Chapter 6

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=Accurate Measurement of Angles and Tapers.=--When great accuracy is required in the measurement of angles, or when originating tapers, disks are commonly used. The principle of the disk method of taper measurement is that if two disks of unequal diameters are placed either in contact or a certain distance apart, lines tangent to their peripheries will represent an angle or taper, the degree of which depends upon the diameters of the two disks and the distance between them. The gage shown in Fig. 16, which is a form commonly used for originating tapers or measuring angles accurately, is set by means of disks. This gage consists of two adjustable straight-edges _A_ and _A_{1}_, which are in contact with disks _B_ and _B_{1}_. The angle [alpha] or the taper between the straight-edges depends, of course, upon the diameters of the disks and the center distance _C_, and as these three dimensions can be measured accurately, it is possible to set the gage to a given angle within very close limits. Moreover, if a record of the three dimensions is kept, the exact setting of the gage can be reproduced quickly at any time. The following rules may be used for adjusting a gage of this type.

[Ill.u.s.tration: Fig. 16. Disk Gage for Accurate Measurement of Angles and Tapers]

=To Find Center Distance for a Given Taper.=--When the taper, in inches per foot, is given, to determine center distance _C_. _Rule:_ Divide the taper by 24 and find the angle corresponding to the quotient in a table of tangents; then find the sine corresponding to this angle and divide the difference between the disk diameters by twice the sine.

_Example:_ Gage is to be set to 3/4 inch per foot, and disk diameters are 1.25 and 1.5 inch, respectively. Find the required center distance for the disks.

0.75 ---- = 0.03125.

The angle whose tangent is 0.03125 equals 1 degree 47.4 minutes; sin 1 47.4" = 0.03123; 1.50 - 1.25 = 0.25 inch;

0.25 ----------- = 4.002 inches = center distance C.

2 0.03123

=To Find Center Distance for a Given Angle.=--When straight-edges must be set to a given angle [alpha], to determine center distance _C_ between disks of known diameter. _Rule:_ Find the sine of half the angle [alpha] in a table of sines; divide the difference between the disk diameters by double this sine.

_Example:_ If an angle [alpha] of 20 degrees is required, and the disks are 1 and 3 inches in diameter, respectively, find the required center distance _C_.

20 ---- = 10 degrees; sin 10 = 0.17365; 2

3 - 1 ----------- = 5.759 inches = center distance _C_.

2 0.17365

=To Find Angle for Given Taper per Foot.=--When the taper in inches per foot is known, and the corresponding angle [alpha] is required. _Rule:_ Divide the taper in inches per foot by 24; find the angle corresponding to the quotient, in a table of tangents, and double this angle.

_Example:_ What angle [alpha] is equivalent to a taper of 1-1/2 inch per foot?

1.5 --- = 0.0625.

The angle whose tangent is 0.0625 equals 3 degrees 35 minutes, nearly; then, 3 deg. 35 min. 2 = 7 deg. 10 min.

=To Find Angle for Given Disk Dimensions.=--When the diameters of the large and small disks and the center distance are given, to determine the angle [alpha]. _Rule:_ Divide the difference between the disk diameters by twice the center distance; find the angle corresponding to the quotient, in a table of sines, and double the angle.

_Example:_ If the disk diameters are 1 and 1.5 inch, respectively, and the center distance is 5 inches, find the included angle [alpha].

1.5 - 1 ------- = 0.05.

2 5

The angle whose sine is 0.05 equals 2 degrees 52 minutes; then, 2 deg.

52 min. 2 = 5 deg. 44 min. = angle [alpha].

