Note AS. - {Paper on lite Principles of Tools for Turning and Planing Metals, by Charles Babbage, Esq., F.R.S., etc. etc.)

Steel of various degrees of temper and under various forms, is almost universally employed for cutting metals. Before deciding on the forms of the different tools it is desirable to inquire into the principles on which their cutting edges act, and to assign special names to certain angles on the relations of which to each other, and to the metals upon which they are used their perfection mainly depends.

In fig. 983, c is a cylinder of steel or other metal, and T is a planing or turning tool acting upon it at the point a. A c is a horizontal line passing through the center c, and the cutting point a. B a, is a line passing through the cutting point a and along the upper plane b a, of the cutting tool T. C a, is a line passing through the cutting point a and along the front plane e a, of the cutting tool. D a, is a line from the cutting point a, at right angles to the radius c a.

The angle D a C, may be called the angle of relief, because, by increasing it, the friction of that face of the tool upon the work is diminished.

The angle C a b, may be called the angle of the tool.

The angle B a A, may be called the angle of escape, because the matter cut away by the tool escapes along it.

The forces to be overcome in cutting a thin shaving of metal from a cylinder or from a flat surface are of two kinds.

1st. It is necessary to tear along the whole line of section each atom from the opposite one to which it was attached. The force required for this purpose will obviously be proportioned to the length of the cutting edge of the tool, and dependent on the nature of the metal acted upon. But it will be quite independent of the thickness of the part removed.

Fig. 983.

2nd. The shaving cut off by the tool must in order to get out of its way, be bent or even curled round into a spiral. This second force is often considerable, tad when thick cuts are taken, is usually far larger than the former force. If the bending were of small extent, then the force to be exerted would vary as the square of the thickness of the shaving multiplied by some constant, dependent on the nature of the metal operated upon. But the bending very frequently proceeds to such an extent that the shaving itself is broken at very abort intervals, and some shavings of iron and steel present a continued series of fractures not quite running through hut yet so complete, that it is impossible even with the most careful annealing to unwind the spiral. This partial severance of the atoms in the shaving itself, will require for its accomplishment a conaiderable exertion of force. The law by which this force increases with the thickness most probably embraces higher powers than the first and second, and may be assumed thus force = a + bt + ct2 + dt3 + For the present illustration it is unnecessary to consider more terms than those already more particularly explained, namely, the constant force, and that which varies as the square of the thickness of the shaving.

If therefore t, be the thickness of the shaving, and A and B two constants, wo shall find amongst the forces required for the separation of the shaving the two terms.

A + Bt2 where A, and B, depend upon the nature of the metal acted upon.

We may learn from this expression, even without being acquainted with the values of the constants A and B, that the force required to remove the same thickness of metal, may vary considerably according to the manner in which it is effected.

For example. If a layer of metal of the thickness of 2 t, is to be removed. It may be done at two successive cuts, and the force required will be equal to

2A + 2Bt2 But the same might have been accomplished at one cut when the force expended would have been

A+4Bt2

Now the force required for the two cuts, will always bo loss than the force required for making one cut, if t2 >A/2B

For let t2=A/2B + v then Force for two cuts =2 A +2 B(A/2B+v) = 3A + 2 Bv.

Force for one cut of twice the thickness which former is always smaller than the latter force by the quantity 2 B v. In the same manner it may be proved that if t2> A/nB or t2 = A/2B+ v it will always require lean force to make n separate slices, than to cut one slice of n times the thickness for

= A + 4B(A/2B+v) = 3A +4Bv.

Force for n slices =nA+nB (A/nB+v) = (n+1)A+ nBv

Force for one slice of n times the thickness

= A + n2 b(A/nB+v) = (n+1) A+ n2Bv which former force is always leas than the latter by the quantity of ((n2-n) Bv.

The angle of relief should always bo very small, because the point a will in that esse have its support nearly in a line directly opposed to that force acting upon it.

If a tool either for planing or for turning is defectively formed, or if it is presented to its work in such a manner that it has a tendency to dig into it; then a very small angle of relief, in addition to a long back a e, will in some measure counteract this defect.

The smaller the angle of the tool, the less will be the force necessary for its use. But this advantage of a small angle is counterbalanced by the weakness which it produces in the support of the cutting point. There is also another disadvantage in making the angle of the tool smaller than the escape of the shaving requires; for the point of the tool being in immediate connection with a smaller mass of metal, will not so quickly get rid of the heat it acquires from the operation of cutting, as it would if it formed part of a larger mass.

The angle of escape A a B is of great importance and it varies with the nature of the material to be acted upon. If this angle is very small the action of the tool is that of scraping rather than of cutting, and the matter removed approaches the form of a powder. If however the material is very flexible and cohesive, in that case shavings may be removed. The angle I have found best for cutting steel is about 27°, but a series of experiments upon this subject is much required.