Chapter_6_CuD.ppt

7/27/2019 Chapter_6_CuD.ppt

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CHAPTER 6: MECHANICAL TRANSMISSION OF POWER

Power may be transmitted from where it is generated to the point where it is used in a

variety of ways, of which electric cables, steam pipes and compressed air ranges are familiar

examples. It is always necessary to use the mechanical transmission either directly, as in the

hammer drill, where the blow of the piston is applied to the drill steel itself, or directly through themedium of shafts, belts, ropes, chains or gears.

Rope Drives

Woven cutton ropes of three or four strand construction form a very efficient and convenient form of

power transmission for driving fans, and generators. From 4 to 12 ropes are commonly employed,

running in a grooved pulley. The rope groove is V-shaped, the angle being about 45 degrees and

the depth about 1-5 times the rope diamter. The rope thus wedges itself in the groove. A great

advantage of rope drives compared with belts is that there is no danger of the ropes

breaking at once or jumping the pulley. They are more flexible and quiter than gears, but

occupy more space and cannot be used for large speed changes.


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Belt DrivesThey are commonly used between shafts that are too far apart to be coupled economically

with gearwheels. Moreover, since belt drives are usually somewhat elastic, they are very

effective in absorbing shock and vibration. Perhaps the most common types of belts in use at

present are the flat, round and vee-shaped ones.

Flat belting is used with very large

pulley diameters and very long

center distances.

The belts can be eitherleatheror

can be fabric and can be spliced.

Pulleys forflat belt applications

may be eitherflanged orcrowned.

The crowned pulley is usually

considered to be superior to the

flanged one because it causes

less wear at the edges of the belt.



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Round belts are usually made from synthetic material and are used only for light duty

applications. Pulleys forround belt applications have a concaved face to fit the belt cross-

section

Vee belts are probably the most popular type because of theirdependability. Their construction

is somewhat more complex than flat belts and round belts. Figure 7-5 shows a vee-belt cross-

setion. Vee belts are used with pulleys like the one shown in Figure 7-6

Belt drives are most frequently used in the open belt configuration shown in Figure 7-7



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If we assume that there is no slippage in the belt, then the linear velocity of each pulley rim is

equal to the belt velocity. Therefore, the rim velocities (linear) of the two pulleys are equal.

This equation gives us the pulley angular velocity as a function of the diameter. Notice that

this equation is very similiar to the one for gear but both pulleys turn in the same direction.

You will recall that we assumed no belt slippage in deriving this relationship. In most practical

cases there will be some slippage. It is usually reasonable to expect the follower pulley to runabout 5% slower than the value indicated by this equation



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In addition to the velocity ratio, we frequently need to know the belt length. It is normally

practical to measure the pulley diameters and the center distance. With these quantities

known the belt length can be found



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Also notice that the contact angles of both pulleys are greater for the crossed belt

arrangement than that for an open belt. As a result of the greater contact angle, the crossed

belt configuration is able to handle somewhat larger loads.

The belt length required for a crossed belt drive is:

With a crossed belt, the velocity ratio is the same value, but since the pulleys turn in opposite

directions we have



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All belts tend to stretch with use. Therefore a provision for tightening the belt must be included

in the belt drive design. If the pulley center distance can be varied, then it may be used for

belt tightening. Another common method is to use an adjustable idler pulley as shown in Figure7-9.

This arrangement has the additional advantage of increasing the contact angles. This idler

pulley must of course be a suitable for use on the outside of the belt. It will normally be a flatpulley for both flat and vee belts and a round pulley for round belts.



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Chain Drives

Chain drives are employed in applications where the center distances are too large for

economical gearing and belt slippage cannot be tolerated. There are several different typesof drive chains. Figure 7-10 shows a few common types of drive chains.

The wire ladder chain has the advantage of being very economical. It is however, quite

difficult to splice and is normally not considered for precision applications.

Bead chains normally have metal stamped beads orplastic beads.

Cog belts may be constructed from metal links ormolded in flexible rubberlike materials.Some means ofpreventing the belt from walking off the side of the sprocket wheel is

necessary

Toothed belts are suitable for precision drives and have the advantage that the sprockets

can be meshed directly with a spur gear



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When two sprockets are coupled by a chain, we can find the angular displacement and

velocity ratios in much the same way as we do with spur gears by using the following equation

Determining the length of chain for use with a given center distance and sprocket ratio is a

design problem. An approximate length (L) can be obtained with

L/P ratio is infact the number of links in the chain. A good practice

is to make the center distance adjustable whenever possible.

Finally an idler sprocket can be used to provide some chain length

adjustments



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Toothed Belts

Some mechanical drive applications require some of the characteristics of a chain or gear

wheel and the fleibility of a belt. The toothed belt is one way to satisfy both of these

requirements.

