Turning and Boring / A specialized treatise for machinists, students in the industrial and engineering schools, and apprentices, on turning and boring methods, including modern practice with engine lathes, turret lathes, vertical and horizontal boring machines

by Franklin Day Jones

Fig. 14. Turning a Conical Surface by using the
Combined Vertical and Horizontal Feeds

Occasionally it is necessary to machine a conical surface which has such a large included angle that the tool-bar cannot be swiveled far enough around to permit turning by the method illustrated in [Fig. 13]. Another method, which is sometimes resorted to for work of this class, is to use the combined vertical and horizontal feeds. Suppose we want to turn the conical casting W ([Fig. 14]), to an angle of 30 degrees, as shown, and that the tool-head of the boring mill moves horizontally ¹/₄ inch per turn of the feed-screw and has a vertical movement of ³/₁₆ inch per turn of the upper feed-shaft. If the two feeds are used simultaneously, the tool will move a distance h of say 8 inches, while it moves downward a distance v of 6 inches, thus turning the surface to an angle y. This angle is greater (as measured from a horizontal plane) than the angle required, but, if the tool-bar is swiveled to an angle x, the tool, as it moves downward, will also be advanced horizontally, in addition to the regular horizontal movement. The result is that the angle y is diminished and if the tool-bar is set over the right amount, the conical surface can be turned to an angle a of 30 degrees. The problem, then, is to determine what the angle x should be for turning to a given angle a.

Fig. 15. Diagram showing Method of Obtaining Angular Position
of Tool-head when Turning Conical Surfaces by using Vertical and
Horizontal Feeding Movements

The way angle x is calculated will be explained in connection with the enlarged diagram, [Fig. 15], which shows one-half of the casting. The sine of the known angle a is first found in a table of natural sines. Then the sine of angle b, between the taper surface and center-line of the tool-head, is determined as follows: sin b = (sin a × h) ÷ v, in which h represents the rate of horizontal feed and v the rate of vertical feed. The angle corresponding to sine b is next found in a table of sines. We now have angles b and a, and by subtracting the sum of these angles from 90 degrees, the desired angle x is obtained. To illustrate:

The sine of 30 degrees is 0.5; then sin b = (0.5 × ¹/₄) ÷ ³/₁₆ = 0.6666; hence angle b = 41 degrees 49 minutes, and x = 90° - (30° + 41° 49') = 18 degrees 11 minutes. Hence to turn the casting to angle a in a boring mill having the horizontal and vertical feeds given, the tool-head would be set over from the vertical 18 degrees and 11 minutes which is equivalent to about 18¹/₆ degrees.

If the required angle a were greater than angle y obtained from the combined feeds with the tool-bar in a vertical position, it would then be necessary to swing the lower end of the bar to the left rather than to the right of a vertical plane. When the required angle a exceeds angle y, the sum of angles a and b is greater than 90 degrees so that angle x for the tool-head = (a + b) - 90 degrees.