11 62 6 5 9 0 7 ARR No. ESHOk

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

O c t o b e r 1945 as A d v a n c e R e s t r i c t e d Report E S H 0 4

RADIAL AIRCRAFT-ENGINE BEARING LWDS

I - CMNKPIN-BEARING LOADS FOR ENGINES HAVING

NINE CYLINDERS PER CRANKPIN

B y Milton C. Shaw and E. Fred Macks

NACA WASHINGTON

NACA WARTIME REPORTS a re reprints of papersoriginally issued to provide rapid distribution of advance research results to an authorized group requiring them fo r the war effort. They were pre-

nically edited. All have been reproduced without change in order to expedite general distribution. ._. - - . I - . 1 - 7 J viousiy ~ p a u u-idzs a seiiiiiitj status =Ut 56% iii&;isi.ffied. Some cf these rcgsrto :"ere RC! k th-

E-26

t

NACA fiRR N o . E5ET04

3 D?-'ITIONAL ADVISCRY COMMITTEE FOR AERONAUTICS

----- -- ADVfQlcE RESTRICTED RIEPORT

---_I-.-

RADIAL AIRCWT-EMGIm BEARING LO-

I - CRkbXI'lN BXARING LOADS FOR ENGIMES HAVING

r:mz CYLINDERS PER CRAMW

BJ- Milton C . Shaw and E . Fred Mack3

SUMMARY

Dimmsinnal ancz1:ai.s and the pr inciple of sim: 1 itudi: are applied t o the ccm-iputation or the crankFin-b<;aring loads of' r ad i a l sngines havi-ng nina cyl.ind;.rs Der c r a n e in . A rr,othod of gensr- z l i z i n g the r i j s 2 1 1 t R of a re la t ivo ly f e w convtntional Inad analyses i-s devtlopad t o determint? crank-nin-b5aring ].(:ads imdm a wi.de range c?f opwat ing cond.it.i ons. Chmts are prGsentd t h a t givs thz ma.xirrium

and m e a n crmkr!Ln-bcaring lcjads f o r a production angin;, a t a11 values of engine s p e d t o 5000 r i?m and a t 811 valuvs af indicatzd m w m e f f e c t i v e yr,':scsure t o 500 pound.8 px sqaarc 'Inch. BJ use of spct;d and load c m r e c t i c n f a c t o r s thcsc chiirts may bz readily app1ii:d t o a l l wiginas having nini; cyljcdcrs per cra-dqGin: and t o i l lus t ra t , t : t h i s extmdcd use two other prc;r?uct,ion i:Iig(in2s art; c ~ n s idcrcd. individual aff w t s of the several cnginL d imas ions ( r t x i p o c a t i n g woip$t, r o t a t i n g wsl.ght connecting-rod lc;n&,h, stroke,, horu, and cornmc.ssion r a t i o ) upon tho crank,.iin-.bearing loads are dc;tsrmi.nod Rnd discussod,

The

It w a s found t h a t optmum combmations of tng in t specd and 1nd:catzd mean of'fzctivc; 2r;ssurc cxfs t f o r which t h e m m n and maxi- mum cr.mk73in-bz.zring loads arc minma for a givtn y w c r , but such combinfit Lona lib in ttn irn?ra.cticahle opt ra t Lng r<&icn. The m b x i m m 2nd ~ c r n crankpin-bcsr ing I.,mds i i i t k t pract icablc rcgion of optra- t i o n a r c dc,crtasd by an i-ncrtasb of indicatcd mean td'fectivt pres - surt , o r cmmrcssian rat7,o. ?ol:tr diagrams of bcaring loads show that t h t shock lead and the ran& Gf 3trLam imposbd on a crankpin bLaring incroasL,s with incr-asc,d indiciltcd m o a n c-ffect ivt u r L s m r G

Fznd corcyr,sslog ratio.

2

A scheme f o r general iz ing a r e l a t tvely f e w conventional bearing-load ana l j ses has been a>plLed t o an in- l ine engine. ref grence 6 ) FIYLth s h i s nethcd . a few bearm8 -load conputations may be sxtsndsrl t o nbtain char t s t k a t & J w the mean md naximm bearing lqad at an:, camb in&ti cf eiigYLne s?t e d an& indicated mean e f f e c t i v e 7,ressure

(See

T h i s rcetliod has been ap211ed t the r d i a l t y p e engine t:: i 1 l u f j t r - t t p f u r t h e r the generalized treatmext tmd l.jad cLarts a r e preserlted hsrc in f'cr a pmductinn en&;ine, which wi 11 bo -designated en&ne A. In crder t o d e m m t r a t e the a , l ~ l i c a b i l i t g of the c h a r t s t o other rarl,al en&:lnes hav:ng nine cy lmders pe r c r e d q i n , t w o c t h e r production eng:nes, d e s i p x t e d engines B and. C , a r e a l s o C O I ~ S i d e r d I

THECRY

The dmensional method of reasoning presented by Buckineham (reference 7 ) h3s been a7?1 I ecl t o the general izat ion of V .Lyye engine bearing lotido i n ref ereme 6. t h a t mey & f a c t a radial-engine bearing load are:

The s qn l f ican t var iab les

t

KACA AIiR No. E5804

The influence of indicated mean e f f e c t i v e pressure and en@m speed on t h e maximum and mean loads a c t i n g upon t h e pr inc ipa l bearings of an aircraft engine is i q o r t a n t i n both t h e design and t h e operation of the engine. I n add-itlon, the e f f e c t s of recipro- c a t i n g o r rotciting weight, cornecting-rod length, s t roke, bore, and com?rssslon r a t i o on the bearing 1oad.s are of i n t e r e s t .

I n 1919 Burkhardt (references 1. and 2) devised a method of com>uting internal-com'bustion-englne bearing loads . a y l i e d t o H. crankpin bearing of a r a d i a l a l r c r a f t englne by Prescot t and. Pocjle (reference 3) i n 1931. Inasmuch as the conven- %-ional com:mt;sliion of betising loads 3.s ted-ious and time consuming, several a?.?roxi.mate aGlutions have been proposed (references 3 t o 51, but none rJf these methods m e e n t i r e l y s a t i s f a c t o r y

This method was

- .

L

. V

4

NACA ARR No. E5H04

Symbol

ri

P

w

Mi

M,

D

%

Pm

r

5

n

V a r i ab 1 e

Engine speed, rpm

Indicated m e a n e f fec t ive pres- sure , pounds per square inch

Stroke, inches

Crankpin bearing load, powids

Reciprocating mass per crankpin, slugs

Rotating mass per crankpin, s lugs

Dlmete;. of bore, inches

LLength of master connectirqT-Yod length

1qani.f old square

C ompi-e 9 s

ixches

p r e s s w e , pounds per inch absolute

on ratio

Cyank angle, degrees

Number of equally spaced cyl- inders

Dimensional f omula

T -1

F L - ~

L

F

FT~I,”-

.FT~L-~

L

L

F L - ~

Bone

3

Relat i.on

Independent

Do.

Do.

*a

*b

*f

The notat ion imed throughout the repor t i s recapi tu la ted i n appen- di.x A.

I f t h e engine speed, the ir,dicated mean e f f e c t i v e pressure, and t h e s t roke are taken as the indppendent, variables,, an application of‘ Ruckin@mn’s fl theorem (reference E ) yields the following equa- t ion :

where <2 i s some function of the nondimensional q u a n t i t i e s within parenthesos.

a

4 NACA ARR No. E5H04

A sim!lar cqixition may b t di-r'lved f o r the d i r e c t i o n c.f t h e r r ; s A l t g : A t bcarinq 1.md. In itdditiljn t o N: p, Ls, Mi, Mc, D, Lfi , nm r, 0 , an4 n, thi- d i r m t i o n of the r e s u l t a n t bearing li i d is dfuct t id by 0 tho anglcj ( i n dsg) between t h c a i s of c ~ l i n d t ~ r 1. and th t r ~ s u l t m t bGarint3 load i n t h e d i r e c t i o n of r o t a - t! 8 X l .

