CHAPTER L I r!'RODUCTION
January 20 1975 1 ·8110,9
!~]11 QI fQ~1EB1£
CHAPTER L I r!'RODUCTION PAGE NUMBERS Scope l 2. Ge n eral Consideratio ns 3. Vibration Ne.:isurement Insti ·limen t at:i.on CHAPTER 2, SYSTEM ANALYSIS 4. Genernl 5 . Dr ive System Torsional Evnlua t ioa G. Torsional InaLability or·ve System Be n ding 8. Installed Engine Vibration 9. Inlet/Exhaust Disto rt ion 6 CHAPTER 3, V I BRATION HEASUREHEN1' EVALUATION LO. G€mn'.'al 11. Analytical Method 12. Fatigue lest Method Figu1. ·~ 1 I Figure II 12 Figu r e III 1.3 Tab1e 1 Percent Occurrence Table II Determination of Se r vice tife 18
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PB:ge iii 8110,9 Cit.\P'l'ER l - 1.:-rRODUCTION 1 . SCOl E The procetlu n,~s desc d bed i n th i s ha nd book p ![, ,v10e informatio n an th( vit,r.:ition ~rnbstantiation .:rnd f.::iti&t•I.' st:rl' g h (•Valu.atio n of pc.,we r crnns ois:;i1-•ns .
~. GF.~tR..IJ.. CONSIDERATIONS.
a. The rower r:rans,nissicn sy:s tern bei:,.ecn the engine a:nc! the varieius other rc,tnttng co111p1~nents o - an oircr.:1ft, (such as a helicopccr VTOL or S'l'OL) may lrnvc many modes of vibrncion , som.e o[ which may be of n h~za ~cus nntu ·e. I hc power transmission could alter the vibr~tional ch~rncter~s~1cs ~ f the bRsic engine to the extent th~r rhc vibrational d3tn d~t r':rl · neu dudnG engine cer~i hc.:::i~ion m.'.ly nc longer bP. aprilicab l e .
h. v-bration in the power transmi~sion system ~an be the -es~-t of engine C:Ncit.1:::irm , aerodynamic: e:~cita~ion , and [ nechanic.al exd tation . It can occur either du ring a teady s ta e or tt" , 1trnient orrnration . \./bun s~n~11::-engtnc inst:a 1ations arc involved variat~cns 1n both r-c- •,1cr .:md ~. ~.m. nre 1rapo r tan t . In multi-e n gine ~r IDUlti- r otor ins~allat1ons, ho~ever, not: only power ancl .L p . m. b~ 1 c also phasing of t he engines an c!
rotors should be c.onsicle r ed to dete r mine whet h er maximum ·,d.bnition uccu rs under 1.n- pr:.'lse ~r out-of-phase 20:nb1.natio n s .
c . E~ch branch of tho drive sys t em should be investigated for both t Qr sional ~nd be n ding type o[ vibration. In reciprocating engine ins t al lations the powc:r trunsraissiCJn system vibrational spectrum !Tla)' be between O and 1 ) 000 cycles per second. ln t u rbine angi ne installa t ions the upper end of the v1bration spectrum could b~ co1~id~rably hig h er if the exci-ation originates in the engine . Certaia modes of ibra tion can be inves t igated and substan t i~ t ~d by ground resting of the compla t e power ransmissicn system or cum~one n ts the r eof . Othe r m odes 0£ vibration, l,,lherc: t.hc excitation does not occur during gr'-lu.nd (Jp~ni tions, shou ltl bf: i m ,· es tiga i: ed f n flight untler the maneuvers that: [ltTJ1.1c1a: the ·;i brat Lem, d . Th~ drive system is "!; esponsi . ve to engine, mechanical. and nircr;:iit ~c r adynamfc farces p~i~a~ily bec;:iuse the various branches of tbe sy5 tem possess certain natural frequencies . R~cona n ce may occu r in t hese branche~ when e~-.c i ta t ion freq1rnndes approach or coinciclr with t he n~ ura! frequ~ncy of the branch. Yhen a compla~ drive syste~ is in resananc~, Che cowpleL syst•m is involved, ~ot ust an indivtduaJ
portion. Each branch ~r ~ system becom~s 1mpo r ~ant wh e n tnves t iga t ing
the •,dhr;iti rial r,;isponse of "he s.:-st m, liowevet'. sorne modes of vib r a· t 1c,n ol .:i complex system may be raore pred'.Jminan in certain bnmchci., Iher~fore, all bnmches l)f the system should be investigate d .
~. St r ess nnd/cr ~mplitode m~asurements on the saoe br~nch of the system rnny ba nacc5snr>· t ev.1luatc the vibration ch.,rncterislks of the power transmission system clurlng ~Jl n~rm~l or~~oting ao n ditions.
Jam 1 ,1ry 20, 1975 8110,9 Eoch b1::mcl1 o.E the system should be invcsti~.1te.d by measurement un less th~r rr.cans ar found m:~c.eplab le. Me~rnurernent s fl.Jr c. ri tic.al sp1rnus ;.n bcrncling (whirl mod.?) made on sha[tin~ sec:~ions~ such as the tn. il rottw 1H int~rc,,nnect£ni.; ~h~fL~ , should include dctermin~tion 1.:1£ thl· ZL'l' {r~quency co,np ,nenl~ sirtce Lhi: &l1,1It met.il does nol ex 1' ·Ti nc-c ;i revers.a o! o;i:;reia;.!'I but 111ere ly .:in · ncrease in steady stress.
foT a pe£fectly bal~nceJ drive shaft, it is possible _ go chrough th~ cricic~l ~h1rlin£ speed withnuc detectin• its location unless the shnfc is desplaced from its nnrmal undeflEcted ~0~1tion. Once .!eflected, ho~~·.t1 ..:r, it c.=:o. remain deilec!:~d i.-C!g8rdlcss ti± speed.
