in which

_r_ = _L_ _l_; _L_ = lead of spiral; _l_ = lead of hob thread.

For example, if a hob has a pitch circ.u.mference of 3.25, a single thread of 0.75 inch lead, and 6 spiral flutes, what compensating gears would be required?

The lead _L_ of the spiral flutes is first determined by dividing the square of the circ.u.mference _C_ of the hob at the pitch line by the lead _l_ of the hob thread. Thus lead _L_ = _C^2_/_l_, or, in this case, _L_ = 3.25^2/0.75 = 14 inches, approximately. Then _r_ = 14 0.75 = 18-2/3.

Inserting these values in the formula for ratio R,

18-2/3 + 1 19-2/3 19-2/3 3 59 _R_ = ---------- = ------ = ---------- = -- 18-2/3 18-2/3 18-2/3 3 56

Hence, the compensating gears will have 56 and 59 teeth, respectively, the latter being the driver. As the gears for 6 flutes listed on the regular index plate are, stud-gear 60 teeth, cam-shaft gear 40 teeth, the entire train of gears would be as follows: Gear on stud, 60; _driven_ intermediate gear, 56; _driving_ intermediate gear, 59; cam-shaft gear, 40. It will be understood that the position of the driving gears or the driven gears can be transposed without affecting the ratio.

=Cla.s.ses of Fits Used in Machine Construction.=--In a.s.sembling machine parts it is necessary to have some members fit together tightly, whereas other parts such as shafts, etc., must be free to move or revolve with relation to each other. The accuracy required for a fitting varies for different cla.s.ses of work. A shaft that revolves in its bearing must be slightly smaller than the bearing so that there will be room for a film of lubricant. A crank-pin that must be forced into the crank-disk is made a little larger in diameter than the hole, to secure a tight fit.

When a very accurate fitting between two cylindrical parts that must be a.s.sembled without pressure is required, the diameter of the inner member is made as close to the diameter of the outer member as is possible. In ordinary machine construction, five cla.s.ses of fits are used, _viz_; running fit, push fit, driving fit, forced fit and shrinkage fit. The running fit, as the name implies, is employed when parts must rotate; the push fit is not sufficiently free to rotate; the other cla.s.ses referred to are used for a.s.sembling parts that must be held in fixed positions.

=Forced Fits.=--This is the term used when a pin, shaft or other cylindrical part is forced into a hole of slightly smaller diameter, by the use of a hydraulic press or other means. As a rule, forced fits are restricted to parts of small and medium size, while shrinkage fits have no such limitations and are especially applicable when a maximum "grip"

is desired, or when (as in the construction of ordnance) accurate results as to the intensity of stresses produced in the parts united are required. The proper allowance for a forced fit depends upon the ma.s.s of metal surrounding the hole, the size of the work, the kind and quality of the material of which the parts are composed and the smoothness and accuracy of the pin and bore. When a pin or other part is pressed into a hole a second time, the allowance for a given tonnage should be diminished somewhat because the surface of the bore is smoother and the metal more compact. The pressure required in a.s.sembling a forced fit will also vary for cast hubs of the same size, if they are not uniform in hardness. Then there is the personal factor which is much in evidence in work of this kind; hence, data and formulas for forced fit allowances must be general in their application.

=Allowance for Forced Fits.=--The allowance per inch of diameter usually ranges from 0.001 inch to 0.0025 inch, 0.0015 being a fair average.

Ordinarily, the allowance per inch decreases as the diameter increases; thus the total allowance for a diameter of 2 inches might be 0.004 inch, whereas for a diameter of 8 inches the total allowance might not be over 0.009 or 0.010 inch. In some shops the allowance is made practically the same for all diameters, the increased surface area of the larger sizes giving sufficient increase in pressure. The parts to be a.s.sembled by forced fits are usually made cylindrical, although sometimes they are slightly tapered. The advantages of the taper form are that the possibility of abrasion of the fitted surfaces is reduced; that less pressure is required in a.s.sembling; and that the parts are more readily separated when renewal is required. On the other hand, the taper fit is less reliable, because if it loosens, the entire fit is free with but little axial movement. Some lubricant, such as white lead and lard oil mixed to the consistency of paint, should be applied to the pin and bore before a.s.sembling, to reduce the tendency of abrasion.