Whtn ongins speed, indicated mcan ef fec t ive pressure, m d mean Rtre)k\, ;ru takc n ~ t s jndepondmt vm-iablcs, and Bucklngham's n thLorcm is appl led. tho f lsllowing equation j B obtaincrd:

w l w r t , iZ' is some f m c t i o n of the nondimonsicmal q u a n t i t i e s within w m , n t h f m ~ s ,

( 3 )

Eq: i e t :on ( 3 ) ostabl.ishas t h e fast t h e t , if

X'/p u t B constant value of' crank ttngl.c:, a smwth curve w i l l be obt;u.inid. S imi l .a r l .y , ejquatic)li ( 4 ) r3tstos t h a t , at il particul.ar crank G i l p l L : a spec i.f i.c rolati .cn exis ts bctwwn tho angh 0 and E'/,?,

W/s i.s plottud against ca

NACA fiFl;i Nd, E5H34 5

Wl? resvl tan? i n e r t i a fsi-ce due t o a l l r o t a t i n g and reciprocat ing 1 n a m t h a t a c t s vcpoii craakpin, pcuiids

Fc r o t a t i n g weight per crankpin (contr ibut ing t o centrifugal f o r c e ) , po:m%

T h f s r e s u l t a n t i n e r t i a force is also reported t o a c t with t h e sans di;-ect ior, and sense 2s tile corresponding rotatisg-weight soapmerit ( t h a t is, radial-1-27 o;;.t:.m*d along t h e crank axis), whic3 i s dsvelopsd i n appendix B., is Tnqortant i n that its use con- s iderably s i q l i i i e s t h e c o q u t a t i o n or' crankpin-bearing loads and it; is a good approxhat ion f o r radial engiiles hav%g 5, 7 , 9, o r 1.1 cylindera.

Equation (5 ) ,

T%e method used i n thls 1-eport v.tlli-zes equatioris ( 3 ) , (4), and (5 ) . f o r am- convenient indicated mcan e f f e c t i v e press-me , i n the US;;^ mminer by adding vec tor ia l ly the gas forces 02 ';he individual cyl- inders. Because of the inherant syxne'ury of the rad ia l - type engine, or!y the craEk-angle interval from Oo to 720°/n need be considered and, therefore , i n this report cnly those events o c c i x i n g a t crank- angle valims fron 0' t o 80' are investigated. Iner t ia-force c i r c l e s corresponding t o a number of engine speeds are then obtained frm equation (5). a r e obta5ned by the :rector addition of correspcnding r e s u l t a n t gas- force and resu l tan t iner t ia-force components. Equations (3 and (4) m a s be used t o F:ot ~ / p agaiFst $/p and CJ against r; /p f o r each value of crank angle imes t iga ted . Thesc p l o t s are appi icable not only t o the v a l w of indisated mean e f f e c t i v e p 'essure f o r which they were derived but t2 a l l val-les of indicazed mean e f f e c t i r e pressui-e. determinations made at a s i n g l e va l ae of indicated mean e f f e c t i v e pressure.

A polar aiagrm of r e s a t a n t ges f o r m is f i rs t determined,

The resid.%ant

Curves of r e s d t a n t bearing lozd

A

?he mean load may L e generaiized i n t h o same manner from

6 - I I

c

Y

Y

HACA ARR No. l75HO4 7

I n t h e appl icat ion of the method of t h i s repor t it i s more zonyenient t o det,emine t h e resul tant of t h e nine individual gas- force components and add t h i s vector t o t h e r e s u l t a n t i n e r t i a force vector (from equation ( 5 ) ) . m*e 5 f o r a ci*ank angle of 20' where is t h e r e s u l t a n t I n e r t i a - force vector, oc is t h e resultant gae-force vectcr (cornpsed of t h e nine individual components numbered 1' t o 9 ' ) , and t h e r e s u l t a n t load on the crankpin obtained by t h e vector addi t ion of vectors OB and- OC. The resu l tan t gae-force curve and the r o t a t i n g iner t ia - force and resul tant i n e r t i a - f o r c e c i r c l e s are a l e o shown i n f i g w e 5.

This method is a l s o l l l u s t r a t e d i n f i g - OB

OD is again

Generalized Load Charts

- M a x i m i i m bearing loads. - -- - Resultant i n e r t i a - f o r c e c i r c l e s were constructed f m m equation ( 5 ) foJ* a number of speeds corresponding t o values of $/p from 3 t o SO,OQO. H e s d t a n t bearing-load vectors were obtained by adding v e c t o r i a l l y value8 of r e s u l t a n t gas force f o r an inaicated mean effect ive pressure of 245 pounds per square inch (from flg. 5 ) t o t h e corresTondinG r e s u l t a n t t o t a l iner t ia - force vectors (from equation ( 5 ) ) . i n f i g w e s 6 and 7 according t o equatlons (3) and (4) with crank angle a8 t h e parameter. crank-angle values of 20° and SOo) of f igure 6 correspond t o t h e maximum value of' W/p $over the e n t i r e range of N2/p shown.

Such data are p l o t t e d

The solid pcr t ions of the Cwvea ( f o r

A useful chart ( f i g . 8) f o r determining maximum crankpin loads is obtained f r o m t h e cui-veo of figilre 6 . The l i n e OA represents t h e locus of optimum combjnations of speed and indicated mean effec- t i v e pressure for* which the max-inum bearing load at, a given power l e v e l i s a minimum.

The bearing loads determined from t h e maximum load chart f o r t h e condjtlons of (1) take-off, ( 2 ) take-off engine epeed and 10 percent above take-off indicated mean effective presswe, and ( 3 ) take-off indicated mean effect ive pressure and 10 percent above take-off engine speed am given I n t h e foliowing t a b l e :

q h s 3ffectiv.s ;vojocted besr ing area was taken as 1 0 . 1 sq i n .

t3 NACA ARR KO. E5E04

Mean bearing loado. - The mean l m d a c t i n g on t h e c r a l l b i n bea::ing waa determined ky p l o t t i n g W a+?nutj 21:.m1k angle, v.sing a pl.anheter t o obtain the average hsight of the cvrve, apd wacl used t c obtain f-igture 9 i n -which G/p is pl.ctted against N 2 / 2 .

I--- --_I_ .-.-

A convenient chart (f . ig. l i ; ) is obtained fi.om f i g u r e 5 by p lo t t ing indicated mean effect;.ive presawe against engine speed with mean bearing load a8 t h e pmmnetor, is i:Llustrated i n the foll.owing excuilple. ;prieviouely tabulated three cond-itions w e as follows :

The uae of the mean load chart The bearing 1.oad.s f o r the

-.--

3 245

taken as 10.1 sq i n .

.--I. &Ihe effect3.ve yr.o,jectod. bc.,ur.ing area vas

Pda:. diagrams. " -- - A palm* dlczgmm CJ' the r e s u l t a n t crankpin- bearing l3ad m y be obt8ained Yor m y c:mbimtion of engine opeed arid indicated map. e f fec t i r e premu-e froni t.he curvos of f i ;p rea 6 and 7 , Rcgresentktive po la r dlsg-auus rr!.th w s p a c t t c t,he engi.ne axis (f'j.2. 11) h a m been constructed f o r t h e fallowing f o w power con- d i t ion8 :

PTACA ARR No. E5€Tr?4 9

Y Pcl-ar die.grms with respect t v the crank axis may be obtained by r o t a t i n g each resu l tan t vector of f i g u r e 11 counter t o t h e d i r e c t i o n of r o t a t i o n through an angle corresGonding t o t h e number of crank- angle degreas indicated a t t h e terminal end of t h e vector .