f. Vibrntions encciLLnc.er!i!tl during t:t:1lnsient ope1·ation o.E ,1 sys i:em r.'la)' bE': m~r ~ impm:t;mt th.1n s te<idy 5 t.i te vi b?:","ltions. Even though the tre:ns ~ it=nt ru..:ir 1a!lt f.::ir only a r.1:l~ ivcl, few c.ycle:s, th~ :sr;ress~s m;iy be of such magoi ude as _c, cause fatigue da:r.,o.ge . In helicopters, such tr .1nsi cnts can occur during clutch engagein.!nt. or discngHgam-nt re covc rJ' from ;.utorotation, :st.uting of the engine, etc: . For other tlri\:e s,stems such .:is SIOL or VTO_ aircrait, transition from verti c.::;.l tci hor · .:ant.al £Ii gh L or other fl 1.ght m.ineuvers m.iy be i nvolvetl.
Where multi-engine or ~ulti-driv.e sys t ems nre used, phasing of the systems ~~y be important, with i~-phase excita~ion being gross1y di fforcnt th~n ou t - of -phase exci tt.tion. It t he design of the system cloes not control such ph .. sint by locking the sys tern in a single relationship, all pcissi ble ph.ising should be e:-:.:mri net!, Where a po rtion of the sys tern incorporates a be It dr{ ve the flexibility of the belts and belt tightness aLe important. Belt designs incorporating iater woven st.eel .Jr me t.:11 cables will have a different rigidi::y torque - wise ~s compared to an all-rubber belc systom . Changing from one
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be 1 t type to :mo:the r may a 1 ter the vi br ation.i 1 ch:ir .ac teri s tics .
J. 1/IBRATIO:' HEASIJREH!::NT KSTrtlNEi'!ATION ~ - The electrical s rain gage has become the mos US4fu1 tool or de i:erm1 nint h vi brat i ona 1 ch,::ir3c t:!ds tics of po,.;er tr.:ins,n· ssion s. strms.
Signuls genora~ed by these transducers atL2chad to the pa rt under in vestigation ctm be .Eed into sui tab!. sign.oJ conditioning equipment nad hen recorded on a multi-ch~nnel device, This e qu ipment can provide stress, amplitudet frequency and phase relaL1onsh ip ot any instant of time. Tn this reg~rd, it is impottant to be a~~~e of the 1·m·ta t1ons of th~ equi~mcnt and h&ir possible effect on the accu racy of men~urem<:!nt.
b. It is ,;_,,s.i.rable to loc~te the. strain gage ,'11. t:he p-oint of grc.icest stress Co provide m~xjmum gnge rc3ponsc, hmiever, in many c~ses th is is impossible: due to component geometry. It th~n bccome;s necessary lo de ermine the stress re la tion..sl1i p be twe:en lhe point where the st r:i in g.ige is 1oc.:itecl -and the point oi max:lmurn stress. Stress ev.:ihrntion of: the part using c:on'lcntional technirjues s 1 Jch a'9 st i:ess coat. photo elas tic 5 trcs s an{! ys 1 6. or other rne l hods <:.Jo pl;"ovidr: th is stress ratio, Stresses measured dudng the flight ~tr:iin .·;rnrvey may then be adjusted by tba:se stress r.:iUos t:u pr0v,dc the higl,cst st r ess to which the part is exposed.
Ch:ir, 1 Page 2 P:1r J 81!0. 9 January 20, 1a75 CHAl:'TER 2 - SYSTEM ANALYSIS ~. CENt:RAL .
,\ Jynnmic .:,nalysis can help to ide n tify criti.:al vibration modes and es t-im:1tc the vibrn t ory response unde r t he most serve re condi t ions th at wl.)uld proOably occl•r. This ..:rnalysis is useful i n d efi n ing the i ns tr ume n taticn needed to invest1gate the power tr{lnsmission system .
5 . DRIVE S\'STrn TORSIONAL FVALUA'rlON .
a. A Pl.'W~r tt·ansmission sys t em is made up of a combi n "1tic>;t of concentr~ttd masses c<'nnected .:ogether by a number of differe nt flexible units. The r:,asses may be in the form of rotors, flywheels, gears, cooling fans, engine componen~s, clutch units, e t c.; while the flexible u nits arc the sha{ t components~ such as the main r otor d r ive shaft, tail ro t o r drive shaft , fan drive , inte r con n ect in g dr:i.ve shafts, et c. Any dy n~mic system has 3s many possible natural modes of vibratio n as it hus combinations of masses and stiffnesses. These natural modes of vibration do not result in potential problems unless the natural. fre quency of a vibt'ation a,ode coincides with an exciting fo r. ce frequency .
Since the dy~amics of the sy ste m can react in either a torsiooJl or bending directioc on its c omponents , this at leas t do u ble s t he nu mb er of critical vibration condi t ions that ca n r esult i n poten t ia l dyoamtc probJ.ems in the transmission system . This is one of the reasons fc.r the need to measure both bending and torsional vibratory s tr esses i n (:ach branch of the sys tern . Si n ce thes~ natural modes of vib r atio;.1 ca n be excited by ei t her steady sta t e or t ransient opera t i ng ccod it io n s, nn inves t igation sho u ld t,e made for al 1 condi t ions . The t ra ns ie nt s can be due co various operating conditions such as changes from one 1'rerati ng regime to another, power chops, ~ust :i.oaclir.g, maneuve rs , etc,; whereas , the steady state operation in·,olves s tabilizied rpm , power, er ni r sp e ed .
