Precision locating and dividing methods

by Anonymous

Locating Work by the Disk Method

Comparatively small precision work is sometimes located by the disk method, which is the same in principle as the button method, the chief difference being that disks are used instead of buttons. These disks are made to such diameters that when their peripheries are in contact, each disk center will coincide with the position of the hole to be bored; the centers are then used for locating the work. To illustrate this method, suppose that the master-plate shown at the left in [Fig. 8] is to have three holes a, b, and c bored into it, to the center distances given.

Fig. 4. Testing Concentricity of Button Preparatory to Boring Hole in Lathe

It is first necessary to determine the diameters of the disks. If the center distances between all the holes were equal, the diameters would, of course, equal this dimension. When, however, the distances between the centers are unequal, the diameters may be found as follows: Subtract, say, dimension y from x, thus obtaining the difference between the radii of disks C and A ([see right-hand sketch]); add this difference to dimension z, and the result will be the diameter of disk A. Dividing this diameter by 2 gives the radius, which, subtracted from center distance x equals the radius of B; similarly the radius of B subtracted from dimension y equals the radius of C.

For example, 0.930-0.720 = 0.210 or the difference between the radii of disks C and A. Then the diameter of A = 0.210 + 0.860 = 1.070 inch, and the radius equals 1.070 ÷ 2 = 0.535 inch. The radius of B = 0.930-0.535 = 0.395 inch and 0.395 × 2 = 0.790, or the diameter of B. The center distance 0.720-0.395 = 0.325, which is the radius of C; 0.325 × 2 = 0.650 or the diameter of C.

Fig. 5. Flange Templet with Buttons Attached

Fig. 6. Hinge Jig Templet with Buttons Attached

After determining the diameters, the disks should be turned nearly to size and finished, preferably in a bench lathe. First insert a solder chuck in the spindle, face it perfectly true, and attach the disk by a few drops of solder, being careful to hold the work firmly against the chuck while soldering. Face the outer side and cut a sharp V-center in it; then grind the periphery to the required diameter. Next fasten the finished disks onto the work in their correct locations with their peripheries in contact, and then set one of the disks exactly central with the lathe spindle by applying a test indicator to the center in the disk. After removing the disk and boring the hole, the work is located for boring the other holes in the same manner.

Fig. 7. Hinge Jig Templet Illustrated in [Fig. 6]

Small disks may be secured to the work by means of jeweler’s wax. This is composed of common rosin and plaster of paris and is made as follows: Heat the rosin in a vessel until it flows freely, and then add plaster of paris and keep stirring the mixture. Care should be taken not to make the mixture too stiff. When it appears to have the proper consistency, pour some of it onto a slate or marble slab and allow it to cool; then insert the point of a knife under the flattened cake thus formed and try to pry it off. If it springs off with a slight metallic ring, the proportions are right, but if it is gummy and ductile, there is too much rosin. On the other hand, if it is too brittle and crumbles, this indicates that there is too much plaster of paris. The wax should be warmed before using. A mixture of beeswax and shellac, or beeswax and rosin in about equal proportions, is also used for holding disks in place. When the latter are fairly large, it may be advisable to secure them with small screws, provided the screw holes are not objectionable.

Disk-and-Button Method of
Locating Holes

The accuracy of work done by the button method previously described is limited only by the skill and painstaking care of the workman, but setting the buttons requires a great deal of time. By a little modification, using what is sometimes called the “disk-and-button method,” a large part of this time can be saved without any sacrifice of accuracy. The disk-and-button method is extensively used in many shops. Buttons are used, but they are located in the centers of disks of whatever diameters are necessary to give the required locations. As three disks are used in each step of the process, it is sometimes called the “three-disk method.”

To illustrate the practical application of this method, suppose six equally-spaced holes are to be located in the circumference of a circle six inches in diameter. To locate these, one needs, besides the buttons, three disks three inches in diameter, each having a central hole exactly fitting the buttons. It is best to have, also, a bushing of the same diameter as the buttons, which has a center-punch fitted to slide in it. First the center button is screwed to the templet, and one of the disks A, [Fig. 9], is slipped over it; then a second disk B carrying a bushing and center-punch is placed in contact with disk A and a light blow on the punch marks the place to drill and tap for No. 2 button, which is kept in its proper place while tightening the screw by holding the two disks A and B in contact. Next the third disk C is placed in contact with disks A and B and locates No. 3 button, and so on until the seven buttons are secured in position. The templet is then ready to be strapped to the lathe faceplate for boring.

Fig. 8. An Example of Precision Work, and Method
of Locating Holes by Use of Disks in Contact

Of course, it is not possible to use disks of “standard” sizes for many operations, but making a special disk is easy, and its cost is insignificant as compared with the time saved by its use. One who employs this method, especially if he also uses disks to lay out angles, soon accumulates a stock of various sizes. While it is desirable to have disks of tool steel, hardened and ground, or, in the larger sizes, of machine steel, case-hardened and ground, a disk for occasional use will be entirely satisfactory if left soft.

