Governing
164. To make an engine run steadily an almost continuous process of adjustment must go on, by which the amount of work done by steam in the cylinder is adapted to the amount of external work demanded of the engine. Even in cases where the demand for work is sensibility uniform fluctuations in boiler-pressure still make regulation necessary. Generally the process of government aims at regularity of speed; occasionally, however, it is some other condition of running that is maintained contact, as when an engine driving a dynamo-electric machine is governed by a electric regulator to give a constant difference of potential between the brushes.
The ordinary methods of regulating are either (a) to alter the pressure at which steam is admitted by opening of closing more or less a throttle-valve between the boiler and the engine, or (b) to alter the volume of steam admitted to the cylinder by varying the point cut-off. The former plan was introduced by Watt and is still common, especially in small engines. From the point of view of heat economy it is wasteful, since the process of throttling is essentially irreversible, but this objection is to some extent lessened by the fact that the wire-drawing of steam dries of superheats it, and consequently reduces the condensation which it suffers on coming into contract with the chilled cylinder walls. On the other hand, to hasten the cut-off involves a gain rather than a loss of efficiency unless the ratio of expansion is already very great. The second plan of regulating is much to be preferred, especially when the engine is subject to large variations of lad, and is very generally followed in stationary engines of the larger types
165. Within certain limits regulation by either plan can be effected by hand, but for the finer adjustment of speed form of automatic governor is necessary. Speed governors are commonly of centrifugal type: a pair of masses revolving about a spindle which is driven by the engine are kept from flying out by a certain controlling force. When an increase of speed occurs this controlling force is no longer able to keep the passes revolving in their former path; they move out until the controlling force is sufficiently increased, and in moving out they act on the regulator of the engine, which may be a throttle-valve or some form of automatic expansion gear. In the conical pendulum governor of Watt (fig. 90) the revolving masses are balls attached to a vertical spindle by links, and the controlling force is furnished by the weight of the balls, which, in receding from the spindle, are obliged to rise. When the speed exceeds or falls short of its normal value they move out or in, and so raise or lower a collar C which is in connexion by a lever with the throttle-valve. The suspension-links may be hung from a cross-bar (figs. 94, 95) instead of being pivoted in the axis of the spindle.
166. In a modified form of Watt’s governor, known as Porter’s, or the loaded governor, a supplementary controlling force is given by placing a weight on the sliding collar (fig. 91). This is equivalent to increasing the weight of the balls without altering their mass. In other governors the controlling force is wholly or partly produced by springs. Fig. 92 shows a governor by Messrs Tangye in which the balls are controlled partly by their own weight and partly by a spring, the tension of which is regulated by turning the cap A.
167. In whatever way the revolving masses are controlled, the controlling force may be treated as a force F acting on each ball in the direction of the radius towards the axis of revolution. Then, if M be the mass of the ball, n the number of revolutions per second, and r the radius of the ball’s path, the governor will revolve in equilibrium when F =4&Mac185;2n2rM (in absolute units), or
n = 1 / F
2 &Mac185; &Mac195; Mr
In order that the configuration of the governor should be stable, F must increase more rapidly than r, as the balls move towards. In the simple conical pendulum governor, any of the three forms shown in figs. 93, and 95, where the balls have no load to raise but their own weight, the controlling force F is the resultant of T, the tension in the link, and Mg, the weight of the ball (fig. 96). Let the height of the pendulum, that is, the distance above the plane of the balls of the point where the suspending-link, or the link produced, cuts the axis, be called h. Then F: Mg::r:h:. Hence __
F = Mgr , and n = 1 /g .
h 2&Mac185; &Mac195; h
Any change of n tends to produce a change of h, and, if the governor itself and the regulating mechanism attached to it were free from friction, only one position of the governor would be possible for any one value of n. It is obvious that neither this governor nor any other stable governor maintains a strictly constant speed in the engine which it controls. If the boiler pressure or the demand for work is changed, a certain amount of permanent displacement of the balls is necessary to alter the steam supply, and the balls can retain their displaced position only by virtue of a permanent change in the speed. The maximum range of speed depends on that amount of change of n which suffices to alter the configuration of the governor from the position which gives no steam-supply to the position which gives full steam-supply; and the governor is said to be sensitive if this range is a small fraction of n.