b. With these potential prob l ems in mind, the evaluation should begin with a det,riled dynamic ~naJyc:cs of tl e i,ngine/drive system/rotor systc:n combination using measu r ed or calculated m.tsses ::in d' spring rates for each elcn,ent of the system. The number of torsional raode·; to be onalyzcd would depend on the c omple x ity of the drive system; ho w ever , for the conventional single main roto r hail rotor helicopte r , the first four modc.s rr.ay be al ch..iL are of interest. More complex dt:ive.
systems require considerably more analytical work which c:m best be h.1ndled by a computer which is prograt1111ed t,ith a :nathem:itical model of the ,Jynamic system. The analysis should defi ne the natural freciuency for each mode, th" mode shap,:, , and the rela t ive torsional deflection throughout the system . A conesprmding study of the engine, :he rotors, c~uplings, unive r sal joints, r~ns, accessory drives, gears , control devices, ate., is required to identify the vibriltion excit.:i t.ion sout'ces ;:incl t h ci-r f r eque n cies, most of which vory di r ec t ly with rot.:.or o r engine rotational speed . f.. cross p l ot of cxci t i ng f r equenc i es Char 2 Page 3 ?;, C 5 8110. 9 J~nu~ry 20, 1975 ant.I che z;-esunan c:ondi ~ions wi 11 de .Ei ne the cri ci cal vi bra ti (In crin tl i ·ons. Also tho ~nalysis will establish che nodes and anti-nodes fwhid, · n urn h lp de fine che type and sens· t:ivity of the inst ·u ment::.ition to be used, ro:r example, strain gages should be placed ;1t or c: lose to nodal points where mmcim1..rm stresses occur. Tm:siographs, .:icc1.::lerome ters and velocity pickups should be placed at nnti-nodal points where rna.·imorn deflection occurs, Of equal imporLanc'i!, an analysis highli~hts he probnble significant vib at·on phenamen~ to be expec ed and provides sufficient insight i.nto the chive system res pens s ta cnab c the evaluator to quickly and accu ri:i te ly c:lassi fy the au tpu t of the inst rume nta ti on.
c. 'Ihe analysis can be exte ded to cover r:insmiss·on ge.ar teeth contact frequencies ,,,hich must be compared t.ii t-h tc rbi ne blade and disc ree o nan t frequency <lat a ( obt ai natl ho:n th11 engine manufacturer) • Any coincident frequencies should be avoided or substantiated.
d. Since ach engine is COl)Gidered ;:is one branch o!: the drive system, the vibrntion cnv;i :r;onmcut of its dynmr.ic cor.1pooents including accessory dri v~s, w · 11 differ from that which was subs t nntiated und~ FAR 33.
This new v·bra ion environment should not . be dam3ging to ·he engine, and the eagine manufacturer should bE encouraged o _ovestignte and st.bstantiate this. An acceptable alternative would be for the air- fr arne rnanu fac turer ta forward his vibration investigation d;:ita to the er-. i ne manufa.c turer. The re,1;u 1 ts of the ~ngi nc. m;,mufac ture 1· 8 n!vi 12"-'
cou'd either confirm the a·rworthiness er the combination or define
special te.st:s to establish this objective. Advance coordin.ition hE tween the: engine manufacturer and the .airfram0 manufacturer is rec:om meruled to maintain s om~ uniformity in the basic test par :;irne l:ers and method of me ssut"emen t ~ o assure the desire(! cr::irapati hi Ht)' of vi.b!',ati on data, 6. TORSIONAL INSTABILITY, a. Some torsional ins tabilil::y can be expected with £N•ernor c.cntrollecl engines. Ynis phenomena is exhici ted as a low frequency tors ·onal oscillation . It occurs when che foel control governor system h.:is a respons~ rate close to the first or second dri\e system to~sional natural frequency. In the extreme situation, this coupling of the exciting force (torque a.sci l lation.s responding di1:ecLy to the fuel control) and the drive system r son.int requency can become di ~:r n::ont ant! dest ·rut: tive, 'T'hc de::-· gncr should de c. nni n· ar ly in I h development pro~ram the probable fi~st nnd second naturnl or resonant frc~uencies of the dynamic components including tbe co pon~n s 01 the cngin~ 11rectly coupled to tha dTive system, the engine mauufacture should be able to provide data on the fuel control response rate, I~ frequency coupling is apparent, redes·gn e( orts by either or both the airframe manufacturer and the engine manufactuter arc rcquir~d to pro- v·de a suitable combination, he reoesign may consis of chans..as lo chap 2 rnr 6 Pager.
8ll O. 9 J:mu:ir:,, 20, 1975 ,woid frequency couplios or impro,:ement in the dempinc characteris ti.cs o f the' S"StCffi , In either case, changes L.:o ch~ fuel control are usu~lty the most prcductive.
h, The suitability of the fi n ~] configur'1tion should be demonstrated by test. 'rhc test pr ogr:im should include cyclic inputs of the collec ti ,1c, anti - torque, eye 1 ic, and most imfdr t:mtly, Lhe fuel o r gover ncr control av.:1ilable to the crew. Frequency of control inp~t should be ::is close as possible to drive system reson:int frequency. \,hile the U$C of mechanical connol inputs is desirable, reasonably good
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test re5ults cao t,e obtained by pilot inputs, although several at tempts m"y be necessary to achieve a meaningful test. Input ampli tud<'! should be a.:lequate to obtain a meaningful record .
c. Instrumentation requirements may vat"y widely with drive system com plexity . Some typical examples arc: torsionally oriented rotor mast strain gages, engine fuel nozzle pressure, engine torque signal, gas generator tachometer, control displac :mient indicators, e· tc .
