235. Problems.

1. Write detailed, numbered directions for cutting a doublethread screw of pitch, on a lathe equipped with plate 2 as given in paragraph 233.

Could this thread be cut with an ordinary face plate by turning the dog over?

Give reason for your answer.

2. State the difference in procedure from that in Problem 1 in order to cut a triple-threaded screw of the same pitch on the same lathe.

3. State exactly how you would direct one not knowing the business to cut a quadruple-thread screw of pitch on a lathe equipped with plate 3.

CHAPTER X

PULLEYS

SECTION 1. RIM VELOCITY. SECTION 2. WEIGHT OF A PULLEY. SECTION 3. VELOCITY RATIO OF PULLEYS. SECTION 4. CENTRIFUGAL TENSION. SECTION 5. BACK GEARS.

§ 1. RIM VELOCITY

236. Velocity in Terms of Radius. In the work-book draw a pulley whose circumference measured to the outside of the rim is C and whose radius is R.

When the pulley has made one complete revolution, any point on the rim has moved through a distance equal to how many times the length of the radius?

When it has made 5 revolutions, the point has moved through a distance equal to how many times the radius?

The circumferential or rim velocity of a pulley is the distance through which a point on the rim moves per time unit.

If V denotes rim velocity, and R is in inches, how many revolutions per second does the pulley make when

V=2TR inches per second?

How many when

V=5×2TR inches per second?

How many when

V=N×2πR=2NR inches per second?

If the velocity is expressed in feet per second and R is

If the velocity is expressed in feet per minute and N denotes the number of revolutions per second and R is in inches,

V=?X2TNR
?

237. Formula for Rim Velocity. The circumferential or rim velocity of a pulley is also known as linear velocity or the distance a point on the rim travels per time unit, if the distance through which it has revolved were laid off on a straight line.

If

D= diameter of pulley in inches,
R=radius in feet,

R=radius in inches,

N=number of revolutions per minute,
V = rim velocity in feet per minute.

Write a formula for V in terms of R.
Write a formula for V in terms of R.

Write a formula for V in terms of D.

238. Problems. Complete the entries in the following table:

§ 2. WEIGHT OF A PULLEY

239. Formulas for Weight of a Pulley. The variation in the proportions of the different parts of a pulley makes any formula for weight an approximation. The following from Cromwell's Treatise on Belts and Pulleys is claimed to be sufficiently accurate for ordinary purposes.

W = approximate weight of pulley in pounds;
R=radius of pulley in inches;

w= width of belt in inches.

The formula may be used to calculate the weight of an unbelted pulley by taking

w=F

in which

F= width of face of pulley in inches.

(2) Clarke's Formula. Unwin gives the following as Mr. D. K. Clarke's formulas:

For rough castings

W=7.6D-1.5 to 12D-9.5.

For finished pulleys

W=7D-1.75 to 11.6D-9.25,

in which

W = approximate weight in pounds per inch of width;
D= diameter in feet.

240. Problems.

1. By Cromwell's formula compute the weight of a 10-inch pulley operated by an 8-inch belt.

2. Compute the weight of the pulley in Problem 1 by Clarke's formula.

3. Compute the weight of some detached pulley in the shops, and test the degree of accuracy of the formula by weighing the pulley.

4. If possible make a second test of the formula with another pulley whose dimensions are considerably different from those of the pulley used in the first test.

5. Compute the weight of some pulley in use in the shops.

6. By Clarke's formula determine the weights of the pulleys in Problems 3, 4, and 5.