Illinois Itzsdmte of Techc-oiogy UNTVERSJTY LIBRARIES AT 545 Jones, L. E. Heat balance of a Hvid engine In '^ ! Digitized by tine Internet Arcliive in 2009. witli funding from CARLI: Consortium of Academic and Researcli Libraries in Illinois http://www.archive.org/details/heatbalanceofhviOOjone Heat Balance of a Hvid Engine A THESIS PRESENTED BY L. E. JONES AND E. C. SCHWACHTGEN TO THE PRESIDENT AND FACULTY OF ARMOUR INSTITUTE OF TECHNOLOGY FOR THE DEGREE OF BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING MAY 27, 1920 APPROVED: ILLINOIS INSTITUTE OF TECHNOLOGY .^-^^^/fx,.^^.-,^^ PAUL V. GALVIN LIBRARY ^^ ?«.»«», ofMechaniCEn^neenns 35 WEST 33RD STREET ^J/^.7]4 . /?^ CWCAGO, IL 60616 De.„of^n^„e.rin«S.udies Dean of Cultural Sludic Th« Heat Balance of a Hvid iLn^lne HEAT BALANCE OF A HVID ENGINE AUTHOR'S NOTB It la not our purpose to offer a coraplete analysis of the Hvid enfiine. Ratiier, the worlj we have done is merely a beginning, and our timo has been largely spent in putting the engine in condition to test. This work is described in detail in the text. We wish to thank Profeasor Roesch for the opportunity he has given us to work on our own initiative, and for his constant aid and advice. Professor Perry has also lent us his aid in the shaking -forces analysis. We are further Indebted to Ur» Larson of the class of 1917, who has done some special work on the characteristics of different fuels in the injector. This work will be presented by Mr. Larson personally. L. E. Jones E. C. Schwachtgen 290S3 Heat Balance of a Hvld Engine Table of Contents X# The Hvld Engine Introductory 1 Explanation of Cycle 3 Operation 6 II. Work Preliminary to Testing Mounting the Engine 11 Design of reducing motion 12 Design of Prony Brake 16 III. The Heat Balance 17 Results of Tests 19 Curves IV. Shaking-Force Analysis 20 The livid Engine HEAT BALANCE OP A HVID ENGINE THE HVID ENGINE The Hvld Engine i3 of necessity a heavily built machine and is designed primarily for heavy duty work. It is built in single and multi-cylinder models, and is used largely for farm and machine shop work- A four cylinder 25 horse-power engine is built by the Common- wealth Motors Co. of Joliet, 111., for marine work. The price of this engine (January 1920) is $2000. This model should prove popular, despite the high first coot (which by the way, is as cheap or cheaper than any other success- ful kerosene engine adapted to this work) be- cause of its reliability and inherent economy. The engine used (Pig* 1) is built by Sears Roebuck & Co. of Chicago, under the trade name "Thermoil". It is of the single cylinder horizontal type and developes 8 horse power. The price is $300. Early medals of this engine gave trouble, due to incomplete development of - 1 - Figure 5 the Injector, but this obstacle has been over- come and the present models are considered as reliable as the ordinary farm enclne. The engine is governed by a high speed centrifugal Governor, geared to the timing gears. Crovernoring is effected by reduction of fuel, and a full-load speed of 450 r.p.m. is maintain- ed. (Hvid engines have been built that operate successfully at 1500 r.p.m.). The inherent advantages of this type of engine are: 1. Mechanical Simplicity 2. Low fuel consumption at all loads 3. Absence of electrical or hot bulb ignition 4. Ability to start cold on any free-flow- ing fuel 5. Absence of oarburetting device 6. Low water jacket losses 7. Ease of lubrication 8. Lack of carbon troubles 9. Constant compression 10. Good torque characteristics -2 - EXPL/NATION OP CYCLE The basic four cycle fotto cyole) principle is used, with this modification, pure air, in- stead of a mixture of air and caseous fuel, is drawn in the cylinder on the suction stroke. Two values are employed, actuated as in the usual gasolene enf^lne by a camshaft (geared from the crankshaft to run at one-half enpine speed. Ir.nition is effected by the compression temperature (900 to 1000 deg. fahr. due to a compression pressure of 425 to 475 lbs. per sq. in.). Referrinc to fi^^uro 2, the phases of the cycle are as follows: SUCTION STROKE; As the piston moves down the stroke (toward the crankshaft), the inlet valve "A" opens and a charce of pure air is drawn into the cylinder. The fuel valve "B", (actuated by the push rod "R" ) opens simulta- neously with the inlet valve, and fuel enters the cup "C", due partly to the action of Grav- ity and partly to inhalation. The amount of fuel admitted is reculated by the metering, - - 3 - FUEL VALVE COLLAR FUEL VALVE LEVER 1 AUXILIARY AIR HOLE FUEL CUP SCREW FUEL CUP ^'^^"^ FUEL INLET VALVE Figure 6. pin "E", which ic linked to the governor. As the fuel enters the cup, a cnall char^je of air la dratm throi;r>h the hole "P" and enters the cup throui^h the ^uide "0". As the piston nuaro the end of tho strcke, ths inlet and fuel valvos are closed. COMPRESSIOS STOCKS; On this stroke all the valves are cloasd and tho entrapped air is com- pressed to a presBure of 425 to 475 lbs. per sq. in. Ac the preasuro builds up, air is forced into the ciip through t>se liolea "H" and a presoure nearly equal to that in the cylinder is firjally attained. At the temperature due to this pres- sure, the more volatile parts of the fuel Ignite spontaneously, and a "primary" explosion takes place within the cup. The force of this explosion drives the heavier constituents of the fuel thru the holes Into the cylinder. At this stage the piston has reached the end of the stroke and the compression is at a maximum, and the temperature Is high enough to ignite the fuel. (The fuel - 4 - bums, rather than explodes). Due to air defi- ciency, the amount of fuel burned In the cup is infinitesimal. PO?fER STROKE; As the fuel is forced into the cylinder it is thoroughly atomized, and is ignited by the temperature due to compression. The consequent expansion forces out the piston, as in the ordinary gas engine. EXH/>UST STROKE! As in the ordinary four cycle engine, the exhaust valve opens at the end of the power stroke and the products of combus- tion are expelled by the piston on the return stroke. - 5 - OPERATION SPEED CONTROL! The spaed control wheel (Fig. 1) regulates the amount the fuel value opens, arfd thus regulates the amount of fuel fed per stroke to the fuel cup. ^"hen the wheel is screwed up ae fs.r as it will go, the maximum value openinc is allowed, and the encine runs at normal speed. Screwing the wheel down reduces the supply of fuel and hence reduces the speed. A noticeable amount of play is observed when the wheel is screwed up. If the wheel is screwed down until this play is elialnated, the fuel supply is entirely shut off. (In order to cut off the supply of fuel quickly, in ease of an eccident, we inserted a stop-cook in the fuel line, close to the Injector). LPBRICATOR AND FUEL PUt^Pi The pressed steel box attached to the back of the water hopper (Pig. 3) contains a combination lubricator and fuel pusip. The box is divided into two sections, one an oil reservoir and ore a fuel reservoir. Oil is pumped from the oil reservoir to the pis- - 6 - ton, and fuel la pumped from a tank in the base to the fuel reservoir* (The oil reservoir la filled by hand). Prom the fuel reservoir, the fuel flows under the action of gravity to the injector. The pumps are actiiated by the cam- alriaft and the link, as shown in Fig. 3. TO START TKE ENGINE; Befoi'e starting the engine, the oil and fuel reservoirs must be filled, and all grease cups should be screwed down. To quote from the Instruction book fur- nished by the manufaetureis : "Release the coiiipression in the cylindar by puiliiig the compression release lever up to the Eltirtirig position (Fig. 4). Turn on fuel by screwing up tne speed control wheel. WiUi the starting crank, turn the flywheels rapidly Uirougii eight or ten revolutions, fiemove the ortink rapiaiy and lm;nediately push the com- pression release lever down to the running posi- tion. The moiaonlum of the flywheels will turn - 7 - S^Pr . SPEED CONTROL- WHEEL STAPTIN6 POSITION the wigine over compression and the engine will start. To shut down the engine, screw down the speed control wheel until the fuel is shut off." The lubricator should be adjusted to give about 16 drops of oil per minute. If the engine is to be started warm (i.e. after it has been in operation, and has not