All parameters should be recorded or. tape or by oscill3graph in order l o detcrmin~ the ph~se relationships of tl1e measured porameters '3nd Lo establish that th~ oscillacory inputs from the controls damp im mediately and at an acceptaule rate.
7 . DRIVE SYSTEM BENDING .
a . Shaft bending in helicopter drive systems falls into two categories, one that is associated with whirl modes, ~hich is essentially zero frequency, and the other that is associated wilh thrust forces at the unsupported end points of the drive system. The component of the cl'tcust load normal to the shaft produces a bendi.ng load, which for two bladed rotors, wil 1 vary, depending on whether bending is measured in - plane with the rotor or perpendicular to the ro t or .
Both conditions should be evaluated . Cyclic bending of shafting also occurs with the use of belt drives, certain gear arrangements, etc., which produce loads normal to the axis of the shaft.
b. Th~ critical (resonnnt) rotncional speed sh~uld be calcula t ed for each segment of shafting. Calculation methods should employ con servatism and should normally show large margi:1s with respect to any rotational speed to be expected. Ovcrspeeds m~y occur during trans ient or speed control failures. Exceptions to this ac~cptancc crit eria would be sh~fting which is designed to operate super-critically, ipc . , a~ spc~ds above the resonant f r equency of the whirJ mode .
Special precautions are in order in this case to insure accurate bal:mcing , relatively high shaft stiffness, reliable support bc;irir.gs nnd shaft protection horn exte~nal forces or druMge inducing conditions >ihich will affect shaft balnnce.
Ch:ip 2 Page 5 Pri r 7 J,nu:try 20, 1975 6110.9 6. UlSTAt.LED ENGit."E VIJ!RATION.
a. Airworthiness ~bjcctivcs in this areo reGuirc that the ~nsine b~ installed and mounted ln such o manne't as to ins11re that external vi bra Lory i nputs tr ansmitted to tho cng; ne ~:,iough mounts and other ;ittach poin t s arc within the limits establi~hed by the engine man· ufa ct urcr . The combi n otion of engine mounting and a ir fram~ vibr$· t io ns inhe rent i n a rotory wing oircroft will produce on cnvi ronmm,t which j ustifies investigation and evalua t io~ .
, b . The cngine manufacturer h expected to est ablish vibrator)• lim! rs for ;ill engi ne co~Fonents and to define t h~ basic instrumentation to det terminc compliance with these l!~its. Usually, the limits or~ defined es an allowable combination o! frequency and a~plitude, or, "10ra simply as an allowable acceleration . The instrurnent~tlon would con· sist of various transducers 1110Unted as presc ri bed by the engine 1t11n· u[aerurer to measure motion in three planes .
c. The test pr og r am should explore- the comple te r ange of r otational speeds of tr.e drive system, both coupled to the engine and in auto rotation . Engine scart nnd acceler:ztion should be examined, and speed/ power s:;~eps shouid be conducted over the expected operatinfl range.
I n soma instances, r oc orc r ~ft center of g ravit y wi ll aCfect test rn· sul ts. Mu lti -engine rotorcraft test progr ams shou ld consider com· binations of inoperative englne(s) and une q ual power from the engines.
Preliminary re>Jiew of the data shoul d be accomplisne-l 3nd any un· usual or raargiaal vibratory condition should be reexplored in rlijtell .
9. INU:T/ElCl!AllST D1STORT10S .
a. The basic pur pose of inlet distc tioo investigations is to establish ~hat tu~bine engine compressor b 1des ore not excited ac reson~nt frequencies by circum!er~ntinl ~nriations in air inflow to the engine.
Ideally, this would be est~bl1.shed by strain gag., ,:,eoscromcnts of comptessor blades during in-flight t:1aneuvers of che al.re-raft under cvatustion . 1n pr accice , the cngtne manuiacLurer detemines cxp~ri mcntal ly the corapressor blade response t o pa rt ia l inlet blu,,:k~gc duri n& test stand r•,ns . Differe nt tlockage patterns arc, used lo ex• cite higher o r ders of inflow distcirtio n and frorn th is basic Lnform11 t ion the engine manu fac tur er cn n determine Lhe tolerance a[ hid comrr~ssor lo in!low d i scurbances. Th,; nlrfranoe manufoccurnr ca n tlrnn moflsure inflow disturbances which c.1n be cumpa red with the distortion limits established by the cngin~ m,inufnclurcr .
b. Instrumentation for tn<?asurin& the inflow disturbances should 1>rovhle data compatible with the pnreffll!ters established by th<! engino manu facturer . These parameters usually involve differential ;iir pressure and are measured by nf.l)tiplc or"ficc p ress ur e probes inSt3llcd directly ln front of the engine eomprQssor. With this insrru~£ntacion lnst~llcd, the aircraft should be flown through its complete flight envclo~c.
Chop 2 P11r 9 8110 . 9 J~nu ~ry 20. 1975 ins ;me s, the engi.n , , nufacturer ir.ay sp cify a particular ut ti 1 • hich _c itl'H!l "insures th:1 ;iir!:"low tc- the corr.
ss~r is no scorted beyond compressor oler;:in es . In _h sc c.iscs. no .iirfl · disto rt ion s by the ;:iitfrnma manufa,::,tu'l:'.1.:.r ar~ r 1uircd.
d, EKh us t gas flew do-flections ,uuocia ed with sever~ duct section dis c ntinuties can r su1t in c:,i:h uat sas pressur rcflectioms bnck nto the turbine s tagea. These pres u e re flee tions s be cv _ unt d for po·si le turb·n blade '-'ihr.1 io , "rrie ecnginc nufacturer is he source o~ hi information and d ,1 regarding C me4Sur:c::.en , nd interpre t ation o: this cond'tion.