168. If the governor is loaded, let M’ be the amount of the load per ball, and q the velocity ratio of the vertical movement of the load to the vertical movement of the ball. Then qM’g is the equivalent increase in the weight of each ball. The effect of the load is to increase the controlling force F from Mgr/h to (M+gM’)gr/h, and the speed at which the governor must now turn to maintain any assigned height h, is __________
N = 1 1(M+gM’) g .
2&Mac185; &Mac195; Mh
The speed of the loaded governor must therefore be greater than that of an unloaded governor of the same height of the ratio &Mac195; (M+qM’) to &Mac195;M.
The sensibility is then the same as that of an unloaded governor of the same height h, but the loaded governor has an important advantage in another respect-namely, its power or capability of overcoming frictional resistance to a change of configuration. This quality in a governor is increased whenever the controlling force F is increased, whether by the addition of a load or by the use of springs.
For let f be the frictional resistance to be overcome per ball, resolved as a force resisting the displacement of each ball in the direction of the radius r. Then if n be the speed normal to any configuration this speed must change by a certain amount &Mac198;n before friction is overcome and the balls begin to be displaced. The controlling force is now F+f when the balls are moving outwards, and F-f when the balls are moving inwards. Hence _____
n + &Mac198;n = 1 F+f .
2&Mac185; &Mac195; Mr
and n - &Mac198;n = 1 F-f .
2&Mac185; &Mac195; Mr
From this, if &Mac198;n be small compared with n, we have &Mac198;n/n=f/2F.
Thus, when a given amount of frictional resistance is to be overcome before the governor can act, the limits within which this friction allows the speed to vary are les the greater is the controlling force F. A loaded governor is more powerful in this respect than an unloaded governor of the same configuration in the proportion in which F is greater—namely, as M+qM’ is to M. A loaded governor may therefore have much lighter revolving without loss either of sensibility or of power.
169. The same results are applicable to governors in which the controlling force is supplied by springs as well as by gravity, or by springs alone. To find the configuration which the governor will assume at any particular speed, or the speed corresponding to a particular configuration, it is only necessary to determine the whole controlling force F per ball acting along the radius towards the axis for various values of r. Let a curve ab (fig. 97) be drawn showing the relation of F to r. At any assigned value of r set up an ordinate QC=4&Mac185;2n2rM. Join OC. The point c, in which OC cuts the curve, determines the value of r at which the balls will revolve at the assigned speed n. Or, if that is given, and the value of n is to be found, the line Oc produced will determine C, and then n2=QC/4&Mac185;2nrM. The sensibility of the governor is determined by taking points a and b corresponding to full steam and no steam respectively, and drawing lines through the them to determine the corresponding values of QA and QB.1 When the frictional resistance f is known, an additional pair of curves drawn above and below ab, with ordinates F+f and F-f respectively, serve to show the additional variations in speed which are caused by friction. The governor is stable throughout its whole range when the curve ab has steeper gradient than any line drawn form O to meet it.