cool- ed off) less fuel will be required. Therefore the speed control wheel should be only partially screwed up. Indeed, it is possible to "flood" the engine by admitting too much fuel, in which case difficulty will be encountered in starting. If the engine pounds upon starting, an excess of fuel is indicated, and the entire supply should be cut off until this excess is used. When the engine begins to slow down, the wheel should be screwed up until proper running conditions are reached. FUEL INLj^T VALVE; The fuel inlet valve some- times leaks, due to the formation of carbon, or - 8 - to dirt. WJaen this condition ocourSf the valve must be ground In. To quote further from the instznictlon booklet: "To grind the fuel Inlet valve, remove the fuel Injector from the cylinder head. Take off the fuel cup and remove valve collar and valve. Place a minute quantity of powdered pummice and oil on the valve seat, and turn the valve slow- ly back and forth on the seat. A gentle pres- sure should be used. After grinding, the parts must be washed in kerosene." In placing the indicator on the cylinder head, the rods which actuated the fuel valve had to be replaced with special rods, made to clear the indicator. As these rods were of different length from the original ones, the timing of the valve was changed. Resetting was accomplished with the crank straight down (180 degrees from the position shown in Fig. 3) and the compression release lever in the running position. At this phase, there is supposed to be between .005 and - 9 - .01 of an Inch clearance between the valve tappet and valve stem. This clearance is ad- justed by the fuel valve adjusting screw shown In Pig. 1. - 10 - Work Preliminary to Testing WORK PRELIMINARY TO TESTING MOUNTING TilE ENGINE ; We received the engine bolted on skids* These were left in place and a bolt was sunk in the concrete floor at each end of either skid. (Special bolts, having a nut on each end, were used. Holes were bored in the skids first, and then the relative positions of these holes were laid off on the concrete floor. Holes were drilled with a star drill and a nut with a bolt threaded in place was inserted in each hole. Melted lead was then poured around each bolt. When the engine is removed, the bolts can be readily withdrawn from the nuts, leaving them in the floor for future use. The engine was run unloaded after being bolt- ed in place, but excessive vibration resulted. Accordirgly, two more holes were placed in each skid, and bolts to correspond were sunk in the floor. A second test proved the vibration to be satisfactorily reduced. For a permanent setting the engine should be mo^inted directly on a concrete base. THE REDUCING MOTION To Indicate the engine a special head with a hole tapped in it to receive the indicator was procured from the manufacturers. The reduc- ing motion, however, had to be made in the shop. A reducing motion must reproduce, point by point, the motion of the piston. V7hen the en- gine has a cross-head, the familiar pantograph motion is usually employed, and the length of card produced la about three Inches. As this engine has a full-trunk type pis- ton (customary in gasolene and small gas engine pi^actice) this method could not be used. Our apparatus consisted of a small eccentric, four and one fourth inches in diameter, having a throw of five eights of an inch. This gave an Indicator card one and one fourth inches in length. The parts were made small, in an at- tempt to eliminate inertia forces and the re- sulting discrepancies. - 12 - The ecoentrlo circle was keyed to the crank- shaft at zero degrees with the crank. A push rod extended along the center line of the engine, close to the indicator* Three bearingB support- ed the rod, which was made of steel, three quar- ters by three eighths of an inch. To reduce weight, the rod was melted out to an I beam section, except at the bearings. The rod must be placed precisely on the center line of the engine. If it is displaced either way, the motion of the piston will not be accurately reproduced, due to a difference in angularity on the forward and return strokes. (This fact is made use of in shaper practice, where a "quick return" motion is realized by the use of an off -set rod). The eccentric was placed on the right hand side of the eAglne, inside the flywheel, and set the flywheel out about seven-eighths of an inch. This seriously interferred with cranking the engine, as room enough was not left to fit - 13 - the crank handle properly on the shaft. Unfortunately, this objection was removed by the failure of the apparatus. After ten minutes of running, the eccentric strap failed, wrecking the entire reducing motion. Whether the failure was due to a seized bearing, or an inherent weakness in the strap, has not been determined. However, it is probable that the strap gave away, as the inertia forces at 450 r.p.m. are large. In redesigning the apparatus, more rugged construction was used. (See blue print of eccentric appended). The throw was increased to one inch, giving a two inch card. To obviate the difficulty in cranking, the new eccentric was placed on the other side of the engine. The push-ixjd used was made of five-eighths cold rolled steel shaft of circular cross- section. Two bearings were used, in place of three, as the larger rod was less subject to flexure. We found by experience that the - 14 » simplest way of lining up such a shaft wag by babbitting the bearings with the shaft lined up In plaoe. (Previous to the babbitting, a steel bearing was used. This bearing seized, but due to the rugged construction employed, little damage was done, beyond bending the rod). - 15 - CONSTRUCTION OP PRONY BRAKE A two -foot brake dznim was made from plans furnished by the Institute. The machine work was done under Mr. Agio's supervision (by the author ' s ) . A large pulley runs "sweeter" than a small one, due probably to the Increased rim veloc- ity. It was for this reason that a two foot pulley was used. A brake band of steel, lined with wood blocks, was made as per the submitted blue print. The brake arm (distance from the cen- ter of the crankshaft to the point of applica- tion of the load) was made 31.5 inches. Sub- stituting this value in the fonnula H.P. s 2TT R N W SSoob there results the equation H.P. - N W 2000 where N z R«P»M. W - net load on scale pan in lbs. - 16 - The Reat. Belanee THE HEAT BALANCE We did not have sufficient time tc run a complete heat balance, but the engine has been left In condition to run this test. Several runs for horse power were made, and a typical indicator card (Pig. 5) is included in this report. / At Professor Roesoh's suggestion, we have included a heat balance, using data taken from an article in the January 1920 number of the Scientific American f'onthly* This article was written by Mr. E. B. Blakely, who used data collected from a series of tests run by Prof. Roesch at the Institute. Further information can be obtained by referring to the "Proceedings of the American Society of Mechanical Engineers" for December, 1919. The heat balance gives the mechanical and thermal efficiencies for both brake and indicat- ed horse power. The engine used by Prof. Roesch was the same size and model as the engine we - 17 - Jki^ c^/siTJO^^^r^o^t^s:^ ^/cpr used (5-3/4 In. bore and 9-in. stroke). For testing purposes, the engine was flex- ibly connected to a Sprague electric dynamosieter by two Spioer universal joints. Engine speeds and fuel weights were obtained by electrically operated devices. The water jacket losses were determined by weighing the water used and recording the temperature dif- ferences. The sensible heat of the exhaust gases was determined by the calorimeter method. Prof. Roesch also took indicator cards, but (to quote from Mr. Blakely's article)" ... because of the probable errors due to the high pressures involved, and the comparatively high speed of the engine, these cards were usdd mere- ly to study the valve settings and general events of the cycle." The engine was operated under various loads and speeds with various adjustments of fuel supply, compression and cup design. The final compression pressure was set at 390 pounds per - 18 - square inch. FiGures 6 and 7 illuBtrate by curves the results of these tests. - 19 - ! 1 9 --i- -7 1 V f/gr/^A/cr^^-^ --■ — i i - 1 1 i ' * 1 '■' TfX^/^^^T^If^Wk. f — *■ ■-i. J/i:^ .r-jV i :''!'".;i ": i ! 1 j -.:.__ J "71 _;_^ ! i 1 :- ■; -j--; ['■ , 1^ . I;-,, ■ -r'r. .. __, i — r* 1- > = p— : : Ti i ■:i' ■■ i ;■' • wmmsmd - 1 ■ ! — 1 — ^ "1 ■-t ■{H-.r 1 ; 1 J .1 ..A.c^^':-:-:..^. : • 1 -:.- . I " \ ) a 1", J^4_- ■l::;:- WBmmmm -i ■ i - 5S r* i - 1 HBr^HBHHiBH / -^^1 ■-■' -i u |Z^ \ ::[;:: Vj-:. :.::,i . ^ m ■ ;.'." "* 1 ■ ::;. , "i T ' _ J 1 •■-';.. . ..-U. — 1 : -1 [ ■'■ ! ! L J |:' r ,"" M ,li-.t^ :/.:! 1 , i ?~j F* - -i- ■■■ r— /-T" i _ .. . _ .' "7 ! - i 1 i \:. i i, .. - '-M ^ WIMImfmM PCS r^^^m >:::d V- i. " ■ ' ; A ' — >■ 1- _/ i 1 ■ '•i-' 1 "' >-iS B^EBiaS a \- , j ■ ■ ■-' j. ... \"~ .. -,- „ ^ •■■'I- k^ SBMIHI i — - — 1 1 - ^ i^ :!,:.■ -.^^ 1 ; . . 1 p^ n c H "T ':' ^ • ■HIBhIbH 1 !■■■ 1^" " ■ r » BHH r 1 r 1^ ■; ', ' '■ - ' 1 ' Sir iB ■/a^^^jRCkk^^J^. ' \' .- . ^^ [j~TT^ ~jT^ i-^ [,^ -_ w /^-/a-.u^ -rp-i~t^d ^/(^c: Ehaklng Force Analysis DETERIIINATION OP THE SHAKING FORCES In addition to tho heat balance proper a study of the shaking forces produced in the Hvid engine was made. 3?.ue prints .-aarked plates #1 and ^2 lllustrete dlagracinatlcally the forces found and c&lculated in the following pages* The x^rsssure produced upon ignition of the kerosene vapor is expended in two ways. First, it accelerates the moving parts; second, it rjroduces a pressure on the crank pin which may bo resolved into two components, one of which produces rotation of tho crank shaft, and the other pressure on the main bearings* In order to get a clear Idoa of just how these foreen act it is necessary to know some- thing about the relative motion of tho various moving parts* The piston has a sinple motion of reciprocation, the crank an approximately uniform motion of rotation, while the connect- ing rod has a complex motion of combined os- cillation and reciprocation* The reciprocating motion requires accelerating forces acting - 20 - alternately in opposite directions, wa does also oscillotion. On the other hand, a r*otery motion induces a centrlfu^i&l force aotine always toward the crank pin. 1'he various forces influeneln^j rotation are llluatratod in Fi£. A, pa£,e where S s Nat gas pressure F = Translational inertia force of piston and parts T = Translational inertia force of connect- ing rod A s Angular inertia force of connecting rod G z Centrifugal force of coimecting rod 0 - Graviti'' force due to the weight of the connecting rod NET PRESSURE The indicator card shown in plate 1 is the net pressure card, as the engine is single actings The engine exhausts at l-l/S pounds above atno- spheric pressure and the ciiarge is drawn in at 1-1/2 pounds bslov; atmosfiierlc pressure. - 21 - FJS.A. £?/A^i?AM or FORCeS^ COf^A/£^CT/N<} /?OC> fRAimi/Tioif/vL imiaau poRCii of pistok /vPd ?if At tha 9nA of ench atroKo tli« voloolty of tho ploton And pin lo zero, «rtiil9 nsar thd old- dlo of tho stroke it is e naxiouQ* To spood up Uieso pfirts froca rest to a guusIbuci velooity and than to brln(; theia back to rest ugain requires an ftltsiYititoly dcooloratinc und rfetardinij foroa. This force F is found and calculated as follows) Stroke s 9" * r s 1/2 stroke s 9/8 « 4»6'* Piston dlmaetor s 5.76" Piston area s lA s 6«76^ z 89»9B9 sn»in» L&t\Q%h of connoctire rod s gfi^S" Ratio v/l z 4.6 s l/S ^ei^it of piston * pin s 25 pounds KasB of piston ♦ pin s S5 2 .777 R s revolutions per sec. s 450 r.p.a. z 7.6 F a «H -^r (COS.© «* r cos. «*) - K W* r - - rvf J' s - ^'12 s - J'(8TFr)2 n^ 2 r - 22 - - M 2 n2 r -4 2 . 39.478. M K^ R r .777 x 56.25 x .375 ^ .632 25.959 P = - 39.476 X .632 x (cos.© ■» l/S cos. 6) DETERiaNATION OP (Cos. © + l/5 Cos. ©) Angle Function Numerical Value 30" 60° 90° 120° 150° 180° (cos. 0° (COB. 30° 1/5 COS. 0°) ,.,__. 1/5 COS. 60°) (COS. 60° ♦ 1/5 COS. 120°) (COS. 90° ■» 1/5 COS. 180°) (COS. 120°+ 1/5 COS. 240°) (cos. 150°* 1/5 COS. 300°) (cos. 180°* 1/5 COS. 360°) 1 4 1/5 X 1) .866+1/5X.5) .5 - 1/5 .5) 0 - l/5x 1) -.5- l/5x.5) -.855+1/5 .5) -1 + .2) ♦ 1.2 ♦ .966 ♦ .400 - .200 - .600 - .766 - .800 F z ' 24.98 (cos.© + l/5 cos ©) Angle (Cos.