American Technical Society. # Cyclopedia of engineering : a general reference work on steam boilers, pumps, engines, and turbines, gas and oil engines, automobiles, marine and locomotive work, heating and ventilating, compressed air, refrigeration, dynamos motors, electric wiring, electric lighting, elevators, etc. (Volume 2) online

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Online Library → American Technical Society → Cyclopedia of engineering : a general reference work on steam boilers, pumps, engines, and turbines, gas and oil engines, automobiles, marine and locomotive work, heating and ventilating, compressed air, refrigeration, dynamos motors, electric wiring, electric lighting, elevators, etc. (Volume 2) → online text (page 7 of 30)

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It is evident that while the piston can push the crank around

during part of the stroke, and pull it during another part, there

are still two places (called dead points) at the ends of the stroke,

where the pressure on the piston, no matter how great, can exert

97

46

THE STEAM ENGINE.

: >.

THE STEAM ENGINE.

47

no turning moment on the shaft. Therefore, if some means is

not provided for making the shaft turn past these points without

the assistance of the piston, it may stop. This means is provided

in the fly wheel, which is merely a heavy wheel placed on the

shaft. On account of the momentum of the fly wheel it cannot

be stopped quickly, and therefore carries the shaft around until

the piston can again either push or pull.

If a long period be considered, the mean effort and the mean

resistance must be equal; but 'during this period there are tem-

porary changes of effort, the excesses causing increase of speed.

To moderate these fluctuations several methods are employed.

Fig. 33.

The turning moment on the shaft of a single cylinder

engine varies, first, because of the change in steam pressure, and

second, on account of the angularity of the connecting rod. Before

the piston reaches mid-stroke the turning moment is a maximum,

as shown by the curve, (Fig. 33). While near the ends of the

stroke (the dead points) the turning moment diminishes and

finally becomes zero. This, of course, tends to cause a corre-

sponding change in the speed of rotation of the shaft. In order

to have this speed as nearly constant as possible, and to give a

greater uniformity of driving power, the engine may be run at high

speed. By this means the inertia of the revolving parts, such

as the connecting rod and crank, causes less variation. When

the work to be done is steady and always in the same direction

(as in most factories), a heavy fly wheel may be used.

The heavier the fly wheel, the steadier will be the motion.

It is, of course, desirable in all factory engines to have steady

motion, but in some it is more important than in others. For

99

48 THE STEAM ENGINE.

instance, in a cotton mill it is absolutely necessary that the ma-

chinery shall move with almost perfect steadiness ; consequently

mill engines always have very large, heavy fly wheels. It is un-

desirable to use larger wheels than are absolutely necessary,

because of the cost of the metal, the weight on the bearings and

the danger from bursting.

If the turning moment which is exerted on the shaft from

the piston could be made more regular, and if dead points could

be avoided, it would be possible to get a steadier motion with a

much smaller fly wheel.

If the engine must be stopped and reversed frequently, it is

better to use two or more cylinders connected to the same shaft.

The cranks are placed at such angles that when one is exerting its

minimum rotative effort, the other is exerting its maximum turn-

ing moment ; or, when one is at a dead center, the other is exerting

its greatest power. These two cylinders may be identically the

same, as is the case with most hoisting engines and with many

locomotives ; or the engine may be compound or triple expansion.

This arrangement is also used on engines, for mines, collieries,

and for hoisting of any sort where ease of stopping, starting

and reversing are necessary. Simple expansion engines with their

cranks at right angles are said to be coupled.

The governor adjusts the power of the engine to any large

variation of the resistance. The fly wheel has a duty to perform

which is similar to that of the governor. It is designed to adjust

the effort of the engine to sudden changes of the load which may

occur during a single stroke. It also equalizes the variation in

rotative effort on the crank pin. The fly wheel absorbs energy

while the turning moment is in excess of the resistance and restores

it while the crank is at or near the dead points. During these

periods the resistance is in excess of the power.

The action of the fly wheel may be represented as in Figs. 33

and 34. It will be noticed that in Fig. 33 the curve of crank

effort runs below the axis toward the end of the stroke. This is

because the compression is greater than the pressure near the end

of expansion, and produces a resultant pressure on the piston.

In Fig. 34 the effect of compression has been neglected. Let us

suppose that the resistance, or load, is uniform. In Fig. 33 the line

100

THE STEAM ENGINE. 49

A B is the length of the semi-circumference of the crank pin, or it

is the distance the crank pin moves daring one stroke. The curve

A M D O B is the curve of turning moment for one stroke. M N

is the mean ordinate, and therefore A E F B represents the constant

resistance. The effort and resistance must be equal if the speed is

uniform ; hence A E F B = A M D O B. Then area A E M +

area O F B = area M DO. At A the rotative effort is zero be-

cause the crank pin is at the dead point ; from A to N the turning

moment is less than the resistance. At N the resistance and the

effort are equal. From N to P the effort is in excess of the resist-

ance. At P the effort and resistance are again equal. From P

to B the resistance is greater than the effort. In other words,

from A to N the work done by the steam is less than the resist-

Fig. 34.

ance. This shows that the work represented by the area A E M

must have been done by the moving parts of the engine. From

N to P the work done by the steam is greater than the resistance,

and the excess of energy is absorbed by or stored in the moving

parts. From P to the end of the stroke, the work represented by

the area O F B is done on the crank pin by the moving parts.

^y ^2

We know from the formula, E , that energy is pro-

u

portional to the square of the velocity. Hence as W and g

remain the same, the velocity must be reduced when the moving

parts are giving out energy, and increased when receiving energy.

Thus we see that the tendency of the crank pin is to move slowly,

then more rapidly. The revolving parts of an engine have not

sufficient weight to store this surplus energy, hence a heavy fly

wheel is used.

In case there are two engines at right angles, two effort curves

101

50 THE STEAM ENGINE.

must be drawn, as shown in Fig. 34. The mean ordinate A E is

equal to the mean or constant resistance. There are two minimum

and two maximum velocities in one stroke. The diagram shows

that the variation is much less than for a single cylinder ; hence

a lighter fly wheel may be used.

The weight of the fly wheel depends upon the character of the

work done by the engine. For pumping engines and ordinary

machine work the effort need not be as constant as for electric

lighting and fine work. In determining the weight of a fly wheel

the diameter of the wheel must be known, or the ratio of the

diameter of the wheel to the length of stroke. If the wheel is too

large, the high linear velocity of the rim will cause too great a

centrifugal force and the wheel is likely to break. In practice,

about 6,000 feet per minute is taken as the maximum linear velocity

of cast-iron wheels. When made of wood and carefully put

together, the velocity may be taken as 7,000 to 7,500 feet per

minute.

We know that linear velocity is expressed in feet per minute

by the formula, V = 2-rr R N, or V = TT D N.

Then if a wheel runs at 100 revolutions per minute, the

allowable diameter would be,

6,000 = 3.1416 X D X 100

6,000 101 , .

= 3^i4ihrLoo = 19 - lfeefc -

If a wheel is 12 feet in diameter the allowable speed is found

to be,

N = Z_

TrD

6,000

= . loy revolutions per minute.

It is usual to make the diameter a little less than the calcu-

lated diameter.

Having determined the diameter, the weight may be calculated

by several methods. There are many formulas to obtain this result

given by various authorities. One formula is given as follows :

W = CX d2 X j

D^ x N2

102

THE STEAM ENGINE. 51

In the above. W= weight of the rim in pounds

d = diameter of the cylinder in inches

b = length of stroke in inches

D = diameter of fly wheel in feet

N number of revolutions per minute

C is a constant which varies for different types and conditions.

Slide-valve engines, ordinary work, C = 350,000

Corliss engines, ordinary work, C = 700,000

Slide-valve engines, electric lighting, C = 700,000

Corliss engines, electric lighting, C = 1,000,000

Automatic highspeed engines, C = 1,000,000

Example. Let us find the weight of a fly-wheel rim for an

automatic high-speed engine used for electric lighting. The cylin-

der is 24 inches in diameter; the stroke is 2 feet. It runs at

300 revolutions per minute, and the fly wheel is to be 6 feet in

diameter.

W = 1,000,000 X C 24 ) 2 X 2

36 X 90,000

W = 4,266 pounds

Another example.. A plain slide-valve engine for electric

lighting is 20" X 24". It runs at 150 revolutions per minute.

The fly wheel is to be 8 feet in diameter. What is the weight of

its rim ?

W = 700,000 X 4 X 24

64 X 22,500

W = 4,666 pounds.

The weight of a fly wheel is considered as being in the rim.

The weight of the hub and arms is simply extra weight. Then,

if we know the weight of the rim and its diameter, we can find the

width of face and thickness of rim. Let us assume the given

diameter to be the mean of the diameter of the inside and outside

of the rim.

Let b = width of face in inches

t = thickness of rim in inches

d = diameter of fly wheel in inches

.2607 = weight of 1 cubic inch of cast iron

Then,

W= .2607 X b X tX ird

= 6 X * X .819 d

103

52 THE STEAM ENGINE.

Suppose the rim of a fly wheel weighs 6,000 pounds, is 9 feet

in diameter, and the width of the face is 24 inches. What is the

thickness of the rim?

W

6,000

,819 X 108 X 24

= 2.83 inches

In this case the rim would probably be made 21| inches thick.

The total weight, including hub and arms, would probably be

about 8,000 pounds.

GOVERNORS.

The load on an engine is never constant, although there are

cases where it is nearly uniform. While the engine is running at

constant speed, the resistance at the fly-wheel rim is equal to the

work done by the steam. If the load on the engine is wholly or

partially removed, and the supply of steam continues undiminished,

the force exerted by the steam will be in excess of the resistance.

Work is equal to force multiplied by distance ; hence, with con-

stant effort, if the resistance is diminished, the distance must be

increased. In other words, the speed of the engine will be in-

creased. The engine will " race," as it is called. Also, if the

load increases and the steam supply remains constant, the engine

will "slow down."

It is evident, then, that if the speed is to be kept constant

some means must be provided so that the steam supply shall at all

times be exactly proportional to the load. This is accomplished

by means of a governor.

Steam-engine governors act in one of two ways : they may

regulate the pressure of steam admitted to the steam chest, or they

may adjust the speed by altering the amount of steam admitted.

Those which act in the first way are called throttling governors,

because they throttle the steam in the main steam pipe. Those of

the latter class are called automatic cut-off governors, since they

automatically regulate the cut-off,

Theoretically, the method of governing by throttling the

104

THE STEAM ENGINE. 53

steam causes a loss in efficiency, but the throttling superheats the

steam, thus reducing cylinder condensation. By the second

method the loss in efficiency is very slight, unless the ratio of

expansion is already great, in which case shortening the cut-off

causes more cylinder condensation. This subject will be taken

up in detail later.

In most governors, centrifugal force, counteracted by some

other force, is employed. A pair of heavy masses (usually iron

balls or weights) are made to revolve about a spindle, which is

driven by the engine. When the speed increases, centrifugal

force increases, and the balls tend to fly outward ; that is, they

revolve in a larger circle. The controlling force, which is usually

gravity or springs, is no longer able to keep the balls in their

former path. When, therefore, the increase is sufficiently great,

the balls in moving outward act on the regulator, which may

throttle the steam or cause cut-off to occur earlier.

With the throttling governor a balanced throttle valve is

placed in the main steam pipe leading to the valve chest. If the

engine runs faster than the desired speed, the balls are forced to

revolve at a higher speed. The increase in centrifugal force will

cause them to revolve in a larger circle and in a higher plane.

By means of some mechanism (levers and gears) the spindle may

be forced downward, thus partially closing the valve. The

engine, therefore, takes steam at a lower pressure, and the power

supplied being less, the speed falls slightly.

Similarly, if the load is increased, the engine slows down,

which causes the balls to drop and open the valve more widely,

steam at higher pressure is then admitted, and the speed is

increased to the regular number of revolutions.

With the Corliss or Wheelock engine the governor of this type

acts differently. Instead of throttling the steam in the steam pipe,

the governor is connected to the releasing gear by rods. An increase

of speed causes the releasing gear to unhook the disengaging link

earlier in the stroke. This causes earlier cut-off, which of course

decreases the power and the speed, since the amount of steam

admitted is less. If for any reason the load increases, the governor

causes the valves to be held open longer. The cut-off, therefore,

occurs later in the stroke.

105

THE STEAM ENGINE.

One of the most common forms of governor is similar to that

invented by James Watt. It is called, from its appearance, the

pendulum governor. It is shown in Fig. 35. To consider the

theory of the pendulum governor, the masses of the balls are

assumed to be concentrated at their centers, and the rods made of

some material having no weight.

When the governor is revolving about its axis at a constant

speed the balls revolve in a circle having a radius r The distance

from this plane to the intersection of the rods, or the rods pro-

duced, is called the height and is equal to h.

Fig. 35.

If the balls revolve faster, the centrifugal force increases, r

becomes greater and li diminishes. We know that centrifugal

force is expressed by the formula,

gr

Then centrifugal force varies inversely as the radius.

While the pendulum is revolving, centrifugal force acts hori-

zontally outward and tends to make the balls fly from the center;

gravity tends to make the balls drop downward. In order that the

balls shall revolve at a certain height, the moments of these two

forces about the center must be equal, or the weight of the balls

multiplied by their distance from the center must equal the

centrifugal force multiplied by the height, or.

W X r = F X A

h W

from which,

or,

from which,

W

gr

gr

106

THE STEAM ENGINE. 55

Now we know that the linear velocity of a point revolving in

the circumference of a circle is expressed as 2 TT r N feet per

second.

Thpr

Since we know the values of g and TT we can write the

formula,

h = 82 ' 16 = - 8146 feet per second, or

4 X 3.1416 2 X N 2 N2

h = ' inches per second.

If N is the number of revolutions per minute, since 00* =

3600 > 2,932.66 ,

h = _ _ feet

, 35,190.7 . ,

h = . 2 inches

From the above formula, we see that the height is independent

of the weight of the balls or the length of the rod ; it depends

upon the number of revolutions. The height varies inversely as

the square of the number of revolutions.

The ordinary pendulum governor is not isochronous ; that is,

it does not revolve at a uniform speed in all positions ; the speed

changes as the angle between the arms and the spindle changes.

The early form consisted of two heavy balls suspended by

links from a pin connection in a vertical spindle, as shown in Figs.

36 and 37. The spindle is caused to revolve by belting or gear-

ing from the main shaft, so that as the speed increases, centrifugal

force causes the balls to revolve in a circle of larger and larger

diameter. The change of position of these balls can be made to

affect the controlling valves so that the admission or the throttling

shall vary with their position. With this governor it is evident

that for a given speed of the engine there is but one position pos-

sible for the governor ; consequently one amount of throttling or

one point of cut-off, as the case may be. If the load varies, the

speed of the engine will change. This causes the position of the

governor balls to be changed slightly, thus altering the pressure

107

56

THE STEAM ENGINE.

But in order that the pressure or cut-off shall remain changed, the

governor balls must stay in their new position. That is to say,

the speed of the engine must be slightly changed. Thus with

the old ball governors there was. a slightly different speed for each

load. This condition has been greatly improved by various

modifications until now such governors give excellent regulation.

While the engine is running with a light load, the valve con-

trolled by the governor will be open just enough to admit steam

at a pressure that will keep the engine running at a given speed.

Now, if the engine is heavily loaded, the throttle valve must be

wide open. The change of opening is obtained by a variation in

the height of the governor, which is caused by a change of speed.

Thus we see that the governor can control the speed only within

certain limits which are not far apart. The difference in the

extreme heights of the governor must be sufficient to open

the throttle its entire range. In most well-designed engines the

speed will not vary more than 4 per cent ; that is, 2 per cent

above or below the mean speed.

From the formula h = ' g ,we can compute the heights

corresponding to given speeds as shown by the following table :

Number of

Revolutions

per Minute.

Height

in

Inches.

Variation of

Height in Inches

4 per cent.

250

.563

.0225

200

.879

.035

175

1.149

.046

150

1.564

.062

125

2.252

.090

100

3.519

.140

75

6.256

.250

50

14.076

.563

In the above table the second column is found from the

formula h =

35,190.7

N 2

The third column is the variation in

height for a speed variation of 4 per cent or 2 per cent either

above or below the mean.

108

THE STEAM ENGINE.

57

From the table we see that for a considerable variation of

speed there is but slight variation in the height of the governor.

Also for high speeds the height of the governor is so small that it

would be difficult to construct it. The slight variation in height

is too small to control the cut-off or throttling mechanism through-

out the entire range.

Other disadvantages of the fly-ball governor are as follows:

it is apparent that the valves must be controlled by the weight of

the governor balls. In large engines this requires very heavy

balls in order to quickly overcome the resistance of the valves.

But these large balls have considerable inertia and will therefore

be reluctant to change their speed with that of the engine. The

Fig. 36.

Fig. 37.

increased weight will also increase the friction in the governor

joints, and the cramping action existing when the balls are driven

oy the spindle will increase this friction still further. All these

things tend to delay the action of the governor, so that in all

large engines the. old-fashioned governor became sluggish. The

balls had to turn slowly because they were so heavy ; this was

especially troublesome in high-speed engines.

To remedy these defects the weighted or Porter governor was

designed. (See Fig. 38.) .It has a greater height for a given

speed, and the variation in height for a given variation of speed is

greater. When a governor has this latter quality, that is, a great

variation in height for a given variation of speed, it is said to be

sensitive. By increasing this variation in height the sensitiveness

is increased. Thus, if a governor running at 50 revolutions has a

109

58 THE STEAM ENGINE.

variation in height of .57 inch, it is not as sensitive as one having

a variation of 1 inch for the same speed.

In the weighted governor, the weight is formed so that the

center of gravity is in the axis. It is placed on the spindle and

is free to revolve. The weight adds to the weight of the balls,

and thus increases the moment of the weight. It does not, how-

ever, add to the centrifugal force, and hence the moment of this

force is unchanged. We may then say the weight adds effect to

the weight but not to the centrifugal force, and as a consequence

the height of the governor, for a given speed, is increased. If we

let W equal the combined weight of the balls as before, and W

equal the added weight, the moments are,

(W + W) X r = F h

(W + W) X r = ^! X A

W X 4 7r2 r 2 N2

(W + W) v <7

-^^~ X 4-

We know that ^ - ' 81

N 2

Hence the height of a weighted governor is equal to the

height of a simple pendulum governor multiplied by

W ) ( W,

For instance, if the height of a simple pendulum is 10 inches,

and the weight of the balls equal to the added weight, the height

will be,

= 2 X 10

no

THE STEAM ENGINE. 69

Thus we see that if a weight equal to the combined weight of

the balls is added, the height of the governor will be doubled.

We know that if the balls fall, the cut-off comes later. If

the belt driving the governor slips off or breaks, the balls will

drop, and, making the cut-off later, will allow the engine to " run

away." To diminish this danger many governors are provided

with some kind of safety stop, which closes the valve when the

governor loses its normal action. Usually a trip is provided

which the governor does not touch in its normal positions, but

which will be released if the balls drop down below a certain

point.

In another arrangement, instead of a weight, a strong spring

is used, and this makes it possible to put the governor in any

position.

Spring Governors. In many cases a spring is used in place

of the weight. This type of governor

is used frequently on throttling engines ;

it consists of a pendulum governor with

springs added to counteract the cen-

trifugal force of the balls. Thus the

height and sensitiveness are increased.

Fig. 39 shows the exterior view of a

Waters governor, and Fig. 40 the same

governor having the safety stop. In

this governor the weights are always in

the same plane, the variation in height

being due to the action of the bell F . 3g

crank levers connecting the balls and

spindle. When the balls move outward the spindle moves down-

ward and tends to close the valve. The governor balls revolve

by means of a belt and bevel gears. The valve and seat are

shown in section in Fig. 41. The valve is a hollow cylinder

with three ports, by means of which steam enters the valve. The

seat is made in four parts, that is, there are four edges that the

steam passes as it enters the valve. The valve being cylindrical

and having steam on both sides is balanced, and because of the

many openings only a small travel is necessary.

Shaft Governors. Usually some form of pendulum governor

ill

60

THE STEAM ENGINE.

is used for throttling engines. For governing an engine by vary-

ing the point of cut-off, shaft governors are generally used ; how-

ever, Corliss engines and some others use pendulum governors for

this purpose. Cut-off governors are called shaft governors because

they are placed on the main shaft ; they are made in many forms,

but the essential features of all are the same. Two pivoted masses

or weights are arranged symmetrically on opposite sides of the

shaft, and their tendency to fly outward when the speed increases

is resisted by springs. The outward motion of the weights closes

the admission valve earlier, and the inward motion closes it later.

Tiiis change is effected by altering the position of the eccentric,

either by changing the eccentricity or the angular advance.

40.

Shaft governors are made in a great variety of ways, no two

types being exactly alike. If the principles of a few types are

understood, it is easy to understand others. The following illus-

trates two common methods of shifting the eccentric.

Buckeye Engine Governor. The valve of the Buckeye en-

during part of the stroke, and pull it during another part, there

are still two places (called dead points) at the ends of the stroke,

where the pressure on the piston, no matter how great, can exert

97

46

THE STEAM ENGINE.

: >.

THE STEAM ENGINE.

47

no turning moment on the shaft. Therefore, if some means is

not provided for making the shaft turn past these points without

the assistance of the piston, it may stop. This means is provided

in the fly wheel, which is merely a heavy wheel placed on the

shaft. On account of the momentum of the fly wheel it cannot

be stopped quickly, and therefore carries the shaft around until

the piston can again either push or pull.

If a long period be considered, the mean effort and the mean

resistance must be equal; but 'during this period there are tem-

porary changes of effort, the excesses causing increase of speed.

To moderate these fluctuations several methods are employed.

Fig. 33.

The turning moment on the shaft of a single cylinder

engine varies, first, because of the change in steam pressure, and

second, on account of the angularity of the connecting rod. Before

the piston reaches mid-stroke the turning moment is a maximum,

as shown by the curve, (Fig. 33). While near the ends of the

stroke (the dead points) the turning moment diminishes and

finally becomes zero. This, of course, tends to cause a corre-

sponding change in the speed of rotation of the shaft. In order

to have this speed as nearly constant as possible, and to give a

greater uniformity of driving power, the engine may be run at high

speed. By this means the inertia of the revolving parts, such

as the connecting rod and crank, causes less variation. When

the work to be done is steady and always in the same direction

(as in most factories), a heavy fly wheel may be used.

The heavier the fly wheel, the steadier will be the motion.

It is, of course, desirable in all factory engines to have steady

motion, but in some it is more important than in others. For

99

48 THE STEAM ENGINE.

instance, in a cotton mill it is absolutely necessary that the ma-

chinery shall move with almost perfect steadiness ; consequently

mill engines always have very large, heavy fly wheels. It is un-

desirable to use larger wheels than are absolutely necessary,

because of the cost of the metal, the weight on the bearings and

the danger from bursting.

If the turning moment which is exerted on the shaft from

the piston could be made more regular, and if dead points could

be avoided, it would be possible to get a steadier motion with a

much smaller fly wheel.

If the engine must be stopped and reversed frequently, it is

better to use two or more cylinders connected to the same shaft.

The cranks are placed at such angles that when one is exerting its

minimum rotative effort, the other is exerting its maximum turn-

ing moment ; or, when one is at a dead center, the other is exerting

its greatest power. These two cylinders may be identically the

same, as is the case with most hoisting engines and with many

locomotives ; or the engine may be compound or triple expansion.

This arrangement is also used on engines, for mines, collieries,

and for hoisting of any sort where ease of stopping, starting

and reversing are necessary. Simple expansion engines with their

cranks at right angles are said to be coupled.

The governor adjusts the power of the engine to any large

variation of the resistance. The fly wheel has a duty to perform

which is similar to that of the governor. It is designed to adjust

the effort of the engine to sudden changes of the load which may

occur during a single stroke. It also equalizes the variation in

rotative effort on the crank pin. The fly wheel absorbs energy

while the turning moment is in excess of the resistance and restores

it while the crank is at or near the dead points. During these

periods the resistance is in excess of the power.

The action of the fly wheel may be represented as in Figs. 33

and 34. It will be noticed that in Fig. 33 the curve of crank

effort runs below the axis toward the end of the stroke. This is

because the compression is greater than the pressure near the end

of expansion, and produces a resultant pressure on the piston.

In Fig. 34 the effect of compression has been neglected. Let us

suppose that the resistance, or load, is uniform. In Fig. 33 the line

100

THE STEAM ENGINE. 49

A B is the length of the semi-circumference of the crank pin, or it

is the distance the crank pin moves daring one stroke. The curve

A M D O B is the curve of turning moment for one stroke. M N

is the mean ordinate, and therefore A E F B represents the constant

resistance. The effort and resistance must be equal if the speed is

uniform ; hence A E F B = A M D O B. Then area A E M +

area O F B = area M DO. At A the rotative effort is zero be-

cause the crank pin is at the dead point ; from A to N the turning

moment is less than the resistance. At N the resistance and the

effort are equal. From N to P the effort is in excess of the resist-

ance. At P the effort and resistance are again equal. From P

to B the resistance is greater than the effort. In other words,

from A to N the work done by the steam is less than the resist-

Fig. 34.

ance. This shows that the work represented by the area A E M

must have been done by the moving parts of the engine. From

N to P the work done by the steam is greater than the resistance,

and the excess of energy is absorbed by or stored in the moving

parts. From P to the end of the stroke, the work represented by

the area O F B is done on the crank pin by the moving parts.

^y ^2

We know from the formula, E , that energy is pro-

u

portional to the square of the velocity. Hence as W and g

remain the same, the velocity must be reduced when the moving

parts are giving out energy, and increased when receiving energy.

Thus we see that the tendency of the crank pin is to move slowly,

then more rapidly. The revolving parts of an engine have not

sufficient weight to store this surplus energy, hence a heavy fly

wheel is used.

In case there are two engines at right angles, two effort curves

101

50 THE STEAM ENGINE.

must be drawn, as shown in Fig. 34. The mean ordinate A E is

equal to the mean or constant resistance. There are two minimum

and two maximum velocities in one stroke. The diagram shows

that the variation is much less than for a single cylinder ; hence

a lighter fly wheel may be used.

The weight of the fly wheel depends upon the character of the

work done by the engine. For pumping engines and ordinary

machine work the effort need not be as constant as for electric

lighting and fine work. In determining the weight of a fly wheel

the diameter of the wheel must be known, or the ratio of the

diameter of the wheel to the length of stroke. If the wheel is too

large, the high linear velocity of the rim will cause too great a

centrifugal force and the wheel is likely to break. In practice,

about 6,000 feet per minute is taken as the maximum linear velocity

of cast-iron wheels. When made of wood and carefully put

together, the velocity may be taken as 7,000 to 7,500 feet per

minute.

We know that linear velocity is expressed in feet per minute

by the formula, V = 2-rr R N, or V = TT D N.

Then if a wheel runs at 100 revolutions per minute, the

allowable diameter would be,

6,000 = 3.1416 X D X 100

6,000 101 , .

= 3^i4ihrLoo = 19 - lfeefc -

If a wheel is 12 feet in diameter the allowable speed is found

to be,

N = Z_

TrD

6,000

= . loy revolutions per minute.

It is usual to make the diameter a little less than the calcu-

lated diameter.

Having determined the diameter, the weight may be calculated

by several methods. There are many formulas to obtain this result

given by various authorities. One formula is given as follows :

W = CX d2 X j

D^ x N2

102

THE STEAM ENGINE. 51

In the above. W= weight of the rim in pounds

d = diameter of the cylinder in inches

b = length of stroke in inches

D = diameter of fly wheel in feet

N number of revolutions per minute

C is a constant which varies for different types and conditions.

Slide-valve engines, ordinary work, C = 350,000

Corliss engines, ordinary work, C = 700,000

Slide-valve engines, electric lighting, C = 700,000

Corliss engines, electric lighting, C = 1,000,000

Automatic highspeed engines, C = 1,000,000

Example. Let us find the weight of a fly-wheel rim for an

automatic high-speed engine used for electric lighting. The cylin-

der is 24 inches in diameter; the stroke is 2 feet. It runs at

300 revolutions per minute, and the fly wheel is to be 6 feet in

diameter.

W = 1,000,000 X C 24 ) 2 X 2

36 X 90,000

W = 4,266 pounds

Another example.. A plain slide-valve engine for electric

lighting is 20" X 24". It runs at 150 revolutions per minute.

The fly wheel is to be 8 feet in diameter. What is the weight of

its rim ?

W = 700,000 X 4 X 24

64 X 22,500

W = 4,666 pounds.

The weight of a fly wheel is considered as being in the rim.

The weight of the hub and arms is simply extra weight. Then,

if we know the weight of the rim and its diameter, we can find the

width of face and thickness of rim. Let us assume the given

diameter to be the mean of the diameter of the inside and outside

of the rim.

Let b = width of face in inches

t = thickness of rim in inches

d = diameter of fly wheel in inches

.2607 = weight of 1 cubic inch of cast iron

Then,

W= .2607 X b X tX ird

= 6 X * X .819 d

103

52 THE STEAM ENGINE.

Suppose the rim of a fly wheel weighs 6,000 pounds, is 9 feet

in diameter, and the width of the face is 24 inches. What is the

thickness of the rim?

W

6,000

,819 X 108 X 24

= 2.83 inches

In this case the rim would probably be made 21| inches thick.

The total weight, including hub and arms, would probably be

about 8,000 pounds.

GOVERNORS.

The load on an engine is never constant, although there are

cases where it is nearly uniform. While the engine is running at

constant speed, the resistance at the fly-wheel rim is equal to the

work done by the steam. If the load on the engine is wholly or

partially removed, and the supply of steam continues undiminished,

the force exerted by the steam will be in excess of the resistance.

Work is equal to force multiplied by distance ; hence, with con-

stant effort, if the resistance is diminished, the distance must be

increased. In other words, the speed of the engine will be in-

creased. The engine will " race," as it is called. Also, if the

load increases and the steam supply remains constant, the engine

will "slow down."

It is evident, then, that if the speed is to be kept constant

some means must be provided so that the steam supply shall at all

times be exactly proportional to the load. This is accomplished

by means of a governor.

Steam-engine governors act in one of two ways : they may

regulate the pressure of steam admitted to the steam chest, or they

may adjust the speed by altering the amount of steam admitted.

Those which act in the first way are called throttling governors,

because they throttle the steam in the main steam pipe. Those of

the latter class are called automatic cut-off governors, since they

automatically regulate the cut-off,

Theoretically, the method of governing by throttling the

104

THE STEAM ENGINE. 53

steam causes a loss in efficiency, but the throttling superheats the

steam, thus reducing cylinder condensation. By the second

method the loss in efficiency is very slight, unless the ratio of

expansion is already great, in which case shortening the cut-off

causes more cylinder condensation. This subject will be taken

up in detail later.

In most governors, centrifugal force, counteracted by some

other force, is employed. A pair of heavy masses (usually iron

balls or weights) are made to revolve about a spindle, which is

driven by the engine. When the speed increases, centrifugal

force increases, and the balls tend to fly outward ; that is, they

revolve in a larger circle. The controlling force, which is usually

gravity or springs, is no longer able to keep the balls in their

former path. When, therefore, the increase is sufficiently great,

the balls in moving outward act on the regulator, which may

throttle the steam or cause cut-off to occur earlier.

With the throttling governor a balanced throttle valve is

placed in the main steam pipe leading to the valve chest. If the

engine runs faster than the desired speed, the balls are forced to

revolve at a higher speed. The increase in centrifugal force will

cause them to revolve in a larger circle and in a higher plane.

By means of some mechanism (levers and gears) the spindle may

be forced downward, thus partially closing the valve. The

engine, therefore, takes steam at a lower pressure, and the power

supplied being less, the speed falls slightly.

Similarly, if the load is increased, the engine slows down,

which causes the balls to drop and open the valve more widely,

steam at higher pressure is then admitted, and the speed is

increased to the regular number of revolutions.

With the Corliss or Wheelock engine the governor of this type

acts differently. Instead of throttling the steam in the steam pipe,

the governor is connected to the releasing gear by rods. An increase

of speed causes the releasing gear to unhook the disengaging link

earlier in the stroke. This causes earlier cut-off, which of course

decreases the power and the speed, since the amount of steam

admitted is less. If for any reason the load increases, the governor

causes the valves to be held open longer. The cut-off, therefore,

occurs later in the stroke.

105

THE STEAM ENGINE.

One of the most common forms of governor is similar to that

invented by James Watt. It is called, from its appearance, the

pendulum governor. It is shown in Fig. 35. To consider the

theory of the pendulum governor, the masses of the balls are

assumed to be concentrated at their centers, and the rods made of

some material having no weight.

When the governor is revolving about its axis at a constant

speed the balls revolve in a circle having a radius r The distance

from this plane to the intersection of the rods, or the rods pro-

duced, is called the height and is equal to h.

Fig. 35.

If the balls revolve faster, the centrifugal force increases, r

becomes greater and li diminishes. We know that centrifugal

force is expressed by the formula,

gr

Then centrifugal force varies inversely as the radius.

While the pendulum is revolving, centrifugal force acts hori-

zontally outward and tends to make the balls fly from the center;

gravity tends to make the balls drop downward. In order that the

balls shall revolve at a certain height, the moments of these two

forces about the center must be equal, or the weight of the balls

multiplied by their distance from the center must equal the

centrifugal force multiplied by the height, or.

W X r = F X A

h W

from which,

or,

from which,

W

gr

gr

106

THE STEAM ENGINE. 55

Now we know that the linear velocity of a point revolving in

the circumference of a circle is expressed as 2 TT r N feet per

second.

Thpr

Since we know the values of g and TT we can write the

formula,

h = 82 ' 16 = - 8146 feet per second, or

4 X 3.1416 2 X N 2 N2

h = ' inches per second.

If N is the number of revolutions per minute, since 00* =

3600 > 2,932.66 ,

h = _ _ feet

, 35,190.7 . ,

h = . 2 inches

From the above formula, we see that the height is independent

of the weight of the balls or the length of the rod ; it depends

upon the number of revolutions. The height varies inversely as

the square of the number of revolutions.

The ordinary pendulum governor is not isochronous ; that is,

it does not revolve at a uniform speed in all positions ; the speed

changes as the angle between the arms and the spindle changes.

The early form consisted of two heavy balls suspended by

links from a pin connection in a vertical spindle, as shown in Figs.

36 and 37. The spindle is caused to revolve by belting or gear-

ing from the main shaft, so that as the speed increases, centrifugal

force causes the balls to revolve in a circle of larger and larger

diameter. The change of position of these balls can be made to

affect the controlling valves so that the admission or the throttling

shall vary with their position. With this governor it is evident

that for a given speed of the engine there is but one position pos-

sible for the governor ; consequently one amount of throttling or

one point of cut-off, as the case may be. If the load varies, the

speed of the engine will change. This causes the position of the

governor balls to be changed slightly, thus altering the pressure

107

56

THE STEAM ENGINE.

But in order that the pressure or cut-off shall remain changed, the

governor balls must stay in their new position. That is to say,

the speed of the engine must be slightly changed. Thus with

the old ball governors there was. a slightly different speed for each

load. This condition has been greatly improved by various

modifications until now such governors give excellent regulation.

While the engine is running with a light load, the valve con-

trolled by the governor will be open just enough to admit steam

at a pressure that will keep the engine running at a given speed.

Now, if the engine is heavily loaded, the throttle valve must be

wide open. The change of opening is obtained by a variation in

the height of the governor, which is caused by a change of speed.

Thus we see that the governor can control the speed only within

certain limits which are not far apart. The difference in the

extreme heights of the governor must be sufficient to open

the throttle its entire range. In most well-designed engines the

speed will not vary more than 4 per cent ; that is, 2 per cent

above or below the mean speed.

From the formula h = ' g ,we can compute the heights

corresponding to given speeds as shown by the following table :

Number of

Revolutions

per Minute.

Height

in

Inches.

Variation of

Height in Inches

4 per cent.

250

.563

.0225

200

.879

.035

175

1.149

.046

150

1.564

.062

125

2.252

.090

100

3.519

.140

75

6.256

.250

50

14.076

.563

In the above table the second column is found from the

formula h =

35,190.7

N 2

The third column is the variation in

height for a speed variation of 4 per cent or 2 per cent either

above or below the mean.

108

THE STEAM ENGINE.

57

From the table we see that for a considerable variation of

speed there is but slight variation in the height of the governor.

Also for high speeds the height of the governor is so small that it

would be difficult to construct it. The slight variation in height

is too small to control the cut-off or throttling mechanism through-

out the entire range.

Other disadvantages of the fly-ball governor are as follows:

it is apparent that the valves must be controlled by the weight of

the governor balls. In large engines this requires very heavy

balls in order to quickly overcome the resistance of the valves.

But these large balls have considerable inertia and will therefore

be reluctant to change their speed with that of the engine. The

Fig. 36.

Fig. 37.

increased weight will also increase the friction in the governor

joints, and the cramping action existing when the balls are driven

oy the spindle will increase this friction still further. All these

things tend to delay the action of the governor, so that in all

large engines the. old-fashioned governor became sluggish. The

balls had to turn slowly because they were so heavy ; this was

especially troublesome in high-speed engines.

To remedy these defects the weighted or Porter governor was

designed. (See Fig. 38.) .It has a greater height for a given

speed, and the variation in height for a given variation of speed is

greater. When a governor has this latter quality, that is, a great

variation in height for a given variation of speed, it is said to be

sensitive. By increasing this variation in height the sensitiveness

is increased. Thus, if a governor running at 50 revolutions has a

109

58 THE STEAM ENGINE.

variation in height of .57 inch, it is not as sensitive as one having

a variation of 1 inch for the same speed.

In the weighted governor, the weight is formed so that the

center of gravity is in the axis. It is placed on the spindle and

is free to revolve. The weight adds to the weight of the balls,

and thus increases the moment of the weight. It does not, how-

ever, add to the centrifugal force, and hence the moment of this

force is unchanged. We may then say the weight adds effect to

the weight but not to the centrifugal force, and as a consequence

the height of the governor, for a given speed, is increased. If we

let W equal the combined weight of the balls as before, and W

equal the added weight, the moments are,

(W + W) X r = F h

(W + W) X r = ^! X A

W X 4 7r2 r 2 N2

(W + W) v <7

-^^~ X 4-

We know that ^ - ' 81

N 2

Hence the height of a weighted governor is equal to the

height of a simple pendulum governor multiplied by

W ) ( W,

For instance, if the height of a simple pendulum is 10 inches,

and the weight of the balls equal to the added weight, the height

will be,

= 2 X 10

no

THE STEAM ENGINE. 69

Thus we see that if a weight equal to the combined weight of

the balls is added, the height of the governor will be doubled.

We know that if the balls fall, the cut-off comes later. If

the belt driving the governor slips off or breaks, the balls will

drop, and, making the cut-off later, will allow the engine to " run

away." To diminish this danger many governors are provided

with some kind of safety stop, which closes the valve when the

governor loses its normal action. Usually a trip is provided

which the governor does not touch in its normal positions, but

which will be released if the balls drop down below a certain

point.

In another arrangement, instead of a weight, a strong spring

is used, and this makes it possible to put the governor in any

position.

Spring Governors. In many cases a spring is used in place

of the weight. This type of governor

is used frequently on throttling engines ;

it consists of a pendulum governor with

springs added to counteract the cen-

trifugal force of the balls. Thus the

height and sensitiveness are increased.

Fig. 39 shows the exterior view of a

Waters governor, and Fig. 40 the same

governor having the safety stop. In

this governor the weights are always in

the same plane, the variation in height

being due to the action of the bell F . 3g

crank levers connecting the balls and

spindle. When the balls move outward the spindle moves down-

ward and tends to close the valve. The governor balls revolve

by means of a belt and bevel gears. The valve and seat are

shown in section in Fig. 41. The valve is a hollow cylinder

with three ports, by means of which steam enters the valve. The

seat is made in four parts, that is, there are four edges that the

steam passes as it enters the valve. The valve being cylindrical

and having steam on both sides is balanced, and because of the

many openings only a small travel is necessary.

Shaft Governors. Usually some form of pendulum governor

ill

60

THE STEAM ENGINE.

is used for throttling engines. For governing an engine by vary-

ing the point of cut-off, shaft governors are generally used ; how-

ever, Corliss engines and some others use pendulum governors for

this purpose. Cut-off governors are called shaft governors because

they are placed on the main shaft ; they are made in many forms,

but the essential features of all are the same. Two pivoted masses

or weights are arranged symmetrically on opposite sides of the

shaft, and their tendency to fly outward when the speed increases

is resisted by springs. The outward motion of the weights closes

the admission valve earlier, and the inward motion closes it later.

Tiiis change is effected by altering the position of the eccentric,

either by changing the eccentricity or the angular advance.

40.

Shaft governors are made in a great variety of ways, no two

types being exactly alike. If the principles of a few types are

understood, it is easy to understand others. The following illus-

trates two common methods of shifting the eccentric.

Buckeye Engine Governor. The valve of the Buckeye en-

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