Ch p 2 Page 7 ( nd 8) p r l
CHAPTER 3 - VIBMl'ION ME.ASURE1'1ENT EVAUMTION
J~nu~ry 20, 1975 8]10.9 CHAPTER 3 - VIBMl'ION ME.ASURE1'1ENT EVAUMTION 10. CENER.t\L Sev~rr1 ..:>f the pl:oblern.s d f.scussed in Chapters 1 ::.ncl 2 can be eval1H1l:ecl by str.'light forusJrd comp;i:-ison of measured or cnlcul.:11:etl lo.1d.s \..iith firmly est:iblished limits. Among these are torsional inst.!!bi it:y, inst;;lled engine: vibration, tnle t/ exlrnus t disto rt ion t and transmission ge.ar tooth excU:ations. Other vibratory phenomena such as drive s. stem torsion and beu'l.l i ng requite special ev;; lu ~ tion tec:hr.iques. Thes If! techniques fa 11 in to I two b-asic cntergories the analytical method or filtigue test method.
I These m ~hods are briefly discussed below; however, use of this informa tion obviously must be. su ~p lerrnmted by iaxperiencE .1nd by guidance from t he extensive text book and handbook data .;!vai l.!!ble to vibration and . atigue investigators, IL !.'\J ALYTIC,.L ~IETHOD • . 1. It is recognized th,:;it:, if olJowable s tr ess levels ,1re estnblished by acceptable means, and the stresses measured during groun<l ~ml flight conditions are lower than these est~blishe.d levels, no fatigue tesc· ng of actual parls is necessary .
~ . At this point it is appropri,ate to discuss !'~t ·guic subst<1ntiation of ge~rboK components ocher Chan critiral components~ such ~s the msia roror shaftJ which should have the same degree of structurnl relia bility as the main rotors. Components sucb as gears, geDrshafts, and be.a:rings do not readily lend themselves to evaluation by flight strain
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survey data, Fatigue margins of safety mQy be comruted for gears .and gea r sh.J"fts. Analysis of t bis type should, whe r e ,1pplic::ible. con sider the simultaneous appl"cation of co bined stresses involving axial bonding, and torsion loads in conjunccion with steady state and vi bratory loads. Equations used for ~1is purpose should be based on a theory of failure appropriate for the component under ct.'lnsiclerat:ion and consistent: wich good industry practice. In this regard. accept.
able standards fot gear design are published by t!:Je American Ge~i: }1 anu fac turers Association (AGHA) , ?ost i ve rnargi ns o £ .s.i (et;• compu tccl by the_ nbove techniques intli cate infinite 1i re .for the part. and therefore, no fur t.her fa1lig1Je evnluation ~ •ould be required. Conversely, ncgtit' ve margins of ~are ty indica e a fi.ni e life which should be established by fatigue tests of actual p~rts.
Fatigue e•,ahi ati on of bearings should be based on acce pt,able indrrs try standards such as those publ "s!1ed by the Anti-Friction Be~,.ing MAnu faeturers J..ssociat .; on (AFENA) Be.'.lrings used · n nort-r.edundant er~ t · cal applications mrry aeces :s i ate s peci.:1 l se lee: ciun c r i l- ria ,. · th tcspecc to tolero1ncos an(f tr1rn.erf als.
Ch:tp J p,,.ge 9 Par 11 Jam.rnry 20t 197S 6110.9 ti. For L' thcr p.:ir ts a me thud, s oroewha t similar co the one d~sc ri beJ :for gears and ge rshafts in Para. 2b, is bas don the use of the modified Goodma11 c:fiagr · m, This method is also cons iclere:d acceptable for est.ab lish i ng an allowabl~ stress level as follows; (lJ Estil:1.;:i:te the meo 2ndur.mte limii: of the part from test -results of specimens witlL simil.n: stress coru:entrations, ""he test: speci men r:n.:lter:i al should be representative of the actual part and suf ficient t~st data should be available to substantiate the can endurance limit. The estimate should account £or surface condi tions, fabrication methods, fretting, chafing, size and shape effects, as well as diffore~ces io stress concentrations between the test sp cimen and the actual part. Referring to figure 1, the me.:in enJurance Hroit may be represem:ed by -a scraigbt line dr awn through the yield stre£s (point A on the hotizo tal axis) and the m,'!ximul'!l oscillatory s i:resi. ~.,hich the :.ive rage s pec.imen can with s ta~d at a given steady s~r.ess (point B) without fRilure for 107 cycles to S X 10 eye les depending on the l'l\l3 teri al. (Alumi num would require at least SX 10 cycles).
(2) A fm:: tor of saft:! c:y of 3 should then be applied to the mean endur
ance limit so that the slope of line AC would be 1/3 of line Aa
(3) If the flight strain measurements indicate ~hat all of the opera ting stresses fall below the operating boundary line (AC), no fatigue testing is necessary. When the m.::asured stresses are above th~ oper~ting boundry line, however, fatigue testin~ of the actual pa~ts ahould be co~ducted .
(4) Limitations of ti,e nnalytical , et:r.od: Caution shoul<l be exercised in the i!pplicatiou of the method aboveJ particul3rly when the .following ·tems are involved: (a) Large partJ ln proportion to the laboratory s pee imens .
(b) Irregularly shaped parts cont.1ia.ing numerous or superi m posed fillets, holes 1 th~cads~ or lugs, (c) Parts of unique design for which oo past service experience is avai ·able, {d) Parts subject to fretting or chafing.
(e) Eoltcd or. pinned connections.
Chap 3 Page 10 Par 11
J. nuat • _o, J97S
llO. 9 {MAX. 0SCI LLATORV STRESS} u, h'.]