Perhaps the main shortcoming of a belt drive is the inherent slippage. The toothed belt shown

in figure 7-14 effectively overcomes this problem. Pulley suitable for use with toothed belts are

a sort ofcomprimise between a round belt pulley and a spur gear. In fact, the pulley teeth are

involute-shaped. Figure 7-15 shows a toothed belt drive that is in fact being driven by a spurgear

Also shown in Figure 15 is an idler pulley being used to take up belt slack. It is worth mentioning

that idler pulley can be used to drive a light load. With ordinary belt drives this is usually not

the case



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For an open belt configuration shown

in Figure 7-16 above, the performance

ratios for the toothed belt drive may

be calculated using the equation

The length of the toothed belt may be found in the usual way with the following Equation



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Toothed belts may be used in a crossed belt drive shown in Figure 7-17. The pulley ratios

remain the same with the exception that the direction of the driven pulley is reversed.



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The minimum crossed belt length is given by the following equation

Where (theta) is this time the belt contact angle on each pulley

One of the important advantages of a toothed belt is its flexibility. The belt may be twisted to

fit many difficult applications. Figure 7-18 shows just a few of the possibilities



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Disc Drives

s is the small disk angular velocity, Lis the large disk angular velocity R is the large disk radius, r is the small

disk radius, D is the large disk diameter, d is the small disk diameter, s is the small disk angular displacement,

Lis the large disk angular displacement, TL is the large disk torque, Ts is the small disk torque

Negative signs reflect a change in the direction of the action

Friction disk drives are used in a variety oflow torque systems from phonograph turntables to lawn movers. It

is possible that they predate gear wheels and may infact have been their anchestors.

Lets look at a single disk pair of the type shown in Figure 7-20. Suppose that these two disks are made of a hard

rubber material and that there is no slippage between them. This being the case, they will act very much like a

gear mesh. The velocity ratios will be



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On of the important advantages of disk drives is that it is possible to have continously variable ratios.

Figure 7.21 shows on type ofvariabe ratio disk drive. The velocity ratio of type of drive are still

However, if we can move the smaller disk along its own axis we can change r2. Ifr2 changes, the

velocity ratio also changes. When this type of drive is used, the smaller wheel is usually the driver.



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Another type of variable ratio disk drive is shown in Figure 7-22. In this case the input disk drives the idler

disk which in turn drives the output disk. Equation below gives ratios. However by moving the idler shaft we

can change both r1 and r2

Notice that there is no change in direction in this case. Also, while there are two chances for slippage,

notice that slight idler deformation does not alter the velocity ratios. As a result, the total error is still

normally about 5 percent.



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Rotary Cams

Cams are used in a great variety of mechanical applications. Consider the rotary cam shown in Figure 7-23.

When it is operating properly the cam rotates with its shaft. The follower rolls over the cam face. The cam

followerthen has a motion which is determied by the cam profile. During the portion of a revolution when the

smaller cam radius (r) is under the follower, the follower arm is in its lower position. As the cam rotates, the

lobe region having the larger radius (R) eventually forces the follower up to its upperposition. This follower

travel is frequently used to operate some other mechanism.



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By controlling the lobe angle and angular velocity of the cam, we can control the on and off time of such

blinking operation. Figure 7-24 shows the cam again with the on and off angles marked. These angles are

often referred to as dwell angles. When the follower is up, we say it is ON the cam. When it is down, we say it

is OFF of the cam. There are of course also two angles during which the follower is neither on nor off of thecam. These are called the transition angles. In high speed cam operations these transitions become

extremely important.

In most practical cases the on and off times will be small fractions of a minute. Consequently it is frequently

convenient express them in seconds



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Shafts and Couplings

As the rotational speed of cam is increased, it becomes more and more difficult for the cam follower to

maintain contact with the cam surface. Figure 7-26 shows the path of a roller centerat low and high cam

speed. The dotted line represents the relative position of follower centers as the cam rotates.

A rotating bar usualy cylindrical in shape, which transmits power is called a shaft. Poweris delivered to the

shaft through the action of an outside tangential force, resuting in a torsional action set up in the shaft.

The resultant torque allows the power to be distributed to other machines or to various components

connected to the shaft.



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Shaft CouplingsIn machine design, it is often becomes necessary to fasten or join ends of two shafts axially so that they will

act as a single unit to transmit power. When this parameter is required shaft couplings are called into use.

Shaft couplings are grouped into two in general classifications: rigid (or solid) and flexible. A rigid coupling

will not provide forshaft misalignment orreduce vibration orshock from one shaft to the other. However,

flexible shaft couplings provide connection of misaligned shafts and can reduce shock and and/or

vibration to a degree.


Universal JointsUniversal joints are used to couple shafts which are angularly displaced one to another. Universal joints

come in many different sizes, types and designs. Perhaps, the simplest one ishe hooked-type universal joint

shown in Figure 7-34. Universal joint of this type can be effectively used for drive angles as large as 30

degrees or even more.

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