Slide valve gears. A new graphical method for analyzing the action of slide valves, moved by eccentrics, link-motions and cut-off gears, offering easy means for properly designing valves and valve-gears, and for establishing the comparative merits of their various constructions

Preface

The most successful method of studying and analyzing the action of the slide valve, in its various modes of application, is that which is based on the use of graphical diagrams, among which the one discovered by Zeuner, * is pretty generally considered the best.

This diagram shows at a glance what, by the aid of working models, can be seen only by carefully watching the movement of the slide valve in relation to that of the piston ; it shows how an alteration of any of the essential members of the valve gear affects the working of the valve ; it is admirably adapted to draw a comparison between different valve gears and link motions on their intrinsical as well as their relative merits ; it also furnishes the means, by a reversed -application, of finding the proper proportions of valves and the valve -moving devices when a given effect is desired, and how any valve gear can be proportioned to the best advantage. In short, it meets all the principal requirements of the case. Only one feature is in some respects adverse to a general use of this graphical method ; in some instances its application requires algebraical calculations, or else an intricate geometrical procedure, and for this reason it can be used only by those engineers who have enjoyed a theoretical education.

In his efforts to fully open this field to every intelligent mechanic, the author found that a modification of the Zeuner

IV

Diagram renders the subject in all its bearings purely graphical, and no knowledge of mathematics beyond the most elementary propositions of geometry is required to understand the demonstrations as well as the applications of this new diagram. Nor is this the only advantage gained over the original form ; for by this modification the diagram profited in several other respects, especially in regard to clearness, and will therefore give better satisfaction, even to engineers familiar with mathematics.

The following discussions will be as brief as is consistent with a thorough and fundamental treatment ; and the leading propositions will be amply illustrated.

V CONTENTS.

INTRODUCTION: paob

PeOPEE DlSTEIBUTION OF STEAM, 1

PART I. The Common Slide Valve, 7

The Valve Diagram,..* •>

The Angle of Advance, IS

Width of Ports, 20

Velocity of the Valve, 22

Practical use of the Diagram (Problems), 25

The Scope of the Common Slide Valve, 32

Irregularities of the Crank Motion (Problems), 34

PART II. Link Motions, 45

The Stephenson Line: Motion, 46

The Theory, 49

The Valve Diagram, , 56

The\Link^and its Suspension, 60

Equalization of the Lead, 62'

Problems, 65

Irregularities and their Rectification, 69

The Gooch Link Motion, 78-

PART III. Independent Cut-off Gears, 87

The Gonzenbach^ Cut-off Geae, 91

The Meyer Cut-off, Geae, 97

The Link Expansion Geae, 107

The Bilgeam Cut-off Geae; 119

Introduction

Proper Distribution of Steam.

The steam engine is a mechanical contrivance for converting the power, developed by the evaporation of water, into such a form that it can be utilized for driving machinery or for other industrial purposes. After its generation in the boiler, the steam is caused to exert its pressure alternately upon both sides of the piston, imparting a reciprocating motion, which is converted into a rotary one by a connecting-rod and crank. The valves admitting the steam alternately to both ends of the cylinder, and opening an exit for the steam after the performance of its duty, are named" distributionvalves " and the mechanism operating them is termed ''valve-gear. ' '

We shall now consider how the admission of steam should be regulated in order that the greatest amount of useful effect will be realized ; this will enable us to judge how near the valve-gears to be considered hereafter approximate to perfection.

I. Expansion. To the engineer, the most valuable property of steam is its elasticity, which can most effectively be utilized by admitting steam to the cylinder for a portion of the stroke only. The production of work per stroke will then comprise two stages : (1) The direct action of steam, for the time of admission, when the steam exerts its initial pressure upon the piston, and (2) The action of the expanding steam ; in which period the pressure is gradually diminishing.

For economy of steam it is most advantageous to expand until the terminal pressure upon the piston equals the average Motional resistance of the engine. In practice, however, the expansion is not always carried thus far, as an engine accomplishing this result generally demands a higher price than one with a single slide-valve, and purchasers of engines frequently prefer to save in the first cost.

When the load on the engine is subject to variation, the admission of steam must be regulated accordingly. The effec tive steam pressure upon the piston is usually more or less reduced by throttling the admitted steam by a valve that is operated by the governor. A more economical plan, however, is to vary the degree of expansion by cutting the steam-off at an earlier or later stage of the stroke, if the valve-gear admits of such a variation.