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~ C (YtELD STREss, A STE ADY STPE SS FIGUR E I 12.
'Ih · fat!.gL.e. strength ,md rot,:n: d-ri .. ~ ""f5 ltl'JY b determi ne d in appri pri C)ry tests. These t cnnclucc:ed in S1Jch a mann c prt'l.l...1cc \•alid faitigue tr •n h tl,1 ,1 for the componen in th• en·• cf both steady Qatl osci]JnLory lands s thl:!y are geneni ~ed hy h r r:mnponc n ts o:t the ro tllrc: raL , N ma l practice is t o obtait\ au a:! i nt: .spccimeo failures to enabl lh • t·valu n or to cstabl!sh a t ti iti~ lly volid S-N carve a~ shown l1 1 Flgur~ II c each steady load sel•cl J .
b. 'Iheo establishment o involves testing .i u icl n nl.lmh~r r f parts at t:~e s~ s t!y tr .sn l~vel am" varyiag l !! O' d lln or: s ress. Thus. in F gur II, if a 2 ,.;: tead)T ~ tress lcv~ l A .,nd :m oscl ] la ory stress of level B. th~ part is tested u II fni ur , ilurc occur ng at i; cyc. lcs, pain on lhe S- • curve Ior !. [ld • ,, U! , Ol lev~l A is deten.ii ,ed. Adi iona oints on hes - : reprcs ntin 4 s CJdy s ress of le .... c. A r.t.1)' b d cnninrd by c.hoDSing a differ•n o c.f.1l4r y r.h p J P,1r 12 P,1 C l] 110,9 art t.o fai ure. lf no fa:lure ec:c:Ut."" for .:it t.et: 107 to 5 X 10 c.yc les, depending on
•
consi<lcred to ha ... e irainite li fc a . that 10000 lSOOO U1 Ln ...J 16000 0:: ~ IJ'l Fotigue e~t D.:::i ta 14000 >-
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rc-d1.1ction (as roqu;red Y
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I V, to a5sur ~hot fci!u re I I I Nor1-f 8 rrous is. • xtr rn ly remove) Fer roLJs [ . I I rna te,1c l m at errn / ( (Sx l 0 ) I
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I N NUMBE~ OF CYCL ES FIGUP.E 1 1 .reau :; ·c Cat:i.gue testing, a arge number of <11i.r:nb e 1n establishing each S - 1 curve. H~,..oer.
ford th cost and i necessary to ob a n of four tes s pecimcns: lilhic.t- wi 11 the '"ange uf osci a:.ory stress er•ic is c .sirleietl acceptabl~ in e-t~b c:urv , l,c lenst one t.:e·t specimen sb.ould !'lurvive th , r~qu red o Jcfine ~ofini e :ife. n order to cat C.[ 1sso ia ec 1..-it tat gue tes ing. t-he an •duecd b" aa .ip?top.riat:e factor. his :ict:or · • f!houltl be ba::~d on the type of materinl b t; cd pnst • c v · c · v.p r l ~m: with the materi ;:il ~ and type of design.
Fer crt~ic 1 c mpon nt , Yh05e fa: lure may be catas tr ophic, the teduct on ·ncco shoulti b 8 l•ct d to ssure ch~t t:be prababili y of ailutc s ex. r mcly r St icll1 methods ~re useful 1n this ,aspect of h h(I c th · res u 1 ing rnduccd curve shou lei b in flu Chap 3 Pnr 12.
Jsnuary 20 1975 S!l0,9 encec: by typic.Jl ptablished S-K data fo r the m.iterial, iJnd c1l1 of the tef: t points shou =d f al 1 above t:he reduced cut:ve. This c::u rve "'10U ld then rep~csent the S-N cut"ve for use in determining the f.atigue lives.
igurc ~l repiesents this method of constructing A typical S- N curve basi?d cm te.s.!:: specimens . A se1rnr~te :>-N curve should be es ' t.ablished for each cd tic a.l te:ady s tt"ess 1e ve1 de l:ermined in the fli gb t strain me asur M · ment survey. lf it is desired to limit the fatigue tests, a single S-N c:urvc t-'tsed on the highes t measured steady stress :nay he usccl in the fatigue life c;ikulat.iocs. iiowever, if this approach tends l:o 1.mdu . ly limit t.hc _atigue life, ~ family of curves rnay be developed from two es ablished S - N curves b~;' means of Goodman or .similar di.a.g1;ams or !:ly r~tionnl w£thods, ti. '!'he r ducr::ion factor Il'.J)' also be based on s atistical .1Jnalysis of the failure data rrojEcted to ~he number of cyclas associated with infinir::~ life . for !:lie particular material. The .shape of the curve drawn tht"ough oach data point is ob tained ~rorn experimentally der:ived constants ,ippro'.)5. rate for the material. The mean enduranc limi c is the statisti c<1l aver.c1ge of the curves projected to L07 or 5 X 107 cycl~s. T he working S-N curve wotild be established at 3 standard deviations below the mean \'.a lue c?S shown in Fi.gu re I I.
(5-N Curve T ypi ca I for a Ferrous Mafe: ria 1} 20000 18000 Fai lure Points I.fl 16000 V'i Projected Dato Points w a:: 14000 i V1 12000
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NUMBER OF CY CL'ES FIGURE UI Cr!ap 3 l] Par 12 P.'.lge J.\1.nuary 20, 1975 S l l 0. 9 c. Using the S-N <l~ta obtained above and a know l erlge of strasses imposed on he co::nponent by flight and gruund cand · tions, tbe fatigue life limi ::ation if .i. plicable, can be est.iblisbed using one of the cumula tive dam~·~ theoric:~ available from cunent literature cm th.is subject.
An cx-1mple of this, using i' inen: s theory, is shol-ln tie law. Note that flight conditions which result in tresses belo~ the endurance limit defined by the S-N curve ai:-c considered t o have na effec on the fatigue life of the componenl under ~valuation.
..
same e cakulatiun based on s- d;,ita; The Cumula ive Dam~ge Hypothesis states that every cycle of stress above a1;1 em1m;,mce limit produces darn.age prapartioaal to the ratio of cycles run at: tha stress 1:0 the fatigue lif at tha stress level. Thus i£ a part is subject to random lo~ding for n cycles at a stress level of S1 nz cy1ces at S i cycles at S · ' and so on~ ,:ntd if N , Nz, NJ at'!.:' the n cor1;espcmdin,g 6.uraber of cycles !o f.ailure for each stress level then fai ure t.::i 11 occur ~-ii ti- the: summation: Using this expression, the calculatad service li fe of a par t subjectEd ta ra~do m loading c~n be derer ined if the percent of life used per hour at each dam~ging stress level is known. The percent of life used per hour at each damaging stress level, can be expressed by: (1) where 1 - pe rcent of 1 ifc. used per hour at the damaging stress level; a percent of tot a operatiag time al lotted to the flight condition during which the damaging sLress : eve! ~as recorded: N -= total number o • cycles o f the da~ging stress level at t'ai h,rc; an<l n = number of cycles he damagi s-ress level occurs rer hour, T us, the calcul~ted service lifc Le of a partic u lar part of compon ent subjec to a random nu mber of damaging stress levels, would be: 10(1 ; '10 (2} /, .=- -·-- -- . l1 - l1 · 1 1··.,.J , ::'i1 chap 3 Page 1 Par 12 8110, 9 J~nuary 20. 1Q75 A sample c~lcul11tion illu~tratins this method for determining t:he calcu Jntcu service li Le is shown in Table II. In this cx.imple. the peak ste~dy nnd vibratory stress levels nssociatcd with each maneuver have been ns:sumed to occur for the duration of t:he ma n e:u·;er (colum n s 3 a nd 4). In ::idd it ion, the eye 1 es of oscillatory st: res s per hour a l!J' o has been conser v :i ti ve ly assumed "lt the maximum level thro1Jghout the flight spec.Lrum (columa 5). If this procedure te n ds to limit the service llfe unduly. it is acceptable to use the actural n1easured strt"ss lt•vel r.!ist:ributi ons if proper .:1ccount of r,oss'ible v;iriations is pt'ovided by rcpe;ited mamwvers.
The number of cycles to failure for each damaguig stress level (coh1mn 6) was determined from Figure II. As an extimp le, consider flight condition IJ(c) of Table II. The percent of total op~rating time (a) considered at this maneuver is 0.5 perc~nr, the damaging oscillaLory stress level i. s l !J, 5CO p~ i, the numb~r of eye les of damaiing s Cress pc r hour (n) is 23,200, and the number: of cycles to failure (N) f.rom the S- N curve (Figure II) is 3,200,000 cycles. Then by equation (1) the percent of Jife used per hour at this damaging stress level ~ould be:
l = ~!! - 0.5 ;,. '.!;1 ,1)[1f)
N_- 3,~00,UUU =o_nn:K~ The smr.Jnation of the i nJi vidua 1 pe rc1.mt ages; of life u.:.ed per hour for each d.::imaging stress level is shovo1n "in column 7 of Tabk II. Therefore, b7 equation (2), the calculated ~ervice lif~ of this part would be: 100 _ ~-051 hows l.= l.:1L-0,15'1S!) ~ A summary c1f the measured stress and peri::ent life used at the various L1 ight conditions should ba aub1ci tted with the fatig1.1e r;.?v.aluation r,rngram in a form similar to Tab l e II.
Chap 3 P.ag~ 15 Par 12 Jnnuory 20 , 1975 8110 . 9 TAllL& 1 Percent Occurrence<, I. GROOND CC!':DITIONS ········· ··----- -·· · · - · · -··------------ - -····· l.5 (n) Rapid increa,;e of rp,:, on ground to quickly cngnsc clutch- - 0 . 5 (b) T;,:,.Hng with full cyclic control-------------------· ······ . 5
(c) Jump t~kcoff ··· · ··· ··----··-····- ···· - - -·····-·--···· ···· (1)
(d) Grcund·ol r·grc1:nd eye le····· - ------ · · ·· - - · - - · • - ---- ··· ···· (1) II . HOVJ::Rl!,G- ·-·· -··· · · ····· · · •• --·-·· ·· · · ·· ·· ·· - · ----- - ----- - -- • · ··· 2 . O (a) Stc~dy hovering----·······-·· ···· ·· · · · ··· ····-·--i---·· ·· · .5 (b) Latornl reversal ··· · · ----------···· · ··-············· ····· · . S (c) Longitudinal reve r sal·····-···· ·········· ···-········ · · -· · . S (d) Rutidor reversal ···· · · ····-··· · ··· ·· · ·· --·--··········· ···· . 5 Ill. FORWARD l'UCHT·PCMR o:;--·······-·· ····· ···· ·· ··--······ ····· ·· - 67.5 (a) Lc'.'c,) flight - 20:., \'~,.. -· ·····-······ ···· · ····-·-···· ······ 1.0 (b) l!!\'el (light · I.Oi,, \'~:i;-----········-----·-········-···· ··· 3 .0 (c) tcvcl flight - 60% V~------···· ······· ··-----····· ····· ·18 , 0 (d) Level fiight · 807. \' . • ········· · ·· · · ·· · ··-············· ·25 . 0 (e) Ha>d,...,m level flightNitbut not greate r than Vi,.t:)··········15 . 0 (!) Vim--·-···· · ·· · --·-·········-···· · · ····· ---·-·-···· ··· ···· 3. 0 (&) 1117. VE······-· · · · · · ··-····-· ·· ···· ····- ----··-· ·· ··---·- . 5
(h) Right furns · :J 60 90~ V ---·--···· · ·· · ····-······· · (2) J . 0
(i) tc(c turns • 30 , 60, 9!Ji; fN&- ········ · -· --··········--(2) 3 .0 (j) Climb (Takeoff power)---·-·-······ ·· · · · ·· ----······ ····· · · 2 .0 (k) Climb {}lax , continuous po..,er)··· ·· ·· · · ·- ----·-··· · · · · · · ··- 1..0 (1) Change to auto r ctatio~ from p~wer-on·flight 30, 60, 901; "!\1::· ··· -··---···· · · ····· ···------·-· ·· · ···· l.!i (c) Partial power descent (including condition of zero flow thr~uzh rotor) ···· ··--······ ··· ···· -· ·------···· · ·· ---- 2.0 (n) Cyclic and collec t i.,e pull·up frora level fllght···-·· ··· ·· (2) (~) Pushovers····· ······· --·-···· - · · · · · · · ··· ·----······ · · ··· - - (2) (rl Gusts····· · · ··· · · ··· · ········-·· · · ······ ······-······· ··-- (2) (q) Quick StO~S-- ····· ··· · ···-------··· ········ ····--··-· · ·- ·· (2)
(r) Flores---···· · ·······---------------··- · - · ···--···--------(2)
(s) Later~! reve r sals at Vn·····--------················ · - ···· .5
(t) Longitudinal reversals at Vu·-· ········· --··---···· ··· ···· .5 (u) !tudder reversals at \'; --------- ······ - · ··--·--····- ······· .5 (v) Landlnr, appro3ch ··· ··-·-·-···-···· ··· -· · · · ··-·----······· - 3 . 0 (x) Sldew~rd !light · · · ········-··············--·-·······-·- ··- . 5 (y) Re3rwaro flight··············--·- · - · ·--·--·-----····· ··· ·· .5 lV . AUIOROTATION • POWER O FF ·---·--········ ···· ··------·-••······-··9.0 (a) Stcndy forward flight--········-···············-·-··-·- ··· 2 . 0 (b) R apid power r e c ove r y from ou to r otatio n al flight··· ·····- ·· . 5 (c) Right turns - 30, 60, 907. VNE · ·· ·····--- --·------······(2)1 . 0 (d) Left turns· 30, 60, 907. VNE ·· - ·····- - · ------····· ·· · ·· (2)1 . 0 (e) Lateral reversals ·· · · ·-·········- · · · -·-------····· ·· · · · ··· .5 (f) Longitudinal r ev e rsals······· · · ··· · ··-- -- - --------· - · -- · ·· . 5 (g) Rudder reversals--··········· · ····· ·· ···--···-·-········ ·· .5 (h) Cyclic and collective pull-ups····· · - - -----········· ·- ··(2) Chap 3 Page lb Pn r 12 SI 10. 9 January 20, 1975 L~nding approach---------------- - -- - --- -- ------- --------------2 .0 (1) flbres - ---------------- ----- ------ -- ----- - ------ -- -------- -(2) (j) 100.0 One fhght every 10 minutes with less frequent rotor stops.
(l) (2) A ve r tical load factor frequency curve should be developed tha t is represen t ~t i ve of the more critical t ypes of operation. Ihe time spe nt in each turn should be odjuec~d to give the specified per cent of occurre nce.
NOTE: Extensive adjustment co lhis table is oomally required to closely appcoximate ,he cocorcraft under evaluation .
Chop 3 Pogc 17 Par 12 J.anun '/ 2U, l 'J75 s H).
TJ LE II
s 6 1
l 2 Cycles o P rc~nt of F3ilurc Li{e Used p ,. ;hour : u)---- 0.5 1~00 ( J---- .5 2100 (1: ---- • 5 2300 II(aJ--·- .5 2 00 3,000,000 0 . 002.32 (li ---- . 5 800 .3,200,000 (~)---- .5 10500 .. 00362
(d)---- .s 3400
Ill(n)---- 1.0 &300 (h)---- 3.0 •.'.HOO (c)---- 8,0 7700
Cu)---- _5_0 a100
....
(e)---- lli,Q 8350 16,000,000 0 . 0217:3 u ;,...
(£)---- 3.0 8200 8,400,000 ,00522 u (g)---- .5 9100 7, 00,000 ,00b7 (h ---- 3. 0 -1: 11200 2.li.00,000 .02900
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(i)---- 3.'0.. ,... 11 00 2,2.50,000 • 03093 M N 2,700 000 I (j)---- 2.0 ; 10900 .017 9 (~)---- .0 ...i 9°00 !.., 0,000 .02203
<•>---- .5 7 00
< )---- 2.0 ,oo
I ,800,0Q .0 I 3 (n)---- 1.0 9/00 (o)---- .5 7800 (p)---- .5 7000 (q)---- .5 7300 (r)---- .0 6700 (s ---- .5 700
(:)---- .s 7900
!IV(n)---- 7100 ."400.000 .002 2
(b ---- .s 9700
6 300,000 .00383
c~>---- .o 93 o
(d ---- .0 9JOO ti. 00.000 . 0058 (e)---- .S 6800
(£ ---- .s 6100
(•)---- .5 5900 (I)---- l.0 7600 (j)---- 2.0 7900 TOT,\T.S '--='1 ~oo~.-=o:---!-----11-..;..;;.~--1--~--+-- - ---t--. l---,,5-2-8 - -9- Ch.i p 3 Pnr 12 .I,