The polar diagrams with respect t o the crank axis f o r t h e four power conditions of the foregoing table are given i n f i g u r e 12 in terms of crank-angle degrees. f o r any engine s;seed and indfcated. mean e f f e c t i v e pressure t o be visualizwd.. Point A i s the e n t i r e polar d.iagram with respect t o t h e crank ax-is f o r an indiceted mean e f f e c t i v e pressure of 0 pounds p3r square Inch. The dis tance frcm 9oint A t o the pole corre- syonding t o aqv engine syeed. is obtained from equation (5 ) . The u-pper and lcwer envelopes of the polar diagrams for Cidferent ind i - cated m e a n effective pressures in te rsec t a t point A . The pole corresponding t o m y engine a p e d i s lccated elong the crank axis by 'pro2scting hor.izontal1.y from the speed sca le =

l i n e f o r c e on the crankpin of engine A with respect t o t h e crank axis a t an engine; speed of 2000 rprri, an indicated mean e f f e c t i v e pressure

sca les f o r engines B end C w i . l l . be discussed under APPLICATION OF TEIE DlXl3NSIOn'AL N?ALYSIS NETHOD TO WilER ENGINES HAVING NINX C n - 1mms PER C M W I N .

Th i s f i g u r e enables t h e polar diagam

For cxmpla, 09 re-gresents t o s c a l e the magnitude and d i r e c t i o n of t h e

: cf 25ci pounds p e r square .inch, and a crank angle of 20". The speed

F-igure 13 shcsws t h a t the Ijc'lsr d ~ a e a m s wj.th rosyect t o the crank axis for a p a r t i c u l a r s p e d and indicated mem ef fec t ive pres - s1n-e ma;{ be cbtmned f r c i m a d.iae,rm for the same indicatod mean cff ec t ive pressiire but a d i f f went angine speed by t . ranslatfng t h e center of the crankpin ( tha polo) a l m g the crrznk ax^.

two po la r diagrams with respect t o the engine axis for t h e same l.ndicatcd Icean er'f ect ive pressure but d i f f e r e n t engi ne s?eeds a r e shown 1.n t h i s f ' i q x e - Line; BC is parall.el.. tcl l:me An and, whan these d!.agramH are ro ta ted t o o b t a a diagams with respect t o the cr;tnk axis, l i n e BC w i l l ro ta te i n t o 3.ine B ' C ' . It 11.8 thus evidznt t h a t the di.agrm w:Lth rosyoct t:? t h e crank axie 1.9 merel j t r s n s l a t e d 1-n a dir; jction para1lt:l t o t h i s axis when the cngfne s?t:ed v a r i e s and the ind.icated int;<Ln d f t;ctive ,?ressine I s constant

Portions of

The polar d.iagraJns with res:)ect t o the master connecting-rod axis arc a l s o of' i n t u r e s t with mt3ard t o loads a c t i n g an tho bcczring surface These dictgmans are obtdrned by r o t a t i n g t h e d.iagram with r e s y m t t o the crsmk a x i s i n thi: d i r e c t i o n of' crankshaft r o t a t i o n throu& an rtng1.k of 130 t ul, where al i a tho angle defi-ned i n f iC,,uro 1. axis f c r an engine s ' x x d . ~f 25PC r p m and indicatod msan e f f e c t i v e :!rsssurm cf 3''ultL 350 pc-mds p:r squari? inch a r e given i n f i g u r e 14

Tolizr dJ.aQraiiS with ros:Jcct t o t h e mast.er ccnmctmg-rod.

1: NASA ARR No. E5H04

V e r i f l c z t i o n 01' W e General ized 1,cad Chwts

c x u i d o r c d 9 sa t i s f ac to i*y check of the

Y

Y

i

NACA ARR No. E5H04 11

Individual Effects of Engine Dinenoions upon Crankpin-Bearing Loads

Reciprocating weight. - It is evident from equation (1) that an incresae i n reciprocating weight may be c m p n s a t e d by a decrease i n engine speed. Crankpin-bearing loads ccrreapcnding t o any recipro- cat ing weight a t any value of crank angle may thus be determined from f igures 6, 7 , and 9 by um of an equivalent engine speed.

From equation (5) :

I . T 1

F i standard reciprocating weight per crankpin, pou.nds

Fi ' new reciprocating weight per crankpin, pounds

Ni equivalent engine spoed with standard reciprocat ing weight ,. r Pm

N actual. engine spesd with new reciprocat ing weight, rpm

Equating ( 7 ) and (8 ) and solving f o r N i :

NI =

Because Ls/2 LR i s q u a l to 0.25 for ongino A ,

(9)

12 NACA ARR No. E5H04

The maximum and mean c r a m i n - b e a r i n g loads f o r any engine speed N, indicated mean ef fec t ive pressure p, and t h e new reciprocatSri weight F i by m e of t h e ac tua l indicated mean e f f e c t i v e p r e s s w e and the equivalent engine speed N i from equation (10)

may be determined. from f i g u r e s 8 and 10,

The r e l a t i v e e f f e c t of a lQ-.percent inci-ease o r deo-ease i n the reciprccatint? weight per crankpin upon maxlmum and mean bearing loads i s i l l u s t r a t e d f o r take-off conditlons i n the following t a b l e , which was obtained from equation (10) and f igures 8 and 10:

--- 10-percent increase i n 10-percent decrease i n

reciprocat ing weight F i = 0.9 Fi

Standard reciprocating reoiprocat ing weight

-- w e i ght Fi' = 1.1 Fi

I I

Rotating -- weight, . - The crankpin-beaying load corresponding, t o my r c t a t i n g weik;ht at any value of cr::nk angle may x l sn be deter- m?'ned fmm figures 6, 7: and 9 by use of an equivaleat engine speed. This equivalent engine speed may be obtained i n A manner similar t c t h a t used t o der ive equation (10)

where

Fc standard r o t a t i n g weight pei- ci*ankpin, pourids

F c ' new r9tatinG w e i @ per crnnkyin, pounds

lVc equivalent engine speed w i t,h standard r o t a t i n g weight ,, rpm

N actus1 en(.ine speed wit,h new r::.tating weight, r.pm

The r e l a t ive influence of a 10-pei:cent tncrease o r a 10-percent decrease of' t,he r o t a t i n g weight p 7 ' cranlqin q o n t h e maxi.mum and mean bemicg loads is i l l u s t r a t s d f o r take-off conditions (2500 q m , 245 lb/sq i n . ) :In t h e following t s b l e , whjck: was obtained fi-om equation (11) and f:igures R and 1.9:

J

c

c

I Y K A ARR No. E5H04 13

-_ --- l$--;ercent r o t a t i n g weight r o t a t i n g weight

St andar6 r o t a ti ng wei ght I?,' = 1.1 F,

FC --I- I - i-

34, OrJQ 3.3 37 ,500 -5 .1 '

---

Connecting-rod length. .. The connectlng-rod length plajrs an -- _I

u n l r n ~ o r . t m t par t i n t h e develoyment cf bearing loads. I-t a f f e c t a orily tho r a t i o of the cornecting-rod iellgth t o t h e crank throw wh1cl1, i n tun,, influence8 tho accelerat ion of tile 2 i s t c n and thus the magnitude .;lf the r.ecip:?oca,ting force. P r a c t i c a l values of 'she ratio of the connecting-rod length t o the crank throw f c r radial ai..Lbcraft engines lie i.n t h e range from 3.0 t o 5.0. fonnd t h a t chauges i n the .:.atfc of rod :!.en@h t o c rmk t h m w (due t o a change i n the ccmectlng-rod length) within t h i s range a f f e c t %he iwmltanb c!-a@in-bearing lcada by lons than 1 p r c e n t .

It has been

Stroke. - The effect ~ f ' a chanGe of stmlce at any valiie of -- crank angle ma$. be determinod fraa ?.'igu:.es 6., 7 , an?! 9 by use of an equivalent. speed. The following expresaim f o r t h e eqxivalent speed dxe t o a cliangt. i n s t roke 'v:.28 derived from equation (5) f,?,llowing tho mothod used f o r a change of reciprocat lng weight :

Ls standard s t roke inches

LIS1 new stroke, inchcs

equlvalent engine speed with standard s t rake , rym

N ac tue l engine speed with new stroke, r p ~

The r e l a t i v e influence of a LE-percent increese OT a 10-percent decrease o f t h e wan stroke upon the max5mum and clean bearjn6 loads

1.4 NACA ARR Nc. E5R04

n l now b o w , inches

,

va7. on t

NACA P3IR No. E5H34 15

- S t andsrd l 7 & Z k n t increase in bore 1 bcre

D 1 D' = 1.1 D i

I

! 1'

lo-pcr-cent decrease i n bore

D' = (3.9 D

I .

