Conical surfaces are ground after the same general methods as cylindrical surfaces, and with grinders of nearly the same general forms, the principal differences being that the grinders are made conical instead of cylindrical, and that they do not admit of being traversed through each other like cylinders to distribute and correct the errors of the grinder itself, and consequently in grinding cones the accuracy of the result depends entirely upon the truth of the grinder, which under the most favourable circumstances transfers nearly all its errors to the work.
Unlike cylindrical works, conical surfaces are not usually ground for the correction of the trifling errors of turning, partly because they are mostly short in proportion to their diameter, and therefore but little liable to spring away from the tool, the principal source of error in turning long cylinders, and partly because the ordinary methods of grinding cones are less perfect than the methods of grinding cylinders, as the conical grinders depend entirely upon the turning lathe for their accuracy, and consequently when the material is sufficiently yielding to allow of the action of cutting tools, the surfaces may be thus produced more correctly than by grinding, which in this case is principally employed for producing accuracy of contact between two cones by grinding them together, and not for improving the general truth of either.
Works in hardened steel are necessarily corrected for accuracy of form by grinding, in order to remove the distortion occasioned by hardening; but in this case the cones, whether external or internal, are prepared exactly to the angle, and only slightly larger in diameter than the required size, by turning them in the lathe while soft, so as to leave but a very trifling amount of correction to be effected by grinding. Internal cones in objects that do not admit of being conveniently chucked, are prepared with the taper broaches, or revolving cutters, described in Chap. XXV., Vol, II., which under proper management produce very accurate and smooth surfaces.
The grinding clamps for cylinders, fig. 1112, are also very generally employed for external cones; the grinder is cast in the same manner, in two halves, either upon the cone itself or upon one of the same angle and a little smaller diameter. The grinder, if cast of the same length as the cone, is liable to round off the smaller end, from this being more constantly exposed to the grinding action, and therefore the grinder is usually made a trifle shorter than the cone. The spring grinder, fig. 1118, is also much used for small cones; it is very nearly a counterpart of the grinder, fig. 1117, for internal cylinders, the principal difference being, that at the opposite extremity to the spring it is bowed out near the ends for the reception of the grinder, and beyond this enlargement a binding screw is added, for closing the grinder gradually upon the cone, and which at the same time serves to prevent the rods from springing sideways.
In grinding the external cone the work in almost all cases revolves in the lathe, and the grinder charged with emery and water is held in the hands. The grinder is gradually twisted round to different positions, and continually traversed endways a small distance, according to the length and acuteness of the cone. The object of the short traversing motion is to distribute the emery uniformly and to keep the particles constantly shifting to different parts of the grinder, as if they were allowed to remain in the same position they would be liable to mark the work with rings. On this account much less force is applied in grinding cones than cylinders, and the grinder is lightly held in an elastic manner so as to permit the emery to roll over between the work and grinder.
At the commencement of the process the grinder should be somewhat smaller in diameter than the required cone, so as to allow for a little enlargement of the grinder, as well as the reduction of the cone, which latter should at first only enter the grinder for about three quarters to seven-eighths of its length, according to the acuteness of the cone. The abrasion of the two surfaces allows the grinder gradually to advance towards the larger end of the cone, and as this is approached the grinder is from time to time slightly closed, to compensate somewhat for the wear. As the work progresses towards completion, increased attention is required to the condition of the grinder, and when it becomes so far worn as to mark the work with rings, or that the smaller end of the cone protrudes, a new grinder is cast for the completion of the work.
In the case of two cones of different angles joining each other as in fig. 1119, a form frequently employed in lathe mandrels, the grinder cast to a counterpart form is first employed to grind both cones at the same time in order to ensure their being concentric with each other. The long and nearly cylindrical cone a, serves as a guide for applying the grinder to the short obtuse cone b, which is completed with a grinder fitting both cones, and finally the cone a is separately corrected with a single cone grinder.
By far the more accurate methods of grinding the external cone are however the employment of the end of a fixed grinder, or the edge of a revolving lap mounted in the sliding rest, while the work revolves in the lathe exactly in the manner explained on page 1237, for the production of cylindrical surfaces, except that the sliding rest is swung round to the suitable angle for the side of the cone. One of these methods is generally resorted to for works requiring the greatest accuracy, as it admits of the cone being corrected with considerable exactness, both for angle and straightness of the sides, and the circular section being derived directly from the lathe, the adjustment of the diameter is the principal object requiring attention.