[Ill.u.s.tration: Fig. 17. Setting Center Mark in Line with Axis of Lathe Spindle by use of Test Indicator]

[Ill.u.s.tration: Fig. 18. Jig-plate with b.u.t.tons attached, ready for Boring]

=Use of the Center Indicator.--=The center test indicator is used for setting a center-punch mark, the position of which corresponds with the center or axis of the hole to be bored, in alignment with the axis of the lathe spindle. To ill.u.s.trate, if two holes are to be bored, say 5 inches apart, small punch marks having that center-to-center distance would be laid out as accurately as possible. One of these marks would then be set central with the lathe spindle by using a center test indicator as shown in Fig. 17. This indicator has a pointer _A_ the end of which is conical and enters the punch mark. The pointer is held by shank _B_ which is fastened in the toolpost. The joint _C_ by means of which the pointer is held to the shank is universal; that is, it allows the pointer to move in any direction. Now when the part being tested is rotated by running the lathe, if the center-punch mark is not in line with the axes of the lathe spindle, obviously the outer end of pointer _A_ will vibrate, and as joint _C_ is quite close to the inner end, a very slight error in the location of the center-punch mark will cause a perceptible movement of the outer end, as indicated by the dotted lines.

When the work has been adjusted until the pointer remains practically stationary, the punch mark is central, and the hole is bored. The other center-punch mark is then set in the same way for boring the second hole. The accuracy of this method depends, of course, upon the location of the center-punch marks. A still more accurate way of setting parts for boring holes to a given center-to-center distance is described in the following:

=Locating Work by the b.u.t.ton Method.=--Among the different methods employed by machinists and toolmakers for accurately locating work such as jigs, etc., on the faceplate of a lathe, the one most commonly used is known as the b.u.t.ton method. This scheme is so named because cylindrical bushings or b.u.t.tons are attached to the work in positions corresponding to the holes to be bored, after which they are used in locating the work. These b.u.t.tons, which are ordinarily about 1/2 inch in diameter, are ground and lapped to the same size and the ends squared.

The diameter should, preferably, be such that the radius can be determined easily, and the hole through the center should be about 1/8 inch larger than the retaining screw, so that the b.u.t.ton can be shifted.

As an ill.u.s.tration of the practical application of the b.u.t.ton method, we shall consider, briefly, the way the holes would be accurately machined in the jig-plate in Fig. 18. First the centers of the seven holes should be laid off approximately correct by the usual methods, after which small holes should be drilled and tapped for the clamping screws _S_.

After the b.u.t.tons _B_ are clamped lightly in place, they are all set in correct relation with each other and with the jig-plate. The proper location of the b.u.t.tons is very important as their positions largely determine the accuracy of the work. A definite method of procedure that would be applicable in all cases cannot, of course, be given, as the nature of the work as well as the tools available make it necessary to employ different methods.

[Ill.u.s.tration: Fig. 19. Setting a b.u.t.ton True Preparatory to Boring, by use of Test Indicator]

In this particular case, the three b.u.t.tons _a_, _b_ and _c_ should be set first, beginning with the one in the center. As this central hole must be 2.30 and 2.65 inches from the finished sides _A_ and _A_{1}_, respectively, the work is first placed on an accurate surface-plate as shown; by resting it first on one of these sides and then on the other, and measuring with a vernier height gage, the central b.u.t.ton can be accurately set. The b.u.t.tons _a_ and _c_ are also set to the correct height from side _A_{1}_ by using the height gage, and in proper relation to the central b.u.t.ton by using a micrometer or a vernier caliper and measuring the over-all dimension _x_. When measuring in this way, the diameter of one b.u.t.ton would be deducted to obtain the correct center-to-center distance. After b.u.t.tons _a_, _b_ and _c_ are set equidistant from side A_{1} and in proper relation to each other, the remaining b.u.t.tons should be set radially from the central b.u.t.ton _b_ and the right distance apart. By having two micrometers or gages, one set for the radial dimension _x_ and the other for the chordal distance _y_, the work may be done in a comparatively short time.

[Ill.u.s.tration: Fig. 20. Testing Concentricity of b.u.t.ton with Dial Gage]

After the b.u.t.tons have been tightened, all measurements should be carefully checked; the work is then mounted on the faceplate of the lathe, and one of the b.u.t.tons, say _b_, is set true by the use of a test indicator as shown in Fig. 19. When the end of this indicator (which is one of a number of types on the market) is brought into contact with the revolving b.u.t.ton, the vibration of the pointer _I_ shows how much the b.u.t.ton runs out of true. When the pointer remains practically stationary, thus showing that the b.u.t.ton runs true, the latter should be removed. The hole is then drilled nearly to the required size, after which it is bored to the finish diameter. In a similar manner the other b.u.t.tons are indicated and the holes bored, one at a time. It is evident that if each b.u.t.ton is correctly located and set perfectly true in the lathe, the various holes will be located at the required center-to-center dimensions within very close limits.