II, Compression. That end of the cylinder towards which the piston is moving must be in communication with the exhaust passage. In condensing engines the exhaust passage is in communication with the condenser, where a partial vacuum is produced by the condensation of the exhaust steam. Other engines exhaust into the air, and have therefore a back pressure equal to, or slightly above, that of the atmosphere.

It is of advantage to interrupt the exhaust a short time before the termination of the stroke, and to compress the thus insulated exhaust steam by the piston. At the first glance this statement may appear absurd ; but it is nevertheless consistent with both theory and practical experience, for the following reasons :

The " clearance/ ' — which is the space left at the end of the stroke, between the piston and the end of the cylinder, together with the space of the steam passage between the valve and the cylinder, — is alternately brought in communication with the steam chest and with the exhaust passage, and is thus filled with steam and emptied again. The direct action of this steam is evidently lost, and only part of the expansive power of the same is made available. This continual loss of power can, however, be moderated by compressing into the clearance part of the exhaust steam, raising its pressure to that in the boiler. "When thereafter the valve opens the port for admission, no steam is required to fill the clearance, and the full power of all the admitted steam will be turned into useful work. If now the steam is cut off so early in the stroke that the terminal pressure will be equal to that in the exhaust passage, the re-expansion of the previously compressed steam will augment the production of work just so much as to restore the work expended in compression. This shows that under the said conditions the clearance will cause no loss of steam. It must, however, be remembered that in the first place we took no account of friction. The space through which the piston travels during compression, is entirely lost for the production of work ; therefore it is evident that an engine with much clearance and corresponding compression, though theoretically equal to one with but little clearance and compression, is practically inferior, for since the travel of the piston must be greater it will involve greater loss from friction. In the second place, we assumed the expansion carried to a degree higher than that generally used. It is, therefore, . advisable to compress to a less degree, especially if not much, expansion is used ; for the work expended for compression will be but partially restored by the following re-expansion.

A second reason for prematurely closing the exhaust is due to the reaction of the compressed exhaust steam upon the piston,— commonly called "cushioning," — which assists in the reversal of the motion of the piston and other reciprocating parts of the engine and lessens the wear in bearings, and also the thumping caused by lost motion which is usually present to some extent.

III. Lead. Experience has taught that both the admission and the exhaust of steam should be commenced a short time before the crank passes the centre. Either port will thereby be opened to some extent at the beginning of the stroke. The width of the opening at that time is termed "lead," while the angle through which the crank passes from the moment of the opening of the port until it reaches the centre is the "lead angle."

Cne reason is obvious. The steam does not fill the clearance, nor does the exhaust steam reduce its pressure to that of the exhaust passage, the very instant the port for either admission or exhaust is opened ; hence the advantage of a premature opening on either side.

As a general rule the lead on the exhaust side is greater than that on the steam side, as the former has the function of releasing the pressure of a volume of steam filling the entire cylinder, while the latter need only fill the clearance with live steam. The opening of the exhaust is mostly effected w7hile the piston is still an appreciable distance from the end of its stroke, and is more commonly called "release," while the admission mostly begins when the piston has practically arrived at the end of its travel.

The most advantageous amount of lead on the exhaust side depends mainly on the terminal pressure of the expanded steam ; and should, therefore, be greater on engines with late cut-off. High speed engines need more lead on both sides than slow running ones, to allow the proper time for the functions of lead. Excessive lead on either side always results in waste of power.

Lead is also a very convenient means for supplementing the cushioning if compression is insufficient for this purpose ; it can be adjusted until the engine ceases to thump. High speed engines and beam engines need more lead on this account, than others^ because of the greater momentum to be overcome.

Part I. The Common Slide Valve

The Common Slide Valve.

The usual form of the common slide valve is shown in Fig. 1, where /Sand 8 ' represent the steam passages of the cylinder, kick i a&vaf

Fig. 1.

and S° the exhaust passage. Tis the valve, the cavity v of which effects alternately a connection of the steam ports with the exhaust port. The valve is encased in the steam chest, into which the live steam is admitted. It is moved by the valve stem passing through a stuffing box of the steam chest.

When the valve is in its neutral position, as shown, its face overlaps the steam ports on both sides. The distance a b is called the outside or steam side lap, andc d is the inside or exhaust side lap.

