CHAPTER IIACCURATE DIVIDING ANDSPACING METHODS

Toolmakers and machinists occasionally find it necessary to locate a number of equally-spaced holes on a straight line between two points, or to divide a circle with holes which are equi-distant within a very small limit of accuracy. Several dividing and spacing methods are described in this chapter; some of these methods can, with slight modification, be applied in various ways.

Fig. 18. Method of Drilling Small Equally-spaced Holes in Rows

It is sometimes necessary to drill one or more rows of small equally-spaced holes. The best method of doing this work naturally depends, to some extent, upon the accuracy required, but even when a high degree of accuracy is not necessary, if an attempt is made to lay out the holes and drill them in the ordinary way, considerable time is usually required and the results are liable to be unsatisfactory. For example, suppose a row of holes ¹/₁₆ inch in diameter and ⅛ inch center-to-center distance were to be drilled in a flat plate. Some machinists would proceed by first scribing a center-line and then laying out the centers of the holes by means of dividers. A much easier and accurate method isillustrated in Fig. 18, and is as follows:Lay out the first hole and drill it; then secure a small piece of flat steel for a drill guide, drill a hole through it, bevel one corner and scribe a fine line on the beveled section, as shown in the illustration. Align the hole drilled in the guide with the hole in the work, by inserting a close-fitting plug, and clamp a scale against one edge of the drill guide so that one of the graduation marks exactly matches with the line on the guide. The edge of the scale must also be located parallel to the center-line of the row of holes to be drilled. Now proceed to drill the holes, setting the drill guide each time, to whatever graduation line represents the required spacing or pitch of the holes.

It is advisable to use a magnifying glass to accurately align the graduation mark on the scale with the line on the drill guide. If two or more rows of holes are to be drilled parallel, the guide block can be drilled accordingly, so that the different rows of holes can be finished at the same time. The drill guide block should be relieved slightly in the center so as to insure the ends of the block bearing against the edge of the scale. A toolmaker or machinist can drill a row of holes accurately by this simple method, in the time required to lay them out in the usual way, and even though accuracy is not necessary, it is quicker to drill holes by this method than by the one more commonly employed.

A simple method of spacing holes that are to be drilled in a straight line is illustrated inFig. 19. Two disks are made, each having a diameter equal to the center-to-center distance required between the holes. These disks must also have holes which are exactly central with the outside to act as a guide for the drill or reamer. The first two holes are drilled in the work while the disks are clamped so that they are in contact with each other and also with the straightedge as shown. One disk is then placed on the opposite side of the other, as indicated by the dotted line, and a third hole is drilled; this process of setting one disk against the opposite side of the other is continued until all the holes are drilled. When it is necessary to drill a parallel row of “staggered” holes, the second row can be located by placing disks of the proper size in contact with the first row of disks.

Fig. 19. Locating Equi-distant Holes in a Straight Lineby Means of Disks and Straightedge

A method of using disks, which is preferable for very accurate work, is shown inFig. 20. The disks are clamped against each other and along straightedgeAby the screws shown, and if the outside diameters are correct and the guide holes concentric with the outside, very accurate work can be done. With this device there may be as many disks as there are holes to be drilled, if the number of holes is comparatively small, but if it is necessary to drill a long row of holes, the disks and frame are shifted along an auxiliary straightedgeB, the hole in one of the end disks being aligned with the last hole drilled by inserting a close-fitting plug through the disk and hole.

An adjustable jig for accurately spacing small holes is shown inFig. 21.

Fig. 20. Special Disk-jig for Precision Drilling

This form is especially adapted for locating a number of equally spaced holes between two previously drilled or bored holes, and the accuracy of the method lies in the fact that a slight error in the original spacing of the guide bushing is multiplied, and, therefore, easily detected. There are two of these guide bushingsAandBwhich are carried by independent slides. These slides can be shifted along a dovetail groove after loosening the screws of clamp-gibC. To illustrate the method of using this jig, suppose five equally-spaced holes are to be located between two holes that are 12 inches apart. As the center-to-center distance between adjacent holes is 2 inches, slidesAandBwould be set so that the dimensionxequals 2 inches plus the radii of the bushings. A straightedge is then clamped to the work in such position that a close-fitting plug can be inserted through the end holes which were previously drilled or bored. Then with a plug inserted through, say, bushingBand one of the end holes, the first hole is drilled and reamed through bushingA; the jig is then shifted to the left until the plug inBenters the hole just made. The second hole is then drilled and reamed through bushingAand thisdrilling and shifting of the jig is continued until the last hole is finished. The distance between the last hole and the original end hole at the left is next tested by attempting to insert close-fitting plugs through both bushings. Evidently, if there were any inaccuracy in the spacing of the bushings, this would be multiplied as many times as the jig was shifted, the error being accumulative. To illustrate how the error accumulates, suppose that the bushings were 0.001 inch too far apart; then the distance to the first hole would be 2.001 inch, to the second hole, 4.002 inch, and finally the distance from the first to the sixth hole would be 10.005 inches; consequently, the distance between the sixth and seventh holes would equal 12-10.005 = 1.995 inch, or 0.005 inch less than the required spacing, assuming, for the sake of illustration, that the first and last holes were exactly 12 inches apart. In case of an error of 0.005 inch, the bushings would be set closer together an amount equal to one-fifth of this error, as near as could be determined with a micrometer, and all of the holes would then be re-reamed.