170. By § 167 it is evident that, if, when the balls are displayed, the controlling force F changes proportionally to the radius r, the speed is constant. In other words, the equilibrium of the governor is then neutral; it can revolve in equilibrium at one, and only one, speed. At this speed it assumes, indifferently, any one of its possible configurations. The slightest variation of speed drives it to the extremity of its range; hence its sensibility is indefinitely great. Such a governor is called isochronous. A gravity governor is isochronous when h is constant for all positions of the balls (since nx&Mac195;g/h). This will be the case if the balls are constrained to move in a parabolic path (fig. 98), it being a property of the parabola that the subnormal QM, which is h, is constant. A useful approximation to the same condition, through a limited range, is secured in Farcot’s governor by the device of hanging the balls by crossed links from the distant ends of a piece (fig. 95). If each centre of suspension were at the centre of curvature of a parabolic arc which coincided with the actual circular locus of the balls at the position of normal speed, the governor would be sensibly isochronous at that speed; by taking the centres of suspension rather nearer the axis, a suitable margin of stability is secured, but the governor is still nearly enough isochronous to be exceedingly sensitive.2 When springs furnish the controlling force, an approach to isochronism can be secured by adjusting the initial tension of the springs, and this forms a convenient means of regulating the sensibility. Thus, in Mr. Hartnell’s apparatus (fig.99), where the balls move in a nearly horizontal direction, and gravity has little to do with the control, the governor can be made isochronous by screwing down the spring, so that the initial force exerted by the spring is to its increase by displacement of the balls as the initial radius of the balls path is to the increase of radius by displacement. When the initial force is increased beyond this the governor becomes unstable. In fig. 97 the condition of isochonism is secured when the line ab is coincides with a straight line though O.
171. In practice no governor can be absolutely isochronous. It is indispensable to leave a small margin of stability for the sake of preventing violent change in the supply of steam, especially when there is much frictional resistance to be overcome by the governor, or where the influence of the governor takes much time to be felt by the engine. An over-sensitive governor is liable to fall into a state of oscillation called hunting. When an alteration of speed begins to be felt, however, readily the governor alters its form, the engine’s response is more of less delayed. If the governor acts by closing a throttle-valve, the engine has still a capacious valve-chest on which to draw for steam. If it acts by changing the cut-off, its opportunity is passed if the cut-off has already occurred, and the control only begins with the next stroke. This lagging of effect is specially felt in compound engines, where that portion of the steam which is already in the engine continues to do its work for nearly a whole revolution after passing beyond the governor’s control. The result of this storage of energy in an engine whose governor is too nearly isochronous is that, whenever the demand for power suddenly falls, the speed rises so much as to force the governor into a position of over-control, such that the supply of steam is no longer adequate to meet even the reduced demand for power. Then the speed slackens, and the same kind of excessive regulation is repeated in the opposite direction. A state of forced oscillation is consequently set up. The effect is aggravated by the momentum which the governor balls acquire in being displaced, and also, to a very great degree, by the friction of the governor and the regulating mechanism. Hunting is to be avoided by giving the governor a fair degree of stability, by reducing as far as possible the static frictional resistances, and by introducing a viscous resistance to the displacement of the governor, which prevents the displacement from occurring too suddenly, without affecting the ultimate position of equilibrium. For this purpose many governors are furnished with a dash-pot, which is hydraulic or pneumatic brake, consisting a piston connected to the governor, working loosely in a cylinder which is filled with oil or with air.
172. In some high-speed engines the governor balls or block revolve in a vertical plane, about a horizontal axis, and the control is given wholly by springs. An example is shown in fig. 100, which is the governor of the Armington and Sims engine referred to in § 197 below. Another example is furnished by the governor of Brotherhood’s engine (§ 203, fig. 128).
173. The throttle-valve as introduced by Watt, was originally a disk turning on a transverse axis across the centre of the steam–pipe. It is now usually a double-beat valve (fig. 89) or a piston-valve. When regulation is effected by varying the cut-off, and an expansion-valve of the slide-valve is used, the governor generally acts by changing the travel of the valve. Fig. 99 illustrates a common mode of doing this, by giving the expansion-valve its motion from an eccentric-rod through a link, the throw of which is varied by the displacement of the governor balls. In fig.100, the governor acts on the main slide-valve of the engine (there being no separate expansion-valve), an the displacement of the revolving masses M, M changes both the throw and the angular advance of the eccentric, thereby producing a change in the steam supply similar to that produced by "notching up" a link motion. The eccentricity B is altered by the relative displacement of two pars C, D into which the eccentric sheave is divided. In other forms of automatic expansion-gear the lap of the valve is altered; in others the governor acts by shifting the expansion-valve eccentric round on its shaft, and so changing its angular advance.
174. In large stationary engines the most usual plan of automatically regulating the expansion is to employ some form of trip-gear, the earliest type of which was introduced in 1849 by G.H. Corliss of Providence, U.S. In the Corliss system the valves which admit steam distinct from the exhaust-valves. The latter are opened and closed by a reciprocating piece which takes its motion from an eccentric. The former are opened by a reciprocating piece, but are closed by springing back when released by a trip- or trigger-action. The trip occurs earlier of later in the piston’s stroke according to the position of the governor. The admission-valve is opened by the reciprocating piece with equal rapidity whether the cut-off is going to be early or late. It remains wide open during the admission, and then, when the trip-action into play, it closes suddenly. The indicator diagram of a Corliss engine consequently has a nearly horizontal admission-line and a sharply define cut-off. Generally the valves of Corliss engines are cylindrical plates turning in hollow cylindrical seats which extend across the width of the cylinder. Often, however, the admission-valves are of the disk or double-beat type, and spring into their seats when the trip-gear acts. Many forms of Corliss gear have been invented by Corliss himself and by others. One of these, the Spencer Inglis1 tip-gear, by Messrs Hick, Hargreaves, Co., is shown in figs. 101 and 102. A wrist-plate A, which turns on a pin on the outside of the cylinder, receives a motion of oscillation from an eccentric. It opens the cylindrical rocking-valve B by pulling the link C, which consists of two parts, connected to each other by a pair of spring clips a, a. Between the clips there is a rocking-cam b, and as the link is pulled down this cam places itself more and more athwart the link, until at a certain point it forces the clips open. Then the upper part of the link springs back and allows the valve B to close by the action of a spring in the dash-pot D. When the wrist-plate makes its return stroke the clips re-engage the upper portion of the link C, and things are ready for the next stroke. The rocking-cam b has its position controlled by the governor through the link E in such a way that when the speed of the engine increases it stands more athwart the link C, and therefore causes the clips to be released at an earlier point in the stroke. A precisely similar arrangement governs the admission of steam to the other end of the cylinder. The exhaust-valves are situated on the bottom of the cylinder, at the ends, and take their motion from a separate wrist-plate which oscillates on the same pin with the plate A.1
175. Fig. 103 shows a compact form of trip-gear by Dr. Proell. A rocking-lever ab is made to oscillate on a fixed in through its centre by a connexion to the crosshead of the engine. When the end a rises, the bell-crank lever c engages the lever d, and when a is depressed the lever d is forced down and the valve c is opened to admit steam to one end of the cylinder. As a continues moving down a point is reached at which the edge c slips past the edge d, and b the valve is then forced to its seat by a spring in the dash-pot f. This disengagement occurs early or late according to the position of the fulcrum piece g, on which the heel of the bell-crack crests during the opening of the valve. The position of g is determined by the governor. A similar action, occurring at the other end of the rocking-bar ab, gives steam to the other end of the cylinder. In one form of Proell’s gear both ends of ab act on the same steam-valve, which is then a separate expansion-valve fixed on the back of a chest in which an ordinary slide-valve works.
