Mechanical Power Transmission: Belts, Chains, and Ropes, Summaries of Theory of Machines

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Flexible Transmitting

Elements

Elements Of Mechanism Sixth Edition

Flexible Connectors

When the distance between the

driving shaft and the driven shaft

is too great (usually less than 6 ft)

to be connected by gears, a

flexible connector is used. If the

wheel A, Fig. 12-1 , is turning at a

certain angular speed about the

axis S, its outer surface will have a

linear speed dependent upon the

angular speed and the diameter

of A.

Flexible connectors may be

divided into three general

classes:

1. Belts
2. Ropes
3. Chain

For convenience the word band may be used as a general term to denote all kinds of

flexible connectors.

Bands for communicating continuous motion are endless.

Bands for communicating reciprocating motion are usually made fast at their ends to

the pulleys or drums which they connect.

Flexible connectors may be

divided into three general

classes:

1. Belts made of leather, rubber, or woven fabrics are flat and thin,

and require pulleys nearly cylindrical with smooth surfaces. Flat

belts are used to connect shafts as much as 30 ft apart.

Belts may be run economically at speeds

as high as 4500 fpm. Belts are also made

with V-shaped cross section to be used on

grooved pulleys. V-belts are usually used

for connecting shafts which are less than

15 ft apart. Speed ratios up to 7 to 1 and

belt speeds up to 5000 fpm may be used.

Pitch Surface and Line of

Connection When this same belt is stretched around a pulley, as in Fig. 12-3 , the

surface i is drawn firmly against the surface of the pulley while the

The outer part of the belt must therefore

stretch somewhat and the inner part

compress. There will be some section

between i and o which is neither

stretched nor compressed, and the

name neutral section may be given to

this part of the belt.

surface o bends over a circle whose

radius is greater than that of the surface

of the pulley by an amount equal to the

belt thickness 2p.

Pitch Surface and Line of

Connection

In a flat belt the neutral section may be assumed to be halfway

between the outer and inner surfaces. An imaginary cylindrical surface

around the pulley, to which the neutral section of the belt is tangent, is

the pitch surface of the pulley, the radius of this being the effective

radius of the pulley. A line in the neutral section of the belt at the

center of its width is the line of connection between two pulleys and is

tangent to the pitch surfaces, and coincides with a line in each pitch

surface known as the pitch line.

Speed Ratio and Directional

Relation of Shafts Connected by

a Belt

That is, the angular speeds of the shafts are in the inverse ratio of the

effective diameters of the pulleys, and this ratio is constant for circular

pulleys. As the thickness of belts generally is small as compared with

the diameters of the pulleys, it may be neglected. The speed ratio will

then become

which is the equation almost always used in practical calculations.

The relative directions in which the pulleys tum depend upon the manner in which

the belt is put on the pulleys. The belt shown in Fig. 12-1 is known as an open belt

and the pulleys turn in the same direction as suggested by the arrows.

The belt shown in Fig. 12-4 is known as a crossed belt and the pulleys turn in

opposite directions as indicated.

Kinds of Belts

Leather belts are made by gluing or riveting together strips of leather

cut lengthwise of the hide, near the animal's back. If single thicknesses

of the leather are fastened end to end, the belt is known as a

single belt and is usually about 3/16 in. thick.

If two thicknesses of leather are glued together, flesh side to flesh side,

the belt is known as a double belt and is from 5/16 in. to 3/8 in. thick.

The manner of uniting the ends of the strips to form a belt, and of

fastening together the ends of the belt to make a continuous band for

running over pulleys, is very important.

Power of Belting

The amount of power which a given belt can transmit depends upon its

speed, its strength, and its ability to adhere to the surf ace of the

pulleys. The speed is usually assumed to be the same as the surface

speed of the pulleys. The strength, of course, depends upon the width

and thickness and upon the nature of the material of which the belt is

made. The ability to cling to the pulley in order to run with little or no

slipping depends upon the condition of the pulley surfaces and of the

surface of the belt which is in contact with the pulleys, and upon the

tightness with which the belt is stretched over the pulleys.

Tension in a Belt

Suppose now that some external force is applied to the shaft S causing

it to tend to turn in the direction indicated by the arrow. This tendency

to turn will increase the tension in the lower part of the belt (say

between m and n) and decrease the tension in the upper part. Let the

new tension in the lower or tight side of the belt be represented by T 1

(which is greater than T 0

) and the tension in the upper or slack side by

T

2

(which is less than T 0

Tension in a Belt

If the belt sticks to the pulley B so that there is no slipping, the force T 1

tends to cause the pulley B to turn as shown by the full arrow, and the

force T 2

tends to cause B to turn as shown by the dotted arrow. As soon

as T 1

becomes enough greater than T 2

to overcome whatever resistance

the shaft S offers to turning, the pulleys will begin to turn in the

direction of the full arrow. The unbalanced force, then, which makes

the driven pulley B turn is the difference between the tension T 1

on the

tight side of the belt and the tension T 2

on the slack side of the

belt. This difference in tensions is

called the effective pull of the belt

and is here represented by the

letter E.