© 4 l/s cos. © ) Constant F_ 0° 4 1.2 30° 4 .966 60° 4 .400 90° > .200 120° - .600 160° - .766 180° - .800 - 24.98 - 29.60 H - 24.06 It - 9.97 N 4 4.98 m 4 14.98 n 4 19.13 » 4 19.95 TRAHSL/iTIONAL IRBRTIA FORCE OF THE CONNECTING ROD To produce the translation of the rod the - 23 - force T Pig* A, page applied at the center of gravity is necessary. This force "T" is resolv- ed into two forces, one "T" acting at the pin and the other "12" acting at the crank pin* T s Ti ♦ T2 Ti z - Uq (L-Zc) W^N (cos. e r_ COS. 6) E L Weight of connecting rod = 30 pounds Mn s mass of connecting rod s 50 = .953. Zq s 22.5 - 14.625 = 7.375 L - Zq = 7.575 = .35 , 22. fe ij Ti = (955. X .55 X .575 x 56.25) ^ constant 25.959 T^ z •271 X constant, or by ratio of masses, Ti = 30.5 X .35 X F : .427 P. 25 Ti or Angle P .427 P Oo ^ 29.60 - 12.63 30° - 24.05 - 10.30 60° . 9.97 - 4.25 90° ♦ 4.98 ♦ 2.122 120° 4 14.98 + 6.40 150° ♦ 19.25 ♦ 8.22 180° ■> 19.95 ♦ 8.53 - 24 - or o T2 - Mq Zn W r (COS.0 4 COS. ©) L L Zc = 14.625 : .65 -~- 22.5 Tg : (.953 g .793 X «575 x 56.25) x constant 25.96 T2 = (1.22 X 65 X P s .793 P T2 or Angle P .793 P 0° ^ 29.60 - 23.43 30° - 24.05 - 19.10 60° - 9.97 - 7.91 90° 4 4.98 4 3.95 120° ♦ 14.98 4 11.89 150° 4 19.13 4 15.20 180° 4 19.95 4 15.83 ANGULAR INERTIA FORCE OF CONNECTING ROD The angular inertia force "A" of the connect- ing rod when rotating about the wrist pin may be determined from the equation: A : Mc Zg w2 r sin d L - KqZq w2 - .953 X 4.625 x 56.25 12 X 25.956 X 4 2 __ 99.50. - 25 - Angle sin © 1/5 : K sin © 0° 0 0 30 .5 .1 eo .866 .173 90 .1 .20 180 .866 .173 150 .5 .1 180 0 0 Angle 1/5 sin © Constant A 0<> ♦ 0 - 99.1 50 0 30« ♦ .1 M - 9.94 eoj ♦ .173 H -17.21 90° t .2 n -19.86 120O + .173 k -17.21 150° 4 .1 m - 9.94 180° 0 « 0 "A^" and '•A2'' are two forces acting at the wrist pin and crank pin respectively, which to- gether give the same result as "S" acting at the center of percussion. ^1 = A (L - S) L t = S : .31416 _§ S r 3.26 t^ 10 suings in 7 seconds .7 sec z time of one suing. .7 x 2 r 1.4 sec - time of 1 period of connecting rod. - 26 - 0 - 0 - 9.94 - 1.47 -17.21 - £.55 -19.85 - 2.94 -17.21 - 2.55 - 9.94 - 1.47 - 0 0 Sx = 3.26 X t^ = 3.26 X .7^ z 1»697. S a D^ (Si - D) ♦ D. D = 14.626" D^ = 14.625" S = 1 (1.597 - 1.22) ♦ 1.22 - 1.597 X IB = 19.17" Ai = A (22.5 - 19.17 = . 148 A 22.5 Angle Cor, a tart A Ai 0© .148 60® " 90° " 180° 150° 180° " Ao = A X S = 19.17 - .853 A. "l" 22.5 Angle Constant A A2 0° .853 0 - 0 80® " - 9.94 - 8.47 60* " -17.21 -14.66 900 * -19.85 -16.91 120° " -17.21 -14.66 150° ■ - 9.94 - 8.47 180° " - 0 0 CENTRIFUGAL FORGIi OP TFiE COWIEGTING ROD The centrlfucal force "C" of the connecting rod acts at the center of gravity, is always - 27 - radial with the rod, and la outward in direction. "C" can be determined from the equation 0 = Uq W^ Zc ( £_ COS.© )^. L MjjZoW^ - 4 2 X .953 x 56.26 x 14.625 = 99.50 12 X 25.96 / 2 Angle Oos.Q 1/6 Cos. 9 0° 1 .04 30 .866 .0299 60 .6 .01 90 0 0 120 .5 - .01 150 .866 - .0299 180 1 - .04 Angle 1/5 cos.e^ Constant C 0<» .04 - 99.60 <»3.98 30 .0299 n ♦2.97 60 .01 n « .99 90 0 N 0 120 -.01 W + .99 150 -.0299 n ♦2.97 180 -.04 n ♦3.98 WEIGHT OP THE CONNECTING ROD The influence of the weight of the connect- ing rod Is slight and is often neglected. -28 - Gi = G (L - Zq) L '^l = gg»5 ~ 14.625 X 30.5 - .412 22.5 25.965 02 = G (Z__) L Og = 14.625 X 30.5 s .764 22.5 X 25.96 Since all the necessary forces have been calculated the resultant effect of the explo- sion pressure and inertia forces on the rotative effort of the crank pin, and on the shaking forces at the center of the main bearing can be determined. The forces at the wrist pin are S^ Fi T^ A^ and Oi resulting in a pressure on the guides and a thrust along the rod. This thrust along the rod combines with forces Tgt Ag, Ggf and 0^ to produce (1) rotation of the crank shaft (2) pressure on the main bearings (3) An unbalanced force tending to shake the engine on its founda- tion. - 29 - These various resultants have been determined graphl ;ally in plates jfl and ^'2. COUNTER BALANCE The counter balance curve Illustrates the principle of reducing the effect of the shaking forces by placing a counter balancing weight in the orank disc of the engine opposite to the cranlc