176. In the ordinary form of centrifugal governor the position of the throttle-valve, of the expansion-link, of the Corliss trigger depends on the configuration of the governor and is definite for each position of the balls. In disengagement governors, of which the governor A shown on the right-hand side in fig. 104 is an example, any reduction of speed below a certain value sets the regulating mechanism in motion, and the adjustment continues until speed has been restored. Similarly a rise of speed above a certain value sets the regulating mechanism in motion in the other direction. If the spindle a (fig. 104) is connected to the regulator so as to give more steam if it turns one way and less if it turns the other, the speed at which the engine will run in equilibrium must lie between narrow limits, since at any speed high enough to keep b in gear with a the supply of steam will go on being reduced, and at any speed low enough to bring c into gear with a the supply will go on being increased. This mode of governing, besides being sensibly isochronous, has the advantage that the power of the governor is not limited by controlling force on the balls, since the governor acts by deflecting a portion of the poser that is being developed by the engine to the work of moving the regulator. It is rarely applied to steam-engines, probably because its action is too slow. This defect has been ingeniously remedied in the supplementary governor Mr. W. Knowles, who as combined a disengagement governor with one of the ordinary type in the manner show in fig. 104.2 Here the spindle a, driven by the supplementary or disengagement governor A, acts by lengthening the rod d which connects the ordinary governor B with the regulator. It does this by turning a coupling nut e which unites two parts of d, on which right- and left-handed screws are cut. Any sudden fluctuation in speed is immediately responded to by the ordinary governor. Any more or less permanent change of load or of steam-pressure gives the supplementary governor time to act. If goes on adjusting the supply until the normal speed is restored, thereby converting the control of the ordinary governor, which is stable, and therefore not isochronous, into a control which is isochronous as regards to all fluctuations of long period? The power of the combination is limited to that of the common governor B.
177. Other governors which deserve to be closed as disengagement governors are those in which the displacement of the governor affects the regulator, not directly by a mechanical connexion, but by admitting steam or other fluid into what may be called a relay cylinder, whose piston acts on the regulator. In order that a governor of this area should work without hunting, the piston and valve of the relay cylinder should be connected by what is termed differential gear, the effect of which is that for each displacement of the valve by the governor the piston moves through a distance proportional to the displacement of the valve. An example of differential gear is shown in fig. 105. Suppose that the rod a is connected with the governor so that it is raised by an acceleration of the engine’s speed. This admits steam to the upper side of the piston and depresses the piston, which pulls down d with it, since the end of a now serves as a fulcrum. Thus by the downward movement of the piston the valve is again restored tot its middle position and the action of the regulator then cases until a new change of speed occurs. A somewhat similar differential contrivance is used in steam-steering engines to make the position of the rudder follow, step by step, every movement of the hand-wheel,3 also, in the steam reversing gear which is applied to large marine engines, to make the position of the drag-link follow that of the hand-lever; and also in certain electrical governor.4
The effect if adding a differential gear such as this to a relay governor or other disengagement governor is to convert it from the isochronous to the stable type.
178. Another group of governors is best exemplified by the "differential" governor of the lat Sir W. Siemens5 (fig. 106). A spindle a driven by the engine drives a piece b (whose rotation is resisted by a friction brake) through the dynamometer coupling c, consisting of a nest of bevel-wheels and a loaded lever d. So long as the speed remains constant the rate at which work is done on the brake is constant and the lever d is steady. If the speed accelerates more power has to be communicated to b, partly to overcome the inertia and partly to meet the increased resistance of the brake, and the lever d is displaced. The lever d works the throttle-valve or other regulator, either directly or by a steam relay. The governor is isochronous when the force employed to hold d in position does not vary; if the force increases when d is displaced, the governor is stable. A governor of this class may properly be called a dynamometric governor, since it regulates by endeavoring to keep constant the rate at which energy is transmitted to the piece b. in one form of Siemens’s governor the friction brake is replaced by a sort centrifugal pump, consisting a paraboloidal cup, open at the top and bottom, whose rotation causes a fluid to rise in it and escape over the rim when the speed is sufficiently great. Any increase in the cup’s speed augments largely the power required to turn it an consequently affects the position of the piece which corresponds to d.6 Siemens’s governor is not itself used to any important extend, but the principle it embodies finds application in a number of other forms.
179. The "velometer" or marine-engine regulator of Messrs Durham and Churchill7 is a governor of the same type. In it the rotation of a piece corresponding to b is resisted by means of a ran revolving in a case containing a fluid, and the coupling piece which is the mechanical equivalent of d in fig. 106 acts on the throttle-valve, not directly but through a steam relay. In Silver’s marine governor8 the only friction-brake that is provided to resist the rotation of the piece which corresponds to b is a set of air-vanes. The inertia is, however, very great, and any acceleration of the engine’s speed consequently displaces the dynamometer coupling, and so acts on the regulator in its effort to increase the speed of b.
