warm when being bored in the lathe, while the shaft is much cooler. When the sleeve cools to the temperature of the shaft, it contracts and seizes or "freezes" to the shaft. In accurate tool work the effect of differences in temperature between the measuring instruments and the work may become serious. For this reason many gages are provided with rubber or wooden handles which do not conduct heat readily. They thus prevent the heat of the hand from getting into the gages and expanding them.

But this is enough to give some idea of the troubles caused by this property of materials; let us now see of what benefit it is. We have already seen the use that is made of the expansion of mercury in thermometers. There are numerous heat regulating devices (called thermostats) which depend on the expansion or contraction of a bar to perform the desired operations. We find these used for regulating house heating boilers and furnaces, incubators, and other devices where uniform temperatures are required. Probably the greatest shop use of expansion and contraction is in making shrink fits. When we want to fasten securely and permanently one piece of metal around another, we generally shrink the first onto the second. This process is used for attaching all sorts of bands and collars to shafts, cylinders, and the like, for putting tires on locomotive wheels, and for similar work. The erecting engineer uses it to put in the links in a sectional fly-wheel rim or to draw up bolts in the hub or in any other place where he wants to make a rigid permanent joint.

The amount of linear expansion which a body undergoes depends upon the kind of material of which the body is made, upon the amount of the temperature change and, of course, upon the original length.

The coefficient of linear expansion of a substance is that part of its original length which a body will expand for each degree change in temperature. Coefficients for different metals have been determined for our use by careful experiments, and can be found in hand books or tables under the head of "Coefficients of Expansion." The values given in different books do not always agree. In fact, the exact compositions of the metals used in the tests were undoubtedly different for the different tests that are on record. Hence, different tables give slightly different rates of expansion. The following values are taken from the most reliable authorities and are sufficiently accurate for most purposes.

The above values are based on a temperature rise of 1° F. For one Centigrade degree change in temperature the coefficients would be of those just given. The student is not expected to memorize these values. Remember that if the length is given in feet the expansion calculated will be in feet, and if the length is in inches the expansion calculated will be in inches. To get the actual expansion per degree for any certain length, multiply the coefficient of expansion by the length. If the temperature change is 100°, the expansion will be 100 times that for 1°.

Example:

The head of a gas engine piston in operation has a temperature of about 400° higher than the cylinder in which it is running. What allowance must be made for this expansion in a 12 in. piston? (The piston is made of cast iron.)

.000006 X 400 = .0024 in. expansion per inch
.0024 × 12 =

= .0288 in. expansion in 12 in., Answer.

The head of the piston must, therefore, be turned at least .0288 in. small to allow for the expansion to take place without the piston seizing in the cylinder.

The law of expansion and contraction may be expressed by a formula as follows:

where

ETXCXL

E is the change in length

T is the change in temperature

C is the coefficient of linear expansion

L is the original length of the body.

Example:

What will be the expansion in a steam pipe 200 ft. long when subjected to a temperature of 300°, if erected when the temperature was 60°?

T=300-60=240; C=.0000065; L=200

E=TXCXL

=240.0000065×200=.312 ft., Answer.

Notice particularly that here we use L in feet and, consequently, the expansion E comes out in feet. This can be reduced to inches if desired, giving 12.312=3.744 in. or 3 in. nearly.

125. Allowances for Shrink Fits.-In making a shrink fit, the collar or band, or whatever is to be shrunk on, is bored slightly smaller than the outside diameter of the part on which it is to be shrunk. It is then heated and thus expanded until it can be slipped into place. When it cools, it cannot return to its original size but is in a stretched condition. It, therefore, exerts a powerful grip on the article over which is has been shrunk.

Practice differs considerably in the allowances that are made for shrink fits. A rule which has been widely and successfully used is to allow in. for each inch of diameter. According to this rule, if we were shrinking a crank on a 6 in. shaft, the crank should be bored .006 in. small or else the shaft turned .006 in. oversize and the crank bored exactly 6 in. For a 10-in. shaft we would allow .010 in, and so on for other sizes. This could be expressed by the following formulas:

A= .001 XD, or, since .001=- this could be written.

1000'

Assuming that an allowance of .001 XD is made, let us see what temperature is necessary in order to give the necessary expansion so that a steel tire can be put over a locomotive driving wheel.

For each degree that the tire is heated, it will expand .0000065 in. per inch of diameter. We must have an expansion of at least .001 in. The number of degrees necessary to get this will be

It would look as if a difference of 154° would be sufficient. However, a greater difference is necessary in practice. There must be sufficient clearance so that the tire can be slipped quickly into place before it has time to cool off or to warm the wheel. Once in place, the tire will grip the wheel when a temperature difference of 154° exists.

PROBLEMS

211. In testing direct current generators, it is customary to specify that under full load the temperature of the armature shall not rise more than 40° Centigrade above a room temperature of 25° C.; that is, the temperature of the armature under these conditions should not exceed 65° C.

In making a test a Fahrenheit thermometer was used. The room was at a temperature of 77° F. and the temperature of the armature at the end of the run was 180° F. Did the generator meet the specifications? What was the temperature change, Centigrade?

212. In erecting a long steam line that will have a variation in temperature of 320°, how far apart should the expansion joints be placed if each joint can take care of a motion of 3 inches?

213. If a brass bushing measures 2 in. just after boring, when its temperature is 95° F., what will it caliper when it has cooled to 65° F.? 214. A steel link 2 ft. long is made

wheel rim into which it is to be shrunk. it will go in?

in. too short for the slot in the flyHow hot must the link be before

215. If a hub bolt is heated until it just begins to show red and is immediately screwed up snug and allowed to cool, what shrinkage allowance per inch of length would we be allowing by such a plan?

216. If we wished to maintain a tempering bath at a temperature of 500° F., what should be the reading on a Centigrade pyrometer?

217. If the brass bearings for a 2 in. steel crank shaft are given a running clearance of .002 in. at a temperature of 60° F., what would be the clearance when running at a temperature of 100° F.?

218. A horizontal steam turbine and dynamo are to be direct-connected, their shaft centers being 3 ft. above the bed plate. If the bearings are lined up at a temperature of 70°, how much will they be out of alignment under running conditions when the temperature of the dynamo frame is 80° F. and that of the turbine is 215° F., both frames being of cast iron?

CHAPTER XX

STRENGTH OF MATERIALS

126. Stresses. When a load is put upon any piece of material, it tends to change the shape of the piece. The material naturally resists this and, therefore, exerts a force opposite to the load. If the load is not too heavy, the material may be able to exert a sufficient force to hold it, but often the strength of the material is exceeded and the piece breaks.

The resistance which is set up when a piece of material is loaded is called the Stress. For instance, if a casting weighing 3 tons or 6000 lb. is suspended by a single rope, the stress in the rope will be 6000 lb.

There are three different kinds of stresses that can be produced,

depending on the way the load is applied.

(1) Tensile stress (pulling stress).

(2) Compressive stress (crushing or pushing stress).

(3) Shearing stress (cutting stress).

Fig. 83 shows how these different stresses are produced.

We sometimes recognize two other kinds of stresses, but these are really special cases of the three just given. These two others

are: