is applied so that the pressure is equal on both faces,--one face will guide the course of the edge, and in paring tools this will always be the lower face, or that next the surface of the work.

The first consideration in placing any paring tool must therefore always be that, _the lower face of the edge should lie as nearly as possible in a line with the direction the cut is intended to follow_, so as to place the whole edge in its natural wedge-like position: for when any edge is compelled to act in a manner contrary to this, it will assuredly assert its natural tendency by digging and chattering in the direction of its lower face. But when the action of the tool is continuous as in turning, planing, or boring, care must be taken that this face of the edge does not actually rub against that of the work; and, to avoid this, Nasmyth recommends that the face of the edge should be inclined from the surface of the work at an angle of 3°. Babbage calls this angle "the angle of relief," because it relieves the friction; and to show how little variation is admissible in this angle, Holtzapffel places its maximum at 6°. In cylindrical work the angle of relief is estimated from a tangent to the circumference. Thus, in Figs. 4 and 7, the lines C, D, may represent plane surfaces or tangents at pleasure, and in either case the lower face of each edge is supposed to make an angle of 3° with these lines respectively.

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 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° } ditto edge 60° } 90° ditto escape 27° }

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.

The best rule for hand-turning is, therefore, to apply the tool to the work, with these ends in view before fixing the rest, and then to bring that up to the necessary position.

When the heel of any hand tool has a firm bearing on the rest, and the edge is applied in the wedge-like position, the preservation of this during the progress of the work depends on delicacy of touch rather than muscular power. But when the edges are applied out of their natural line, it puzzles a strong wrist to keep them to their cut at all without digging into the work. This affords the best practical illustration of the necessity of careful attention to the position of slide-rest tools, which are deprived of all power of accommodation to the sense of touch, and which therefore require accurate adjustment in the first instance.

For the motion of the tool is now confined to that of the rest, and as this moves in horizontal planes, the edge of the tool must be applied to the work on that parallel plane which passes through the lathe centres. The reason for this rule will be at once apparent, if the edge be not placed on this central line in facing up a plate--for then it will lose its cut before reaching the centre, leaving a core untouched. Now although it would require an exaggerated error in the position of the edge to lose cut altogether in turning a cylinder, yet this example proves that, unless the edge be applied exactly on the central line the relative position between it and the surface of the work, on which the cutting action depends, will imperceptibly change with the reduction of the work; and supposing this to vary much in diameter, the same tool may cut beautifully on one part and badly on another. Fig. 4, which illustrates the cutting action of the edge, has been purposely placed on a part of the circle where a slide-rest tool could only act for a very short time, in order to draw attention to the difference between those conditions which govern the cutting action, and those which depend on the motion of the rest from which the tool is used. It is obvious that if Fig. 4 were moved inwards on a horizontal line the edge would pass over the smaller circle without touching it. The illustration is of course exaggerated, but it proves that Fig. 7 is the only position in which the tool will cut over varying diameters without some change in the relative positions of its lower face and that of the work. Hence the usual instructions to apply the edge about the centre of the work. But Babbage has observed, that however good this direction may be as far it goes, it is insufficient and liable to mislead when given alone. It is impossible to do away with elasticity when the tool is supported at some lateral distance from the line of strain, as in the slide rest or planing machine; and unless this elasticity is counteracted by the position of the tool, it may upset the best position of the edge. To meet this, Babbage gives the following rule--First, consider whereabouts the tool itself will bend under strain on its edge, when fixed in the rest; and then take care that this part of the tool, which Babbage calls "the centre of flexure,"--is placed above a line joining the centre of the work and the edge of the tool. Fig. 7 will explain the reasons for this rule and the consequences of neglecting it when there is much strain put on the edge.

Let E, I, F, be the line joining the centre of the work and the edge of the tool. Then if G above this line be the centre of flexure, when the tool bends its edge must follow some part of the arc, H, I, J, from G as a centre, and will be thrown out of the work. But if K below the line, E, I, F, be the centre of flexure, then, under the same circumstances, the edge will follow some part of the arc L, I, M, from K as a centre, and must dig into the work. It is important to recognise this principle, because while it shows that every tool in which the top of the edge stands _above_ the shaft must be liable to the evils resulting from elasticity, it shows also that even cranked tools may fail to obviate the danger, unless care is taken to place the weakest point in the shaft above the central line. Babbage remarks, that although it is not always possible to strengthen any part of a tool, it is always possible and sometimes desirable to make some particular point weaker than the rest, by cutting away a little where the weak point should be. Fig. 9 shows that the crank principle may be applied in another form, and although the crank is upwards in this case, the same object is attained by making P the weakest point, and placing it above the central line, N, O. This form, however, is only used for light finishing cuts; for any unnecessary length of crank evidently adds elasticity, and Holtzapffel observes that, "in adopting the crank form tools the principle must not be carried to excess, as it must be remembered we can never expunge elasticity from our materials, whether viewed in relation to the machine, the tool, or the work." The crank, therefore, should only be just sufficient to give the edge the right direction if the tool should spring; and Holtzapffel remarks, that as a tool will generally bend somewhere in the central line of its shaft, it is sufficient if the top of the edge is kept on or just below this line, as in Fig. 8. Referring again to Fig. 7, and looking at the line C, D, as a plane surface, and I, F, as a line perpendicular to that surface, the same arguments and illustrations apply to the form of a tool in the planing machine. The point at which the tool is now applied ceases to be of moment.

Having considered the conditions necessary to insure the best cutting action of acute edges and the preservation of that action during the progress of the work, it remains to treat of the edges most suitable to particular materials, the method of giving them any desired angle, and the manner of applying slide-rest tools so as to obtain the best work with the least expenditure of force and time.

Willis observes that different metals and qualities of the same metal require to be treated with edges differing in their degree of acuteness, and all the standard authorities concur in giving the following code as near enough for all practical purposes. The modification of these angles is ruled by the general principle that fibrous and cohesive materials require more acute edges than crystalline and granular substances, as will be apparent in the following code:--

Wrought iron and steel 60° Cast do. do. 70° Roughing brass 80° Finishing do. 90°

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.