I 4'

7- _- W

J

-- T/! kl

Becmse from equation ( 1 2 ) a change i n bearing load due t o EL change in s t roke may be determined by u8e cf an equivalent engine speed,

( p e r - ( l b ) (pot-.- cent ) cent ) cent )

-4 .G 40,300 1.3

equation (13) map be replaced by a second when conbined with equation (14) yie lds a l e n t spoed:

(lb) (per- cent )

34,500 4.6

equivalent spsed, which s ingle resultant equiva-

This cquivalent engine speed ND ckimge the funct ion 6i

with standard bore and st roko w i l l i n the same way as a chanee i n bo;-e.

Inasmch as L s appears outside of the funct ion I;] i n equa- i n t h e t i n n (1) and has been conajdered t o vary inversely with D

foregoing disciiss! on, it is where

must be applied t o the load

evident t h a t a corroction f a c t o r

cbtalned frcm tho char t s ( f i a e . 6, 8, 3, and 10) by us6 of t h e equivalent speed f o r t h e 1m.d an@.c; 5 (equation ( 2 ) ) Ls d3es not appear outside t h e function IZ' and thus no load-angle ccri-ection f a c t o r need ba used. use of the equivalent engine s p e d

ND. I n t h e expression

The loud angle foil any bore may be 3b.tained from f igure 7 by ND.

The r e l a t i v e influence of a lO-porcent increase or decrease of bore upcn t h e maximum and mean bearlng loads is i l l u s t r a t e d f o r take-cff conditions (2500 r p and 245 l b / q i n . ) i n t h e follcwing t a b l e ? the values of which were obtained from eguations (15) and (16) and figures 8 and 3.0:

MACA ARR No. ESH05 16

compression r a t i o . - The compression ra t ic a f f e c t s the s h q e of ------.-- t h e indi.cator diagrafm and therefcre the gas force developed i n t h e engine cylinder. The e f f e c t of compression r a t i o xpon gas force during the exhaust s t m k e , the intake s t roke, and most of the com- pression stroke is qui te small. The compression r a t i o has a con- s iderable e f f e c t upon the gas f w c e , however, during t h a t port ion of the expansion s t roke when the pis ton i s near the top-center pos i t ion .

Inasmuch as t h e nondimensional compression r a t i o r enters equations (1) and ( 2 ) apart from the other var iab les , an equivalent speed o r indicated mean ef fec t ive pressure cannot bG used t o cornpen- s a t e f o r a change of compression r a t i o ( t h a t i s , the pr inc ip le of simili tude cannot bo appl ied) . It i.s therefore necessary t o con- s t r u c t a new indicator diae;,rm and repeat t h e ana lys i s f o r each d i f - fe ren t value of compression r a t t o . It i s seen i n t h e fcllowing t a b l e , h9wever, t h a t t h e muxiawn and mean crankpin-bearing loads change very l i t t l e when the compression r a t i o changes from 6.i? t o 7 .4 .

Crank andlo (de&)

Standard compression r a t i o

1 !

0 1c; Zc; 30 40 50 6 1? 70

Mean I__

2 2,500 1 36 . 0 25,500 56 .O

132,000 58.5 57,000 61.0

3O,S0@, 71.5 36,500 f '19.0

39,500 6 5 . 5

33,r30C?j -.--- --

I*---

10-percent increme decrease i n cornpeasion r a t i o

1__ -.-- ------ I W I 0 3

- Y I

c cnt in- crease)

.6

- Maximum-load and mean-load char t s ( f i g s . 15 and 1 6 ) and polar diagrams ( f i g . 1 7 ) with mKpeCt t o the crank ax ie are presented f o r t h e high valuos Of cornpromion r a t i o s of 6.0 and 9.C: whore t h o loads were S i g - n i f icuntlS i z l t o r o d .

PJACA ARR No. E5H04 17

Dimension Incmam ( Increase i n mi- i n mean

lmum load load I (poi-cent) ( p e r c m t )

Hsciprocating weight 6.3 6 .I Rotating weight 5.1 ! 3.3

10.1 10.6 -1.3 1 -4.6

Stroke Bore

Connecting-rod lengtha 0 1 0

C9mprossion r a t i o -T -2.s , -3.0

Y

c -1 Increase !Increase i n m a x i - I i n moan mum load ' load ( p e r a n t ) 1 (iiorcent)

1 -9.1 1::; 1 -7.6 3 ci

-11.4 I -13.6 1.3 4.6 0 3.0

I

APPLICATION OF THF: DIMENSIONAL-ANALYSIS METHOD TO OTHER ENGINES

HAVING NIXE CYLINDERS PEP, C R A I " I N

Mothod. - By uao of an oqtlivalont speed and load correct ion f a c t o r , as discussed i n tho fcrogcing s e c t i m , t h e char t s shown In f iguree 6 t o 10 a r e applicable t o any engine having nine cyl inders per crankp-in. speed IT, f o r charyges of reciprocating weight, r o t a t i n g w e j g h t , s t m k e , and bore was obtained by comblning equstions (10): (ll), (12), and (15):

The following equation of over -a l l equivalent engine

112 D r LLs Lsl (Fc + 0.516 3'1') (TC' + '2.516 Fi)] N, = (17)

I>' 1,s (F, + 0.516 Fi)

An eqLtivalent speed factor C is obtained by s u b s t i t u t i n g standard values f m m appendix C i n t o equation ( 1 7 ) :

3112 fLSl ( 3 2 . 7 2 + (3.516 Fill (Fcl + 4 i . m ) i - L - (18) C = - = 0.0315

N n ,

I. P, NACA AXR No. E5H04

4. load corrzct ion f a c t o r f o r a changs of bore is giv6.n i n G q m t i on (16) . whm D aq?tndix C :

This exiressl on reduces t o the fol lowing equation 1s re !laced by t he valuc f o r tha s tmdard bore given i n

(1s) 2 K = 0.02E6 (D')

Thl: ali.ncmant charta of f i g u r o 18 arc; prosmted j.n ordijr t h a t C and cSlindors 3ar crmk,nin. Tht: for tgolng method. i s illustratud by a.:?ly q; it t c twl addi t 1 onal nin6 -cy l indor rad.lid enginus.

K m y be conwcicnt ly d.ctormj.ned. for any ang:inu having nlne

F r c d u c t i m mgino B. - The s?ucificati .ons of engine B aro - " -- -.- -_ - I _ - -_-.- -.-.-.-.- given i n a?pend.i.x D. From f i g ~ ~ ~ . 18 t h e equivulunt-sp&ed f a c t o r i s s e m t o be ir.966 and tho load corrcct;on f a c t o r , 0.8RC. The crttnkpin, bonri.r,t; loada a t my eng-:nu speed o r indicc.ited mem- offec . t i v u prw3uro m y bo dotsrm:i.nud frcm f i g u r e s 6 to 10 bj: us:ing tht: uquimlsnt -s:wc;d q u a t i o r , (N,. = CM) and t h e load corrc:cti.cn f n c t c r I(, For. cx*mple, thc m a x i m u m a d . n;t;'ttn load on the crsnk-:iin of erLgi.ne B a t an Gngincj speed. of' 25(!0 rpm and an .Lnd..icatd niem ~;ffecC,.ive prcssurti of 300 ;)ounds :per 3qaarl; inch arc: found. t o bo 35,30() (aid 2 C , l . O ( ! pounds, r e : s ~ ~ e c t i v C 1 y ; by mi: c f fi.gurus 8 and. 1.0.

corrt;ction f 'actcrs, a y:,lur diagram was constructed f o r oneino B i n tli-.. convcnt cml. aari1c.r a t rn engine s p w d . ;.f 3000 r p n m d . an lndi c;ite,d nc.an t;ffl-c.t::.ve ?rZssx-e of 363 pounds p:r square inch. The vs1ui:a obtainod f'rc-rn tho locd charta are c o q a r e d with thy: values f rc,m t h o canvontionul ana lys i s i n t h e f , l l r?wi.n@, tnbl t : :

Tn erdor t(, v e r i f y t.hc usc. of tht..: c;quivali:nt r.;i:ed and t h o load

NACA ARR No. E5804 19 I .

t u

I .

