These formulæ are both based upon the assumption of arms of uniform section, either straight or else symmetrical with respect to hub and rim.

Other formulæ might be deduced which assume a variable section, but it would not seem to be worth while, in view of the fact that the bending moment is probably unequally divided among the arms. Hence the students confined themselves to computing the values off from each of the above formulæ, thus obtaining average values of the constants to be used in these formulæ for the purpose of determining approximately the strength of the pulleys. (See table of the results on previous page.)

CONCLUSIONS FROM THESE TESTS.

1st. A low value of the modulus of rupture of cast iron should be used in the ordinary formulæ for designing pulley arms, due to the fact that a load at the rim acts more upon some arms than upon others, as shown by the fact that, in four out of eight of the tests, one arm broke first, and this one always occupied the same position. 2d. In every case but one, of these four, a greater load than the original was afterwards put upon the pulley, and no other arm broke, but the rim gave way by crushing. In this one case excepted, the arms afterwards stood a greater load proportional to their number before breaking.

3d. In the tests on the single arms to be described next, the modulus of rupture rose as high as 55,000 lbs. in some cases, and in no case went below 35,000 lbs.

TESTS OF THE SEPARATE ARMS.

In the cases of numbers, 5, 7, 8, 9 and 10, some of the arms were not broken, the rims were now broken off, and the remaining arms were tested separately, the pull being exerted by a yoke hung over the end of the arm, the lower end being attached to the link of the machine.

The arms were always placed so that the direction of the pull was tangent to the curve of the rim at the end of the arm. The actual outside fiber stress at fracture was then determined by calculation from the experimental results, and is recorded in the following table:

In order to show how the results in the preceding table were deduced from the experiments, the calculation will now be given in full for the first, or 5-1 (Fig. 33).

The force OW, which is equal to the load upon the arm, is resolved into two components, OB and B W. Both these compo

nents act on the arm at the point O, OB in the direction OB, and BW in the direction OA.

The first, OB acts as a pull at the end of a cantilever of length OC, and is calculated accordingly; the second, BW acts as a pull in the direction OA, and produces stresses similar to those acting in a hook, where the distance from the line of pull to the center of the most strained section is CM.

The formula used for the cantilever is f

My

=

where M equals

I

the pull times the length of the arm, y equals half the depth and I equals the moment of inertia of the section.

The formula used to determine the greatest tension due to the force BW is

where Pequals the pull, A equals the area of the section =

equals the distance CM, and y equals the half depth.

πbh

n

The sum off, and f2 gives us the greatest fiber stress at fracture, or the modulus of rupture of the iron of the arm. The breaking load of this arm was 1645 lbs.

Hence:

Hence fi+f=45396, as recorded in the table.

The other values are similarly calculated.

An inspection of the table will show that the modulus of rupture figures out higher when the bend of the arm is with the load than when it is against it, and the value will be found to be very much. higher than the values of ƒ derived for the pulleys with the rims on.

TESTS OF THE HOLDING POWER OF SET SCREWS.

These tests were all made by using pulley No. 12, the pulley being fastened to the shaft by two set screws and the shaft keyed to the holders; then the load required at the rim of the pulley to cause it to slip was determined, and this being multiplied by

gives the holding power of the set screws.

The number 6.037 is obtained by adding to the radius of the pulley one-half the diameter of the wire rope, and dividing the sum by twice the radius of the shaft, since there were two set screws in action at a time. The set screws used were of wrought iron, of an inch in diameter, and having ten threads to the inch; the shaft used was of steel and rather hard, the set screws making but little impression upon it. The set screws were set up with a force of 75 lbs. at the end of a ten-inch monkey wrench. The set screws used were of four kinds, marked respectively A, B, C, and D. They may be described as follows:

A, ends perfectly flat," diameter.

B, radius of rounded ends, about inch.
C, radius of rounded ends, about inch.

12 144

D, ends cup shaped and case hardened.
The results are given in the following table:

The following remarks should be made in regard to each kind of tests:

A. The set screws were not entirely normal to the shaft; hence they bore less in the earlier trials before they had become flattened by wear.

B. The ends of these set screws, after the first two trials, were

found to be flattened, the flattened area having a diameter of about of an inch.

C. The ends were found, after the first two trials, to be flattened as in B.

D. The first test held well because the edges were sharp, then the holding power fell off till they had become flattened in a manner similar to B, when the holding power increased again.

KEYS.

The experiments on keys were made with pulley No. 11 except those marked C which were tested with pulley No. 12. In all cases where the keys were not as wide as the keyway they were wedged in with hardened steel pieces, the hardened steel piece in the pulley hub being as long as the hub was wide.

The load was applied as in the other tests, the shaft being firmly keyed to the holders. The load required at the rim of the pulley to shear the keys was determined, and this multiplied by a suitable constant, determined in a similar way to that used in the case of set screws, gives us the shearing strength per square inch of the keys. The keys tested were of eight kinds, denoted, respectively, by the letters, A, B, C, D, E, F, G and H, and they may be described as follows, the first dimension being the length, the second the width, and the third the height:

32

571

32 9

32

constant = 18.5184.

constant = 18.5184.

A, were of Norway iron, 2" x 1" x 15";
B, were of refined iron, 2′′ × 1′′ ×
C, were of cast or tool steel, 1" x 1" × 15"; constant = 49.78.
D, were of machinery steel, 2" x 1"x"; constant = 18.5184.
E, were of Norway iron, 13" x 3"x"; constant = 18.5184.
F, were of cast iron, 2 × × 15; constant = 18.5184.
G, were of cast iron, 1 ×
H, were of cast iron, 1 ×

7

×; constant
= 18.5184.
×; constant = 18.5184.

The shearing stresses per square inch, as determined from the experiments, are given in the following table: