T APPLICATIO E PRACTICAL A PPLICATIONAIO OF THE SLIDE VALVE AIND LINK MOTION TO STATIONARY, PORTABLE, LOCOMOTIVE, AND MARINE ENGINES, WITH NEW AND SIMPLE METHODS FOR PROPORTIONING THE PARTS. BY WILLIAM S. AUCIINCLOSS, C.E., MEL. AM-ER. SOC. CIV. ENG. SECOND EDITION. NEW YORK: D. VAN NOSTRAND, PUBLISHER, No. 23 MURRAY STREET, AND No. 27 WARREN ST. 1869. Entered, according to Act of Congress, in the year 1869, by WILLIAM S. AUCHINCLOSS, In the Clerk's Office of the District Court of the United States for the Southern District of New York. Electrotyped by SMITH & McDOUGAL, 82 & 84 Beekman Street. PRE F ACE. THE main object of this Treatise on the Link and Slide Valve, is to place in the hands of the Mechanical Engineer and Draughtsman, a simple method for determining the proportions suitable to any Link Motion, without the assistance of an expensive and cumbrous model, or the delays incident to its manipulation. Secondarily, to supply the Student of Steam Engineering with a comprehensive view of those causes which regulate both the form and dimension of the cylinder, slide valve and eccentric. This portion of the work has grown incidentally out of the first; for as the link merely combines the action of the two eccentrics, it was obviously necessary that the functions of one of these should be clearly understood before an attempt was made to develop the laws of their joint action. It is hoped, however, that these Parts I. and II. will not prove entirely devoid of interest to the skilled designer, but that they will at least receive a hasty survey, for the sake of the light they throw on the general subject through the medium of Part III. WVe are aware, that most Engineers consider the use of a model as absolutely indispensable to the proper adjustment of a Link Motion, and that they are wont to look with skepticism upon all efforts made to solve the problem by other means. So far as these feelings are entertained against an algebraic or trigonometric solution they rest on a firm foundation and receive our hearty approval; for -we have been led to believe from careful investigation that it is utterly impossible to construct for this case a formula of any practical value, since the question involves from sixteen to iv P REY F ACE. twenty variable quantities, the majority of which exert a controlling influence on the motion and many introduce irregularities quite beyond the powers of algebraic expression. But at the very point where such analysis fails, geometric construction tenders its most efficient aid and furnishes a simple solution of this abstruse problem. The method of investigation has been copiously illustrated with cuts-Part IV —showing the link template drawn in all of its important positions. These have been considered of greater importance for a clear understanding of the subject than the employment of a more diffuse explanation. They are however apt to produce at first sight an erroneous impression regarding the conciseness of the method, but this will always be corrected by a single construction trial, which at once reveals how smnall an amount of work is actually required for accomplishing the object in view. The Table of crank angles for different locations of the piston cannot fail to effect a great saving of time, for it enables the designer to instantly locate the eccentrics for any piston position, without resort to laborious construction. Besides treating of the various methods by which a link should be suspended for accomplishing certain results, the manner of attaching the eccentric rods has been carefully examined and diagrams presented that show what form should be adopted for meeting most directly the requirements of an accurate adjustment. A brief discussion of the subject of independent cut-offs will be found in Part Y., together with general remarks on Friction, Clearance, Travel, &c. We have added an Appendix for the benefit of those who desire a mathematical investigation of the subject of crank and piston motion and who would fain inquire more minutely into the principles involved in the STROKE TABLE. This has purposely been separated from the body of the work, which we have aimed as far as possible to preserve free from all algebraic formula, in order to render it more acceptable to the majority of mechanics. We trust that these will appreciate the peculiar directness of the PREFACE. V solutions effected by the TRAVEL SCALE, in that it determines immediately the very dimensions desired, without taxing the investigator's patience by leading him through intricate constructions to an uncertain result. The work is now presented to the Engineering community, not without consciousness of its imperfections, yet with the hope that it will tend to simplify in many minds the subject of eccentric and link motion and serve as a stepping-stone to further discoveries. W. S. A. NEW YORK, Ml/arch, 1869. CONTENTS. PART I. PAGE. THE SLIDE VALVE-ELEMENTARY PRINCIPLES AND GENERAL PROPORTIONS... PART II. GENERAL PROPORTIONS MODIFIED BY CRANK AND PISTON CONNECTION.. O... PART III. ADJUSTABLE ECCENTRICS. 78 PART IV LINE MOTIONS..,..89 PART V INDEPENDENT CUT-OFF, CLEARANCE, ETC.. 147 APPENDIX. FORMULAS RELATING TO CRANK: AND PISTON MOTIONS O. 161 TRAVEL SCALE. ATTACHED TO THIE BACK COVER. PART I. TIE SLIDE VALVE. ELE MENTARY PRINCIPLES AND GENER AL PROPORTIO NS. POWER AND WORK. THE fundamental query in designing a steam-engine has reference to the power required to accomplish a given amount of work. The term work, when employed in a mathematical sense, signifies the continuous overcoming of an offered resistance along a definite path. The, quantity of work is the product of that resistance into the space passed over. As the standards of weight and distance differ throughout the world, the expressions for quantity of work also differ. With the English standard of pounds avoirdupois and feet, the quantity of work is said to consist of a certain number of foot-pounds. But with the French standard of weight, the kilogramme (=2.20462 lbs. avoirdupois) and of distance, the metre (=3.28089 ft.), the expression becomes a certain number of kilogrammetres. Thus the quantity of work expended in raising a weight of 300 lbs. through a vertical'height of 10 ft. =3,000 ft.-lbs. and that of elevating a weight of 50 kilogrammes to a height of 20 metres =1,000 kilogrammetres. The quantity of work performed by the steam in the cylinder of an engine, equals the mean effective pressure exerted upon the entire area of the piston multiplied by the space passed over in a 12 HORSE POWER given time. The interval of time usually taken is one minute; hence, if the distance traveled by the piston during a single revolution of the crank be multiplied by the number of revolutions made per minute, their product will equal the required space. Suppose, for instance, the mean effective pressure on each square inch of a piston, having an area of 1,500 sq. ins., is 60 lbs.; then the total pressure will be 1,500 x 60 =90,000 lbs., and if the crank makes 40 revolutions per minute, with a piston stroke of 3 ft., the speed of the piston becomes 3 ft. x 2 x 40 = 240 ft. per minute; consequently the quantity of work -=90,000 lbs. x240 ft. =21,600,000 ft. -lbs. I.-HO0RS:E POWER. A force capable of raising a weight of 33,000 lbs. one foot high in one minute is termed a Horse power. The expression originated at the time of the discovery of the steam-engine from the necessity which then arose for comparing its powers with those of the prevailing motor. In its early history this unit had three prefixes-Nominal, Indicated, and Actual —derived from the various methods of estimating the power. The nominal horse power was based on the general practice of the age, which dealt with low pressures and slow piston speeds. These quantities have of late years been greatly increased and the old formula in consequence, grown of less and less importance as a true expression of relative capacity. Indicated horse power designates the total unbalanced power of an engine employed in overcoming the combined resistances of friction and the load. Hence it equals the quantity of work performed by the steam in one minute, HORSE POWER. 13 divided by 33,000. Thus, in the above example, the indicated horse power equals 1,600,000 3)21,600 2100,000 = 11)7,200 3,000 654 HP The mean effective pressure can alone be determined by means of an instrument called the Indicator. The Actual or net horse power, expresses the total available power of an engine, hence it equals the indicated horse power less an amount expended in overcoming the friction. The latter has two components, viz: the power required to run the engine, detached from its load, at the normal speed, and that required when it is connected with its load. It is customary in designing massive engines-in the absence of reliable data-to estimate the loss of available pressure by the unloaded friction at 2 lbs. per square inch, and subsequently to deduct 71 per cent. for the friction of the load. Thus, if the mean pressure of the steam within the cylinder...................................... 60 sq:i n. 2 It becomes 58 after allowing for unloaded friction, 58 And 71 % of this for the friction of the load....... 4-.4 Gives a net pressure of................... 53.6 lbs. But for small engines of the ordinary design the total loss by friction will, in many instances, amount to 15 or 20 % of the mean pressure. Thus, if the mean pressure..................... = 60 lbs. 15 ~ of 60 = total loss by friction.............. = 9 " Gives an available pressure of............ 51 " The French apply the term Force de cheval to a power capable of raising 4,500 kilogrammes 1 metre high 14 MEAN EFFECTIVE PRESSURE. in 1 minute. Reducing these quantities to their equivalents in pounds and feet and multiplying together, we find that their horse-power equals a force capable of raising 32,549 lbs. 1 foot high in a minute, which is about 1 less than the English unit of measure. The following TABLE furnishes the Force de cheval equivalents of horse powers ranging between 10 and 100: Horse Power. Force de cheval. Horse Power. Force de cheval. 10 Io.14 60 60.83 15 I5.20 65 65.89 20 20.28 70 70.97 25 25.34 75 76.03 30 30.41 80 8. I I 35 35.48 85 86. 7 40 40.55 90 91.25 45 45.62 95 96.31 50 50.69 I00 I01.3856 55 55.75.... For powers greater than 100, and less than 1,000, multiply these terms by 10; or, if in excess of 1,000, multiply by 100. I I. —MEAN EFFECTIVE PRESSUiRE. The character of the connections between the boiler and steam cylinder, their length, degree of protection, number of bends, shape of valves, etc., must all be considered in forming an estimate of the initial steam pressure in the cylinder; while the mean effective pressure will depend upon the point of cut-off of the steam, and the freedom with which it exhausts. The exact portion of the stroke that should be completed before this closure or cut-off takes place is a vexed question among engineers, and its discussion is foreign to the object of this Treatise, in which-with the exception of noting cer MEAN EFFECTIVE PRESSURE. 15 tain limits prescribed by different valve motions —it will be considered as predetermined. Having chosen a point of cut-off, and having estimated the initial pressure of the steam for a given boiler pressure, the question of mean pressure exerted by the steam throughout the piston's stroke, can be approximately solved by the subjoined Table, which has been computed in the ordiMean Pressure, Volume, and Temperature Table. Pi ~ STROKE I... MEAN PRESSURE FOR VARIOUS CUT-OFFS.. 4 1or 3 or 8 or 4 or or or or.= 0.25 0.375 0.5 0.625 0.666 0.75 0.875 Lbs. Deg. Lbs. Lbs. Lbs. 20 260 765 II.9 14.9 I6.9 I8.4 I8.7 I9.3 I9.8 25 267 677 14.9 i8.6 21.2 23. 23.3 24. I 24.7 30 274 608 I 7.9 23.3 25.4 27.6 28. 28.9 29.7 35 281 552 20.9 26. 29.6 32.1 32.7 33.7 34.6 40 287 506 23.9 29.7 33.9 36.8 37.3 38.5 39.6 45 293 467 26.8 33.4 38. 4I.3 42. 43.4 44.5 50 298 434 29.8 37.1 42.3 45.9 46.7 48.2 49.5 55 303 406 32.8 40.8 46.6 50.5 5I.3 53. 54.4 6o 308 381 35.8 44.5 5o.8 55.I 56. 57.8 59.4 65 3 12 359 38.8 48.2 55. 59.7 60.7 62.6 64.3 70 3I6 340 4I.7 52. 59.3 64.3 65.3 67.5 69.3 75 320 323 44.7 55.7 63.5 68.9 69.9 72.3 74.2 80 324 307 47.7 59.4 67.7 73.5 74.6 77-I1 79.2 85 328 293 50.7 63. I 7I.9 78. I 79.3 81I.9 84. I 90 332 281 53.7 66.8 76.2 82.7 84. 86.7 89. I 95 335 269 56.7 70.5 80.4 87.3 88.7 91.6 94. 100 338 259 59.7 74.2 84.6 9I.9 93.3 96.4 99. I05 341 249 62.6 77.9 88.9 96.5 97.9 OI.I I03.9 I10 344 239 65.6 8i.6 93. I Ioi. I oi.6 105.9 108.9 115 347 231 68.6 85.3 97.4 Io5.6 106.3 I IO.8 I I3.8 I20 350 223 71.6 89. IOI.6 1 10.2 110.9 I I5.6 II8.8 725 353 2I6 74-6 92.7 I0o5.8 I4.8 I15.6 120.5 123.7 130 356 209 77.6 96.4 I Io. 119.4 120.3 I25.3 128.7 135 358 203 8o.6 Ioo. 1 114.2 I24. I25. I30.I 133.6 140 360 I97 83.5 I03.8 I I8.5 I28.6 I30.6 I34.9[ I38.6 145 363 I9I1 86.5 107.5 I22.7 I33.2 I35.3 I39.7 I43.5 750 365 I86 89.5 111.2 1 26.9 137.8 I40. I44.5 48.5 Common difference. 3.0 3.7 4.2 4.6 4. 7 4.8 5.0 16 MEAN EFFECTIVE PRESSURE. nary manner with the aid of logarithms (Naperian Base). The first column is given for pressures above that of the atmosphere, or the same as registered by an ordinary steam-gauge. The second and third, for temperature and volume, are taken from Mons. Regnault's Experiments on Saturated Steam. In the estimate for volume, that of the water producing the steam was considered equal to Unity. If from the mean pressure we subtract the mean value of the back pressure, or that which may arise from imperfections in the exhaust, which is usually taken for lowpressure engines at from 1 to 2 lbs. per square inch, the resulting pressure will be the mean effective pressure (in pounds) exerted on each square inch of the piston and may be represented by the letter P. For high-pressure engines (having an ordinary slide valve) a more exact determination of the mean effective pressure may be secured from the subjoined table, which embodies the results of 50 experiments made by Mr. Gooch, in 1851, with the locomotive "Great Britain," whose boiler pressure varied from 60 to 150 lbs. per square inch. Mean Efgective Pressures incident to a Simple Slide-Valve zMotion for various Cut-offs. Cut-Off at- Mean Pressure. Cut-Off at Mean Pressure. (Boiler press. =.oo.) - - (Boiler press..oo.) 0.I. I5 0.45 0.62 o.I25-=8 0.2 0.5 =o- 0.67 0.15 0.24 0.55 0.72 0. 175 0.28 0o.625 — 0.79 0.2 0.32 o.666=-2 0.82 0.25 =4 0.4 0.7 0.85 0.3 0.46 0.75 =-4 0.89. 333 3 0.5 =1 o.8 0.93 0.3757= 0.55 0.875-=7 o.98 0.4 0.57..... SPEED OF PISTON. 17 EXAMPLE. jGiven Boiler pressure = 70 lbs. per sq. in. Steam cut off at 2 of the stroke. Required. —The mean effective pressure P a We learn from the table that this pressure for a cut-off f the stroke is 0.82 of the boiler pressure. Then 70x0.82=57.4, or The mean effective pressure P = 57.4 lbs. per sq. in. II.-SPEED OF PISTON. The speed S, or number of feet travelled by the piston in one minute, like the subject of cut-off, rests with the judgment of the individual designer. Nothing more will be attempted in this connection than the presentation of quantities most frequently found in ordinary practice: Small stationary engines from....... 170 to 230 ft. per min. Large stationary engines............250 to 300 (Rarely as high as 350 ft.) River and Sound steamer engines.... 350 to 500 " Marine engines.....................250 to 600 " The Corliss stationary engine........400 to 500' (Usually 50 revolutions.) Locomotive engines about...........600 (Occasionally 700 or 800 ft.) The Allen engine................... 600 to 800 " (Generally the former speed.) It is interesting to note that a fine specimen of the latter 2 18 DIA3METER OF PISTON. form of engine was operated successfully by Mr. Charles T. Porter, during the late "Exposition Universelle," at the astonishing speed of 1,400 feet per minute. IV. —DIAMETER OF PISTON. Having decided the questions relating to indicated horse power, mean available pressure P and piston speed S, all the elements are at hand for determining the area of the piston, and consequently its diameter. The formula for indicated horse power, solved with reference to such area, will read: A_ 3,3000 x Horse power SxP or, Area of piston is found by multiplying the required indicated horse power by 33,000, and dividing the product by speed of piston multiplied by the mean available pressure. The corresponding diameter can be obtained from an Area Table. EXAMPLE. Suppose that the indicated horse power=100. Piston speed=300 ft. per minute. Mean available pressure=21 lbs. Then the 33,000 x 100 Area 300x21 -523.8 sq. in. Which gives a diameter of about 26 inches. STROK:E OF PISTON. 19 V.-STROKE OF PISTON. The general expression for the stroke of an engine (in feet) is, Piston Speed Stroke= 2x No. of Revolutions' conversely, No. of Revolutions —Piston Speed 2 x Stroke There are many circumstances tending to limit the stroke of a piston. Among other considerations the diameter of a paddle-wheel influences the number of revolutions that can advantageously be made by the crank of a sidewheel steamer, and consequently determines the stroke when the piston speed is chosen. Peculiarities of design.requently make it desirable that an engine should be run at a slow speed and transmit its power through gearing. Again, the diameters of pulleys for shafting exert an influence, as when the main shaft of a shop is' required to run at 120 revolutions per minute, then 60 revolutions for the crank of the engine, will allow a ratio of 2: 1 between the diameter of the band wheel and shaft pulley. With a very rapid piston speed, the stroke of the engine is due more to a length imposed on the connecting rod by the necessities of the design, than to the number of revolutions of the crank. In the case of the locomotive, the stroke is generally about 24 inches, and the piston speed 600 feet per minute, while the speed of the engine which depends on its power and the diameter of its drivers, ranges between 20 and 60 miles per hour. The accompanying table has been calculated, for drivers of different diameters, to represent the number of revolu 20 STROKE OF PISTON. tions they will make per minute, irrespective of slip, when the engine travels at given speeds per hour. Rezvoltions made by 2Driving W/z/eels of locomotive at given speeds. SPEED IN MILES PER HOUR. RevoluDriving-wheel diam- tions eter. eter. 20 miles. 25. 30. 35. 40. 50. per mile. 4 ft. oin. I40 I75 2 I.... 420. 4 "3 I132 i65 198 395.5 4" 6" I24 I56 I86.. 373.6 4 "9" I18 I48 I77 207.. s 354. 5 I140 I68 I96 336. 5 "3 134 16o 187 320.2 5 "6 c c 128 I53 I79 204 o 305.9 5 9. I 46 170 I95 F 292.3 6 "o 0 I40 63 I87 280.3 36 "3.. I35 I57 I79 224 269. 6"6 " 129 I50 I72 216 258.6 7 0( o'c.. I20 I40 I6o 200 240. The subjoined table is applicable to stationary and marine engines: NVo. of Revolutions of Crank for Given Stroke and (approximate) Piston Speed. PISTON S FU Stroke. Ft. Ft. I I IFt. 200 210 2,0 2 925. 0 240 250 260 2 79 2S 290 00 320 3 40 350 I ft.6in. 67 70 73 75 76 80o 83 86 90go 93 97 100II06 113 1166 I' 8 6o 63 66 68 70 72 75 78! 81 84 87 9o 96100105 i"I0 55 57 6o 6 63 66 68 71 74 7679 82 88 93 96 2 0 "~50 5 5 55 56 576063 651 67 70 7275 8o 85 87 2" 3" 44 47 49 50 5 53 55 581 60 62 64 66 721 76 78 2 cc 6 " 40~ 42 44 45 46 48 50 521 54 56 58 60 64 68 70 2 cc 9. 38 40 41 42 43/ 45 471 49 5153 551 581 62 64 30 o.0 335 36 37 38 40( 421 431 45 47 48 5~0 531 56[ 58 3" 3". 32 33" 34 35 37 381 40 41 431 44 46 50 52 54 3 cc 6.. 30 3II 32 33 341 36 371 38 40 41 43 461 481 50 3 "9".. 291 3~0 3I 32j 331 34j 36 37 39 401 43 45 47 4 0... 27 28 29 30 31 32 34 35 5 36 38140 4o2 44 4 3.... 25 26 27 28 29 30 32 331 34 35 38 40 441 4" 6".2 *| 25 26 27 28' 29 30 3I32 33 351 381 39 4" 9" 23 24 25 261 27 28 29 30 3I1 33 36! 376 5 1 23 24 25 26 27 281 29 301 32 34 35 APrEA OF STEAM PORT. 21 These dimensions, the stroke of piston and diameter of cylinder, are so constantly used in comparing engines of different powers, that, as far as possible, they should consist of whole numbers quite free from all fractions of an inch. VI.-AREA OF STEAM PORT. This dimension ranks next to cut-off in its controlling influence upon the proportions of the valve seat and face. It may justly be considered as a Base from which all the other dimensions are derived in conformity with certain laws. Its value depends greatly upon the manner in which the port is employed, whether simply for admitting the steam to the cylinder, or for purposes both of admission and exit. In cases of admission it is evident that the pressure will be sustained at substantially a constant quantity by the flow of steam from the boiler. But in cases of exit or exhaust, a limited quantity of steam, impelled by a constantly diminishing pressure, forces its way into the atmosphere with less and less velocity. If, then, the engine is supplied with two steam and two exhaust passages, the ports will be correctly proportioned when tlue areas of the latter exceed those of the former by an amount indicated by careful experiment. When, however, one passage performs both duties, it should have an area suitable for the exhaust and be opened only a limited amount for the admission of the steam. Very excellent results have been found to attend the employment of an area equal to 0.04 of that of the piston, and a steam-pipe area of 0.025 of the same, when the speed of the piston does not exceed 200 ft. 22 AREA OF STEAM PORT. per minute, but widely-different factors are demanded by higher speeds, like those peculiar to locomotives. In tile year 1844 M. M. Gouin and Le Chatelier instituted a series of experiments for ascertaining the value of such terms. These were continued about six years later by Messrs. Clark, Gooch, and Bertera, upon engines of British manufacture. The various results having been collated and analyzed by 3Mr. Clark, were finally presented to the public in his valuable work on "Railway Locomotives." From this it appears that with a piston speed of 600 ft. per minute, an area of 0.1 that of the piston was found to give practically a perfect exhaust, a steam-pipe area of 0.08 a fiee admission of steam to tile chest, and a port opening of from 0.6 to 0.9 the entire width of the port, depending on the humidity of the steam, a free admission to the cylinder. The following table has been prepared for intermediate speeds of the piston on the assumption that the area increases directly as the speed, and that a higher speed is usually attended by increased pressure: Speed of Piston. Port Area. Steam-Pipe Area. 200 feet per minute..04 area of piston..025 area of piston. 250 " 4.047 " ".032 " 300 ".055 ".039 4 350 " ".062 ".o046 " " 400 ".07.053 " " 450 c".077 " ".o6 " " 500 ".085 ".067 " " 550 ".092 c ".074 " 600 " ". I C.o8 c c I-Iaving determined the area of the steam port, the next step will be to resolve it into its factors, length and breadth. When a small travel of the valve is essential, the length should be made as nearly equal to the diameter of the cylinder as possible; then the port area divided by the length, furnishes of course the value of the breadth or S in Fig. 1. AREA OF STEAM3 PORT. 23 The extent to vwhich the valve should open this 2ort for the admission of the steam will equal from 0.6 to 0.9 of the value of S, and the minimum travel of the valve, that which with a given cut-off just opens the steam port the amount of this limit. The maximum travel is governed by expediency, the general tendency of an excess over the minimum travel is to render the events of the stroke more decisive, the cut-off takes place wi'th greater brevity, avoiding unnecessary wire drawing of the steam and the release opens rapidly, affording a more perfect exit. Where the travel is small, these good qualities should be secured by increasing this term, until the valve gives an opening equal to or even greater than the width of the steam port. With a large travel no such attempt should be made, since it would inevitably sacrifice much work in friction and cause a far greater loss than gain. EXAMPLE. Diameter of a certain piston=26 inches. Area=531. Piston speed=350 ft. per minute. ]Required. —Width of steam port, minimum width of port opening and diameter of supply steam pipe. From the Tables we have: Sq. inches. Area of steam port=531 x.062-33 sq. inches. The length of the port=diameter of cylinder=26"'. And the width= -- a -=1.3 inches or 1-16 Minimum width of port opening=0.6 x 1.3=- inch. Sq. inches. Area of steam pipe =531 x.046=24.4 sq. inches. Consequently the diameter-5-I inches. In the Corliss Engine, where the steam is admitted and exhausted through different valves, it is customary to give the steam passage an area of I to f6 that of the piston, and the exhaust an area of from — L to l-. 24 AREA OF STEAM3 PORT. In this connection a few remarks may appropriately be made with reference to the formation of the valve edge and the walls of the steam port. The experiments of scientists like Weisbach, D' Aubuisson and Koch, prove that the various phenomena of contraction in the fluid vein observed in the flow of water are equally true for gases, the formulae of discharge however have slightly different coefficients of efflux. The character of the discharge will evidently vary with the extent of opening offered by the valve edge, from what is termed "discharge through a thin plate" at the commencement, to that through a " short tube" with the full opening. Fig. 1 illustrates the natural convergence FIG. 1. which takes place in the filaments of the steam vein with the common slide valve. If the edge were formed as in Fig. 2 the discharge would be much improved and rendered similar to that which occurs through an ordinary "mouth piece." The curvature of the valve edge should commence far which taks~place n h itmn o e ea i wh the ~ ~ ~ N cmo ld ave t eg r fmd i AREA OF STEAM PORT. 25 FIG. 2. II /,O enough above the rubbing surfaces to permit a limited amount of wear without altering the proportion of the parts. Every effort should also be made to reduce the amount of clearance for the steam and loss of head by friction, to a minimum value. Hence the passage from the port to the cylinder must be constructed as short as possible, be of uniform cross section and bend with easy curves if bending is indispensable. PISTON, CRANK AND VALVE MOTIONS. In essaying the study of an intricate subject like the relative motions of the piston and the ordinary slide valve of a steam engine, it is of the utmost importance to first divest the parts of all the complicating influences which arise from special constructions and present them in such simple and elementary forms, that the discovery of the fundamental laws governing their motions may be facilitated. If these are clearly defined, the deduction of others adapted to special cases will subsequently be accomplished with comparative ease. The entire series of events which take place within the cylinder of an engine, occur when the piston has reached definite positions in its complete stroke. It follows since there is in practice no fixed limit to the stroke, that an infinite number of such positions may be occupied, and in order to express them by a standard which shall apply equally to all cases, a unit scale must be adopted. The stroke of all pistons therefore will be regarded throughout this Treatise as equal to Unity, and their positions at certain important periods, as decimal portions of the entire stroke. If a movable point is caused to travel around a fixed PISTON, CRANK AND VALVE MOTIONS. 27 one, in the same plane, at a constant distance therefrom, it will describe a curved line called a circle. For the purpose of locating any position in the path of the movable point, the circle has from remote ages —though not wiselybeen divided into 360 equal parts called degrees (360~), each degree into 60 minutes and each minute into 60 seconds. While the piston of an engine performs a single stroke, the crank-pin makes a semi-revolution (180~) about the centre of the main shaft, each position of the former consequently corresponds with some angular position of the crank-arm, and if these angles are arranged in a Table we can instantly determine therefrom the number of degrees over which the pin must pass in order to bring the piston to any desired position. FIG. 8. 80 8 le'o ___________20...o. 4 0 302000 o W,. | |I: N S ROD ~~7r/ r ~~~~~~~~ o 1~~~. 28 PISTON, CRANK AND VALVE MOTIONS. Since the "slotted cross-head" shown in Fig. 3 is the only form of connection between the crank-pin and piston, in which the piston moves from one extremity of the stroke to the other at the same speed as the crank-pin —measured on the stroke line-it will answer our purpose for determining the fundamental principles of the piston and valve motions. The arrangement of the parts are clearly shown in the Figure. The crank-pin is surrounded by blocks BB, these slide freely up and down the solid frame FHI to which the piston-rod is welded, so that while the crank-pin advances from D to G the block mounts towards F, returns as it approaches E and descends towards H on the return stroke ED. For convenience, the cylinder will always be regarded as lying on the right-hand side of the main shaft and the point of the crank-pin circle nearest to the cylinder as the zero or starting point of the forward stroke. TABLE A. Piston Position. Crank Angle. Piston Position. Crank Angle.: Piston Position. Crank Angle. Deg. Deg. Deg. 0 I 36 13 1285 O.I 364 o.5625= 96 97-4 o 8I3 1- I283 o. I25 = 4 83 05 75 988- 0.82 I29 -. I5 45 - o.6 IOI4 0.83 I3 I O. 175 494 0.625 = 1041 0.84 132 7 0.2 534 o.65 I071 0.85 I34a 0.225 56~ o.666 = Iog091 o.86 I364 0.25 =- 60 o.68 I I I8 o.87 I374 0.275 631 0.687 =16 I12 o.875 = 138,5 0.3 66 o.69 I I 2 o.88 139g 0.325 694 0.7 II38 0o.89 14I8 0.333= 70 ~ o. 71 II44 ~.9 I43: 0.35 724 0.72 ii64 o.9I I45, 0.375= 754 0.73 II78 0.92 I478 0.4 78 - 0.74 II84 0.93 I498 0.425 8I- 0.75 -3 I20 0.94 I5I8 0.437-= 82I 0.76 I2I 0.95 1 544 0.45 84- 0.77 I228 0.96 i5647 0.475 878 0.78 124- 0.97 I6o0 0.5 =- 90 0.79 I2 o.98 I633 0.525 927 o.8 I267 0.99 I68 0.55 95 0.8I.1281 I..oo I80 PISTON, CRANK AND VALVE MOTIONS. 29 The foregoing Table furnishes angular positions of the crank-arm corresponding with the various points in the stroke which may at times be occupied by the piston. To illustrate its application, suppose forEXAMPLE. The stroke of a certain piston=36 inches. Query. —How many degrees will the crank have passed over when the piston reaches points respectively 9" and 232" distant from the commencement of its stroke? 9f 6)9.00 1st. 36,=6)1.50=0.25 of the stroke. 0.25 2d. 239 = 30.649 of the stroke. 36 36 Then by the Table: 0.25 of the stroke=an angular passage of 60~. 0.65' - 107 0~ The required angles. AGAIN: Suppose the stroke of a piston=361", and that the crank has passed over 1120. How far will the piston have advanced? The Table gives for 112~ a piston position of 0.687 of the stroke. Therefore 0.687x36"= 24k"1 the distance advanced by the piston while the crank has advanced 112 degrees. There is securely fastened to the crank shaft a device called an "eccentric," which serves to impart a reciprocating motion to the slide valve. Upon close inspection it appears that this is only a mechanical subterfuge for a small crank. The travel of any valve being small compared with that 30 -PISTON, CRANKl AND VALVE MOTIONS. of its piston, the crank required for its motion has frequently an arm or "I throw" c b shorter than one-half the diameter a e of the main shaft, Fig. 4. Hence to avoid cutFIG. 4. 7, 7, ting the shaft and the expense of forming the crank c b, the pin in, n, and enclosing strap of the rod are greatly enlarged until they attain the common diameter M N, the former may then be slipped on, and keyed fast to the shaft a e. Of course the motion will not be altered by this change, but the same reason that led to the adoption of the slotted cross head for tracing the piston's progress, now compels us to substitute a small slotted cross head and rod for the eccentric rod. In the sequel therefore both the crank pin and the eccentric pin (or centre of a centre) will be considered as transmitting their motions through slotted cross-heads to the piston and the valve. (See Fig. 5.) The axes of the cylinder and of the valve stem do not always pass through the centre of the main shaft. V'When that of the latter lies above and parallel to the former, as shown in the figure, some expedient must be adopted for carrying the motion of the eccentric pin up from the point q in the central plane of the engine to e in that of the valve. PISTON, CRANK AND VALVE BIOTIONS 31 This is frequently accomplished by aid of a bar q d e called a " rocker," free to oscillate on its firmly supported axis d. The direction of the motion then becomes the reverse of that produced by the eccentric pin and if the pins q and e are made to operate in vertical slots no irregularity will be introduced by this arrangement. Having explained the general features of these controllers of motion, the crank and the eccentric, and having resolved them into their elementary forms, we pass to consider the parts moved and seek the law of their proportions. The plain slide valve of a steam-engine is a device by which the entrance and exit of the steam is regulated for the opposite sides of the cylinder. It is essentially a case A, resting on a plane surface c c as seen in cross section in Figs. 5 and 11. Through this surface are cut three passages S', S", and E, separated by the partition walls B, B, called " bridges." The two former lead to the opposite extremities of the cylinder, and the passage E called the "exhaust" leads through an oval pipe to the atmosphere. The valve A is sufficiently large to cover both the passages S', S", when standing in its neutral position. A second case D, ID, called the " steam chest," encloses the valve A and is secured rigidly to the plane surface c c. Being larger than the valve it leaves, over it much unoccupied space to which the only entrance is through the aperture F. This space is the "reception room "'-so to speak-of the cylinder; to it, the steam is admitted from the boiler through F and kept in waiting during such times, as the valve in its motion completely covers the two ports. Figure 5 represents the crank-pin at the zero point of its path, the piston at the extremity H of its stroke, the valve in the neutral position and all the parts ready for motion. A complete revolution of the crank will carry the piston 32 PISTON, CRANK AND VALVE MOTIONS. forward to K and return it to the starting point H. Whatever events take place in the journey from H to K should be repeated in the same order on the return route from K to HI, hence in studying the motion we will seek to render it perfect for the trip from H to K and leave the parts when the latter point is reached in the same relative positions as those occupied for HI, so that the one will become simply a counterpart of the other. The first point evident, is that the port S' must be opened and again closed for the proper admission of the steam during the stroke of the piston from H to K; in other words, while the piston is making one entire stroke the valve must accomplish a half and a return half of its stroke. Such an operation can only be brought about by securing the eccentric pin in the positionf or b on a line at right angles to the crank-arm, that of f being suitable for a direction of the crank indicated by the arrow. Let us trace the two motions throughout one revolution of the crank. Moving it from the zero to the 90~ point will draw the piston from the position II to the half stroke or the line c", c",ll will advance the eccentric pin from f to k, the rocker from e q to e' q', the centre of the valve from V to V" and completely open the port S'. As the crank progresses from 90~ to 180~ the eccentric pin will travel from k towards b, gradually closing the port S' and completely covering it when the 180~ point is reached, thus leaving the valve in the same position at the terminus of the stroke that it occupied at the commencement. On the return stroke from K to IH the port S" will in like manner be opened and again closed. In thus hastily following the two entrances of the steam to the cylinder, we have lost sight of its mode of escape after performing the work of forcing along the piston. Let us suppose that one revolution has been completed and the piston is prepared for a second journey from PISTON, CRANK AND VALVE MOTIONS 33 the position H. The space J is now filled with steam and some passage of escape must be opened. This is provided in the port and pipe E, which are thrown into immediate communication with the passage S" when the valve commences its motion, the opening becoming wider and wider as the travel progresses, only closing when the piston reaches the point K and is ready to receive fresh steam through the passage S" for the return stroke. Such is a brief outline of the parts and functions of the simplest form of slide valve, in which the steam is admitted at the commencement of the piston's stroke and not excluded until that stroke is completed. This arrangement, however, is not attended with economic results, for it entirely ignores that remarkable property of steam, its elasticity. To render this latent power available, the steam should be admitted during only a portion of the piston stroke, the valve should then be closed and the confined volume of steam allowed to complete the remaining portion, by developing its power of expansion. But how can our elementary form of valve and position of eccentric be modified for attaining this desirable result? Suppose a cut-off were required at a piston position of 0.93 of the stroke. By carrying the crank to the 1503 position (as in Fig. 6) we observe that the port S remains opened a distance I and the most ready means for effecting its closure is to lengthen the valve face by this amount. Since the cut-off must take place at relatively the same piston position in both strokes, an equal addition must be made to the other edge of the valve. Such additions to the outer edges of the valve, for the purposes of cut-off, are called overlap or simply "lap." The extent of this lap in the present case is evidently equal to the horizontal distance of the eccentric's centref" from the 90~ line, because 3 34 PISTON, CRANK AND VALVE MIOTIONS. without lap it would naturally close at this line. The same distance expressed in degrees would be equivalent to a "lap angle" of 30~. But on referring to Fig. 6 it is clear that no such addition can be made without necessitating a change also in the eccentric location, for it would render the admission 30~ too late. Hence if we add a lap to the valve equivalent to an eccentric motion of 30~ from its neutral position, we must at the same time unkey the eccentric, and having advanced it also 300 refasten it on the main shaft. The number of degrees by which the eccentric is thus carried forward from a position at right angles to tlhe crank-arm is termed the'6 angqtdlar advance" of the eccentric. When tile eccentric stands at right angles to tile crank the exhaust closes and release commences at the extremnities of the stroke, consequently if the eccentric be moved ahead 30~ not only will the cut-off take place 30~ earlier, or at a crank angle of 120~ instead of 150~, but the release as well as the exhaust will take place 30~ earlier or at the 150~ crank angle. Although we have not secured by this process the cut-off aimed at, yet the investigation distinctly points out the means at our command for the accomplishment of any cut-off and will enable us to construct a Scale for determining the magnitudes of such alterations. For a cut-off of 1400 there would be required an angular advance of 20~ and a lap equivalent to the distance these degrees remove the eccentric centre from the line at right angles to the crank; for a cut-off of 1600, an advance of 10~ with a corresponding lap, and so on; the exhaust closure taking place respectively at the 160~ and 170~ crank angles. This closure of the exhaust confines the steam in the cylinder until the port is again opened for the return stroke; consequently the piston in its progress will meet with in / I' I ~ ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~/ i'/ I ". 1/ \ -"' I I!I~! I \ *\ I' I' I~~~~~~' _,.............. _,').., -,- --;9- 4 -._!/>s tIl;- ___ "? *. - -" 9/ -f,_ I',' — -, 1A~~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ i ~Y.9 j Lf:;>~~~~ ~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~',,-.,, ~'.Y~~.5.~,' 3n f~~~~~ l, --,, -— __',-: 7V7,/'J' - ___ _____._______________-_________ \ IK j7 I -- - -' 10~ ~~ ~~ ~........,:'.;-.,\ _ l _ = - 3........ -'1::J,___=_ /...... \t/ ~ - X~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..J -nEe f..;S0 \AO..'/ ~Y13 ~ iI \./' / _ ~ P; _I __ ~r~m! i~~~~~~~~~~~~~~~~~~~~~~ /,''',,,~~~~~~~~~~~~~~~~~~~~~~~~~~~Q;lhii v dC/d ~ ~ ~ ~ ~, ~~~~~~~~~~~~~~~~~sn~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.,,:/X ~~~~~~~~~~~~~~L ~ ~ ~ ~ ~ ~ ~ ~ ~ _ ~ —-- Jr ~,. — ~::,) I~ ~ ~ ~ ~:.:::-I.:~:_~~ i-: I::~......:!i1~I~-~:':::ii~l::~-:~ PISTON, CRANK AND VALVE MOTIONS. 35 creasing resistance from the steam which it thus compresses into a less and less volume. Such opposition when properly proportioned aids in overcoming the momentum stored up in the reciprocating parts and tends to bring them economically to a state of rest at the end of each stroke. Since the closure of one port is simultaneous with the opening of the other, a release will take place of the steam which was previously impelling the piston. Within certain limits this also is conducive to a perfect action of the parts, for an early release enables a greater portion of the steam to escape before the return stroke commences, whereas a release at the end of the stroke would be attended by a resistance of the piston's progress, from the simple fact that steam cannot escape instantaneously through a small passage, but requires a certain definite portion of time dependent on the area of the opening and the pressure. The larger the opening then the less the occasion for anticipating the moment of exhaust. We learn therefore that the moments of exhaust closure and release are, when the valve has neither " inside lap " nor its converse " inside clearance," directly dependent upon the angular advance of the eccentric, and that an angular advance of 20~ produces a closure at a crank angle of 1600, one of 30~ at 150~ and so on, the resistance becoming continually greater as the angular advances increase. A limit at length is reached where this resistance really becomes detrimental, and an amount of power is absorbed quite inconsistent with economy of action. On this account the single eccentric is rarely used to effect cut-offs of less than 3 the stroke. Earlier cut-offs require two valves and two eccentrics, the one set for regulating the cut-off of the steam, the other its admission and escape. This subject will be more fully discussed in Part V. 36 PISTON, CRANK AND VALVE MOTIONS. The principles just developed can be embodied in a single Diagram called the TRAVEL SCALE, whose construction is illustrated by Fig. 7. FIG. 7.,,:~: 1o5.z,._ 4 /TRAUV..~ To Jtheo Reader. —A Cop\\\ \ 4 \ ^, per-plate engraving of the I\,, \TRAVEL SCALE will be 3-8\&\ \ found attached to the back eovcr. B0~ low PISTON, CRANK AND VALVE MOTIONS. 37 Let E F D represent the path traversed by the centre of an eccentric whose throw equals 3- inches, consequently the travel of its valve=7 inches. Then C F at right angles to D E will be the normal position of the eccentric from which the angular advances must be laid off. Extend this line to some convenient point A and join the extremity D of the travel with A. Divide the line C A into 7 equal parts, and through these points draw lines parallel to ID E to represent all the travels less than 7 inches. Finally project each degree of the arc D F upon the line D C and join the points thus found with the point A. The distances from the Base Line C A, at which this group of lines intersect the travel lines, will indicate what lap should be given to accomplish various cut-offs, and their distances from the extreme travel line D A will give the width of the steam-port opening due to these travels and cut-offs. Thus for 7" travel and a cut-off of 120~ the eccentric must have an angular advance of 30~ and the valve a lap equal to 12 C, giving thereby a port opening 12 D; while a travel of 4 inches with the same cut-off only requires a lap of 1' C3 and has a port opening of 13 d3. The exhaust closure of course takes place in both cases at a crank angle of 150, or piston position of 0.93 the stroke. It will be observed that this SCALE may be applied with perfect accuracy to travels greater than 7 inches by making these lines represent their multiples; for instance, a 4-inch travel may stand for one of 8 or 12 inches; a 6-inch travel for one of 12 or 18 inches, and so on. In such cases the values of the true lap and lead will be double or thrice those given by the SCALE. Since the same principle holds for travels less than 2 inches, it is clear that the SCALE must apply to all possible dimensions. A slip of paper and a pencil are the only paraphernalia of the Travel Scale. To illustrate its use take for 38 PISTON, CRANK AND VALVE MOTIONS. EXAMPLE. Extreme width of port opening must= 11 inches and the valve must cut off steam at 0.82 the stroke. Required. -Angular advance of the eccentric, travel of valve, lap and point of exhaust closure. Table A gives for a piston position of 0.82 the stroke a crank angle of 130~, for this cut-off an angular advance of 250 will be required (see line C D of the TRAVEL SCALE). Apply the edge of a slip of paper to the Inch Scale and mark off the desired width of the port opening a, b, as in FIG. 8. ANGULAR ADVANCE. 900 20~ PORT OPENING.. —. —LAP ---- -1 43/1 RA VEL! COUT OFF= 1300 I IEXHAUST OLOSURE= 155 Carry the same to the Travel Scale, place the mark a over the 90~ line C A and slide the edge-parallel to the line C D —until the mark b stands directly over the 25~ angular advance or lap-angle line. The 43 inches line of travel, upon which the slip of paper here stops, will be the correct travel for the valve. Before removing the paper mark the position c of the Base line. Finally return the slip to the Inch Scale and measure the lap b c, which gives 16 of an inch. The exhaust closure on one side and release on the other will of course take place at the 155~ angle of the crank (see line C ID) or at a piston position of about 0.95 of the stroke. Angular Advance-25~. Travel of valve-=4 inches. ANSWERS.. Lap=- 1 inch. Exhaust closes at 0.95 of tle stroke. The solution of such problems as the subjoined, will DIRECTION OF CRANK MOTION. 39 tend to familiarize the Reader with the method of using this Travel Scale: 1st. To cut off at -2 the stroke, with port opening of 1] inches. -Required.-Angular advance of the eccentric, travel of valve, lap and point of exhaust closure. 2d. To cut off at - the stroke, with port opening uf 1-5 ins. 3d. " " " " " " 3 4th.. 8 " DIRECTION OF CIRANK MOTION. The direction of any crank motion depends on two conditions-1st. The presence or absence of a rocker for transmitting the motion; 2d. The location of the angular advance with reference to the central line of the valve motion. Both of these may be conveniently expressed in a single Diagram like the accompanying Fig. 9, in which the posiFIG. 9. 180 9 90 ~ ~; tive sign (+) represents a motion in the direction of the hands of a watch, the negative (-) a reverse motion. To 40 LEA D. produce a positive motion in any engine, whose eccentric acts through a rocker, lay off the angular advance from the line bf in the 1st quadrant (the crank standing at the zero), but for one without a rocker, the angular advance must be laid off from the same line in the 3d quadrant. The 4th and 2cd quadrants in like manner belong to the negative motion. The reason for making such a disposition of tile angular advance will at once appear upon tracing out either of these imotions. When the power of an engine is transmitted through a wide belt to the machinery, the direction of its crank motion will be determined by the relative locations of the main and crank shafts. The strain should invariably be made to fall upon the lower portion of the belt, the upper being thereby relaxed, sags upon its pulleys, increases the frictional surface, and materially improves the adhesion of the belt. L EAD. This term is applied to an alteration made in the plan of the valve motion for the purpose of concealing and neutralizing an effect, due to imperfect workmanship as well as continual wear in the boxes of the crank and cross head pins. The difficulty may be best explained with the assistance of Fig. 10. Suppose, for instance, both boxes of the connecting rod A B, fit loosely upon the crank and cross-head pins, that the crank moving in the direction indicated by the arrow, has reached a location C A within 8 degrees of the zero, and that the piston (on account of the lost motion in the boxes) falls short of its true position B, a distance B B. If now the LEAD. 41 momentum of the motor carries the crank-pin past its zero, the piston, which at the moment of passage is no longer urged or restrained by the connecting rod, will by virtue FIG. 10................. -- -;_I80 _ A _ o. _ 8 _ _ = * _-_ _9_ a of its own momentum continue moving in the direction of H until all the lost motion being expended, its progress is suddenly checked and it is itself again brought under the control of the connecting rod, which then draws it forward upon the return stroke. These concussions are reproduced at the end of each stroke with a degree of force and sound directly dependent on the extent of the lost motion and the momentum of the piston with its connecting rod. Where the parts are of great weight, as in a marine engine, the sound becomes very loud and the engine is said to " thump" or "pound>" on the " centres." Two ways pre sent themselves for counteracting this effect; the one, by making the boxes so durable and the workmanship so perfect that lost motion becomes almost impossible; the other, by introducing a resistance to the momentum of the piston capable of cogmpletely overcoming it before the end of the stroke, in other words by allowing the steam to enter the cylinder a short time previous to the termination of the stroke. With small engines the first method is practicable, but in large ones both are more commonly employed be 42 LEAD. cause with these, a very small amount of lost motion suffices to produce a disagreeable sound. The width of port opening given by any valve at the moment its crank passes either centre, is called the "lead" of the valve; and the angular distance of the crank from its zero at the instant this opening commences, the "lead angle." The opening together with the angle (or time) limit the power of the steam in its effect upon the lost motion; for even a small opening continued through a long time may prove as efficient for the admission as a large opening during a very short time. Since sound, the effect of lost motion, depends upon the weight and velocity of the reciprocating parts, the lead requisite must vary for different engines and also for the same engines at different velocities. The exact amount cannot be predicated in any particular case, but after the engine has been constructed it may be experimentally determined by gradually increasing the angular advance of the eccentric until some position is found which results in a smooth and noiseless movement of the reciprocating parts. W;Ve have before alluded to the effect of compression by a premature closure of the exhaust, but it must be distinctly understood that this agency unassisted cannot neutralize the evils of lost motion without injuring the admission of the return stroke. In this respect it differs from lead. It should then usually be supplemented by lead in order to accomplish a smooth action of the parts and free opening of the steam port for the return stroke. Observe also, that so long as the lead angle amounts to only a few degrees no impression can be produced on the continuity of the crank motion, for the lever arm will be too small for the power to exert any influence over the crank. LEAD. 43 The limits of the leacd angle are commonly zero and 8S for stationary engines; while for any given angle the width of opening will depend upon the travel of the valve and the point of its cut-off. It remains to be shown that the Travel Scale is quite as applicable to valves having a certain lead as to those without any. Referring again to Fig. 6, imagine an increase in its angular advance of 5~, the valve will then close at 115~ instead of 120~ and reopen its port 5~ before the crank reaches the extremity of the stroke; but if the lap be reduced 5~ when the angular advance is increased 65, the cut off will still remain 120~, while the port commences to open 10~ before the end of the stroke. Consequently if we wish to arrange a valve for a certain number of degrees lead, without altering the point of cutoff, it will simply be necessary to find the angular advance for a valve without lead, add 1 the lead angle for a new angular advance, and subtract the other I for an angle by which to measure the lap. If in the Example of Fig. 8 a lead of 8 degrees had been required, with the same cut-off, the angular advance would have become 25~+4~=29~ iand the lap angle 25~-4~21~ and by applying the port opening marks a and b to the 90~ and 21~ lines,-instead of the 900 and 25~ lines, —we would have obtained a travel of 3 inches and a lap of I 1 inch; while the distance between the angular advance line of 290 and the lap angle line of 210 would have equaled inch, the width of the lead opening at the extremity of the piston stroke. The change in the angular advance of course changes the exhaust closure from 155~ to 151~ or about 0.93 of the piston's stroke. 44 LEAD. Supposing then a lead angle of 80 for the same problem the answers become: Angular Advance........................... =29~. Lap angle................................. =21~. Travel..................................... = 37s inches. Lap _ 11 inch. Lap...................,..................... I inch. Lead..................................... inch. Exhaust closes at 0.93 of the stroke. Similar suppositions made and applied to the other trial problems will give all the practice requisite for successfully using the TRAVEL SCALE. It seems almost unnecessary to observe that the SCALE effects with equal readiness and precision solutions directly the converse of that just accomplished. Thus, if the above lap, lead and travel were given, to determine the exhaust closure and cut-off, we would mark the lap and lead on a strip of paper as in Fig. 12, apply the same to the 37 inch travel line of the scale, which would show at once an angular advance of 29~ and consequently exhaust closure of 0.93 the stroke; also a lap angle of 21~ with lead, or 25~ without, the same as a cut-off of 130~-0.82 the entire stroke. A moment's reflection will also show that-during the progress of the crank-the varying width of the port opening from the simple lead out to the maximum width and back again to the period of cut-off, might readily be traced on the SCALE, and all the information common to the popular method of ellipse or other construction, be immediately obtained. But the facts thus gained, would prove of very trifling moment, so long as the valve had received a correct maximum port opening. C FpG. 11. cTE w- \\\-l \ - vlC UTRAL POSI tON t, f o its t, at T T BEAdER- thie KW v lW & ~ edges during motion. C WIDTH OF BRIDGE. 47 WIDTH: OF ]BRIDGE. This dimension is usually made of equal thickness with the cylinder, in order to secure a perfect casting, but at times it becomes necessary to increase its width. The only danger from a narrow bridge is an overtrarve of the valve, by which the exhaust passage would be placed in direct communication with the "live steam" in the chest, and followed by continual waste of the power. Obviously this cannot occur while the difference between the port opening and the steam port does not exceed the width of the bridge. (Fig. 11.) But to prevent even the possibility of a leakage: Add about I of an inch to the width of the opening and from their sum subtract the width of the steam port. Thus the width of the steam port in the example of Fig. 8, should have been at least:14 + 1"-1"=- inch. When however the width of the opening is less than that of the steam port, the danger of such an escape entirely vanishes. WIDTH OF EXHIAUST PORT. The main difficulty to be avoided in nproportioning the width of this port is the possibility of a reduction in its area, when the valve attains extreme travel, to an opening materially less than that of the steam port from which it derives its supply. Suppose that the valve in Figure 11 has reached the end of its half travel, or the exhaust edge V moved a distance 48. INSIDE LAP. R from its neutral position V2; then by the above condition, E will evidently equal (S + R-B). Which furnishes the following general RUL E For determining width of Exhaust port. Add the width of the steam port to 2 the travel and from their sumn subtract the width of the bridge. When called upon to perform the addition or subtraction of many fractional portions of an inch, it will generally be found more convenient to express these decimally than by those very awkward subdivisions sixty-fourths, thirtyseconds, etc. Fractions of an inch expressed decimally. of inch=.nch inch4.34381 8+~ I of inch=.6875 -. =.0313 8 - 375 8+3.7 88 -~1 =.o625 +- 3 =. 4063!l " = 75 3 c 3),, -=.0938 S 4+-1 =.4375 43 + " =.78I3 =.125 3 + c =.46881 i - ".8125 ~8+ 3z ".I563' f " 5 |4+3 -.8438 s T1 _" =-.I875 1 +1 " =.53I31 =.875 ~}=.5 +T-3 =-.59381 7 + = 4 32 =.28I3 " =.625 - 8 -3.9688 l + -1- =.3125 + "1 - =.6563 I inch I.ooo INSIDIE LAP. The effect on a valve motion of inside lap is toProlong tk7e Expans9ion, and Hasten the Compression. (A contrary effect for inside clearance.) INSIDE LAP. 49 The former is occasionally added in the case of highspeed engines having very late cut-offs. In such instances the compression is arranged to commence at about i of the stroke, or at an angle of 138 degrees, and the release at an angle not exceeding 160~. For example, if the angular advance equals 32~ (with a travel of 45 inches) the compression would commence at a crank angle of 148~ or 10~ later than the above limit; hence if we give the valve an inside lap of 10~ or 8 of an inch found as in Fig. 12, the expanFIG. 12, ANGULAR ADVANCE 90~ -...3' 2 26~ 1.0 o BeA...............>. PORT OPENING. -... LAP. — - sion will continue from thepoint of cut-of to 148~10~ sion will continue from thepoint of cutommence-off to 1480~-+100= 158 degrees, and the compression commence at 148o-10o= 138 degrees, instead of both events taking place at the 148~ angle of the crank. We think the foregoing investigations fully sustain our remarking in conclusion that any questions, relating to the travel of the valve, the varying widths of the exhaust and steam-port openings for every possible position of the crank, the moments of closure and release, and other points of interest, can not only be determined with perfect precision by means of the TRAVEL SCALE, but their solution will prove well nigh instantaneous when compared with the indirect and tedious methods that have heretofore obtained in popular usage. 4 50 GENERAL EXAMPLE. GENE 1RAL EXAMPLE. What dimensions should be given to the cylinder and valve of an engine like Fig. 5 to secure an indicated horse power of 150 with Pressure of steam in boiler at 65 lbs.; The crank to make 50 revolutions per minute, and the steam to be cut off at 2 the stroke? The mean effective pressure (page 16)=65 x0.82=53.3 lbs. Piston speed (page 17)= say 250 ft. per minute. Area of piston, page 18, 33,000 x 150 132 x 150 250x = 3-71 sq. inches..50 x 53.3 53.3Therefore diameter of piston=21- ins., say 22 inches. Stroke of piston (page 19)= -15-2.5 ft. -2 ft. 6 inches. Port area (page 22)= 371 sq. inches x.047=17.4 sq. inches. If the length of the steam port=20 inches then its width 17.4 will=7-: = inch. Width of port opening W (by page 23) may vary between 0.6 and 0.9 the width of the entire port, but for the sake of greater precision in the cut-off and freer opening of the port at the commencement of the stroke, let us make its width equal about 1.5 width of steam port, orW=1.5 x "- =14 inches. Area of steam pipe (page 22)-=371 sq. inches x.032= 11.9 square inches. Area of exhaust pipe=area of steam port=17.4 sq. ins. The respective diameters of these pipes will therefore be 4 and 4- inches. By the Travel Scale, the angular advance GENERAL EXAMPLE. 51 for the given cut-off of 110~ equals (without lead) 350 and with a lead angle of say 60, Angular advance will= 35~ + 3= 38 degrees, And lap angle will=35~-3-=32 degrees. Now apply the width of port opening 14 inches to the 90~ and 32~ lines of the Travel Scale, as page 38, and we find that the Travel must=5- inches. After marking the Base line and angular advance we haveLap=1-7 inches; lead= inch. The bridge, page 47, should not be less than' -q 1i" -i-" -= inch. If, however, the cylinder has a thickness of 1 inch the bridge must be made of the same width. Width of exhaust port, page 48, E-= 7 + 2:-1" = 225 inches. Also we have the width of each valve face F and N=width *of steam port+lap Equals, i" l+ Il- 1= 27-5 inches, And the total length of the valve or L=exhaust port + 2 bridges + 2 faces=25+2+4i=91 inches. The angular advance being 38~ the exhaust will close and release commence at the 142~ angle of the crank (see Travel Scale) or at 0.895 of the stroke=30" x0.895=267 inches and the cut-off take place at x 30"=20 inches; which embraces all the required dimensions. PART II. GENERAL PROPORTIONS MIODIFIED BY CRANK AND PISTON CONNECTION CRANK AND PISTON CONNECTIOIN. Tius far we have confined our attention to a form of connection called the " slotted cross-head," and have been able therewith to deduce laws governing the proportions of the various parts of the valve, as well as to devise a most simple and rapid method for determining their magnitudes. But since this connection seldom obtains in practice, it becomes necessary for us to analyze the.form shown in Fig. 13, to modify their general proportions to accord with the new conditions and to eliminate as far as possible all the irregularities they tend to create. It will be observed, by inspecting this Figure, that the cross head pin is drawn a distance BB" beyond its half stroke position B", when the crank attains an angle of 90~, that this irregularity is due to the want of parallelism of the connecting rod, with its original position-during the progress of the crank pin in its semi-revolution-and that a rod of virtually infinite length produces a motion of the piston identical with that of the cross-head. It follows that the irregularity BB" will vary with the different ratios that may exist between the length of the crank arm and the connecting rod. In subsequent comparisons of these two terms, the length of the crank arm will always be regarded 56 CRANK AND PISTON CONNECTION. as the Unit measure and that of the connecting rod as a certain number of times the length of the crank arm. Let the crank arm C A be equal to unity and the connecting rod A B=4, then their ratio is that of 1 to 4, (1: 4.) When the arm occupies the 90~ position the cross-head pin will be drawn a distance B B" beyond the half stroke point FiG. 13.: 6 ~o.-:................... o-':. / i o: B". With B as a centre and A B as radius, describe the arc A A". If the occasion required, it might be readily proved that A", the point of its intersection with the line D E, is the same distance from C that B is from B". Placing the crank in other positions-as at 300, 600, 1200 and so on -and describing similar arcs there will result like irregularities but of a less degree, all of which however vanish at the extremities of the stroke D and E. It becomes evident therefore that the effect of this form of connection is; to carry the piston ahead of its proper positions throughout the forward stroke and on the return stroke to maake it lag behind the positions due to the locations of the crank pin. Consequently the one crank angle, for a given piston position (as in Table A), will no longer serve both the forward and return strokes, but a new table must be -an decibigsmlrac r wl eutlk reu laite but ofals ere l fwihhwvrvns at~~~, th xrmte ftesrk I n.I eoe vdn CRANK AND PISTON CONNECTION. 57 constructed which shall furnish at sight the proper angles of the crank for various piston positions in both the Forward and the Return strokes, and these for every important ratio of crank to connecting rod between 1: 4 and 1: 8 with which intermediate values may readily be determined by interpolation. Such is presented in the following STROKE TABLE. * The fractional portions of a degree have been given as small as can conveniently be laid off with a protractor. By transposing the terms Forward and Return the angles in the Table will apply to the case of a "Back Action " Engine. For the irregularities of the motion are necessarily reversed in such instances, because the cross head and cylinder lie on opposite sides of the main shaft instead of on the same side. FIRST EXAMPLE. The connecting rod of a certain engine=8' 31"=99t". The crank arm= 18 inches. Cut-off takes place at 0.65 of the stroke. Resuired —The forward and return stroke crank angles. Divide length of connecting rod by that of the crank arm: thus 99 18 2 Their ratio therefore will be that of 1: 52. t * The trigonometric formula pertaining to this Table are furnished in the Appendix and angles, for any special case may be found by their aid. t A Ratio commonly adopted by the builders of stationary engines. 58 CRANK AND PISTON CONNECTION. STROKE TABLE. CRANK ANGLES. (FOR ORDINARY CONNECTING ROD.) Piston Position. (Stroke=unity.) RATIO 1: 4. RATIO 1' 4:. RATIO 1:5. Forward Return. Diff. Forward Return. Diff. Forward Return. Diff. dege. deg. deg. deg. deg. deg. de- deg., deg. 0.1325 7 837 46 94 37-3 46 8 45 7' 0.125 1 7 3~~~~~~~~~~~4 0.2 48 459 - 5 o 48: 58 - 9 -1 ~~~~~3 ~~66 I 2 -4 7 66 II- 6 3 0.25 — 4 544 4 8 548 66 i 55 6 6o 6I28 5 6 0.3 6o 734 1 3 6 724 8 6i 72 o 0.333-1 64! 774 I33 643 76 I2 1 65 76' io 0.375 — 68a 824 13 69, 82 I 21 87 I 0 i 68 8`;12 70 0-7-a 8 4 8 8 0.4 7 71 4 85 13- 72 8 4 2 73 844: 0.45 77 I414 784 900 I25 788 90 I11 0.5 = - 823 974 144 83 961 2 844 95 114 0.55 88- 1Q24 14- 894 0' ii- 121 90 i2oi 417 0.6~~~~~~~~~~~~~~~~~~~~~~~)' lO8 2 1~~~~~~~~~~6 1 2 84" 6 94 io84 13 1 95 7 I2 95, 107 II 0.625=- 97 111 9 134 o 98 I T 2 9 094 1004~III I~ 3IO 128 2 go 2 3 1I3 o.65 O 138 134 3 2 o.6-5 - i i8 I` 1 I 51I o.666= 124 115t 134 103 1154 12 1039 i 4 iO o.68 10o4 1174 13-4 ~ 104 6 12 1051 161 o o.7 O6 II9a 13 07 4 18 118 O 0.71 I027 I2oI 12 lo83 120II 1 I090 I194 IO 0.73 1io0 1231 I2'~ I111 I22-~ IIa 3 I1 10- I10.75 31 [25 1 1 1 04 1 12 11 1256 117 ii4 ii5 o 0.77 i6 I:128 123 II6 1276 i1 117 127210 9 0.78 112 128 0o1.79 1198 73i I2o0 12 118 1301 0 0 I 1 1297o 9 I!67 12 1 1 21 32 10 42 IO o.8i 1224 133~~~~~~~1 2l 122Iii 132 2 10 1 II23 13221 9O 0.82 123'34.." 141234' 94 12 I33 8 0.7 15 38 7 9 i II86 1285 98 122I 9: o.812- 38 I2 12931312O 120 1293 0.86 11430410' 11 440 8' I3I 8194 8 0.87 1324 142, a I98 133, 141 8'334 41 7 0.875 1334 142o 19 33 12 7 8 13' o.88 34o 132 I1 I321- 123I' 8'IO 11 I42 7 0.81 1 I223 I341293 4 137 I228 "334 IB 4 4 Io I23~ T32:t.5.54 0.82 1238 14342 I 13 146 7' 25I3 1331 87 11 14 4 4 9 0.83 I251 136 8 124 1 35 71 9 I264 I3s - 1 0.92 142- 50 I274 143 37 I, 128 9 1 14 64 4 0.85 12i85 15 38 11 9 5389 1' 1 138 15 8 1 I2~ 36 IO 12 I 35s ~ 9 I26, I-; 8 0.86' 8 8 8 ) -t I3o2z 14o7~ 91' 13II 14o 8' 4 I 3 30~ s 0.87 I3-I42 9~ 33 141{ 8 { Is13II3,514 7 } o.875= 4 2 1 28 5 33 142~ 9 3 i42 8s 1340~ I3 8 7 o.88 9 I 384 I43 1 293 81 I354- I42 7 ~34' 4432 8 4 o.89 136'~ 44 I37 140 I 344 7`513 0.9 I 8~ I38~ t3 46'~ 7a t3 9 1- 46i~ 8 8 4: 4 3 o.87 I323 142 15 8 -, o.9t i~~~~oI 148~ 8 14~ 148~} 7:~ ~4~a~~~~~~~-4 i 1 148 6i 99 13 11 1 411 5 7 -30.92 142- 15 ~ I 71 143 I542 1 34-3 I492 6 0.95 I5o~- 156~ 6} ~5Ig! I564 5 4 A563 7 4 4 4(il 1 5s I5I~ 4s CRANK AND PISTON CONNECTION. 59 STROKE TABLE. CRANK ANGLES. (FOR ORDINARY CONNECTING ROD.) Piston Position. (Stroke=unity.) RATIO 1 5-. RATIO 1-: 6. RATIO 1I 61. Forward Return. Diff. Forward Return. Diff. Forward Return. Diff. deg. deg. deg. deg' deg deg. deg. deg. deg. o 125' 381 45 7 38 44 61 384, 441 5 o, r25 -8 ~ ~ ~ 6 384 44~ 5~7161 8a 0.2 49 571 81 494j 574 7 494 563 7 0.25 = - 554 64 9 561 64 8I 563 64 74 0.3 6 71 9 624 71 8 6245 o 8 0o333 — 65~- 75- 94 661 751 9 664 743 gi 0.37533 — 7o8 75 4 84 94 87. 80o 1 I798 3 7 5 at 4 8 4 8~ 8 8 0.4 73I 835 101 73 8341 98 741 82 3 8 1 5 Iol 1 88 7 91 8 o 8858 0.45 794 89-' 1o 790 88 9 8 88 8 0.5: 84 4 95 10 4 85 3 45 91 8 943 83 go, 9 4' l, 91 8 94~ 8 0.55 904 10 101 91 1 91 91 1oo 81 1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0.6 964 io6' 10o 96 10o6' 94 972 105 81 -,5 1 j: 1 3 90 97~ 1o5 8' 0.625- -991 I109 IO 999 10o8 9s 1OO 1o85 8' o.65 1023 1 121 97 102I 1113 9 1o3 11I I 80 8 4 8 4 4 9 08Bo.666 1044 I4' 93 104 I I3' 9 105' I133 8' I08 8 ~ 4 4 4 4 II U 0.68 O 106 1 II5 io6- 115 88 1068 115 8' 8 I I 5 9 8. 0.7 lo8} ii8 98 09 I 7 8 9 3 117' 8 0-7 109 I IIs7 I14 I 7 8~ o.71 109, 119. 94 1io' ii87 8! o II!8 7' 0.73 1 II2' I2I 91 121 81 3 121I 73 4 84 t3 8 I2 73 0.75 — " 1151 1241 9 1I5 1234 81 ii6 123 7 0.76 ii6- 125' 81 II7 125' 81 II7 I247 71 0.77 118 I263 83 118' I261 8 II87 126J 70.774 4 2 2 8 4 E8 1~~~~~~~~~~~~~~~ 0.78 i19I 128' 80 120 1274 74 1204 127' 71 0.79 121 I2988 8 I2I 129 74 121 I284 7 0.8 122 I30 81 122' 13 7 1234 1304 7 2 I343 8 3 4 7 A 1 3 81~~~~~~~~3 14 16 o.8r I24 132 8 I24 1310 73 124' 1311 64 o.82126 1256 t338 0.82 125 II33 8 1126 1338 7' 126' 1327 64 0.83 1274 I34 75 1271 1341 7 27 1344 64 O. 83 8 4 127 4 8 0.84 1284 I36 7 1 i29 136 66 29 12 35 64 o.85 I3 8 I 37 Z3 7 83 I03 f372 2 I34 137 8 o.85 1304 137' 74 I30~ [37' 6' 1311 13 74 64 0.86 132 I39 32 39 6 132 I387 64 4 132e: 132 13 0.87 1334 141 7 I34 140o 6 I34 - I40o 6 8 8 8 13421 40. 0.875= 7 135' 14I1 6 3 I4I 3 4 4 I35A2 14II 5 0.88 1354 I424 64 136' 1,42' 6 I36' I421 53 0.89 1370 1'441 64 138 144 6 138' I43: 51 09 1394 1454 64 140% 145 51 140 145't 5' 09 I394~~~~~~~~~~~~ 8 8.5 3 6~~~~~~~~~~~~~~ 3 34 o.91 141 147 6 1 42' 147' 5' I42 147 5 4 4 143J 41 0.92'441' 51 44 1491 56'4 1492' 1553 3: 0.95 151 4 156 44 152 856 4 152j 32 152 41 5 -41 3-t. 60 CRANK AND PISTON CONNECTION, STROKE TABLE. CRANK ANGLES. (FOR ORDINARY CONNECTING ROD.) Piston Position. (Stroke = unity.) RATIO 1: 7. RATIO 1 7'. RATIO 1 8. Forward Return. Diff. Forward Return. Diff. Forwvard Return. Diff. deg. deg. deg. deg. deg. deg. deg. deg. deg. o. I25 -- 39 441 51 39 44 47 391 437 4 - 1 ~~~~~~~48 394 43~ 4g84 0.2 50 56. 6, 5o1 563 6 50 564._5 2' 1 504 0 6 5~~~~~~~~~~~~~~~ 0.25-'4 564 634 7 56 634 64 574 63" 64 6243 70o - 63 63; 0.3 8 23 69 4 6 1 66 04 742 0 9.333- 667 74:4 7} 674 74 7 1 673 74 62 0-333 8 8 H a 4 Y o.375= 7I1 794 74 7 19 79 7 1 72-I 79, 7 0.4 74' 82' 8 74 82 74 75 82 7 8041 883 8 ol4 88 0.45 8o4 88 8 7 80 o4 874 7 0.5 941 8 1 861 934 74 864 93 7 8 4 4 8 9 3 73i 0.55 98 994 8 92 991 7 921 991 7 i o 8l 8 984 gg 0.6 97 105' 8 97 4 Io5I 74 98 105 7 0.65 032 II: 7 033 I 33 74 I04 I10o 64 0.666 I05' II3 75 I053 1124 74 io6 I I25 6 I07 3~ 71- i5:2 }!i6i[~6 0.68 1071 "74I 7 I1o7 I14, 7 [:o73 III41 6:7 i 6 7:[o-1i6 0.7 0943 4 74 IO ii6 6 116 64 I~9' I ii ii-Ii 8 7 6:8o 0 71 83 7i84 4 74 - 1 I -68 6 1 II7 0.7 1 6 IJ 4 8' 11 I 7 71 767 I1 200 6 37 6I 0.73 113 120 74 113 120o I I 4 4 0.75 -:[:I6', I238 7:ii65 123' 6 5 i64 1i22' 61 0.75 4 ~ 8 I _2 __83 _ __ __ 4 _ 84__ __ _ 8 5 34~0.76 1174 1I244 7 1I74 I244 61 ii8: I24' 6 0[:76 I I8 10.77 I19, i26 64-l 3 I254 61 9 8255 0. 77 8 4 8 8 -2 3 0.78 120'- I271 64 I20 1 I27 61 121 I26 5 0.79 61221 2 I28 64 1221 28- 5 0.8 2 13 6' 29 6 23 5 0~79 ~~~~~I22 I28-1. 6 I 12 I28 6 1 I ) I 28'I 0-79 2 4 8 8 5 0.8 I23 I30~~~~~~~~6 I 2 129_3 6-1 I2" 7 5 I238 I 23, 10 8 8 o.8r 125 I31' 6' I25 1 311 6 125- 1304 5 0.82 1:[26 I32 6' I26 32 3 1 1324 5' 0.84 129 35 6 130,5 30 129~~~~~~~S:[28 I33~:[:[33~ 5 0o.85 13 37~ 1 I357 5 13 1362- 5 I281 I 6 I2 I281:[29 5 I33~, I~ ~~3:[~ I3 0.8638I4 1338 4 ~o.86 33 I38 15 56 I33' 13 5 I33 8 4 0.87 13443 140' 5' 1:35 I40o 54 1354 140 4? o.875= 1354 5 I36 140 45 136 13406 4 0142 4 4713 147 ~36'~I: [42 5 1 I3 61 137 I4 s 4 0.89 ~38- I43:~ 5 3 8 I34I431 44 1388 I43 4 0.9' r4o} I458 4J I40o!' I45,1 1 414o 4 1 o.91 I42 471 48 I42 I47 4a I43 147 4 0.92 1448 I491 41 145 149 4 I45 I49 37 0.95 52 1550 31 152' 55 1 5 2 I55 4 8 5 52 I5 8 ECCENTRIC AND VALVE CONNECTION. 61 Referring to this Ratio column in the Stroke Table we obtain: Crank angle of the forward stroke for the 0.65 position =1129-. 8. Crank angle of the return stroke for the 0.65 position =122o. Difference between the return and forward=9s~. SECOND EXAMPLE. Stroke of piston=45 inches. Ratio of crank to rod =1: 61. Forward. stroke crank angle= 131?. Return stroke crank angle=134-1. What locations will the piston occupy for these angles? From the Stroke Table we learn that: —131 3 forward= piston location of 0.85 the stroke and 134-~ return —=piston location of 0.83 the stroke-consequently: 45"1 x 0.85 = 384 inches from commencement of forward stroke. 45" x 0.83=373 " " " return "s ECCENTRIC AND VALVE CONNTECTION. The principle of this connection has already been illustrated by Fig. 4, its standard motion in Fig. 5, but as the latter rarely occurs in practice it becomes necessary to study the former with reference to its influence on the events of the valve motion. It has been observed that the combination is nothing more nor less, than that of a small crank with a long connecting rod, the valve will therefore move in precisely the same manner as the piston, and will have in its progress from one extremity of the travel to the 62 LENGTH OF ECCENTRIC ROD. opposite, like irregularities, differing only in degree. In other words, when the eccentric arrives at the positions for cut-off and lead, the valve will be drawn beyond its true position-measured towards the eccentric-by a distance dependent on the ratio between the throw of the eccentric and the length of its rod. Since this difficulty is corrected by lengthening the rod, it follows that the width of the port opening in one stroke, will slightly exceed that in the other. This is practically the only effect produced by the use of the true eccentric connection; although strictly speaking there is besides a slight difference in the equality of the exhaust closure, yet in no case does this become sufficient to affect the general action. Neither is the difference in the opening appreciable in stationary engines, for their ratio of eccentric throw to length of rod is usually that of 1: 20 or 30, which gives a variation too small to influence the general admission of the steam. (See Example 4 of Appendix.) LENGTH OF ECCENTRIC ROD. To find this dimension geometrically, after the proportions of the valve have been determined with the Travel Scale, proceed as follows:1st. Map the centre lines of the cylinder, valve, rocker, and main shaft. 2d. Place the crank at the zero and the valve in such a position that its edge F (Fig. 11) will give the proper opening for the forward stroke lead. 3d. Find the position of the centre of the eccentric by laying off the angular advance from the 90~ line. Finally CORRECT CRANK ANGLE. 63 measure the distance from this centre to the rocker pin —or that of the valve stem as the case may be —for the correct length of the eccentric rod. CORRECT CRANK A:NGLE. In finding the travel, lap, etc., of a valve appropriate to a given cut-off, by means of the Travel Scale and Stroke Table, the Relurn Stroke crank angle should be invariably employed. This will result in a correct cut-off for the return stroke although a later one than desired in the forward stroke. A method of correction for this inequality will presently be explained. EQUALIZATION OF LEAD OPENING. Since the lead opening is measured at the moments when the crank pin passes the central line, there can exist no irregularity between the piston positions, and if the length of the eccentric rod be determined as above the width of the lead opening in the return stroke will equal that of the forward stroke. EQUALIZATION OF EXHAUST CLOSURE. The nearer we approach the half stroke positions of the piston the greater becomes the inequality between the crank angles, and as the uniformity of the exhaust closure and cut-off depends directly upon these values, it is evident 64 EQUALIZATION OF EXI-EATST CLOSURE. that they also will prove unequal for the forward and return strokes. The equalization of the exhaust closure is always possible, because for a direct-action engine a small amount of inside lap added to the face iNi (Fig. 11) of the valve and clearance taken from the face F, tends to hasten the moment of closure in one stroke and delay it in the other, without producing the slightest effect on either the periods of cut-off or the extent of the lead, both of which are controlled solely by the outer edges of the valve face; vice versa for a back-action engine. Hence, any valve that is found on examination to give unequal exhaust closure, clearly proves a great lack of appreciation on the part of its designer, of those simple means which lie at his disposal for the accomplishment of a perfectly correct exhaust and release. To illustrate this mode of equalization, Suppose that in the General Example of Part I, the crank and rod ratio was 1: 4. Its mean exhaust-closure angle being 142, or a piston position of about 0.89 of the stroke, we have by the Stroke Table a difference angle of about 9 degrees. If then one-half of this difference angle, or 4- degrees, be laid off from the Base line on the 5-11 travel line of the Scale (as in Fig. 12) we will obtain a correction of -4 inch, which added to the face N givesN=2-1 +-" 2 —9- inches, and subtracted, F —-- 2" -=2- inches. The true dimensions of the faces F and N, for imparting equalized exhaust closure with the given ratio of 1: 4. EQUALIZATION OF THE CUT-OFF. 65 EQUALIZATION OF THIE CUT-OFF. WVhere an attempt is made to equalize the cut-off, that of the exhaust closure should be disregarded, for the only process that it is possible to adopt in such a case would practically achieve both results. Since the four periods, at which lead opening commences and cut-off occurs, are regulated by only two edges of one valve actuated by a single eccentric, it must be evident that where inequalities exist between any two of the four angular positions of the eccentric, their mutual dependeace will be such that the periods for these can only be equalized at the expense of the other two. Hence the equalization of the cut-off depends entirely on the expediency of giving a greater amount of lead to the one stroke of the piston than to the other stroke. With high-speed engines, such a change cannot be considered as desirable, but with those of low speed it may be made with very beneficial results. For with high speed the effect of lost motion can be most successfully overcome by a valve having equal lead in both strokes, but if the workmanship be perfect and the boxes carefully set up, the adjustment becomes applicable to all speeds. To equalize the cut-off only two alterations are required in the valve motion, viz: 1st. An increase of the angular advance. 2d. A lengthening of the eccentric rod. To illustrate the process, suppose we were required to equalize the cut-off and exhaust closure of an engine, differing only in respect to the connections, from that described in the General Example of Part I. 5 66 EQUALIZATION OF TIEE CUT-OFF. Let the ratio of crank to connecting rod=1: ~ 51 and the forward stroke lead angle*=4~. From the Stroke Table we find that the return-stroke angle for the above crank and rod ratio with 2 cut-off= 114~, or an angular advance for a valve without lead of 33~. With a lead angle of 4~ the trial angular advance becomes =350 and the lap angle=31~. As the port opening equals 11 inches, we readily find from the Travel Scale the following terms: Travel-51. Lap=1-5-l", and forward lead-9 — inch, nearly. The difference between the forward and return-stroke crank angles for the above ratio and cut-off=-9~. Onehalf of this difference or 4s~ forms the correction appropriate to the angular advance. Adding this quantity to the trial angular advance, we obtain 40~ for the true angular advance of the eccentric. We thereby secure all the terms necessary for determining the length of the eccentric rod as already explained. With an angular advance of 400 and no irregularity in the piston motion, the exhaust would close in both strokes at a crank angle of 140~, or a piston position (Table A) of 0.883 the entire stroke=26k inches. The lengthening of the eccentric rod, however, corrects the irregularity produced by the connecting rod and preserves this same point of exhaust closure to the motion. By measuring the distance between the true and trial angular advances-400 and 35~ —we obtain a distance f6 inch, by which it is necessary to increase the minimum width of the bridge B, making its new value=- + -6=- - inch. * Since from the nature of the case, the return-stroke lead angle must greatly exceed that of the forward stroke, the latter quantity should be taken at only 3~, 4~ or 5~ to prevent the former becoming excessive. EXPERIMENTAL TEST. 67 The lead angle of the return stroke will equal that of the forward stroke added to the difference between the cut-off angles of the crank, or 4~+9 - =13 degrees. The lead opening of the return stroke, will equal twice the measured distance between the angular advances added to the forward lead, or -1" x 2 + 36 = -96 inch. It should be observed that lengthening the eccentric rod increases the width of the return stroke port opening at the expense of that of the forward stroke, but so long as the width of the latter exceeds the minimum limit (page 23) for perfect admission, such inequality is actually a matter of not the slightest consequence. To guard against the danger of a contracted opening, it will be advisable when finding the travel for a corrected motion to estimate the width of the port opening at least 1 or.l1 times tehe width of the steam port. EXP ERIIME INTA L TEST. The greatest nicety and refinement of adjustment may be employed to produce an equal admission and exhaust of the steam throughout both strokes, and yet the attempt to equalize the power fail from lack of a judicious arrangement of the steam pipes and passages, on account of which the steam will enter one end of the cylinder with a lower average pressure than the other. This inequality occurs more frequently with vertical cylinders than horizontal ones, its extent can only be detected by the Engineer's most valuable friend, the Indicator, whose card ever furnishes clear and indubitable proof of the character, time 68 EXPERIMIENTAL TE S T. and correlation of the various events taking place within the cylinder.* To illustrate the character of this inequality, a few cards are here inserted which were taken from a shop engine, having a vertical unjacketed cylinder. The engine has been in service for several years. Its steam pipe, supported by the roof girders, descends to the centre of the cylinder's length where it enters passages for conducting the steam to the upper and lower ports. Fromn the nature of tile case the passage to the lower port is more direct than that to the upper, hence the steam encounters less opposition and enters with a higher average pressure than through the other. The dimensions of the engine are the following: Diameter of cylinder= 10-";' Stroke=20,'r. Connecting rod=51 "; Ratio 1: 5. Eccentric rod= 621". Travel of valve=35"; Lead=- inch. Steam ports-= 7' x 10~" Outside lap=-"; Inside= -". Average boiler pressure=65 lbs.; Velocity=100 Rev. For the purpose of securing a well-defined card the boiler pressure was reduced to 42 lbs. per square inch, and the revolutions of the fly wheel-by means of a brake-to 40 per minute. The result is given in Fig. 14, where the full line represents the card of the forward stroke, the dotted that of the back. In making comparisons of this kind it should al-'"4 For a complete analysis of this instrument, its practical operation, etc., the reader is referred to Mr. Charles T. Porter's Treatise on the IRICHARD'S STEAM INDICATOR., enlarged by F. W. Bacon, M. E., and published by D. Van Nostrand, New York. EXPERI 3MENTAL TEST. 69 ways be borne in mind, that the steam line of the one card must be combined with the exhaust of the other before the FIG. 14. Seule. -40o.bs AIR LIN/. -I true relation is expressed between pressure and resistance. The difference in the steam pressure for the two strokes amounted to about 2 lbs. The cut-off took place at17~-l inches in the forward stroke 15. " return stroke. Difference= 1 inches. The compression commenced at 181" forward. "9's " 171 return. Difference= 1 inch. This case is that of a valve motion in which no attempt has been made to equalize either the points of cut-off or exhaust closure. Had the exhaust closure been equalized the lines a b, c d, would have coincided. Subsequently, the equalization of the cut-off and exhaust closure was accomplished with the same valve, by increasing its angular advance 5~ and extending its eccentric rod. The effect of these changes is shown in Fig. 15;* both * The anrles are constructed on the supposition that the piston is connected with the crank by means of a slotted cross-head and rod. The true angles of 70 EXPERIMENTAL TESTS. FIG. 15. AIRINEsteAM _ __ _.._....32_ __S _ LEAi LEA/ i RURNWAR STROKE. AIR [.IN-',v EXHA[II.,L!! —-- "- \= ~-! SCALE i! cut-offs took place at 158 inches, compressions at 17(return stroke locations), the lead angle of the forward stroke became 4]~ and that of the return 14k, corresponding with an Ad inch lead forward and an 2 inch back. the crank, however, for any ratio of crank to connecting rod, may readily be determined from these by first finding tihe piston positions due to these angles in Table A and then searching the Stroke Table for the forward and back stroke angles, appropriate to such positions. stroke angles, appropriate to such positions. TO SET A SLIDE VALVE. 71 It should be observed that this great inequality in the lead, so long as the port opening was ample, produced but trifling effect on the area enclosed by the card. The two cards of Fig. 15 have been combined to form Fig. 16, showing an equality of the cut-off, exhaust closure FIG. 16. Scae _t) FOR WARNE AIR LIMT o and, release, but the same excess of pressure as before on the return stroke. Had the cylinder lain in a horizontal position, the latter inequality would have entirely disappeared, and equalized power been applied to both strokes of the piston. 11OW TO SET A SLIDE VALVE HAVING EQUALIZED EXHAUST. 1st. Place the crank at the 180~ location, mark on the cross-head and one of its guides opposing " centre punch" points. 2d. Bring the crank to the zero and mark a second point on the guide. The two points thus found, measure the length of the stroke. Move the eccentric until the valve has the required lead for the forward stroke. 3d. Advance the crank in the direction of the motion T2 TO SET A SLIDE VALVE. until the exhaust of the opposite stroke closes; scribe a line across the guide which shall pass through the point on the cross-head. 4th. Move the crank until the other exhaust closes and scribe a second line on the guide. 5th. If now the exhaust should close at equal distances from the commencement of each stroke the motion would be in adjustment; if not, alter the length of the eccentric rod until the closure becomes equalized, then return the crank to the zero position, and alter the angular advance of the eccentric until the required lead of the forward stroke is secured. The position of the valve at the moment of closure may readily be fixed by means of a " valve gauge" fitting centre punch points on the valve stem and its stuffing box. The above process will serve also to equalize the cut-off if the valve be proportioned for this object. PART III. ADJUSTABLE ECCENTRICS. ADJUSTABLE ECCENTRICS. THE intensity of the resistances, opposed to the action of steam upon the piston of an engine, fluctuates in a very marked manner, and were it possible to meet variations instantaneously by an increase or diminution of the power applied, the result would be an impulsive action of the working parts instead of a smooth continuous motion. It is obvious then that the power of an engine must be exerted at different periods of time in overcoming a more and more determined resistance or even one acting in an opposite direction. Slight variations in the resistances are controlled or absorbed by the momentum of the working parts, as by the fly wheel of a stationary engine, the drivers and coupled wheels of a locomotive, and the screw or paddle wheel of a steamer. But variations in degree must be met by an increase or diminution of the power applied. This may be accomplished in two ways, either by controlling the pressure of the steam before it enters the cylinder or by limiting it after an entrance has been effected, that is by cutting off at an earlier or later point of the piston' s stroke. The first method 76 ADJUSTABLE ECCENTRICS. deals with the throttle valve, the second relates to the closing of the steam port by its valve, while for marine purposes both of these agencies are usually employed. The throttle may be operated either by hand or by an automatic device called a " governor," the principle of which has been so clearly elucidated in almost every work on the Steam Engine that it would appear superfluous to repeat it in this connection. The governor is also at times used as a regulator of the cut-off, a work it most beautifully and delicately executes in such stationary engines as the " Corliss" and the " Allen." In these the steam and exhaust ports are perfectly distinct, so that a change in the cut-off does not affect the action of the exhaust, which remains from the beginning to the end of the stroke free of the back pressure peculiar to a single eccentric motion. The principal regulator of the cut-off in modern practice, however, is the "link," or combined double eccentric motion, which retains, while presenting itself in various kindred forms, the individuality of the double eccentric. On this account the study of the action of an adjustable single eccentric forms the best introduction to a complete understanding of the link motion. Hitherto we have considered the eccentric as a fixed body keyed to the main shaft, with its centre line or throw inclined at a certain angle to the crank arm. Thus in Fig. 17 the eccentric has an angular advance of 33 ~ or a position C F, suitable for a positive or forward motion of the crank if a rocker intervenes between the eccentric and the valve. It will be remembered (Fig. 9) that the same eccentric, when located with an opposite angular advance C B, holds a position appropriate to a negative or back motion of the crank. Hence if it be required to change the direction of the engine's motion, it is only necessary to unkey the ADJUSTABLE ECCENTRICS. 77 eccentric, slip it around the shaft and secure its throw in a position C B, opposite to that of C F. But if in addition to a change of direction a variation in the cut-off for the forward and back motions of the crank were demanded, subject to the single condition that the lead opening and lap shall remain unaltered, then it would be very clear that'the eccentric must be slotted in such a manner that its centre can pass in a direct line from F to B (Fig. 17) instead of following the arc F q B. By this FIG. 17, I AD PIN means the throw of the eccentric and consequently the travel of the valve would be reduced between F, the full gear forward of the eccentric, and B the full gear back, while the minumum value would lie at the point M midway between these extremes, or at the mid gear of the eccentric. When the eccentric is placed at f2, the I travel of the valve equals c f2; at f3 cf3 and at the mid gear=C M. It need -scarcely be told one already familiar with the use of 78 ADJUSTABLE ECCENTRICS. the Travel Scale, that by thus reducing the travel of the valve —while the lap and lead opening are preserved constant-we obtain a reduced port opening, an increased angular advance, and consequently an earlier cut-off. Before proceeding, however, to analyze the effects of these changes one other case should be considered, namely that in which the lead opening admits of slight variation. The most common form in which this occurs is for the lead opening to increase from the full gears towards the mid gear as in Fig. 18, where the centre of the eccentric travels in an are. FIG. 18.. —2. -'2-7 The reverse, or case of diminution, is so similar in principle, that the examination of one will serve to indicate the nature of the other. Suppose, FOR EXAMPLE, that C F, the full gear throw of the eccentric................................ - inches. Then the greatest travel of valve............. -5 Let the lap................................. =1 And lead opening.......................... "- ADJUSTABLE ECCENTRICS. 79 These dimensions are chosen on account of no peculiar fitness in their relation to one another, but merely to illustrate the effect of reduced travel, constant lap, and a variable or constant lead upon the cut-off, lead angle, port opening and exhaust closure of a simple slide valve. With a Constant Lead opening the centre of the eccentric should be moved in a direct line from F to B, Fig. 17. When located at F, the travel of the valve equals twice C F=5 inches, the lap —11", and lead=-"ll; if now we mark the lap and lead on a slip of paper and apply it in the usual manner to the 5 inches line of the Travel Scale, we find that The cut-off=1230=0.77 stroke. The lead angle=-10 degrees. The port opening=11 inches. The exhaust closure=146~"=0.92 stroke. Upon removing the centre of the eccentric from F tof' the travel will be reduced to twice C F'2=4". Lap and lead opening remaining unchanged, we find by applying them to the 4" line of the Travel Scale thatThe cut-off=106~=0. 64 stroke. The lead angle=14 degrees. The port opening=l inch. The exhaust closure=136~=0.86 stroke. Since bY is removed the same distance from B that f is from F, the two positionsf2 and b2 will give precisely the same results for opposite motions of the crank. In like manner the cut-off, etc., for the positions"f, 0b, and M may be readily found, but their mutual relation can best be exhibited by grouping their results in a Table like the following for 830 ADJUSTABLE ECCENTRICS. Constant Lead. a a Eccentric P. Cut-off. P M Exhaust Closure. location. r ~, _ _ deg. deg. ins. deg. deg. deg. deg. deg. F or B 5 I 8 123 =0.77 stroke. Io iI 33 I46-=0o.92 stroke. Of' or b2 I 8 Io6 =0.64 " 4 I 44 I36 =o.86 f or b53 I 8 7 I =7 ~ " 25 1 67 113 -0.695 M 2 I 8 4343 o.14 43 43 90 90 = Again, with Variable Lead opening, diminishing from the mid gear toward the full gears (from t" to "t) the centre of the eccentric must move in the arc of a circle, as shown in Fig. 18, where the points f, f are drawn a little nearer toward the centre of the shaft, thereby reducing the travel of the valve. A Table similar to the above has been constructed for showing the effect on the motion ofVariable Lead. bbebb |iEccentric. Cut-off. Exhaust Closure. locations. 0 0 ct a 0. a a t deg. ins. deg. deg. deg. deg. deg. F or B 5 I I29'=0.82 stroke. 3 12 27 153 =0.945 stroke. f2 or 2 34 I + 4 +- oI07 -o.65 " Io4 14 4 1 I 384=1 f~ orb3 24- I 16 -+-:3- 71 =- " 24 -16+-3L 661 113=0-7 M - I 8 434 ='-4 " 43 8 90 90 =g - c From a comparison of the foregoing tables we are enabled to draw the following general conclusions: I. That whether the eccentric centre be moved along a straight line, or upon an arc, the cut-off and exhaust closure will take place the earlier, the nearer its approach to the mid gear; while the lead angle and angular advance of the eccentric will be increased in magnitude. ADJUSTABLE ECCENTRICS. 81 II. At the mid gearThe port opening=the lead opening of the valve. Cut-off angle=lead angle of the valve. Angular advance=90~. Hence the exhaust closes at the -l stroke. III. If the port opening= O, in the mid gear, then the lead opening=O, and the lead angle=90~. The steam consequently is not admitted to the cylinder for either stroke of the piston. IV. Since the free admission of the steam depends directly on the area of the port opening, and this is gradually reduced towards the mid gear, it must be evident that the.most influential element upon the perfect action of a link nmotion, or adjustable eccentric, will be this width of lead opening in the mid gear; at which location it invariably equals the port opening. V. Whether the lead opening remains constant or varies from the full to the mid gear, the lead angle —or angular distance of the crank from the nearest centre at the moment the port commences to open for the admission of steam-increases in magnitude from the full to the mid gear. At this point, if the lead opening=O, the angular distance becomes=90~. This condition is of course incompatible with motion, for the port opening being 0, no steam can enter to urge forward the piston, but could this be moved to the 90~ or — stroke point by extraneous force, it would then be repelled by the steam admitted for the supply of the return stroke. VI. To estimate, therefore, the effect of any lead on the continuity of the crank motion, it is necessary to know not only the width of the lead opening (or lead) at the end of the stroke, but also the angular distance of the crank (or lead angle) at the moment lead commenced. In other 6 82 ADJUSTABLE ECCENTRICS. words, we must know the area of the opening and the time required to produce it. Thus with a constant lead of 3 inch the port commenced opening for the full gear when the crank was within 10~ of the end of the stroke, but for the mid gear when the crank was within 431~ of the same position, a portion of time nearly 41 times greater for the same opening. Since the volume of steam admitted through a contracted passage, depends more directly upon the time that passage is kept open than upon its area, it manifestly would be absurd to imagine that a valve motion, having constant lead, was capable of admitting steam with invariable effect for all points between the full and mid gears. So far as preadmission alone is concerned, the lead opening should grow smaller on the approach towards the mid gear. The relations between travel, lap, lead and port opening for the different positions F,f', f3, M, M, b2, B of the eccentric, are conveniently expressed by a single diagram like Fig. 19. Describe the travel circle a' F B, lay off on both sides of the centre or exhaust-closure line c' C, the lap and lead, and draw the cut-off and lead lines. Through the various positions, f2f, etc., draw indefinite lines parallel to the central line of motion a' d', and upon these lay off on each side of the exhaust-closure line the I travel for the location in question. Thus, from c' lay off c' d and c' a each equal to C F the - travel; from c2, c2h and c: e each equal to Cf2, and so on. Finally, draw the curved lines d M d2, a AIM a' through the extremities of the travels for their boundary lines,* and we obtain a sort of travel scale expressive * The resulting curves will invariably constitute the branches of an equilateral hyperbola. ADJUSTABLE E CCENTRICS. 83 of the character of the motion at the different gears of the eccentric. FIG. 19. -RAVEL. - k-POR7TOPEENINGP7 / —POR9 OPENING.-,/ a — L-.AP — kAP —:y- A-",' AD_. LE.D \ | " 60. / 2 22 I -- \ \ -, " IC I ece....r m 6. \ gears, titill na/ us hereafter to trace the analogy between link 2 a - a.. - B. a.. Since for any particular case the lap absorbs a constant ecceportion of the travel, across e distance shaft, it is proper to indicat have reduced its excess F or B d over the lead in e full 84 ADJUSTABLE ECCENTRPICS. The devices are naturally grouped under two classes: 1st. Those capable of acting upon the eccentric while the engine is in motion. 2d. Those that require a state of rest for their manipulation. The idea of moving the centre of an eccentric directly across its shaft, by means of two wedges with reversed points, first originated with Mr. Dodd, of Newcastle, England, and a device similar to that shown in Figure 20 was patented by him in 1839. His object was simply to obtain a reversable valve motion, little dreaming at the time of its latent powers as a variable cut-off. These were subsequently developed by Mr. Dubs of Glasgow and successfully applied, with slight modifications of design, to many locomotives, In the accompanying figure the crank A is placed at the zero, as well as at right angles to its mate G. The valve motion of its cylinder is operated by the eccentric pulley D, whose centre f2 may be moved across the shaft to any other position between F and B, by withdrawing or inserting the wedges d d secured on one side of the sliding pulley H. In its opposite side are two similar wedges e e, for operating the pulley E, which controls the valve of the cylinder belonging to the crank G, and consequently moves in a line n n2 at right angles to F B. If now the pulley H be slid along the crank shaft until brought in contact with the eccentric D, the centref2 will be transferred from f2 to B, and in like manner n' to n2, locations appropriate to a back or negative motion of the crank. When however it comes in contact with the eccentric E, the two eccentrics will stand in the full gear forward positions F and n, and the nearer the pulley Hi approaches the mid position between * c ~0Z'-;lns/Li(,- —-- I \ I,\ aZ _iZE; —-;( .I1IBU1)1\\ \\\ 1 \,I IBIW I \\ \\\\i 1 II i I — I'I I:, ir s. ~os2i ~1\~=;;~;-,~,\(,!I aielat I I I cWi j)l a~ i -ft- I ~~ "-I~1: ~ ~' I I, a; (II t liJ I! I I B \ T II11 1)( ii 1/1 I Z V i;;I I', I ~\ t I I, i --- ~ i 1. ~r %r r L ~;I u.m+ I / ADJUSTABLE ECCENTRICS. 85 D and E the earlier will the cut-off take place, as already shown in Fig. 17. A moment's reflection will satisfy the mind, that the Dodd Wedge Motion cannot be corrected for inequalities of cut-off and exhaust closure due to angularity of the connecting rod, without introducing mid gear inequalities of port opening, far more pernicious in their effects than the evils we seek to abate. The second class of motors find their chief application in connection with portable engines where it is seldom necesary to reverse the direction of the crank motion. The mechanical arrangement of the parts is shown in Fig. 21. FIG. 21. The claIIbngfrlkeeupnt CENTRAL LINE. The collar A, being firmly keyed upon the main shaft c A, carries on one side a bolt A which performs the office of a pivot to the slotted eccentric pulley E. Through the oppo 86 ADJUSTABLE ECCENTRICS. site side passes the bolt D fitting loosely the slot D d, and capable of clamping the pulley in any desired position. The eccentric has an angular advance of 30~ and its centre occupies the full gear forward position F. To place it in the full gear back position at B, the bolt D should be loosened and the pulley E turned on its pivot A until the point d assumes the position D. This motion will transfer the centre F, upon an arc whose radius equals A F, across the shaft to B, and give as in Fig. 18 an increasing lead from the full to the mid gear. If however it were required that the lead be preserved constant for all gears of the eccentric, the curvature of the slot D d should be formed with a shorter radius than D A, a similar change should be made in the large slot, and the hole for the bolt A should be oval in the direction of the line A F so that the pin D might force the centre of the eccentric to adhere practically to the straight line joining F and B. Figure 21 illustrates a simple method for determining the diameter of the eccentric pulley and for arranging the centres in such a manner that the large slot shall be disposed symmetrically on opposite sides of the diameter A F. The process is carried out as follows: - 1st. About the centre C describe a circle e g, with a diameter equal to that of the proposed shaft. 2d. Decide upon a suitable diameter for the eccentric pivot A and locate the bolt as near to tile shaft c g, on the central line of motion, as consistent with the strength of the pulley. 3d. W~ith A as a centre and A C radius describe an are C c; join A with its point of intersection c of the shaft circle. Bisect the angle C A e by the line A F. 4th. Lay off the required angular advance line C F. Its intersection with the line A F locates the centre of the eccen ADJUSTABLE ECCENTRICS. 87 tric in the full gear forward. About F as a centre strike a circle for the eccentric enclosing the pin A by a distance sufficient to give ample strength to the eccentric pulley. The distance C F will then equal the - travel of the valve, with which radius the travel circle F B may be described, and the lap readily determined. The angular advance is usually taken at about 300 or the; cut-off, but of course the larger the advance the greater will be the travel of the valve, lap, &c PART IV. LINK MOTIONS. LINK MOTION. The various mechanical devices embraced under this general term, have many strong points of resemblance and subserve a common object. By means of them, the Engineer is able at will to change the direction of the crank rotation, with only the loss of the time required for overcoming the momentum of the moving parts, and developing the like in a reverse direction. More than tlhis simple result was not contemplated in the original discovery of the link. Subsequently, however, it was found to be capable of regulating the cut-off of the steam, so that the power could always be adjusted to the work required. This feature greatly enhanced its value, and placed the engine under the complete control of the operator. The extreme simplicity of the parts of the link motion, has enabled it to contend successfully with all rivals, and at the present day it remains in substantially its primitive form. It is applied principally to locomotive and marine engines, where the power demanded is quite variable, and the motion at one time direct, at another reverse. The designs may be divided into four classes: I. The shifting link motion. II. The stationary link motion. III. The Allan link motion. IV. The WalschaSrt link motion. 92 SHIFTING LINK MOTIONS. The first form was invented by Mr. Howe, in 1843, and applied to the locomotives of Messrs. Robert Stephenson & Co. It is in fact the representative link motion, which, excepting slight modifications in the mode of suspension, remains unchanged by the accumulated experience of a quarter of a century. Simultaneous with the appearance of this motion was that of the second, the discovery of Mr. Daniel Gooch. It accomplishes perfectly analogous results, and has met with much favor throughout Great Britain and the Continent. The " Allan" combines the characteristic features of the Howe and Gooch link motions in such a manner that the parts are more perfectly balanced, consequently it dispenses with the counter weight or spring peculiar to the former of these motions. The Walschaert motion is extensively applied in Belgium, but probably will not receive much attention from locomotive Engineers, beyond the limits of that Kingdom, unless future designers succeed in reducing the number of its connections. It is proposed to confine our investigation to the shifting link motion, to develop the general laws governing its action amid varied conditions, to present graphic methods for determining the proportions of the parts, and briefly to point out the general application of the same to the link motions of the other three Classes. SIIFTING LI:NK MOTIONS. A link, operated by two fixed eccentrics, forms when properly suspended an exact mechanical equivalent of the movable eccentric. Unlike the latter, however, its motion is SHIFTING LINK MOTIONS. 93 capable of an accurate adjustment, which practically nullifies the effect of irregularities in cut-off and exhaust closure, attributable to the angularity of the main connecting rod. The general form in which its parts are arranged in American locomotive practice, is clearly shown in Fig. 22. Upon the main shaft are keyed the forward and backing eccentrics, with their centres at F and B, the two extreme positions of the single movable eccentric in Fig. 17. Their straps. are bolted to the eccentric rods, and these in turn are pinned to the "link." The slide valve is attached by its stem to one of the rocker arms, and a "block" surrounds the pin of the opposite arm, which fits the main link and slides freely therein. The centre of the link is spanned by a plate called the " saddle," on which is formed the pin or stud that supports the link and eccentric rods. This pin is embraced by a bar called the "hanger," or sometimes the suspending or the sustaining link, from its position and the service rendered to the motion. The former term is preferable on account of its conciseness, and can lead to no confusion. The opposite extremity of the hanger is attached to one arm of the tumbling shaft. Both arms of this shaft are rigidly secured, and form upon it a "bell crank." The shaft itself freely oscillates on properly supported bearings, but is limited in its motion by the action of the reversing rod. The link has been dropped into the full gear forward, thus throwing the entire influence of the eccentric F upon the valve motion to the almost complete exclusion of that of its mate B. By drawing back the reversing rod and raising the link until the pin of the other eccentric rod is brought in line with the pin of the rocker arm, the link will be made to occupy a location appropriate to a negative crank movement (as with B, Fig. 1.7) and intermediate suspensions will in like manner be pro 94 SHIIFTING LINK NI OTIONS. ductive of earlier cut-off and exhaust closures. In order to clearly demonstrate that such similarity exists between these motions, it will be necessary to reduce Fig. 22 to a skeleton form like Fig. 23, and follow the journeyings of the "link arc" throughout a complete revolution of the crank. Let the path of the main crank pin be represented by the circle E D in Fig. 23. This being divided into 12 equal parts, gives a sufficient number of positions for the purpose of tracing the motions of the link arc. The zero will be known as position No. 1, the 180 as position No. 7, and so on. Within this circle describe the path of the eccentric centres by means of the circle F B bY. This should first be divided into 12 equal parts, with F as the origin of one eccentric's motion, and again into 12 other equal parts with B as an origin, so that when the crank moves front position No. 1 to 3 the new positions f and b3 of the two eccentrics may be instantly found, and the same with other locations. The original positions F and B are of course laid off with the angular advance due to the proposed maximum cut-off. At tlhe distance C t from the centre of the shaft erect the perpendicular T t and locate T the fixed centre of the tumbling shaft. T h will represent the arm which supports the link through its hanger and h h' h" the arc described by this arm. A second perpendicular at the distance C A will contain the point R, the centre of the rocker shaft, whose arm R A sweeps the are r A r. The motion of the upper arm, being merely the reverse of the lower, need. not be considered, and so long as the angular advance is properly located no error can arise from the omission. In the motion of the lower arm there are five locations of vital importance, viz: one at which the exhaust of the valve opens or closes, two appropr ate to the lead at full gear of the SHIFTING LINK MOTIONS. 95 link, and two at which cut-off takes place or the valve closes its ports. The 1st is evidently the normal position R A of the rocker, the 2c R d, R d', that in which the rocker pin is drawn aside a distance A d equal to the sum of the lap and lead, and the 3d R 1, R I' corresponds with a removal A I equal to the lap. Hence, so far as the slide valve is concerned we can confine our attention to the motion of the rocker arm pin upon the arc r r. The five positions in question can be distinctly located by sweeping a circle d d', with a radius equal to the lap plus the lead of the valve, around the exhaust point A, and inscribing a second circle I 1' with a radius equal to the lap of the valve. Then the four points in which these circles intersect the are r r will give the 4 positions of the pin corresponding with the lead and cut-off positions of the valve, and the centre of these circles will give the exhaust closure positions. As these locations will be constantly referred to in the seqnel, it should be remembered that the " lead circle" d d' fixes those points on the are r r which the pin of the rocker arm must occupy when the valve has a given lead; and that the "lap circle" I I' locates the positions of the same pin for the moments at which the steam ports are closed against the admission of steam to the cylinder. Our next duty will be to reduce the link to its simplest form. It appears on examination that the rocker pin is entirely subject, in its motion, to the guidance of the link arc, and that this are swept with a radius C A is rigidly connected with three moving points, viz. the saddle pin, and the two eccentric rod pins. In following the motion of the link arc, the connection of the parts can best be maintained by the use of a template, cut from white holly veneer or other hard wood and shaped like L L in Fig. 23, upon which are 96 SHIFTING LINK MOTIONS. made V shaped incisions for locating the points f, S and b of the pins. We are now prepared to find position No. 1 of the link corresponding with No. 1 of the crank. Of course when the crank is at the zero the steam port should be opened an amount equal to the lead of the valve. The rocker arm therefore will occupy the position R d, and the point d lie in the link arc. Since the eccentric centres F, B are found in a line perpendicular to the central line of motion, and the eccentric rods are of equal length, the link must occupy a nearly perpendicular position. Place the template so that its are coincides with the point d and mark the point f upon the paper, then the distance from F to f will equal the length of the eccentric rod. WVith this length as a radius describe about F as a centre the small are f g, likewise with B as a centre describe the small are b A. Apply the template to these arcs so that the points f and b shall be found in them and the point d on the link arc n c d, after which, draw the link are on the paper and we obtain position No. 1 of the link. WTith the saddle pin S as a centre and the length of the hanger h S as a radius, the position T h of the tumbling shaft arm is readily found for full gear of the link and conversely the arc c S c is fixed along which the saddle pin must travel during the revolution of the crank. The preparatory stages of our solution are now complete, the link motion of Fig. 22 has been reduced to its skeleton form and the first position of the link located. Our next step is to follow the link are during its journeyings in a single revolution of the crank. Suppose then, the crank is made to occupy position No. 2, the eccentrics will be carried forward from F and B tof2 b2. Since the length of their rods remains unchanged the arcs f g, b h, will be I I - VALVE 57EZV7 77///BL//@NG S//AF --. 5IC!P S~~~i3,~, 4. / /S I 1 /? O C / (E / / 5 / A F T I L-%C0-4jTEN Rolo C FEN 7 ~RA Z- Z INZ OF / — -e- - ~ ( ~ / s~\ " I;'I' __ __ _ _ _ _ _ _ _ _ _ SHIFTING LINK MOTIONS. 97 FIG. 24. 10 7 PIN f. 7 98 /N.- -. _ d__ _ - k7'AE OF MOTION a \./' removed from their first position and the link template will follow them with its points b and f. The only restraint 7 98 SHIFTING LINK MOTIONS. upon the course of this template is that the point S must travel on the hanger arc c c. If therefore we describe new arcs about the centres f2 b2, and adjust the template so that f and b shall be found in those arcs and S in the arc c c there will result a new link position with its arc standing like 2 2 in Fig. 24 and intersecting the rocker pin are r r at a point k. But as the rocker pin necessarily follows the course of the link arc it will by this change be drawn aside from d to k, co:lsequently the steam port will be opened wider by the extent of the horizontal measurement of this distance. In like manner when the crank is carried to position No. 3 the link arc will be removed to 3 3 as in Fig. 24, and the rocker pin to V, producing thereby a still wider opening of the steam port. The same process applied to the remainder of the 12 crank positions will give the other locations of the link arc (as in Fig. 24) for the full gear of the link. Now observe that the link position 3 3 produces the widest opening of the steam port, and as the crank advances to 4 and 5 this opening grows less and less, until between 5 and 6 the rocker pin reaches the point i, where the steam is finally cut off. During its further progress expansion goes on and at last when A is attained the exhaust opens and the steam escapes. At position No. 7 (the 180~ location of the crank) the link are is brought again in contact with the lead circle and a like process is repeated throughout the return stroke. A duplicate set of link are locations, might readily be obtained by raising the link to the full gear back position and a similar set for the mid gear, but an examination of the one just found will develop the character of the motion. Draw curved lines* tangent to the * Hyperbolic curves with semi-transverse axes ehorter than their semi-con. jugates. SHIFTED LINK MOTIONS. W extreme positions of the link arc to represent the bounday lines of the valve travel, as B B' B" and D D" in Fig. 25. From the centre of the main shaft, with a raFIG; 25. B.... T/I RAiVEL 11 —..