In the following considerations we shall term "positive " any movement of the valve from its neutral position towards the valve stem, in contradistinction from a movement in the opposite or "negative" direction. A positive movement of the valve connects the port 8' with the exhaust passage 8° through the cavity 0, and opens the port 8 for admission of steam from the steam chest. The width of the opening of either port depends en the distance of the valve from its neutral position, for the time being. This distance, or the "movement " of the valve, must exceed the inside lap before he port S' will be opened for exhaust ; and it must be greater than the outside lap, to effect an opening of the port S for admission of live steam. For a given movement of the valvewe find the opening of the steam ports for either exhaust or

Fig. 2.

admission by deducting from this movement the inside or outside lap respectively. When this difference is equal to or greater than the width of the port, the latter is fully opened. The effect produced by a motion of the valve in the opposite (negative) direction is similar, but reversed as regards the passages #and S\

The valve is moved by means of the eccentric I, (Fig. 2), which can properly be considered as a small crank, the pin of which is enlarged so much as to assume the form of a disc that allows the shaft 0 to pass through it. The eccentric can therefore be represented by the line 0 J, that connects the centre of the shaft, O, with the centre of the eccentric disc, I, and which is supposed to act like a crank.

The Valve Diagram.

We shall first consider horizontal engines of the usual construction, m which both the connecting rod and the eccentric rod, are operated in parallel directions.

The eccentric of such engines is keyed to the crank shaft so that the centre line 01 (Fig. 2) of the eccentric forms an obtuse angle with the centre line OK of the crank. As the •crank shaft rotates, the end P of the eccentrie rod, being .guided in a right line by the valve stem, receives a reciprocating motion while the rod itself is caused to oscillate. The reciprocating motion of the end P is transmitted by means of the valve stem to the slide valve. The oscillating movement introduces a very intricate factor, since it affects the horizontal -extension of the eccentric rod. We shall, however, at present leave this factor altogether out of account, and shall examine it later.

It is necessary to locate the centre of vibration of the endP of the eccentric rod on account of its corresponding relation to the neutral position of the valve. The vibration of this point being a direct result of the circular movement of the other end, I, of the eccentric rod, it is evident that the centres of both movements must correspond. Therefore, if the end I of the rod IP be transposed to the centre of its motion, (which is the centre 0 of the 'crank shaft) its other end P will occupy the centre of its' vibration. It will now be understood that the movement of the pin P depends on the horizontal movement of the centre, 7, of the eccentric ; and can therefore be measured by the horizontal distance of the point /from the vertical centre line 0 Y.

When the crank is on its centre OK (Fig. 3) and J is the corresponding position of the eccentric, the distance Iy will represent the valve movement.

As the crank moves from JTto IP through the angle a, the eccentric will move through the same angle to T, and Tyy will now be the distance of the valve from its neutral position.

Let us now mark the point Q in the circle Z representingthe orbit of the eccentric ; making the angle XOQ equal to the angle 10 Y (lioth of which are marked 6 in Fig. 3), and draw the line Q k perpendicular to the extension of the line OK of the crank. The triangles QOk and T 0yy will then be equal, since the angles QOk and Q JcO are equal respectively to the angles T Oy' and Vy' 0, and the side OQ equals the side 01 ; hence the line Qk equals l'yy and therefore is equal to the movement of the valve for the crank angle a. The same relation can be showTn, in the same manner, for any other crank angle, and the interesting fact is thcreb/ demonstrated that, for any angle of the crank, the distance of the point Qfrom the centre line of the crank is equal to the corresponding movement of the slide valve.

To find the openings of the ports for either admission or exhaust, the inside or outside lap is to be deducted from this movement. This subtraction can be graphically performed by sweeping two circles, L and I, fromQ with radii equal to the outside and inside laps, as shown in Fig. 3. For the considered position, K, of the crank, the movement of the valve was found to equal the distance Q k, and hence the opening of the steam port S (Fig. 1) for admission of steam is equal to ka, and that of the port S' for exhaust equal to ka' ; these distances being equal to the movement Qk, minus the respective laps. The port openings are therefore represented by the shortest distances between the centre line of the crank and the lap circles L or l} respectively.

Had the point Q\ instead of Q, been selected, the result would have been the same, since Q k equals Q'k'.

To prevent any misunderstanding it may be here stated that Fig. 3 now represents two distinct diagrams, one showing the position of the eccentric, I, in relation to the crank, OK, when on its centre, and another in which the point Q figures and which will be called the "valve diagram." The latter can be obtained from the former by making the angle XO Q = angle YOT, or also, by rotating the first diagramthrough a right angle, when the eccentric will arrive at J," and subsequently inverting it. This last mode of converting one diagram into the other, can very conveniently be performed by means of a piece of tracing paper, viz., by tracing the diagram of crank and eccentric, KOI, turning this tracing over and setting the crank-line, OK, in a vertical position, pointing downwards. The position of the eccentric, I, will then locate the point, Q, whose mate, Q\ is diametrically opposite.