Fig. 21. Adjustable Jig for Accurate Hole Spacing

Sometimes it is necessary to machine a number of holes in a plate so that all the holes are on a circle or equi-distant from a central point, and also the same distance apart, within very small limits. A simple method of spacing holes equally is illustrated atA,Fig. 22. A number of buttons equal to the number of holes required are ground and lapped to exactly the same diameter, preferably by mounting them all on an arbor and finishing them at the same time. The ends should also be made square with the cylindrical surface of the button. When these buttons are finished, the diameter is carefully measured and this dimension is subtracted from the diameter of the circle on which the holes are to be located, in order to obtain the diameterd(see illustration). A narrow shoulder is then turned on the plate to be bored, the diameter being made exactly equal to dimensiond. By placing the buttons in contact with this shoulder, they are accurately located radially and can then be set equi-distant from each other by the use of a micrometer. In this particular case, it would be advisableto begin by setting the four buttons which are 90 degrees apart and then the remaining four. The buttons are next used for setting the work preparatory to boring. (See “Button Method of Accurately Locating Work.”)

Fig. 22. Four Methods of Accurately Dividing a Circle

Another method of securing equal spacing for holes in indexing wheels, etc., is illustrated atB,Fig. 22. This method, however, is not to be recommended if the diameter of the circle on which the holes are to be located, must be very accurate. The disk or ring in which the holes are required, is formed of two sectionseandf, instead of being one solid piece. The centers for the holes are first laid out as accurately as possible on ringe. Partseandfare then clamped together and the holes are drilled through these two sections. Obviously, when the holes are laid out and drilled in this way, there will be some error in the spacing, and, consequently, all of the holes would not match, except when plateeis in the position it occupied when being drilled. Whatever errors may exist in the spacing can be eliminated, however, by successively shifting plateeto different positions and re-reaming the holes for each position. A taper reamer is used and two pins should be provided having the same taper as the reamer. Ringeis first located so that a hole is aligned quite accurately with one in the lower plate. The ring is then clamped and the hole ispartly reamed, the reamer being inserted far enough to finish the hole in plateeand also cut clear around in the upper part of platef. One of the taper pins is then driven into this hole and then a hole on the opposite side is partly reamed, after which the other pin is inserted. The remaining holes are now reamed in the same way, and the reamer should be fed in to the same depth in each case. If a pair of holes is considerably out of alignment, it may be necessary to run the reamer in to a greater depth than was required for the first pair reamed, and in such a case all the holes should be re-reamed to secure a uniform size.

The next step in this operation is to remove the taper pins and clamps or turn index plateeone hole and again clamp it in position. The reaming process just described is then repeated; the holes on opposite sides of the plate are re-reamed somewhat deeper, the taper pins are inserted, and then all of the remaining holes are re-reamed to secure perfect alignment for the new position of the plate. By repeating this process of shifting plateeand re-reaming the holes, whatever error that may have existed originally in the spacing of the holes, will practically be eliminated. It would be very difficult, however, to have these holes located with any great degree of accuracy, on a circle of given diameter.

When an accurate indexing or dividing wheel is required on a machine, the method of securing accurate divisions of the circle illustrated atC,Fig. 22, is sometimes employed. There is a series of circular disks or bushings equal in number to the divisions required, and these disks are all in contact with each other and with a circular boss or shoulder on the plate to which they are attached. The space between adjacent disks is used to accurately locate the dividing wheel, engagement being made with a suitable latch or indexing device. When making a dividing wheel of this kind, all of the disks are ground and lapped to the same diameter and then the diameter of the central boss or plate is gradually reduced until all of the disks are in contact with each other and with the boss. For an example of the practical application of this method see “Originating a Precision Dividing Wheel.”

