Now, all this is very simple and easy to understand, and when you have mastered this much, you will be in a fair way to understand more. The second part of the subject, nevertheless, requires very close attention, and very likely may not become quite clear to you when explained. I shall therefore draw a line here, and make this lesson a special paragraph, which you can look back to some other day, when you are grown from a boy-mechanic to a man, and have had more experience in cutting and turning wood and metal.
The tools above described have their cutting edges formed by the meeting of two planes at a given angle,—these planes being the flat bevels (or the flat top and one bevel) formed by the grindstone. But in some tools three planes meet to form an edge instead of two, and the angle of the cutting edge is not the same as that of either of these, although it depends upon them, and can be nicely calculated. This calculation, however, requires a knowledge of some higher branches of mathematics than the young mechanic is supposed to be acquainted with, and therefore a table is added instead, by which, when the angles of two of these planes are known, the third may be at once seen, which last determines, of course, the angle of the edge.
As an example, take the graver, of which you will find a drawing among the other tools, but which I give again in this place. M, Fig. 45, is the tool, looking at the face or bevel which has been ground upon it, making a lozenge-shape or diamond. But this face is a third plane, and the cutting edges, a and b, depend for their angles upon all three of these. Now, for iron we want an angle of 60°. How are we to make the edges, a b, of that exact size? The bar is first of all square in section, like N, which would be its shape before the third face or bevel is ground, and all the angles are now right angles of 90° each. But instead of this, we want two of them 60°, the other two being of no importance. We simply proceed thus:—Determine which angle is to become the point of the tool (it is no matter in the present case, as all are alike), then grind away underneath till the new bevel forms an angle of 45° with the back (by which I mean the edge which runs along from the sharp point towards the handle—the edge x in fig. O). Trigonometry enables us to find out that an angle of 45° is the one required, but you will find it in the table annexed to this chapter, and an explanation of this table is also given to enable you to use it easily. Thus ground, the edges a b of fig. O will be each formed of two planes meeting at an angle of 60°. You can make a gauge of card or tin, P, to work by, of the required angle.
Fig. 46.
Fig. 47.
In order to understand the use of this table, it is necessary to give names to the several angles of a tool. That upon the front or face of the tool, as A of the point-tool, is called the plan-angle; that made by the upper surface and the front edge, as B (a, being the angle in question), is called the section angle, because, if you were to saw right through the central line lengthwise, this is the angle that would appear at the point, viewing it sideways. Now, if we look at C, Fig. 47, we shall be able to understand how the front line, b c, is obtained, which constitutes one side of the section angle of a tool. It results from the meeting of the two diamond-shaped planes at the sides formed by the grindstone, but is dependent also on the plan-angle. These two side-planes are to be generally ground at an angle of about 3° from the vertical, which is to give the clearance of the tool if held in a fixed position, as in the tool-holder of a slide-rest, the tool being supposed horizontal. This is in accordance with what I have before told you, viz., that the cutting edge should be presented to the work at the smallest possible angle, 3° being very small indeed. This angle is generally measured by placing the side ground in contact with a cone of wood or metal, turned to an angle of 3°, such as D,—k being a tool the front of which is evidently 3°; or a piece of tin, l, cut to the same angle, and stood on its edge, will answer the same purpose. By 3°, I mean an angle of 3° measured on the circumference of a circle, as I have already explained in a former page, such angle being of course at the centre of the circle where the lines drawn from the several degrees on the circumference meet.
Now, when you have ground these two surfaces, the line b c of B (or C) will have a certain slope or inclination depending on the plan-angle of the point. The exact inclination of it may be therefore said to be accidental; but, whatever it is, it becomes of great importance in the final result, being one side of the angle which will give any particular angle of cutting edge. And here the table comes into use:—Suppose I wish to have an edge of 60°, for cutting iron. Measure the plan-angle,—say it is 90°, which is that of the graver; then, on the table, under the words “plan angle,” you will see 90°, and opposite, above 60° of “cutting edges,” you will see 45°. You have only to grind back the upper face of the tool, until it makes an angle of 45° (section angle) with the front edge or line, b c, and the edges x x will be angles of 60°. Or take the tool E, of which the plan angle is 120°, and suppose you want cutting edges of 80°, for brass, opposite 120°, and above 80°, is 78° 5″. Grind back the top face to an angle of 78° 5″ (or 78½) with the point line, and it is done.
Until you have practically proved it, you can have no idea of the vast importance of having correctly-formed cutting edges, and of placing them within a hair’s-breadth of the proper position. But it is in slide-rest work especially, and in cutting metal with tools held rigidly in one position, that this is of such paramount importance. It makes all the difference between cutting off a clean shaving, and tearing from the material by main force a quantity of disjointed particles, the latter process leaving a rough unfinished surface, the former producing one as smooth and polished as a sheet of glass; and the advantage of this short table is, that you can at any time shape your own tools for the particular work in hand.