pin. The centrifugal force of this ??e1ght is unifora for a constant speed and is always radial. TURNING P:FP0RT The force T E found on plate I in the force polygons acts at right angles to the crank and represents the turning effort in pounds per sq. in. of piston area. While the piston makes a stroke equal to twice the crank length, or 2 , the crank passes a distance r. Hence, in Pig. I, plate II, the turning effort at the va- rious crank positions is laid off from the datum line equal to 4 r. (2 revolutions per cycle - 30 - in a 4 cycle engine) at the point corresponding to the ortink pin position, in a circular path. This process results in a curve and the area between it and the datum line represents an amount of work in foot pounds (equal to that of the Indicator card). Prom the form of the turning effort curve it follows that if the load is constant the speed of the engine must fluctuate during each stroke. The mean ordinate represents the uniform crank effort which would do the same work per re^/olu- tion as the actual effort. During part of the stroke, the flywheel gains speed and stores up kinetic energy which Is restored during the remainder of the stroke. - 31 - CALCULATION OP VELOCITY AND DISPLACEMENT CURVES F s S (Scale of spring) x P (ozxiinate in inches taken froa mean ordinate of turning effort curve ) . A 2 ftJ^OPL of piston 2 f5''>'65S bQ* inches* d V = r d t s F R K = 15 ^ 2 (4.5) (TF-) dv-PR rdt Ht of 2 flywheels = 2 x 204 = 408 dt - 60 = 1 = .00371. "480 X 36 ~g75 dv 2 P X 20 X 25.959 x 4.5^ x 12^ x 32.2 x .00371 12^ X 15.5^ X 408 = dv : .0127 P F T. "DV" is then the velocity imparted to the flywheel, ii<easured on the crank pin circle, during each interval by the force corresponding to P. The d V will then represent the total velocity imparted to the crank pin, measured from any given starting point. The crank pin velocity curve is found by plotting d V's on a datum linoi 4 r inches long, - 32 - divided into 3C equal paij-ts. iiaeh of thts 36 equal parws corr-espond to thosa of the turning effort curve. The reaulting curve represents the variation in •rslooity of the cranic pin through out 2 revolutions. By niaans of a planlaeter the mean ordinate of this curve was found, and drawn giving a line of average velocity of crank pin. After getting the cranit pin velocity curvo, the crank pin diaplaceaent curve is found In a siailar Bianner* d c = d Vg dt = .00371 dVg. Since d B is the Increment of 3i.Tace pacsed over in each interval. It la evident that the d s ;; total distunco passed over by the crank pin during any nunher of intervalo* This sumniation was plotted for every IQO and the resulting curve of Fig. 3, plats II obtained. Tho aean ordinate of this curve represents the displacement of the crank pin, or the distance in feet through which the crank wo^ild pass in unit time if its motion ¥/ere unifona. - 33 - g O cd o H M fe w o ^:i CQ 2: < O H M Ej ;3 01 o CQ Eh O O 01 iH O] 0> 0) H 0> to 02 I kO r-t 00 01 • • o> IS I I 00 to w CO -* <» to (O 01 H 01 <0 ^ lO rH 00 01 OS to iO 01 iH 00 0> o> 01 w to o rH lO a> o to o OS »o H o to "*> t-i o» a> 00 01 CO 01 00 0) OS iH •^ • 9 • • • • • • • • • • • to o> b- M iH lO to \o iH to IS OS to 01 iH H H f-l H rH H 01 1 1 1 ♦ ♦ ♦ ♦ + ♦ ♦ • 1 1 01 01 to o lO 01 o 01 to 01 o 01 lO O to fD w 01 H -* 01 10 Ol "* rH 01 to (0 m • • • * • • • • • • • • 01 o '«*' 01 to 00 CO 00 <0 01 "* o 01 iH H H r-i 1 • 1 ♦ ♦ + ♦ ♦ ♦ ♦ 1 1 1 01 01 to o <0 c«- 0> 0) <o 01 OS IS <X) O tf> o ■* iH o 01 ^ to '^ 01 o r-{ ^ o • « • • • • « • • • • • • v> O) 01 o 00 to ■* to 00 <o 01 OS o to Ol rH rH 01 01 Ol rH i-i 01 to 1 1 1 •► ♦ ♦ ♦ ♦ •» ♦ 1 • • o irj t- 00 00 to lO to 00 00 t- lO o (0 o 0» o> 0> «-t 0> rH o> o» OS o <0 • • • • • • • • • • ■ • • Ob -«*• Ok -^ '^ o (^ Oft 'it '^ OS •««• o> 01 01 iH H H l-i t-i 01 01 1 1 1 ♦ ♦ ♦ ♦ ♦ ♦ ♦ 1 1 1 o o o o o s o o o o o 8 1 OO to «0 Ok 01 OO H *<• N o <0 0} H H H a 01 0) to 10 tOJS - 34 - TABLE 2 VSLOCITY NO e° P" Px.0127 or dv = ft. dv ft. I 6 .04 .0005 .0005 Z 15 3.00 .0381 .0386 s S6 7.45 .0945 .1331 4 36 7.33 .0930 .2261 6 45 6.57 .0834 .3095 6 55 5.50 .0698 .3793 7 05 4.44 .0564 . .4357 e 76 3.70 .0470 .4827 9 85 3.23 .0410 .5237 10 05 2.95 .0574 .5611 11 105 2.75 .0348 .5959 12 115 2.48 .0314 .6273 13 125 2.17 .0276 .6549 14 135 1.83 .0232 .6781 15 145 1.32 .0162 .6943 16 155 .53 .0067 .7010 17 165 0 0 .7010 18 175 - .39 -.0049 .6961 19 185 - .68 -.0085 .6876 20 195 - . 