Another example of the differential type is the Allen1 governor, which has a fan directly geared to the engine, revolving in a case containing fluid. The case is also free to turn, except that it is held back by a weight or spring and is connected to the regulator. So long as the speed of the fan is constant, the moment required to keep the case from turning does not vary, and consequently the position of the regulator remains unchanged. When the fan turns faster the moment increases, and the case has to follow it (acting on the regulator) until the spring which holds the case from turning is sufficiently extended, or the weight raised. The term "dynamometric governor" is equally applicable to this form; the power required to drive the fan is regulated by an absorption-dynamometer in the case instead of by a transmission-dynamometer between the engine and the fan. In Napier’s governor the case is fixed, and the reaction take s place between one turbine-fan which revolves with the engine and another close to it which is held form turning by a spring and is connected with the regulator.
180. Pump governors form another group closely related to the differential or dynamometric type. An engine may have its speed regulated by working a small pump which supplies a chamber from which water is allowed to escape by an orifice of constant size. When the engine quickens its speed water is pumped in faster than it can escape, ad the accumulation of water in the chamber may be made to act on the regulator through a piston controlled by a spring or in other ways. This device an obvious analogy to the cataract of the Cornish pumping-engine (§ 163), which has, however, the somewhat different purpose of introducing a regulated pause at the end of each stroke. The "differential valve-gear" invented by Mr. H. Davey, and successfully applied by him to modern pumping-engines, combines the functions of the Cornish cataract with that of a hydraulic governor for regulating the expansion.2 In this gear, which is shown diagrammatically in fig. 107, the valve-rod of the engine (a) receives its motion from a lever b, on end of which (c) copies, on a reduced scale, the motion of the engine piston, while the other (d), which forms (so to speak) the fulcrum, has its position regulated by attachment to a subsidiary piston-rod, which is driven by steam in a cylinder e, and is forced to travel uniformly by a cataract f. The point of cut-off is determined by the rate at which the main piston overtakes the cataract piston, and consequently comes early with light loads and late with heavy loads.
181. The government of marine engines is peculiarly difficult on account of the sudden and violent fluctuations of lad to which they are subjected by the alternate uncovering and submersion of the screw in a heavy sea. However rapidly the governor responds to increase of speed by closing the throttle-valve, an excess of work is still done by the steam in the valve-chest and in the high-pressure cylinder. To check the racing which results form this, it has been proposed to supplement the control which the throttle-valve on the steam-pipe exercises by throttling the exhaust or by spoiling the vacuum. Probably a better plan is that of Messrs Jenkins and Lee, who give supplementary regulation by causing the governor to open shunt-valve which connects the top and bottom of the low-pressure cylinder, thus allowing a portion of the steam in it to pass the piston without doing work. In Dunlop’s pneumatic governor3 an attempt is made to anticipate the racing of the screw by causing the regulator to be acted on by the changes of pressure on a diaphragm which is connected by an air-pipe with an open vessel fixed under the stern of the ship. A plan has recently been introduced by Mr. W. B. Thompson to prevent the racing to marine engines by working the valves from a lay shaft which is driven at a uniform speed by an entirely independent engine. So long as this lay shaft is not driven too fast the main engine is obliged to follow it; if the lay shaft is driven faster than the main engine can follow the main engine pauses so as to miss a stroke, and then goes on. Reversing the motion of the lay shaft reverses the main engine.
182. In connexion with governor mention may be made of an apparatus introduce by Mr. Moscrop to give a continuous record of fluctuations in the speed of engines.4 It resembles a small centrifugal governor, but the displacement of the balls actuates, not a regulator, but a pencil which moves transversely on a ribbon of paper that is moved continuously by clockwork. The recorder responds so rapidly to changes of speed as to show not only the comparatively slow changes which occur from stroke to stroke, but also those short-period fluctuations between a maximum and minimum, within the limits of each single stroke, which will be discussed in the next chapter.
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