[Ill.u.s.tration: Fig. 21. Drilling a Bushing Hole]

Fig. 20 shows how one of the b.u.t.tons attached to a plate in which three holes are to be bored is set true or concentric. The particular indicator ill.u.s.trated is of the dial type, any error in the location of the b.u.t.ton being shown by a hand over a dial having graduations representing thousandths of an inch. Fig. 21 shows how the hole is drilled after the b.u.t.ton is removed. It will be noted that the drill is held in a chuck, the taper shank of which fits into the tailstock spindle, this being the method of holding small drills. After drilling, the hole is bored as shown in Fig. 22. The boring tool should have a keen edge to avoid springing, and if the work when clamped in position, throws the faceplate out of balance, it is advisable to restore the balance, before boring, by the use of a counter-weight, because the lathe can be rotated quite rapidly when boring such a small hole.

[Ill.u.s.tration: Fig. 22. Boring a Bushing Hole]

When doing precision work of this kind, the degree of accuracy will depend upon the instruments used, the judgment and skill of the workman and the care exercised. A good general rule to follow when locating bushings or b.u.t.tons is to use the method which is the most direct and which requires the least number of measurements. As an ill.u.s.tration of how errors may acc.u.mulate, let us a.s.sume that seven holes are to be bored in the jig-plate shown in Fig. 23, so that they are the same distance from each other and in a straight line. The b.u.t.tons may be brought into alignment by the use of a straight-edge, and to simplify matters, it will be taken for granted that they have been ground and lapped to the same size. If the diameter of the b.u.t.tons is first determined by measuring with a micrometer, and then this diameter is deducted from the center distance _x_, the difference will be the distance _y_ between adjacent b.u.t.tons. Now if a temporary gage is made to length _y_, all the b.u.t.tons can be set practically the same distance apart, the error between any two adjacent ones being very slight. If, however, the total length _z_ over the end b.u.t.tons is measured by some accurate means, the chances are that this distance will not equal six times dimension _x_ plus the diameter of one b.u.t.ton, as it should, because even a very slight error in the gage for distance _y_ would gradually acc.u.mulate as each b.u.t.ton was set. If a micrometer were available that would span two of the b.u.t.tons, the measurements could be taken direct and greater accuracy would doubtless be obtained. On work of this kind where there are a number of holes that need to have accurate over-all dimensions, the long measurements should first be taken when setting the b.u.t.tons, providing, of course, there are proper facilities for so doing, and then the short ones. For example, the end b.u.t.tons in this case should first be set, then the central one and finally those for the sub-divisions.

[Ill.u.s.tration: Fig. 23. Example of Work ill.u.s.trating Acc.u.mulation of Errors]

=Eccentric Turning.=--When one cylindrical surface must be turned eccentric to another, as when turning the eccentric of a steam engine, an arbor having two sets of centers is commonly used, as shown in Fig.

24. The distance _x_ between the centers must equal one-half the total "throw" or stroke of the eccentric. The hub of the eccentric is turned upon the centers _a--a_, and the tongued eccentric surface, upon the offset centers, as indicated by the ill.u.s.tration. Sometimes eccentrics are turned while held upon special fixtures attached to the faceplate.

[Ill.u.s.tration: Fig. 24. Special Arbor for Turning Eccentrics]

When making an eccentric arbor, the offset center in each end should be laid out upon radial lines which can be drawn across the arbor ends by means of a surface gage. Each center is then drilled and reamed to the same radius _x_ as near as possible. The uniformity of the distance _x_ at each end is then tested by placing the mandrel upon the offset centers and rotating it, by hand, with a dial indicator in contact at first one end and then the other. The amount of offset can also be tested either by measuring from the point of a tool held in the toolpost, or by setting the tool to just graze the mandrel at extreme inner and outer positions, and noting the movement of the cross-slide by referring to the dial gage of the cross-feed screw.