9 -.0115 .6761 21 205 - 1.12 -.0142 .6619 22 215 - 1.26 -.0160 .6459 23 225 - 1.38 -.0175 .6284 24 235 - 1.46 -.0185 .6099 25 245 - 1.46 -.0185 .5914 26 255 - 1.34 -.0169 .5755 27 265 - 1.14 -.0145 .5610 28 275 - . 9 -.0114 .5496 29 285 - .53 -.0067 .5429 30 295 - .08 -.00111 .5418 31 305 4 .22 -.0028 .5446 32 315 4 .3a -.00445 .5480 33 325 4 .40 -.0057 .5537 34 335 4 .35 -.00445 .5581 35 345 4 .2 -.00254 .5606 36 355 - .18 -.00228 .5583 37 365 - .83 -.0105 .5478 38 375 - 1.23 -.0156 .5322 39 385 - 1.44 -.0183 .5139 40 395 - 1.53 -.0194 .4945 - 35 - TABLE 2 (continued) VELOCITY H® P" Px.0127 or dv « ft. dv s ft. 41 405 - 1.53 - .0194 .4751 42 415 - 1.44 - .0183 .4568 43 425 - 1.34 - .0170 .4398 44 435 - 1.24 . .0157 .4241 45 445 - 1.18 - .0156 .4091 46 455 - 1.06 - .0135 .3956 47 465 <- .19 - .0024 .3932 48 475 ♦ .23 - .0029 .3961 49 435 .23 - .0036 .3997 50 495 .20 > .0025 .4022 51 505 .08 - .0011 .4033 52 515 - .07 . .0009 .4024 53 525 - . 2 - .00254 .3999 54 535 - .38 . . 00482 .3951 55 545 - .62 - .0078 .3874 56 555 - .90 . .0114 .3759 57 565 - 1.25 - .0158 .3601 53 575 - 1.42 - .0180 .3421 69 585 - 1.47 - .0185 .3236 60 595 - 1.46 - .0185 .3051 61 605 > 1.42 - .0179 .2872 62 615 - 1.42 - .0179 .2693 63 525 - 1.46 - .0185 .2508 64 635 - 1.46 - .0185 .2323 65 645 . 1.42 - .0179 .2144 66 655 - 1.32 - .0165 .1979 67 665 - 1.35 > .0169 .1810 68 675 - 3.40 - .0425 .1385 69 685 - 4.40 - .0550 .0835 70 695 - 4.29 - .0535 .0300 71 705 - 3.07 ~ .0380 -.0080 72 715 - 1.29 - .0161 -.024 - 36 - DISPIAGIi^JEKT TABLE ] Px.0037 N2. f) r- or de - ft. < ivs= ft. 1 10 ^ 4.02 . .0148 .0148 2 20 ~ 3.40 . .0126 - .0274 3 50 . 2.55 - .0073 . .03526 4 40 - 1.5 - .0056 - .04082 5 50 - .G4 - .0024 - .04319 6 60 - .08 - . 00029 ~ .04348 7 70 4 .43 4 .00159 . .04189 8 80 4 .80 4 .00296 - .03893 9 90 4 1.21 4 .0045 - .03443 10 100 + 1.55 4 . 00575 - .02368 11 110 + 1.88 4 .00696 . .02172 12 120 4 2.22 4 .00816 - .01356 13 130 4 2.48 4 .0092 . .0043 14 140 4 2.65 4 .00965 4 .0054 15 150 4- 2.77 4 .0103 4 .01519 16 160 4 2.77 4 .0103 4 .0261 17 170 4 2.70 4 .0100 4 .0361 18 180 4 2.60 4 .00965 4 .0451 19 190 4 2.56 4 .0095 4 . 0552 20 200 * 2.30 4 .0085 4 .0636 21 210 4 2.16 4 .008 4 .0716 22 220 4 1.97 4 .0073 4 .0789 23 230 4 1.79 4 .0066 4 .0855 24 240 4 1.62 4 . 0060 4 .0915 S& 250 4 1.47 4 .0055 4 .0970 86 260 ♦ 1.55 4 .00493 4 .1019 27 270 1.24 .0046 .1065 28 280 1.20 .0045 .1109 20 290 1.24 .0046 .1155 80 300 1.27 .0047 .1202 81 310 1.32 .0049 .1252 38 320 Z.36 .0050 .1302 33 330 1.39 .0061 .1353 54 340 1.37 . 0051 .1404 35 350 1.30 .0048 .1452 36 360 1.19 .0044 .1496 37 570 1.02 .00379 .1534 38 380 .84 .00312 .1565 30 390 .63 .00234 .1588 40 400 .42 .00156 .1604 - 37 - DISPLACEMiiNT TABLE (continued) ds = ft. No. 6 p« or Px.0037 ds = ft. 41 410 .26 .00096 .1614 48 420 4 .10 ♦ . 000371 .1617 43 430 - .06 - .00022 .16150 44 440 - . 2 - .00074 .1608 45 450 - .28 - .00104 .1587 46 460 - .30 - .00111 .1576 47 470 - .28 - .00104 .1557 48 480 _ .22 - .00082 .1548 49 490 _ .20 - .00074 .1541 50 500 - .21 - .00077 .1533 51 510 - .24 - .00089 .1524 52 520 - .27 - .001 .1514 53 530 - .32 . .00118 .1502 54 540 _ .42 > .00156 .1487 56 550 - .54 ~ .0020 .1467 66 560 - .71 - .00263 .1440 67 570 - . 9 . .00334 .1407 68 580 - 1.09 - .00404 . 13669 59 590 - 1.26 > .00467 .1320 60 600 - 1.45 - .00537 . 12665 61 610 _ 1.65 - .0061 .12055 62 620 - 1.84 - .0068 .11373 63 630 - 2.04 - .00766 .10617 64 640 - 2.21 . .0082 .09697 66 650 . 2.39 - .0088 .08810 66 660 . 2.65 -. .0098 .07826 67 670 . 3.17 - .0117 .06656 68 680 - 3.72 - .0138 .05276 69 690 - 4.09 . .0152 .03756 70 700 - 4.20 - .0155 .0220 71 710 - 4.23 - .0157 .0063 72 720 - 4.23 - .0157 - .0094 - 38 - ,f»0^- ^ Ty/=JC/)L HVJO CAH^ F'LATEL I iisffii III. v^B llll. t' l!!H9!te4= isill t^^^^SBBr nSIIIII mB^BI ^0/^C£: 7=>o/.y(io/^s / n LJi 'HAn/NL a HP Hl^/D SNE//V^ IS^ 1^1 ^ ■iwi. 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