ACCURATE DIVIDING AND SPACING 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.
[Illustration: Fig. 18. Method of Drilling Small Equally-spaced Holes
in Rows]
Locating 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 is illustrated 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.
Use of Disks for Locating Equally-Spaced Holes
A simple method of spacing holes that are to be drilled in a straight
line is illustrated in Fig. 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.
[Illustration: Fig. 19. Locating Equi-distant Holes in a Straight Line
by Means of Disks and Straightedge]
A method of using disks, which is preferable for very accurate work, is
shown in Fig. 20. The disks are clamped against each other and along
straightedge _A_ by 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 straightedge _B_, 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.
Adjustable Jig for Accurate Hole Spacing
An adjustable jig for accurately spacing small holes is shown in Fig.
21.
[Illustration: 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 bushings _A_ and _B_
which are carried by independent slides. These slides can be shifted
along a dovetail groove after loosening the screws of clamp-gib _C_. 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,
slides _A_ and _B_ would be set so that the dimension _x_ equals 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, bushing _B_ and one of the end holes, the
first hole is drilled and reamed through bushing _A_; the jig is then
shifted to the left until the plug in _B_ enters the hole just made.
The second hole is then drilled and reamed through bushing _A_ and
this drilling 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.
[Illustration: Fig. 21. Adjustable Jig for Accurate Hole Spacing]
Methods of Accurately Dividing a Circle
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 at _A_, 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 diameter
_d_ (see illustration). A narrow shoulder is then turned on the plate
to be bored, the diameter being made exactly equal to dimension
_d_. 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 advisable to 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.”)
[Illustration: Fig. 22. Four Methods of Accurately Dividing a Circle]
Correcting Spacing Errors by Split Ring Method
Another method of securing equal spacing for holes in indexing wheels,
etc., is illustrated at _B_, 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 sections _e_ and _f_, instead
of being one solid piece. The centers for the holes are first laid
out as accurately as possible on ring _e_. Parts _e_ and _f_ are 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 plate _e_ is in the position it occupied
when being drilled. Whatever errors may exist in the spacing can be
eliminated, however, by successively shifting plate _e_ to 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. Ring _e_ is first located so that a hole is aligned quite
accurately with one in the lower plate. The ring is then clamped and
the hole is partly reamed, the reamer being inserted far enough to
finish the hole in plate _e_ and also cut clear around in the upper
part of plate _f_. 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 plate _e_ one 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 plate _e_ and 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.
Circular Spacing by Contact of Uniform Disks
When an accurate indexing or dividing wheel is required on a machine,
the method of securing accurate divisions of the circle illustrated
at _C_, 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.”
Spacing by Correcting the Accumulated Error
Another indexing method of spacing holes equi-distant, is illustrated
by the diagram at _D_, Fig. 22. An accurately fitting plug is inserted
in the central hole of the plate in which holes are required. Two
arms _h_ are 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 bushing _k_ located 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,
divide 360 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
360
——————— = 16.36 degrees.
2 × 11
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.
Originating a Precision Dividing Wheel
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
sketch _B_, 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 clamping about 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 sketch _C_, Fig. 22.
The wheel described in the following, which is illustrated in Fig. 23,
was made in this way.
[Illustration: Fig. 23. Precision Dividing Wheel]
Disks _A_ are clamped against an accurately ground face of the wheel
_B_ and are supposed to just touch each other all around, and to be
each of them in contact with the ground cylindrical surface at _x_.
They are held in proper position by bolts _C_ and nuts _D_. The bolts
fit loosely in the holes of the disks or bushings _A_ so 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 diameter _y_
is 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 by
locating 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 bushings _A_ in
place. Instead of providing each bolt with a separate washer, a ring
_F_ is used. This ring fits closely on a seat turned to receive it on
the dividing wheel _B_. When one bushing _A_ has 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 bushings _A_, 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.
Wheel _B_ was 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 surface _x_ was 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 ring _F_. The next bushing was then
pressed up against it and against the surface _x_ of the wheel and
clamped in place. The third one was similarly clamped in contact with
its neighboring bushing and the wheel, and so on, until the 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 surface _x_, and a repetition of the fitting of the bushings _A_
until they exactly filled the space provided for them.
[Illustration: 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
resulted from 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 in Fig. 24. It is operated
by a handle or lever pinned to rock-shaft _H_, to which is keyed arm
_J_. Pivoted to _J_ is a pawl _K_ engaging the teeth of ratchet _L_,
which revolves loosely on shaft _H_. This ratchet _L_ controls the
movement of locking finger _E_. The parts are shown in their normal or
locked position in the engraving.
As the handle on shaft _H_ is pulled in the direction indicated by the
arrow, arm _J_ is raised, carrying the ratchet wheel around to the
right. This allows flat spring _M_ to drop off of the ratchet tooth,
permitting helical spring _O_ to raise latch _E_ and thus leave the
wheel free. The continued movement of the hand-lever and of rock-shaft
_H_, by means of gear _N_, intermediate pinion _P_ and gear _Q_, causes
the indexing pawl _R_, which is pivoted to gear _Q_ and acts on the
head of one of the bolts _C_ (see Fig. 23), to index the wheel one
step. Just before reaching its new location the new tooth of ratchet
wheel _L_ coming up, bears down on the top of spring _M_, pressing
latch _E_ into place against the tension of coil spring _O_. By this
means the wheel is locked in position.
When the operator pushes the handle on shaft _H_ back again to its
position of rest, the pawl _R_ is retracted into position to act on the
next bolt head for the next indexing. Star-wheel _L_ remains stationary
on this backward movement, being prevented from revolving by the notch
on the top of the tooth into which spring _M_ fits. Pawl _K_ on its
return engages with the next tooth of this wheel, ready for the next
indexing operation.
A slight rotary adjustment of dividing wheel _B_, independent of this
indexing mechanism, is required for the feeding of the machine. This
is accomplished by the end movement of latch _E_, which is pivoted in
slide _S_. This slide is pressed to the right by spring plunger _T_,
and is adjusted positively in the other direction by feed-screw _U_,
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.