Allowances for Different Cla.s.ses of Fits

(Newall Engineering Co.)

+-----+--------------------------------------------------------------+ | | Tolerances in Standard Holes[1] | |Cla.s.s+------------+---------+---------+---------+---------+---------+ | | Nominal | Up to | 9/16"-1"| 1-1/16"-| 2-1/16"-| 3-1/16"-| | | Diameters | 1/2" | | 2" | 3" | 4" | +-----+------------+---------+---------+---------+---------+---------+ | | High Limit | +0.0002 | +0.0005 | +0.0007 | +0.0010 | +0.0010 | | A | Low Limit | -0.0002 | -0.0002 | -0.0002 | -0.0005 | -0.0005 | | | Tolerance | 0.0004 | 0.0007 | 0.0009 | 0.0015 | 0.0015 | +-----+------------+---------+---------+---------+---------+---------+ | | High Limit | +0.0005 | +0.0007 | +0.0010 | +0.0012 | +0.0015 | | B | Low Limit | -0.0005 | -0.0005 | -0.0005 | -0.0007 | -0.0007 | | | Tolerance | 0.0010 | 0.0012 | 0.0015 | 0.0019 | 0.0022 | +-----+------------+---------+---------+---------+---------+---------+ | Allowances for Forced Fits | +-----+------------+---------+---------+---------+---------+---------+ | | High Limit | +0.0010 | +0.0020 | +0.0040 | +0.0060 | +0.0080 | | F | Low Limit | +0.0005 | +0.0015 | +0.0030 | +0.0045 | +0.0060 | | | Tolerance | 0.0005 | 0.0005 | 0.0010 | 0.0015 | 0.0020 | +-----+------------+---------+---------+---------+---------+---------+ | Allowances for Driving Fits | +-----+------------+---------+---------+---------+---------+---------+ | | High Limit | +0.0005 | +0.0010 | +0.0015 | +0.0025 | +0.0030 | | D | Low Limit | +0.0002 | +0.0007 | +0.0010 | +0.0015 | +0.0020 | | | Tolerance | 0.0003 | 0.0003 | 0.0005 | 0.0010 | 0.0010 | +-----+------------+---------+---------+---------+---------+---------+ | Allowances for Push Fits | +-----+------------+---------+---------+---------+---------+---------+ | | High Limit | -0.0002 | -0.0002 | -0.0002 | -0.0005 | -0.0005 | | P | Low Limit | -0.0007 | -0.0007 | -0.0007 | -0.0010 | -0.0010 | | | Tolerance | 0.0005 | 0.0005 | 0.0005 | 0.0005 | 0.0005 | +-----+------------+---------+---------+---------+---------+---------+ | Allowances for Running Fits[2] | +-----+------------+---------+---------+---------+---------+---------+ | | High Limit | -0.0010 | -0.0012 | -0.0017 | -0.0020 | -0.0025 | | X | Low Limit | -0.0020 | -0.0027 | -0.0035 | -0.0042 | -0.0050 | | | Tolerance | 0.0010 | 0.0015 | 0.0018 | 0.0022 | 0.0025 | | | High Limit | -0.0007 | -0.0010 | -0.0012 | -0.0015 | -0.0020 | | Y | Low Limit | -0.0012 | -0.0020 | -0.0025 | -0.0030 | -0.0035 | | | Tolerance | 0.0005 | 0.0010 | 0.0013 | 0.0015 | 0.0015 | | | High Limit | -0.0005 | -0.0007 | -0.0007 | -0.0010 | -0.0010 | | Z | Low Limit | -0.0007 | -0.0012 | -0.0015 | -0.0020 | -0.0022 | | | Tolerance | 0.0002 | 0.0005 | 0.0008 | 0.0010 | 0.0012 | +-----+------------+---------+---------+---------+---------+---------+

[1] Tolerance is provided for holes, which ordinary standard reamers can produce, in two grades, Cla.s.ses A and B, the selection of which is a question for the user's decision and dependent upon the quality of the work required; some prefer to use Cla.s.s A as working limits and Cla.s.s B as inspection limits.