Another indexing method of spacing holes equi-distant, is illustrated by the diagram atD,Fig. 22. An accurately fitting plug is inserted in the central hole of the plate in which holes are required. Two armshare closely fitted to this plug but are free to rotate and are provided with a fine-pitch screw and nut at the outer ends for adjusting the distance between the arms. Each arm contains an accurately made, hardened steel bushingklocated at the same radial distance from the center of the plate. These bushings are used as a guide for the drill and reamer when machining the holes in the plate.

To determine the center-to-center distance between the bushings, divide360 by twice the number of holes required; find the sine corresponding to the angle thus obtained, and multiply it by the diameter of the circle upon which the holes are located. For example, if there were to be eleven holes on a circle 8 inches in diameter, the distance between the centers of the bushings would equal

The sine of 16.36 degrees is 0.2815, and 0.2815 × 8 = 2.252 inches. The arms are adjusted to locate the centers of the bushings this distance apart, by placing closely fitting plugs in the bushings and measuring from one plug to another with a micrometer or vernier caliper. Of course, when taking this measurement, allowance is made for the diameter of the plugs.

After the arms are set, a hole is drilled and reamed; an accurately fitting plug is then inserted through the bushing and hole to secure the arms when drilling and reaming the adjacent hole. The radial arms are then indexed one hole so that the plug can be inserted through one of the arms and the last hole reamed. The third hole is then drilled and reamed, and this operation is repeated for all of the holes. Evidently, if the center-to-center distance between the bushings is not exactly right, the error will be indicated by the position of the arms relative to the last hole and the first one reamed; moreover, this error will be multiplied as many times as there are holes. For instance, if the arms were too far apart, the difference between the center-to-center distance of the last pair of holes and the center-to-center distance of the bushings in the arms, would equal, in this particular case, eight times the error, and the arms should be re-adjusted accordingly. Larger bushings would then be inserted in the arms and the holes re-reamed, this operation being repeated until the holes were all equi-distant.

As will be seen, the value of this method lies in the fact that it shows the accumulated error. Thus, if the arms were 0.0005 inch too far apart, the difference between the first and last hole would equal 8 × 0.0005 = 0.004 inch. This same principle of dividing can be applied in various ways. For instance, the radial arms if slightly modified, could be used for drilling equally-spaced holes in the periphery or disk of a plate, or, if a suitable marking device were attached, a device of this kind could be used for accurately dividing circular parts.

There are various methods employed for making accurate indexing wheels for a definite number of divisions. One of these methods, suitable particularly for small numbers of divisions, employs a split wheel with a series of taper holes reamed through the two divisions. By shifting the two divisions from point to point (as explained in connection with sketchB,Fig. 22) and reaming and re-reaming the taper holes at each shifting, they may finally be brought very accurately into position. Another method that has been employed consists in clampingabout the rim of the dividing wheel a number of precisely similar blocks, fitting close to each other and to the wheel itself. These blocks are then used for locating the wheel in each of its several positions in actual work. A third and simpler method (a modification of the one last described) consists in grinding a series of disks and clamping them around a rim of such diameter that the disks all touch each other and the rim simultaneously, as explained in connection with sketchC,Fig. 22. The wheel described in the following, which is illustrated inFig. 23, was made in this way.

Fig. 23. Precision Dividing Wheel

DisksAare clamped against an accurately ground face of the wheelBand are supposed to just touch each other all around, and to be each of them in contact with the ground cylindrical surface atx. They are held in proper position by boltsCand nutsD. The bolts fit loosely in the holes of the disks or bushingsAso that the latter are free to be located as may be desired with reference to the bolts.

One or two improvements in the construction of this type of dividing wheel may be noted before proceeding to a description of the way in which it is made. For one thing, instead of having an indexing bolt enter the V-space between two adjoining disks, a smaller diameteryis ground on each of them, over which locking finger or pawl passes, holding the wheel firmly from movement in either direction. This construction has the advantage of a probable lessening of error bylocating on each bushing instead of between two bushings; moreover, it gives a better holding surface and better holding angles than would be the case if this smaller diameter were not provided.

A second improvement lies in the method of clamping the bushingsAin place. Instead of providing each bolt with a separate washer, a ringFis used. This ring fits closely on a seat turned to receive it on the dividing wheelB. When one bushingAhas been clamped in place, the disk is locked from movement so that there is no possibility, in clamping the remaining bushings, of having their location disturbed in the slightest degree by the turning of the nuts in fastening them in place.

The bushingsA, of which there were in this case 24, were all ground exactly to the required diameters on their locating and locking surfaces. The important things in this operation are, first, that the large or locating diameter of the bushing should be exactly to size; and second, that this surface should be in exact alignment with the diameter in which the locking is done; and, finally, that the face of the bushing should be squared with the cylindrical surfaces. A refined exactness for the diameter of the locking surfaces is not so important, as the form of locking device provided allows slight variations at this point without impairment of accuracy. This dimension was kept within very close limits, however. The truth of the two cylindrical surfaces and the face of the bushing was assured by finishing all these surfaces in one operation on the grinding machine.