9

The close apeemant between the valuos obtained is c o n s i d s r d an adequate chick of tht: two methods umd herein. w a l e s for t h i s engine havt; bucn -Lncludcd on the p o l a r diagrams ,g:Lven i n fSguros 12 m d 1 7 .

Speed and load

Production bngine C . -- Tht s p s c l f i c a t i o n s of engine C w e given -_.-IC --

in a2pendix E . t o be 0.955 and the load correction f a c t o r . 1.000. Tho mttximm and mean crankpin-bcarjng loads f o r t h i s engin6 a t an cngino spcjud of 260C r n m and an indicated mean uffect ive pressure of 300 pounds pe r squart: inch arc found t o bc- 37,703 and 30,.3OC) nounds by use of f i g - ures P .and 1.0. included on f 'Lgures 1 2 md 1.7.

From f iguro 18 the s q u i v a l m t s p e d f a c t o r I s w e n

S p e d m d load scale8 for t h i s engine have becn

APTLICATION OF TBE DIMZNSIONKL-LIALYSIS METHOD TO A DESIGN PROBLEM

Tho foregoing $anal: sis cnublcs a broad =valuation of thc mla- t i v o influctncc of both oporating and design var iablcs . Svvzral exmmlts have beun p r e s o n t d t o illustrate tha us(; of t h i s < a n a l y s i s i n p r d i c t i n g tho change i n crankpln-b(;aring lead t h a t i s broug$t about by a changt: af thId rzpratinq variables. AlthGUglh tht; scvdral dcsign var lablcs have been indtptndLntly t r o a t d , thcsz q u m t l t i e s ar.j intGrrL>latcd m d onz cannot be changod without inf'lucncing t h e o thers . t h e foregoing snalgsj .3 may be a p p l i d t o a d\;sign problem.

Thc following discus.sion i l l u s t r a t c s t h i mauur i n which

It is customary i n unginuoring dcs ign t o ;valuate thc perform- ance of a device i n terms of' it r;lativs. off ic icncy. A g o u p of -9ossiblc cnginos, havjng nlnc cy1.indc.m p u r crankpin, might b< con- siderod on tho bas is of thc rclilt.ivc) m a s i t u d i of thi; crankpin- bcar:ing load pcr ind-i cated horsopowcr d o m l o y d . Many other dos ign crr i tor ia milst? of courm, be considsrid i n a r r t v i n g a t thu most dcsirablo ongino dimmsions.

1 h

'In ordur t o fictmnlnt cqproximatelg tho variat-ion of b t a r i n g oad pe r unlt i n d l c n t d horsopowm with tht, bord of a radial engini . a ~ i n g a f i x e d stsok-. , t h z rLlciprocdt :ng m d tho r o t a t i n g wl=i ( r f i t s

arc asaumd t o vary as t h c cubu of thc bort:, according t:, gdombtric s L m i l a r i t y . m q t h m bi? oxlsrcsszd

Thr: r t c i p r o c a t m g md the r o t a t i n g weights p c r crankgin

%. K2 En,?: ntj.

A I;. 34s ci * 14.2

C , 33s .146 3 , 532 .

(22)

8

NACA f;Rx No. E5H04

DISCUSSION

The maximum a n d mean loads a c t i n g on t h e c r w i n bearing of a

h increase i n indicated mean e f f e c t i v e pressure r a d i a l engine increase s ign i f icant ly with speed i n t h e prac t icable operating rcgion. c a u w s a sl:ght reduction i n the bearing loads e x i s t i n g a t practi-a cable values of engine speed. Optimum Combinations cf indicated m e a n e f f e c t i v e prassuro and eagme spoed f o r which the maximum boaring load is a minimum at an2 power l e v e l are seen t o exist ( f i g . a), but such optimum conditions do not l i e i n t h e range of prac t icable engine operation. When a r a d i a l engine i s operated at f u l l - t h r o t t l e s e t t i n g t h e w i m m ard mean crankpin-bearing loads w i l l be minima f o r t h e engine speed obtaining. (Soe f i g s . 8 and 10.)

It c a ~ bo s w n i n f igire 12 t h a t t h e d i f fe rence between t h e maxi- l~l'lcl and mifiimun; loads increases d i r e c t l y with indicated mean s f f s c t i v e yressure. high values of comprossim r a t i o . beering is sub5ected is taken aa t h s c r i t e r i o n sf f a t i g u e s w e r i t y , bearings operating under hi@ valwcs Qf indicated mean ef fec t ive pres- .sure or i n conjunction with high values of c o q r a s s i o n r a t i o shculd be the first t o f a i l by fa t igue .

Figure 17 shows t h a t t h i s range of load i s accentuated a t If the range of s t r e s s t o which a

Representative val.ues of the crankpin-bearing o p r a t ing character- i s t i c s OF productt.cn ungincs A: B, and C;, obtained from t h e maximum m d m e a n load char t s of t h i s reyort , a r o given j.n t a b l e I .

CONCLUSION

A m c t h d of computing the load a c t i n g on t h e crankpin cf a r a d i a l engino under a l l operatmg cond:rtions has bean developod by use of d3mmsional ana lys i s . By the yrrncLp1:: of s imi l i tude t h e r e su l t s obtained f o r a pur t icx lar ongina a r e r e a d i l y appl icable t o an2 r a d i a l an@.ne having th2 same number of' cyl inders .

Ai rcraf t Engine Research Laboratory,

Clcvcland, Ohio. National Adviscry Clmmitt-:c: f 'n r Aeronaut ? c s ,

22 NACA ARR NG. E B 0 4

APPEITDIX A

NOT AT I O N

C

D

D'

Fc

equ-lval ent - syeed f a c t o r

diameter of b w e , i n ,

new bore, in .

v*otating wei@t per cranlrpln, l b

reciprccat in& wejcht pet' cylinder, 1.b

stroke, i n .

nsw stroke, i n .

equivalent s t roke with standard. bore and equivalent erq;ine speed, in .

r o t a t i n g mass peri crankpin; slugs

i-ecIprccatin;: nas~ per crankpm, sl.ugs

rimber of equally spaced cylinders

NACA ARR No. E5H04

N S

p

i-'m

iiF

M

23

over-al l equivalent engine speed, rg;?l

equj Val-ent engine speed with standard rec iproca t ing weight, rpm

eqirivalent engine speed with standard S t roke j rpm

indicated mean ef fec t ive preasxre, lb / sq in.

nanifolSt pressure, l b / s q in. absolute

iwbbinh frllctor, ( f t - l b ) / ( sq i n , ) ( scc)

c m p c s s i o n r a t i o

crankpin-bearing load, l b

mean ci>ankpin-bearing load Ib

r o t a t i n g inertia force per crankpir,, lb

r o t a t i n g i n e r t i a force per crankci-n, lb

reciprocat ing i n e r t i a force per cy l inder , l b

r e s u l t a n t i n e r t i a force di:e to a l l r o t a t i n g and rocip- rocatin:; mass t h a t a c t s upon c r a n e i n , l b

angles defined in. figure 1

crank angle, de&

angle between axis of cylindor 1 and r e s u l t a n t bearing load i n t h e dxrection of iwt5tion, de3

functions

indtviduiL cy1 inder number

I i

=> L4

N'PENDIX B

NACA ARR No. E5H04

Y E 3 TOTAL IIUTERTIi:, FORCE ACTTDTG UPCN THE CRANICPIN OF A W1.G ENGINE

The arLalyses discussed. i n the body of t he paper u t i l i z e an expression f a r t he r e su l t an t i n e r t i a force ac t ing upon the crankpin. This t a t a l imr t i a force i s the vector 8um of the rctating; i n e r t i a force and t h e individual rec iproca t ing i n o r t i a fo rces f o r each cyl- indel.. The mtatint-j i n e r t i a force per crankpin ITc may be deter - mined from t he fol.lowing equation:

The following expression f c r t he rec iproca t ing i n o r t i a force per cy1inde.t. 7FJ-j."

t40 9 very p g A approxi'mtion; i s giveii I n reference 11 (with a change i n nota t ion)

where F:" i s the rec i .y r*~ca t ing weight por cylinder i n pounds

P rescz t t and Poole ( reference 5 ) give the following equation ( w j t h EL change of no ta t ion) for the r e s d t a n t iner't3a force per 2 rmky irL:

This force is repsr ted t o act along the crank i n the d i r e c t i o n of the r o t a t i n e fc rce Ilc. Therofore. from equation (B3) the oxpres- SLOP f o r the r s c i p r ~ c a t i ~ g i n e r t i a force Wi per c r d q i n is

NACA ARR No. ES04 25

(where the subscript m an engine having nine cylinders). t o compute ana ly t ica l ly the magnitude R and t he d i r ec t ion 7 of the vector sum of these n acceleration f ac to r s follows:

is the number of an indlvldual cylinder of A n ou t l ine of operations required

and where m

1

n - 1

E - 3

e

- 720 + e

2 (T) + e

n

11 - 5 3 (Lo) n + e ( n - 6 ) (y): pim . . . . . . . . . . . . . . . . . . . . . . . . .

2

n

n - 2

3

?+) (F) + e

n - 4 (e) L (321 n / + 8 ( n - 5 ) ( ? ) - + , . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2 - 1) (T) 720' + 9

( R - 1) (?)-- &

(E - 3) (T) - & \

\ I

and where Frn i s the angle between the Y axis (fig. 1) ar,d the c ~ m o c t i r ~ g rod of cylimter m.

26 NACA ARR No. E5H04

The vector eum of the n accelerat ion f a c t o r s given by Prescot t and P e d e (l*eference 3) is compared w i t h t h e exact a n a l y t i c a l prc- cedure fa’ a number of representat ive cases i n t a b l e 11. It i s evi- dent tha t t h e resu l tan t i n e r t i a force may be obtained t o a very good approximation from equation (B3) f o r radial engines having 5, 7 , 9, 31 11 cylinders. endine.

The equation does not apply t o a three-cyl inder

!

NACA ARR No. Ea04

AF'PEXDIX C

27

SPECIFICATIONS OF PRODUCTION ENGImE A

' .

riumbcr af cyl inders . . . . . . . . . . . . . . . . . . . . . . S firranzement of cylinders . . . . . . . . . . . single-row r e d i a l Numbering of cyl inders viewing

anti-gro~e1I.er end . . . . . . clockwise; to2 cylinder, number 1 F - i r b g order . . . . . . . . . . . . . 1, 3 , 5, 7 , 9 , 2, 4, 6, 8

vjewing an t iproyel le r and . . . . . . . . . . . . . . clockwise

Stroke, i n . . . . . . . . . . . . . . . . . . . . . . . . 6.8'15

Direction of' cr.rtnkshaft ro ta t ion

acre, i n . . . . . . . . . . . . . . . . . . . . . . . . . 6.125

Pis ton area, sq i n . . . . . . . . . . . . . . . . . . . . 29.46 Eng3.m speed st take-off, rpm . . . . . . . . . . . . . . . . 2500 Indicated mean of fec t lve Fressure

a t take-off, lb/sq i n . . . . . . . . . . . . . . . . . . . 245 brake mean offec t ive pressure a t

take-off, l b / s q i n . . . . . . . . . . . . . . . . . . . . 200 Assumed mechanical a f f iclency a t

take-off', Tercent . . . . . . . . . . . . . . . . . . . . . 85 Mmif old pessure a t take-off ,

In. Hg absolute . . . . . . . . . . . . . . . . . . . . . 47.5 Com2reseion r a t i o . . . . . . . . . . . . . . . . . . . . . 6.7C Xastcr-rod length, in. . . . . . . . . . . . . . . . . . . 13.75 Art iculatad-rod length, i n . . . . . . . . . . . . . . . . 1C.81

length t o crcvlk tlirow . . . . . . . . . . . . . . . . . . . 4.GG STmk advance (both plugs), d6gB.T.C. . . . . . . . . . . . . ZC!

Intake valve optms, deg A.T.C. . . . . . . . . . . . . . . . 15 I n t d w valve c l o w s , deg A.B.C. . . . . . . . . . . . . . . 44 Erh:iust valve opens, at;.& B.B.C. . . . . . . . . . . . . . . '74 Erh5ust valve c lcses , deg B.T.C. . . . . . . . . . . . . . . 2 5

C r a n e i n d.iamstor, in. . . . . . . . . . . . . . . . . . . :3.25C Effec t ive length of c rwkpin bewing, i n . . . . . . . . . , 3 . 1 1 PrnJostcd crrznkyin bearing uta, sq in. . . . . . . . . . 1 0 , l O

Total w e i g h t of p i s t m assecibly, lb . . . . . . . . . . . 7 . 1 3 Weight of ugycr 2nd of master r.A, l b . . . . . . . . . . 3.36 Weight of E p p r er,d of art1cula;ed. rod, l b . . . . . . . . 1.60 Average t ,o t t l l r w i p x a t i n g w a i p j h t Fe r cylinder, l b . . . . 8.93 Weif&t of lowar cnd of mastor rod, l b . . . . . . . . . 13 .62 Kci&t of crank2j.n boaring, lb . . . . . . . . . . . . . . 1.19 bra!@t of lowdr end of a r t icx la tod rod, Ib . . . . . . . . 1.30 Total trox&t of small rotat:Lr,g ;?arts, lb . . . . . . . . . 1.39 Tcta l r o t a t i n g weight p e r crank7)i.n, i b . . . . . . . . . 32.72

Rat io of rr;zstar connecting-rod

Valve timing:

Rcciyrocating and r o t a t i n g ~0fgit.3:

\{sight of kniickld 1111, lb . . . . . . . . . . . . . . . . 6.675

20 NACA ARR Eo. E5H04

SPECIFICATIONS OF PRODUCTION ENGINX B

AFPENDTX E

29

S.l'ECll?ICATICS OF FRODUCTIOTJ ENGINE C

Number of cylindern . . . . . . . . . . . . . . . . . . . . . . 18 ArY*arqpment of cyl inders . . . . . . . . . . . double-row r a d i a l Bumbor ing of cy liridcrs vi . swing

ant1prop:llor elid . . . . . c3.ockwise; t o p cy l inder of r ea r m w . number 1; odd numbr;rs i n rem row

Firi.nT. o r b r . . . . . . . . . . . 1, 12, 5, 16. 9. 2. 13. 6. 17. 10. 3. 14,, 7 . 18. 11. 4. 15. 8

Direction o f crankshaft ro ta t ion viewing a i kiprope l l o r end . . . . . . . . . . . . . . c lociwise

Bor.e,, in . . . . . . . . . . . . . . . . . . . . . . . . . 6.125 Stroke. i n . . . . . . . . . . . . . . . . . . . . . . . . 6.31.2

Englne speed at taka-oi'f. r?m . . . . . . . . . . . . . . . . 2800 1nd.icated mean otffectivi: pi*i.ssuro

a t take-of 'f . lS/sq i n . . . . . . . . . . . . . . . . . . . 219 Brakt; mt:an e f fec t ive p - e a m m at takv-af'f. lb/sq i n . . . . . . . . . . . . . . . . . . 186

Asaimed mchanlca l cff lc ioncy at tako-off. psrccnt . . . . . . . . . . . . . . . . . . . . . . 85

M m i . f o l d . prmsure at taki-:-off . i n . H& abso:!.utt: . . . . . . . . . . . . . . . . . . . . . . . 46

Cclrnprossion r a t i o . . . . . . . . . . . . . . . . . . . . . . 6 . ;35 Maatar-rod length, i n . . . . . . . . . . . . . . . . . . . 13.937 Arti.cxl.ixtcd-rod lmgth. i n . . . . . . . . . . . . . . . . 10.f;l Ra+u'. o of master connect Ing.rod .

length t o crank throw . . . . . . . . . . . . . . . . . . . 4 . 4 2

Piaton area. ~ l q in . . . . . . . . . . . . . . . . . . . . 29.47

S?ark czdvaqce (both plu@.s). aeg 13.T.C. . . . . . . . . . . . . 20 Valvf.-: . t im€ng :

Intt.k.1 valv. . (2pcina . dog L.T.C. . . . . . . . . . . . . . . . 15

Exhaust va.lvr. c..xns. de6 B . 3 . C . . . . . . . . . . . . . . . . 74 Exhiztlst vclvr: C~.OSLS, ddg 3 . T . C . . . . . . . . . . . . . . . 25

Crm?q!in d.-ianotor, . . . . . . . . . . . . . . . . . . . . . . 5.625

I n t a h va1.v;. Clrjsee. deg A.B.C. . . . . . . . . . . . . . . . . 44 .

Eff ect.ivc 1i;ngth c;f' crwtnkK! i11 .bo.tr':'i.ng. i n I . . . . . . . . . 5"C!3 Fro.joc.tt;d crmi1Tpin b e a r : ng .;l.o.~. sq 2x1 . . . . . * . . e . 1.0, 23 Reci:>rocating and ro ta t ' tns w e i & t s :

Total we.ight of ?.!.ston assembly. 3.b . . . . . . . . . . . . 6:77 Vel.& of u;?per end of rncster rod. l b . . . . . . . . . . . 3 . 3 3 Weight of ii:4Fer end of art'i.culated rod. 1.b . . . . . . . . 1.60 Welpht of lower end of' master rod,, lb . . . . . . . . . . 14.24 Weight of crank.?in.bearing. lb . . . . . . . . . . . . . . 1.53

T o t a l weight of knuckle pin. 1.b . . . . . . . . . . . . . . 0.66

Average t o t a l reci.procat.ing weight per cylinder. lb . . . . 9.57

Weight of lower end of a r t i cu la t ed rod. lb . . . . . . . . 1.39

Welght of s m a l l . r o t a t i n g parts. lb . . . . . . . . . . . . 1 . 7 9 TOlI:'l .?C.<~,.??,G. IJ?i<:i'L >C,:.' . ,. ....... Ib . . . . . . . . . . 3.j . 96 -7.-

NACA ARR No. ESIIO4

REFERENCES

30

1. Burkhardt, Otto M.: On Propcx.tionin3 Engine Bearings. Auto. Ind., vol . 40, no. 1 2 , March 20, 1919, pp. 551-655.

SAX Jour . , vol. 4, no. 4, A y r i l 1919, pp. 216-226. 2. Burkhwdt, Otto M . : Progressive and RotroGroasive Designing.

3. Prescot t , Ford L. ; an& h o l e , Roy B. : Bearing-Load Analysis and

SAJ3 Jour . , vo l . XXIX, no, 4, Oct. 1931, pp. 296-515; Permiosiblc Loads as Affected by Lubrica t lon In Aircraf t Engines. I1 - vol . XXIX, no. 5 , Nov. 1931, p j j . 379-389; diacuusion, pp. 389-390.

4 . Jmnway, Robert N . : Rapid Calculation of Bearing Loads Can Be M;de with Simplified Fo.ms - P a r t I. Auto. Ind . , vol. 64, no, 22, May 1931, pp. 631-1337; Pa r t 11. Auto. Id.:

June 6, 1931, py. 875-979.

5 , S:muols, William: Engine 3em-ing Loading;. Ed.wm4.a Broe., Inc. (Ann Arbor, Mlch.), 1035.

6. S l a w , Milton C., a i d bIackB, E. Fmd: In-Line Ai-rcraft-Engine Bearing Loads. I -. Crankpin-Boaring Loqds. NiXA ARR No. E5Hl0:~, 1945.

7 , Buckingliam, E. : On Physically Sini3xr Systems; I l lua t r -a t ions of tha Use of Xmensiond. Xquations. Phys. Rev., vol . IV , no. 4, Zd sei-., Oct. 1914, pp. 345-376.

8. Brldkgy, I?. V. : Dlmeneional Analysis. Yale Uriiv. Press (New Iinven, , rev. sd., 1931.

10. Gibson, A. H.: Tho Principle of Dynm-Jcal S imi l a r i t y , with Spoclal ReTerence t c ~ Modo1 Expcriments . 1924, py. .3:'7-35?; vo l . 117, Merch 20, 1924, pp. 391-393; v01. 1 1 7 , A p l l 4, 1!j24, pp. <22--423.

Engineel-in(;, V O ~ . 117, liIpXch 14, 1924, pp. 325-327; V O ~ . 1 1 7 , Bki~ch 21,

11. Lichty, L o s t e r C, : Intornal Combustion En&ines. McGmw-Eill Book Co., Inc. , 5th ed., 193'3, p. 453.

XACA ARR I?;). E5H\?4 31.

TABLE I - CRANKPIN-BEARLCXG OPERATING CBLWTERISTICS FOR

NACA ARR N o . E5H04

N

..--_-..-

I

F: 0

-1Nrlr-i r - C O l - l r i d _. . . , I . . G . . .

3 0 0 0 0 0 ~ 0 0 2 0 0 0 1 . e . . o c o o o . . . . .

-- 3 0 0 0 3 rl . . . .

. . . . 3

. . . . * d * d

. . . .

3 L? rl

3 . . .

i m c o . . . 3

. . . n u i u:

. . . oocn c u m

ri ri Pi r - l r l d

. . . 0

N A C A A R R N o * E S H O Y

Rotation

(viewing ontiprcp//cr e&)

NAT 1 ONAL ADV I SORY C W I T T E E FOR AERONAUTICS

f i g u r e 1. - S c h e a r t i c d i r g r r n o f t h e mechanism o f a n i n e - c y l i n d e r r r d i r l e n g i n e .

WACA A R R . N o * ESHOY

U 0 L

L Q c a

U 0 L I L u Y O

,

0 c a Y

ul c

0, + nl + 4

l r ,

-a w w

V

F i g . 2

L 0 * Y c t

N A C A A R R NO. E 5 H G l l F i g . 3

c 01

W 3

.-

L W U C a s c)

L u H

en c .- L V C V e I -

ul u I-

* 2 a < 0 2 UlO - a w w

a 2 " a 0 <LL 1 o w - w c c z- f z 0 u

a a, C

01 c Q)

L 0 *

...

-9) E

N A C A A R R Hoe E S H O V F i g , 5

- R e s u l t a n t f o r c e , I b -O--+--c+ R e s u l t a n t gas f o r c e , I b ----- R o t a t i n g i n e r t i a f o r c e , l b ------- R e s u l t a n t i n e r t i a f o r c e , I b

NAT I ONAL ADV I SORY COMMITTEE FOR AERONAUTICS

F i g u r e 5. - P o l a r d i a g r a m showing t h e m a g n i t u d e o f t h e r e - s u l t a n t f o r c e on the c r a n k p i n of p r o d u c t i o n e n g i n e A a n d i t s d i r e c t i o n w i t h r e s p e c t t o t h e e n g i n e a x i s . € n g i n e speed , 2500 r p m : i n d i c a t e d mean e f f e c t i v e p r e s s u r e , 245 Pounds p e r s q u a r e i n c h : c o m p r e s s i o n r a t i o , 6 . 1 .

N A C A A R R N o * E S H O V F i g , 6

I .