[2] Running fits, which are the most commonly required, are divided into three grades: Cla.s.s X for engine and other work where easy fits are wanted; Cla.s.s Y for high speeds and good average machine work; Cla.s.s Z for fine tool work.

=Pressure for Forced Fits.=--The pressure required for a.s.sembling cylindrical parts depends not only upon the allowance for the fit, but also upon the area of the fitted surfaces, the pressure increasing in proportion to the distance that the inner member is forced in. The approximate ultimate pressure in pounds can be determined by the use of the following formula in conjunction with the accompanying table of "Pressure Factors."

=Pressure Factors=

+-----+-----++-----+-----++-----+-----++------+------++------+------+ |Diam-|Pres-||Diam-|Pres-||Diam-|Pres-||Diam- |Pres- ||Diam- |Pres- | |eter,|sure ||eter,|sure ||eter,|sure ||eter, |sure ||eter, |sure | |In- |Fac- ||In- |Fac- ||In- |Fac- ||In- |Fac- ||In- |Fac- | |ches | tor ||ches | tor ||ches | tor ||ches |tor ||ches |tor | +-----+-----++-----+-----++-----+-----++------+------++------+------+ |1 | 500 ||3-1/2| 132 ||6 | 75 || 9 | 48.7 ||14 | 30.5 | |1-1/4| 395 ||3-3/4| 123 ||6-1/4| 72 || 9-1/2| 46.0 ||14-1/2| 29.4 | |1-1/2| 325 ||4 | 115 ||6-1/2| 69 ||10 | 43.5 ||15 | 28.3 | |1-3/4| 276 ||4-1/4| 108 ||6-3/4| 66 ||10-1/2| 41.3 ||15-1/2| 27.4 | |2 | 240 ||4-1/2| 101 ||7 | 64 ||11 | 39.3 ||16 | 26.5 | |2-1/4| 212 ||4-3/4| 96 ||7-1/4| 61 ||11-1/2| 37.5 ||16-1/2| 25.6 | |2-1/2| 189 ||5 | 91 ||7-1/2| 59 ||12 | 35.9 ||17 | 24.8 | |2-3/4| 171 ||5-1/4| 86 ||7-3/4| 57 ||12-1/2| 34.4 ||17-1/2| 24.1 | |3 | 156 ||5-1/2| 82 ||8 | 55 ||13 | 33.0 ||18 | 23.4 | |3-1/4| 143 ||5-3/4| 78 ||8-1/2| 52 ||13-1/2| 31.7 ||.... | .... | +-----+-----++-----+-----++-----+-----++------+------++------+------+

a.s.suming that _A_ = area of fitted surface; _a_ = total allowance in inches; _P_ = ultimate pressure required, in tons; _F_ = pressure factor based upon a.s.sumption that the diameter of the hub is twice the diameter of the bore, that the shaft is of machine steel, and the hub of cast iron, then,

_A_ _a_ _F_ _P_ = --------------- 2

_Example:_--What will be the approximate pressure required for forcing a 4-inch machine steel shaft having an allowance of 0.0085 inch into a cast-iron hub 6 inches long?

_A_ = 4 3.1416 6 = 75.39 square inches;

_F_, for a diameter of 4 inches, = 115 (see table of "Pressure Factors"). Then,

_P_ = (75.39 0.0085 115)/2 = 37 tons, approximately.