In order to know the direction of the valve-movement we must consider that the valve will be in its neutral position when the crank passes through Q or Q\ the distance of Q from the crank-line being zero. As the crank moves from Qy through K' to Q, the movement of the valve is positive, and while moving from Q to Q' this movement is negative.

When the engine is required to rotate in an opposite direction, the position of the eccentric will be 1°, in relation to the crank, OK ; and the valve diagram will be reversed or left-handed.

The valve diagram as explained affords an easy means of studying the influence of form and motion of the valve on the distribution of steam. The most important positions of the crank, as regards the admission and the exhaust of steam, •are shown in Fig. 4. When the crank is on its centre, at K,

Fig. 4.

13 the distance ka shows the opening of the port for admission,, or the lead on the steam side, and ka' represents the openingof the port for the exhaust, or the lead on the exhaust side. The valve attains its maximum movement when the crank is. at Ns forming right angles with the line OQ; hence the greatest port-opening for admission of steam is equal to Ob. This distance may be greater than the width of the steam port, showing that the outside edge of the valve overrunsthe inside edge of the port, allowing an unobstructed admission of steam. The word " port-opening " will be used independently of the width of the steam ports, and may therefore exceed the latter. As the crank proceeds, the port-opening will be reduced again ; and when the crank arrives at E, the port, S, (Fig. 1) will be closed and the admission of steam cut off; the valve movement being equal to the outside lap. At C the valve movement will be equal to the inside lap, hence the port, S', (Fig. 1) will be closed, and compression will commence. OQ is the position of the crank when the valve passes its neutral position At B the negativemovement of the valve equals the inside lap and the port, 3, is opened for exhaust. At A the port, S't will be opened for admission of steam for the following stroke. For the crank-angles X\E' ', C\B\A\ the results will be merely a repetition of what has already been said, with this difference only : that the ports exchange their respective functions. The lead angle for admission is shown in the diagram by the angle A' OK ot AOX, and that for exhaust by the angle JR' OK or BOX.

This diagram may perhaps seem, to a beginner, somewhat complicated, especially as it is necessary for some crank angles to extend the crank-line over the centre, 0 ; and further, as it requires some practice to determine which of thetwo ports is being opened or closed. It can, however, be so drawn that the operation of the valve on each port may bo represented separately, as in Fig. 5, relating to the port, 3*

(Fig. 1) and in Fig. 6, relating to the port, S9. By a comparison with Fig. 4, these diagrams may be readily under stood without further comment. These diagrams indicate the port to which they relate to be opened, for either admission or exhaust, as long as the crank-line is outside of the respective cross-lined surface and each of them may again be regarded as combining two diagrams ; one for admission, and the other for exhaust.

These two diagrams, Figs. 5 and 6, can readily be combined by drawing the upper half of Fig. 5 and the lower half of Fig. 6 in full lines and the rest in dotted lines. Some of the following diagrams will be executed in that manner ; and it is only to be remembered that the crank-angles for cutting-off and for release (relating to the port on the steam side of the

<rP piston) will always be tangent to solid circles, while the crank-angles for compression and the beginning of admission (relating to the port on the exhaust side of the piston) will be tangent to the dotted lap circles.

When the valve possesses no inside lap, the inside lap-circle shrinks into the point, Q, and hence Qand Qy are the positions of the crank where the exhaust is closed for one port and at the same time opened for the other port. Sometimes the valve may be constructed as shown, in Fig. 7, possessing the converse of an inside lap. The distance, cd, is properly called "negative lap." Some engineers call it "inside lead," others, again, "inside clearance/ ' but both these terms are apt to lead to confusion, for "lap" is measured when the valve is in its neutral position; "lead" is measured when

•tf'JV

Fig. 7.

the crank is on its centre ; and " clearance " is the conventional name for the space left between the steam-valve and the piston at the end of its stroke. To find the opening of the port for exhaust in such a case, the distance, cd, must evidently be added to the movement of the valve, and hence the opening is not Jca7 (Fig. 3) but Jca" and- the diagram represented in Fig. 5 becomes like Fig. 8, which shows that in this case the exhaust remains opened for more than a semirevolution of the crank shaft.

It has been stated before that the greatest port-opening of the valve sometimes exceeds the width of the port. The dia gram shows without difficulty the angles for which the port -remains opened to its full width. We sweep a circle, s, from

JJL -Sk--..H»^fc: t „

Fig. 9.

"^ (Fig. 9), the distance of which from the lap circle, Z, is equal to the width, w, of the port. For the two crank angles, OK and OIC, which form tangents to this circle, the port -opening will be equal to the width of the port, and between K and IP it will be in excess of the latter.