The sizing of the outer diameter of the bushing, which was 1.158 inch, must be done so accurately that it was not thought wise to trust to the ordinary micrometer caliper. An indexing device was therefore made having a calipering lever with a long end, in the ratio of 10 to 1, which actuated the plunger of a dial test indicator of the well-known type made by the Waltham Watch Tool Co. The thousandth graduations on the dial of this indicator would then read in ten-thousandths, permitting readings to be taken to one-half or one-quarter of this amount. The final measurements with this device were all taken after dipping the bushings in water of a certain temperature, long enough to give assurance that this temperature was universal in all the parts measured. It will be understood, of course, in this connection, that getting the diameter of these bushings absolutely to 1.158 inch was not so important as getting them all exactly alike, whether slightly over or slightly under this dimension; hence, the precaution taken in measurement.

WheelBwas next ground down nearly to size, great care being taken that it should run exactly concentric with the axis. As soon as the diameter of the surfacexwas brought nearly to the required dimension as obtained by calculation, the disks were tried in place. The first one was put in position with its loose hole central on the bolt and clamped in place under ringF. The next bushing was then pressed up against it and against the surfacexof the wheel and clamped in place. The third one was similarly clamped in contact with its neighboring bushing and the wheel, and so on, untilthe whole circle was completed. It was then found that the last disk would not fill the remaining space. This required the grinding off of some stock from surfacex, and a repetition of the fitting of the bushingsAuntil they exactly filled the space provided for them.

Fig. 24. Precision Dividing Wheel and its Indexing Mechanism

This operation required, of course, considerably more skill than a simple description of the job would indicate. One of the points that had to be carefully looked out for was the cleaning of all the surfaces in contact. A bit of dust or lint on one of the surfaces would throw the fitting entirely out. The temperature of the parts was another important consideration. As an evidence of the accuracy with which the work was done, it might be mentioned that it was found impossible to do this fitting on a bench on the southern or sunny side of the shop, the variations of temperature between morning and noon, and between bright sunshine and passing clouds, being such that the disks would not fit uniformly. The variation from these minute temperature changes resultedfrom the different coefficients of expansion of the iron wheel and the steel bushings. The obvious thing to do would be to build a room for this work kept at a constant temperature and preferably that of the body, so that the heat of the body would make no difference in the results. It was found sufficient in this case, however, to do the work on the northern side of the shop where the temperature was more nearly constant, not being affected by variations in sunshine.

The dividing wheel, the construction of which has just been described, was made by the Fellows Gear Shaper Co. It is used for indexing the Fellows gear cutters in the machine in which the teeth are ground. The indexing mechanism of this machine is shown inFig. 24. It is operated by a handle or lever pinned to rock-shaftH, to which is keyed armJ. Pivoted toJis a pawlKengaging the teeth of ratchetL, which revolves loosely on shaftH. This ratchetLcontrols the movement of locking fingerE. The parts are shown in their normal or locked position in the engraving.

As the handle on shaftHis pulled in the direction indicated by the arrow, armJis raised, carrying the ratchet wheel around to the right. This allows flat springMto drop off of the ratchet tooth, permitting helical springOto raise latchEand thus leave the wheel free. The continued movement of the hand-lever and of rock-shaftH, by means of gearN, intermediate pinionPand gearQ, causes the indexing pawlR, which is pivoted to gearQand acts on the head of one of the boltsC(see Fig. 23), to index the wheel one step. Just before reaching its new location the new tooth of ratchet wheelLcoming up, bears down on the top of springM, pressing latchEinto place against the tension of coil springO. By this means the wheel is locked in position.

When the operator pushes the handle on shaftHback again to its position of rest, the pawlRis retracted into position to act on the next bolt head for the next indexing. Star-wheelLremains stationary on this backward movement, being prevented from revolving by the notch on the top of the tooth into which springMfits. PawlKon its return engages with the next tooth of this wheel, ready for the next indexing operation.

A slight rotary adjustment of dividing wheelB, independent of this indexing mechanism, is required for the feeding of the machine. This is accomplished by the end movement of latchE, which is pivoted in slideS. This slide is pressed to the right by spring plungerT, and is adjusted positively in the other direction by feed-screwU, which is finely graduated to permit accurate adjustment. The accuracy in indexing obtained by the use of a wheel thus made was required to bring the finished cutters within the very narrow limits allowed for them in the final inspection.

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