=Allowance for Given Pressure.=--By transposing the preceding formula, the approximate allowance for a required ultimate tonnage can be determined. Thus, _a_ = 2_P_ _AF_. The average ultimate pressure in tons commonly used ranges from 7 to 10 times the diameter in inches.

a.s.suming that the diameter of a machine steel shaft is 4 inches and an ultimate pressure of about 30 tons is desired for forcing it into a cast-iron hub having a length of 5-1/2 inches, what should be the allowance?

_A_ = 4 3.1416 5-1/2 = 69 square inches,

_F_, for a diameter of 4 inches, = 115. Then,

2 30 _a_ = -------- = 0.0075 inch.

69 115

=Shrinkage Fits.=--When heat is applied to a piece of metal, such as iron or steel, as is commonly known, a certain amount of expansion takes place which increases as the temperature is increased, and also varies somewhat with different kinds of metal, copper and bra.s.s expanding more for a given increase in temperature than iron and steel. When any part which has been expanded by the application of heat is cooled, it contracts and resumes its original size. This expansive property of metals has been taken advantage of by mechanics in a.s.sembling various machine details. A cylindrical part which is to be held in position by a shrinkage fit is first turned a few thousandths of an inch larger than the hole; the diameter of the latter is then increased by heating, and after the part is inserted, the heated outer member is cooled, causing it to grip the pin or shaft with tremendous pressure.

General practice seems to favor a smaller allowance for shrinkage fits than for forced fits, although in many shops the allowances are practically the same in each case, and for some cla.s.ses of work, shrinkage allowances exceed those for forced fits. In any case, the shrinkage allowance varies to a great extent with the form and construction of the part which has to be shrunk into place. The thickness or amount of metal around the hole is the most important factor. The way in which the metal is distributed also has an influence on the results. Shrinkage allowances for locomotive driving wheel tires adopted by the American Railway Master Mechanics a.s.sociation are as follows:

Center diameter, inches 38 44 50 56 62 66 Allowance, inches 0.040 0.047 0.053 0.060 0.066 0.070

Whether parts are to be a.s.sembled by forced or shrinkage fits depends upon conditions. For example, to press a driving wheel tire over its wheel center, without heating, would ordinarily be a rather awkward and difficult job. On the other hand, pins, etc., are easily and quickly forced into place with a hydraulic press and there is the additional advantage of knowing the exact pressure required in a.s.sembling, whereas there is more or less uncertainty connected with a shrinkage fit, unless the stresses are calculated. Tests to determine the difference in the quality of shrinkage and forced fits showed that the resistance of a shrinkage fit to slippage was, for an axial pull, 3.66 times greater than that of a forced fit, and in rotation or torsion, 3.2 times greater. In each comparative test, the dimensions and allowances were the same.

The most important point to consider when calculating shrinkage fits is the stress in the hub at the bore, which depends chiefly upon the shrinkage allowance. If the allowance is excessive, the elastic limit of the material will be exceeded and permanent set will occur, or, in extreme cases, the ultimate strength of the metal will be exceeded and the hub will burst.

CHAPTER IV

THREAD CUTTING IN THE LATHE

When threads are cut in the lathe a tool _t_ is used (see Fig. 2), having a point corresponding to the shape of the thread, and the carriage is moved along the bed a certain distance for each revolution of the work (the distance depending on the number of threads to the inch being cut) by the lead-screw _S_ which is rotated by gears _a_, _b_ and _c_, which receive their motion from the spindle. As the amount that the carriage travels per revolution of the work, and, consequently, the number of threads per inch that is cut, depends on the size of the gears _a_ and _c_ (called change gears) the latter have to be changed for cutting different threads. The proper change gears to use for cutting a given number of threads to the inch is ordinarily determined by referring to a table or "index plate" _I_ which shows what the size of gears _a_ and _c_ should be, or the number of teeth each should have, for cutting any given number of threads per inch.