Or, it may happen that the greatest port-opening for admission is less than the width of the port, which then will become fully opened for the exhaust only. The greatest port-opening for admission should, however, never be less than 75 per cent, of the width of the port.

The manner of comparing the motion of the crank with that of the piston will be explained later.

The Angle of Advance.

On horizontal engines the centre-line 01 of the eccentric forms, as already mentioned, an obtuse angle with the centre line OiT(Fig. 2) of the crank. This relation will be modified when both the connecting rod and the eccentric rod are not operated in parallel directions, as may be the case with beam engines, or where a rocker or some other lever connection is interposed, for instance as shown in Fig. 10. But no matter whatever the general arrangement of the engine may be, the centre line of the eccentric forms most always approximately right angles with the eccentric rod when the crank is in line with the connecting rod, or "on its centre.' ' It should, however, never be precisely at right angles, but always more or less in advance of this position, in the direction of the rotation of the crank shaft, for else the valve would be in its neutral position at the beginning of the stroke ; and since the port on the steam side is required to be opened, the eccentric must be advanced to make the lap and lead. The angle measuring this advance, namely, the angle formed between the eccentric line 01 (Fig. 10) and the line OY drawn at right angles to the mean direction of the eccentric-rod, is called the ''angular advance" or "angle of advance." The mean or neutral direction of the eccentric rod may be determined, in the drawing, by transferring the end 7 of the same into the centre 0 of the crank-shaft, and is shown, in Fig. 10, by the dotted line 0P°. Whenever the end P of the eccentric-rod is guided in an arc, as in Fig. 10, this construction does not give a perfectly accurate result, but it will be sufficiently accurate for practical purposes, as the valve performs its principal operations when near its central position.

The "angular advance" plays an important part in the action of the slide valve and shall be denoted by the letter 6, as has already been done in the former diagrams.

In order to investigate the operation of its valve motion, any type of engines may be compared with a horizontal engine having the same slide valve, with equal travel, and equal angular advance. The valve diagram can therefore be drawn by first sweeping a circle for the path of the eccentric and then carrying in it the angle of advance from the horizontal centre-line in a direction opposite that of the rotation of the crank. From the points thus obtained in the circumference of the circle the lap circles have to be swept to complete the diagram.

It need hardly be mentioned that in cases where the motion of the eccentric-rod is transmitted to the val^e by rockers or levers of unequal leverage the radius of the "path of the eccentric" of the diagram should not be made equal to the throw cf the eccentric, but equal to one-half the travel of the valve.

In designing engines other than such where the connecting-rod and eccentric-rod are operated in a parallel direction, beginners often find difficulty in drawing the eccentric in its proper position to the crank, the angle of advance being given. The course to be pursued in such cases is as follows. Draw the crank OK (see Fig, 10) on one of its dead centres, and then draw the line 0 F, at right angles to the mean direction, OP°, of the eccentric-rod and cany the angle of advance, S, from the last mentioned line, in the direction of therotation of the crank-shaft. The resulting line determines the angle of the eccentric, but it must be decided yet whether I or I9 (see Fig. 10) is the correct position. This can be done by assuming the movement of the crank to proceed, and considering which of the two points J or J' would cause thevalve to open that port that will admit the steam on the proper side of the piston.

Width of Ports.

The sectional area of the steam-ports should be made so large as to impede the ingress and egress of the steam as little as possible, and yet, on the other hand, so small as not to unduly increase the amount of clearance. By a series of carefully conducted experiments, it was found that the greatest velocity of the steam in the passages should be from 8,000 to 9,000 feet per minute, in small engines and such of a low pressure and low mean piston speed, and from 9,000 to 10,- 000 feet in large ones and such of high piston speed.

To compute, from these data, the area of the ports in any one special case, the maximum velocity of the piston must be found, which is equal to that of the crank pin, and hence equal to the product of the number of revolutions per minute into the periphery of the crank-pin circle. The conventional measure for the speed of engines, however, is the mean

^velocity of the piston, which is equal to the number of revolutions into twice the diameter of the crank-pin circle. The proportion of the mean speed to the maximum speed is therefore as two diameters to the circumference of a circle, or ap proximately as 7 is to 11 ; and hence the maximum speed of & piston is equal to its mean speed multiplied by the fraction y. The ratio of this speed to the allowed maximum speed of the steam in the passages furnishes the ratio of the area of the steam-ports to the area of the piston.

After the area of the ports is thus determined and a suitable length of the ports is selected, their width is found by dividing the area by the leng:h.