Figure 6 . - Varlatlon of W/p with N2/P for engine A at a compression r a t l o of 6 .7 . For a ~ p l l c a t i o n of this chart t o ather radial engines having nlne cy l inders per

crankpin s e e APPLICATION OF THE DIMENSIONAL ANALYS.13 METHOD TO OTHER m c l I N G HAVING NINE CYLINDERS PER C R A M P I N . )

N A C A A R R N O * E S H O U F i g . f a

h

a Q( 0

0 4 e, fd k C 0 -4 La VI a2 k a 0

fd e, a a al E d 40

8

s . k 0 a a \ cu 2

5 4' B

N A C A A R R N o * ESHOII F i g . 7 b

N A C A A R R N O . E 5 H O U F i g . 8

C .4

a

rl t

Fi ure 8 . - Yaxlmum load on crankpin of production engine A at a compression ratioof f . 7 for valuer of lndlcated mean effective pressure from 0 to 500 pounds per sqwre Inch and values of engine speed Fom 0 to 5000 rpn. rquare inches. (For appllcatlon O f this chart to other radial engine8 havlng nlne cylinders per crankpln see APPLICATION OF THE DIMENSIONAL ANALYSIS METHOD TO OTHER

Effective bearlng area, 10.1

ENGINES HAVING N I N E CYLJNDWS PZR CRANKPIN.)

NACA A R R N O . ESHOU F i g . 9

Figure 9 . - variat ion of G / i uitiirN2/p f o r engine A a t a compression ratlo of 6 .7 . g i n e s having nine cyl inders per crankpin see APPLICATION OF THE DIMENSIONAL ANALYSIS METHOD TO OTHER ENGINES HAVING NINE CYLINDERS PER CRANKPIN. )

(For application Of t h i s chart t o other radial en-

LI a f

N A C A A R R N O . ESHOU Fig. IO

N A C A A R R NO. E S H O U

Crank a n g l e ,

,

F i g . I I I

80*

u Force scale, lb

imep Wean l o r d ( I b / c q i n . ) ( I b )

------+ 0 45,200 - I50 36,500 &---*---a 250 32.000 ----- 350 ao.ooo

NATIONAL ADVISORY COMMITTEE COR A € m U T I C S

F i g u r e I I . - P o l a r d i a g r a m s showing t h e m a g n i t u d e o f t h e r e - s u l t a n t f o r c e on t h e c r a n k p i n o f e n g i n e A and i t s d i r e c t i o n w i t h r e s p e c t t o t h e e n g i n e a x i s a t a n e n g i n e speed o f 2500 r p m and v a r i o u s i n d i c a t e d mean e f f e c t i v e p r e s s u r e s f o r a

. c o m p r e s s i o n r a t i o o f 6.7.

N A C A A R R N o * ESHOY

0

/ooc

I500

1750

325C

F i g . 12 .

I

mglncr A and C

Ehglnc B I \ \\\\\\\ ?orce scala, 16

P o i n t A 0 '45,200 . Y 5 , Z O O NATIONAL ADV I SORY Y 1,300 36 t 5 O 0 C O W 1 TTEE FOR AERONAUT ICs - 150

+---*---+ 250 39,200 32 ,600 &.-A - -p. 350 37,000 30,000

F i g u r e 12. - P o l a r diagrams showing t h e magnitude of the r e - s u l t a n t f o r c e on. t h e c r a n k p i n s o f p r o d u c t i o n e n g i n e s A , 8 , and C , and i t s d i r e c t i o n w i t h r e s p e c t t o t h e c r a n k a x i s a t v a r i o u s eng ine speeds and i n d i c a t e d mean e f f e c t i v e ere$= surea for a comgresslon r a t i o of 6.7.

H A C A A R R NO. ESHOV F i g a 13

.

ant Crankpin -bearin4 ,-r speed N

l t o n t qos - force di'agram

NATIONAL ADVISORY COWITTEE FOR AERONAUT I cs

F i g u r e 13. - G r a p h i c a l v e r i f i c a t i o n t o show t h a t t h e p o l a r d i a g r a m w i t h r e s p e c t t o t h e c r a n k a x i s i s t r a n s l a t e d i n a d i r e c t i o n p a r a l l e l t o t h i s a x i s when t h e e n g i n e speed v a r i e s and t h e i n d i c a t e d mean e f f e c t i v e p r e s s u r e i s k e p t con s t a n t a

N A C A A R R N O * E 5 H O U F i g l IU

lnep Mrxinum l o r d Mean l o a d ( I b / r q i n . ) ( I b ) (Ib)

- 0 95 ,200 9 5 , 2 0 0 -------- 350 37,800 90,000 NATIONAL ADVISORY COMMITTEE FOR AERONAUT I CS

F i g u r e I y . - P o l a r d iagram showing t h e magnitude of t h e r e - s u l t a n t f o r c e on t h e c r a n k p l n b e a r i n g o f p r o d u c t i o n eng ine A and i t s d i r e c t i o n w i t h r e s p e c t t o t h e master c o n n e c t i n g r o d a x i s a t an e n g i n e speed o f 2500 rpm, i n d i c a t e d mean e f f e c t i v e pressures o f 0 and 350 pounds p e r square i n c h , and a compression r a t i o of 6.7.

N A C A A R R N O , E5HO4 F i g . I

NACA A R R N O . ESHOY F i g . 15b

(b) Compression ratio, 9.0. P i p r e 15. - Concluded.

WACA A R R Mom ESHOU F i g . 16a

. - - la) Comprerrion rat io , 1.0. Figure 16. - Yean load on crankpin of production engine A a t two compression rat ios ror n l u e

of indicated mean ef fect ive pressure from 0 to 500 poundn per square inch and values of en- gine from 0 to 5000 rpm. Effective bearing area, 10.1 Square inches. (For applicatl o f t h i s chart t o other radial englnes having nine cylinders per crankpin see APPLICATION OF THE DIMENSIONAL, AtJAL,YSIS METHOD TO OTHER I G I N E 8 HAVING N I N E CYLINDERS PER C F U N K P I N . )

S

on

M A C A A R R No. E5H09 F i g . 16b

N A C A ARR N O . E 5 H O U

m

m u c .- c w

0

IO00

150

1750

ZCKX) t s

a 2 2 0 5 .r a .- 0.

2500 Is

2 75C

39ao

32a

F i g . 17a

I Engines A and c

Engine B I \\\\\\\\ Force scols,fb i

. i m r p Maximum load Mean l o a d

( I b l r q i n . ) ( I b ) ( I b )

4 s 200 4s 200 NAT IONAL ADV I SORY

38,300 30,000

P o i n t A 0

4---0---9 250 c - A - ~ 350

COWITTEE FOR AERONAUTICS - is0 wo : 800 3c:too

36,000 28.000

( a ) Compression r a t i o , 8 .0 . F i g u r e 17. - P o l a r d i a g r a m s showing t h e m a g n i t u d e o f t h e r e -

s u l t a n t f o r c e on t h e c r a n k p i n s of p r o d u c t i o n e n g i n e s A , B, and C , a n d i t s d i r e c t i o n w i t h r e s p e c t t o t h e c r a n k a x i s a t d i f f e r e n t e n g i n e speeds and i n d i c a t e d mean e f f e c t i v e pres - s u r e s *

M A C A A R R N O . E S H O U F i g . 17b l a .-

m* c W

0

,000

i300

I750

2000

275C

SGGC

325t

Engines A and C

I Engine I) Force I ttm scale, lb i

NATIONAL ADVISORY COMMITTEE FOR AERONAUT ICs

Point L 0 U5.200 45.200

4--0--0 250 37,600 29.100 - 150 $0.300 au, ooo c--c-+ 350 35.200 28.U00

(b) Conpression r a t i o , 9.0.

F i g u r e 17. - Concluded. '

N A C A A R R NO. E5HOU

c

, m a

..a

man w . -- .- 0 3

0 . Y

N

b 0 . L

v)

s u F i g . 18

c 0

2 b

In N -

. n L 0 Y 0 cp c c 0

Y 0

L L 0 0

W (I 0

._ m

- W c (I

w 1: .. . _-

m u " c O C C . .

0 o m c h

- 0 0 . - .- .- .a 0 - * . u u - L S S - l . I L L * Y O . .

. C L * f b.- c c .

1- .- 0 c W .- c c . .- .- .

O C C Q

s a v - -

- rn I - n * + . - o n n k

WACA A R R No* E5HOS F i g . 19 -

Bore, in . Figure 19. - Variation of specific bearing-load factor with bore.