[Ill.u.s.tration: Fig. 25. Turning an Engine Crank-pin in an Ordinary Lathe]

=Turning a Crankshaft in a Lathe.=--Another example of eccentric turning is shown in Fig. 25. The operation is that of turning the crank-pin of an engine crankshaft, in an ordinary lathe. The main shaft is first rough-turned while the forging revolves upon its centers _C_ and _C_{1}_ and the ends are turned to fit closely the center-arms _A_ and _A_{1}_.

After the sides _B_ and _B_{1}_ of the crank webs have been rough-faced, the center-arms are attached to the ends of the shaft as shown in the ill.u.s.tration. These arms have centers at _D_ and _D_{1}_ (located at the required crank radius) which should be aligned with the rough pin, when attaching the arms, and it is advisable to insert braces _E_ between the arms and crank to take the thrust of the lathe centers. With the forging supported in this way, the crank-pin and inner sides of the webs are turned and faced, the work revolving about the axis of the pin. The turning tools must extend beyond the tool-holder far enough to allow the crank to clear as it swings around. Owing to this overhang, the tool should be as heavy as possible to make it rigid and it is necessary to take comparatively light cuts and proceed rather cautiously. After finishing the crank-pin and inside of the crank, the center-arms are removed and the main body of the shaft and the sides _B_ and _B_{1}_ are finished. This method of turning crankshafts is often used in general repair shops, etc., especially where new shafts do not have to be turned very often. It is slow and inefficient, however, and where crankshafts are frequently turned, special machines or attachments are used.

[Ill.u.s.tration: Fig. 26. LeBlond Lathe with Special Equipment for Crankshaft Turning]

=Special Crankshaft Lathe.=--A lathe having special equipment for rough-turning gas engine crankshaft pins is shown in Fig. 26. This lathe is a heavy-duty type built by the R. K. LeBlond Machine Tool Co.

It is equipped with special adjustable headstock and tailstock fixtures designed to take crankshafts having strokes up to about 6 inches. The tools are held in a three-tool turret type of toolpost and there are individual cross-stops for each tool. This lathe also has a roller steadyrest for supporting the crankshaft; automatic stops for the longitudinal feed, and a pump for supplying cutting lubricant. The headstock fixture is carried on a faceplate mounted on the spindle and so arranged as to be adjustable for cranks of different throw. When the proper adjustment for a given throw has been made, the slide is secured by four T-bolts. A graduated scale and adjusting screw permit of accurate adjustments.

The revolving fixture is accurately indexed for locating different crank-pins in line with the lathe centers, by a hardened steel plunger in the slide which engages with hardened bushings in the fixture. The index is so divided that the fixture may be rotated 120 or 180 degrees, making it adjustable for 2-, 4- and 6-throw cranks. After indexing, the fixture is clamped by two T-bolts which engage a circular T-slot. The revolving fixture is equipped with removable split bushings which can be replaced to fit the line bearings of different sized crankshafts. The work is driven by a V-shaped dovetail piece having a hand-nut adjustment, which also centers the pin by the cheek or web. The crank is held in position by a hinged clamp on the fixture. The tailstock fixture is also adjustable and it is mounted on a spindle which revolves in a bushing in the tailstock barrel. The adjustment is obtained in the same manner as on the headstock fixture, and removable split bushings as well as a hinged clamp are also employed.

The method of chucking a four-throw crank is as follows: The two fixtures are brought into alignment by two locking pins. One of these is located in the head and enters a bushing in the large faceplate and the other is in the tailstock and engages the tailstock fixture. The crankshaft is delivered to the machine with the line bearings rough-turned and it is clamped by the hinged clamp previously referred to and centered by the V-shaped driver. The locking pins for both fixtures are then withdrawn and the machine is ready to turn two of the pins. After these have been machined, the fixtures are again aligned by the locking pins, the two T-bolts of the headstock fixture and the hinged clamp at the tailstock are released, the indexing plunger is withdrawn and the headstock fixture and crank are turned 180 degrees or until the index plunger drops into place. The crank is then clamped at the tailstock end and the revolving fixture is secured by the two T-bolts previously referred to. After the locking pins are withdrawn, the lathe is ready to turn the two opposite pins.

[Ill.u.s.tration: Fig. 27. Diagrams showing Arrangements of Tools on LeBlond Lathe]

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