Another example of work is shown in [Fig. 10]. This is a jig templet similar to the one illustrated in Figs. [6] and [7]. Sketch A gives its dimensions and sketch B shows the disk-and-button way of locating the holes. A steel square is clamped with its stock against the right-hand edge of the templet and its blade extending across the top. The lower edge of the blade should be located 0.250 inch from the upper edge of the templet by the use of size blocks. A 2½-inch disk, touching both blade and stock, locates hole C. Another 2½-inch disk, touching the first disk and the square blade, locates hole B. Next a disk 1.600 inch diameter is placed in contact with the two upper disks and locates the center hole A; and, finally, the disks for holes B and C are used to locate holes D and E.

Fig. 9. Locating Holes on a Circle and Equi-distant
by using Disks and Buttons in Combination

Two other jobs that illustrate this method may be of interest. The first one, shown in [Fig. 11], required the locating of nine equally-spaced holes on a circumference of 7⅜ inches diameter. In any such case, the size of the smaller disks is found by multiplying the diameter of the circle upon which the centers of the disks are located by the sine of half the angle between two adjacent disks. The angle between the centers of adjacent disks equals 360 ÷ number of disks. 360 ÷ 9 = 40; hence, in this case, the diameter of the smaller disks equals 7⅜ multiplied by the sine of 20 degrees, or 7⅜ × 0.34202 = 2.5224 inches. 7⅜-2.5224 = 4.8526 inches, which is the diameter of the central disk.

The templet shown in [Fig. 12] required two holes on a circumference 6½ inches diameter, with their centers 37 degrees 20 minutes apart. To find the diameter of the smaller disks, multiply the diameter of the large circle by the sine of one-half the required angle, as in the preceding example; thus 6½ × sin 18 degrees 40 minutes = 2.0804 inches, which is the diameter of the two smaller disks. The diameter of the larger disk equals 6½-2.0804 = 4.4196 inches.

Very accurate results can be obtained by the disk-and-button method. Of course, absolute exactness is equally unattainable with buttons and a micrometer, or any other method; the micrometer does not show the slight inaccuracy in any one chordal measurement, while in using the disks the error is accumulative and the insertion of the last disk in the series shows the sum of the errors in all the disks. It is only in cases like the one illustrated in [Fig. 9] that we note this, and then, though in correcting the error, we may change the diameter of the circle a very slight amount, an exceedingly accurate division of the circumference is secured.

Use of Two- and Three-Diameter Disks

[Fig. 13] illustrates, on an enlarged scale, a piece of work requiring great accuracy, which was successfully handled by an extension of the three-disk method. Fourteen holes were required in a space hardly larger than a silver half-dollar, and, although the drawing gave dimensions from the center of the circle, the actual center could not be used in doing the work, as there was to be no hole there; moreover, a boss slightly off center prevented the use of a central disk, unless the bottom of the disk were bored out to receive this boss, which was not thought expedient. Hence, the method adopted was to make the plate thicker than the dimension given on the drawing, and then bore it out to leave a rim of definite diameter, this rim to be removed after it had served its purpose as a locating limit for the disks.

Fig. 10. (A) Layout of Jig-Plate.
(B) Disk-and-Button Method of Locating Holes

As the holes A and B, which were finished first, were 0.600 inch apart and 0.625 inch from the center, the rim was bored to 1.850 inch and two 0.600-inch disks, in contact with the rim and with each other, located these holes. As hole C was to be equi-distant from holes A and B, and its distance from the center was given, the size of the disk for this hole was readily determined. The disks for holes A, B and C have two diameters; the upper diameters are made to whatever size is required for locating the disks of adjacent holes, and they also form a hub which can be used when setting the disks with an indicator. Hole D was 0.4219 inch from B, and calculations based on this dimension and its distance from the center showed that it was 0.4375 inch from hole C.

A “three-story” disk or button was made for hole D. The diameter of the large part was 0.46875 inch and it overlapped disks C and B (the upper sections of which were made 0.375 inch and 0.4062 inch, respectively), thus locating D. Then hole F and all the remaining holes were located in a similar manner. The upper diameters of disks E and D were used in locating disks for other adjacent holes, as well as a hub for the indicator; for instance, to locate a hole with reference to holes C and D, the diameter of the new disk and the diameter of the upper part of disk D, were varied to give the required location. The relation between the disks B, D and F is shown by the side view.

Fig. 11. Example of Circular Spacing
requiring a Large Central Disk

It had been decided that no screws should be used in attaching the buttons or disks to the work, as it was feared that the tapped holes would introduce inaccuracy by deflecting the boring-tools; therefore the following method was employed. After all the disks were fastened in place by clamps, a soft solder of low melting point was flowed about them, filling the work to the top of the rim. When the solder had cooled, the clamps were removed, the work transferred to the lathe faceplate, indicated in the usual way, and the holes bored by a “D” or “hog-nose” drill, guided by an axial hole in each disk, which had been provided for that purpose when the disks were made. It was thought that the unequal contraction of the solder and the plate in cooling might throw the holes “out of square;” however, careful measurements failed to show any appreciable lack of parallelism in test-bars inserted in the holes.

Fig. 12.Locating Holes at an Angle by use of Disks and Buttons

Fig. 13. Locating Holes by Means of Two- and
Three-Diameter Disks in Contact