[Ill.u.s.tration: Fig. 1. Measuring Number of Threads per Inch--Setting Thread Tool]

[Ill.u.s.tration: Fig. 2. Plan and Elevations of Engine Lathe]

=Selecting the Change Gears for Thread Cutting.=--Suppose a V-thread is to be cut on the end of the bolt _B_, Fig. 2, having a diameter of 1-1/4 inch and seven threads per inch of length, as shown at _A_ in Fig. 1, which is the standard number of threads per inch for that diameter.

First the change gears to use are found on plate _I_ which is shown enlarged in Fig. 3. This plate has three columns: The first contains different numbers of threads to the inch, the second the size gear to place on the "spindle" or "stud" at _a_ (Fig. 2) for different threads, and the third the size of gear _c_ for the lead-screw. As the thread selected as an example has 7 threads per inch, gear _a_ should have 48 teeth, this being the number given in the second column opposite figure 7 in the first. By referring to the last column, we find that the lead-screw gear should have 84 teeth. These gears are selected from an a.s.sortment provided with the lathe and they are placed on the spindle and lead-screw, respectively.

[Ill.u.s.tration: Fig. 3. Index Plate showing Gear Changes for Threading]

Intermediate gear _b_ does not need to be changed as it is simply an "idler" for connecting gears _a_ and _c_. Gear _b_ is mounted on a swinging yoke _Y_ so that it can be adjusted to mesh properly with different gear combinations; after this adjustment is made, the lathe is geared for cutting 7 threads to the inch. (The change gears of many modern lathes are so arranged that different combinations are obtained by simply shifting a lever. A lathe having this quick-change gear mechanism is described in the latter part of this chapter.) The work _B_ is placed between the centers just as it would be for turning, with the end to be threaded turned to a diameter of 1-1/4 inch, which is the outside diameter of the thread.

=The Thread Tool.=--The form of tool used for cutting a V-thread is shown at _A_, Fig. 4. The end is ground V-shaped and to an angle of 60 degrees, which corresponds to the angle of a standard V-thread. The front or flank, _f_ of the tool is ground back at an angle to provide clearance, but the top is left flat or without slope. As it is very important to grind the end to exactly 60 degrees, a gage _G_ is used, having 60-degree notches to which the tool-point is fitted. The tool is clamped in the toolpost as shown in the plan view, Fig. 2, square with the work, so that both sides of the thread will be cut to the same angle with the axis of the work. A very convenient way to set a thread tool square is ill.u.s.trated at _B_, Fig. 1. The thread gage is placed against the part to be threaded, as shown, and the tool is adjusted until the angular sides of the point bear evenly in the 60-degree notch of the gage. The top of the tool point should be at the same height as the lathe centers, as otherwise the angle of the thread will not be correct.

[Ill.u.s.tration: Fig. 4. Thread Tools and Gage for testing Angle of End]

=Cutting the Thread.=--The lathe is now ready for cutting the thread.

This is done by taking several cuts, as indicated at _A_, _B_, _C_ and _D_ in Fig. 5, the tool being fed in a little farther for each successive cut until the thread is finished. When these cuts are being taken, the carriage is moved along the bed, as previously explained, by the lead-screw _S_, Fig. 2. The carriage is engaged with the lead-screw by turning lever _u_ which causes the halves of a split nut to close around the screw. The way a lathe is handled when cutting a thread is as follows: After the lathe is started, the carriage is moved until the tool-point is slightly beyond the right end of the work, and the tool is fed in far enough to take the first cut which, ordinarily, would be about 1/16 inch deep. The carriage is then engaged with the lead-screw, by operating lever _u_, and the tool moves to the left (in this case 1/7 inch for each revolution of the work) and cuts a winding groove as at _A_, Fig. 5. When the tool has traveled as far as the thread is wanted, it is withdrawn by a quick turn of cross-slide handle _e_, and the carriage is returned to the starting point for another cut. The tool is then fed in a little farther and a second cut is taken as at _B_, Fig.

5, and this operation is repeated as at _C_ and _D_ until a "full"

thread is cut or until the top of the thread is sharp. The thread is then tested for size but before referring to this part of the work, the way the carriage is returned to the starting point after each cut should be explained.