ML20100P264
| ML20100P264 | |
| Person / Time | |
|---|---|
| Site: | Shoreham File:Long Island Lighting Company icon.png |
| Issue date: | 09/17/1984 |
| From: | Sunny Chen POWER & ENERGY INTERNATIONAL, INC. |
| To: | |
| References | |
| OL-I-018, OL-I-18, NUDOCS 8412140090 | |
| Download: ML20100P264 (57) | |
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DOCuTiNG & h s I Crankshaft Torsional Stress Calculations p *CEERANCH 16,8 M j for 8 L 17x21 Engine-Generator Set O s m D CCNSUL.TANTS D
D CRANKSHAFT TORSIONAL STRESS CALCULATIONS FOR 8 L 17x21 ENGINE-GENERATOR SET
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8412140090 840917 PDR ADOCK 05000322 G PDR BY Dr. Simon K. Chen
> July 19,1984 i
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TABLi 0F CONTENTS -
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SusaECT .....................................................
1 SCOPE .......................................................
EXECUTIVE SIM SRY ..................................... ,.... 2 6
)
SUmutY AND RECOMENDATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . g. . . . ,,
3 ,y ETH005 0F CALCULATION ON NOMINAL TORSIONAL STRESS .g
/ b.T.
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RESULTS ANO DISCUSSION .......... ~ ... 7' W- g. . .~1. -
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AP PEND I X . . . . .~. . . . . . . . . . . . . . . . . . . . .~. . . . . . . . . . . . . .~. ..... ... 18 I. . Tnna. s.~,-am g --
) III. TORVAP Program Inputs and Outputs l IV. Torsional Stmss at Rated Condition for Second and Third Modes per TORVAP R V. Reference List
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- I Crankshaft Torsional Stress Calculations July 16,1984 for 8 L 17x21 Engine-Generator Set Page 1 l j
CONSLA.TANTS SU6 JECT
)
Independent calculations are presented here concerning the torsional character-istics of the Shorenam TOI inline 8 cylinder,17 x 21 engine with replacement crankshaft. The rating of the engine is 4889 hp at 450 rpm. The corresponding beep is 225 psi. The TOI diesel engine is used as the prime mover to drive a 60 bz electric generator, rated at 3500 kw at 450 rpm. The diesel generator system is required to serve as the emergency power system for the Shoreham ,
Nuclear Power Station. The replacement crankshaft hcs 13" main and 12" crank- 's
)
pin (13 x 12), the failed shaft has 13" main and 11" crankpin (13 x 11).
SCODE
) .
In October and November of 1983, PEI consultants were asked by LILCO project management to evaluate the suitability of the TOI 81.17 x 21 engine with re-placement crankshaft (13 x 12) for service intended at Shoreham Nuclear Power
)
Station (SNPS). A preliminary analysis was made and it indicated the new . .
I placement crankshaft was satisfactory and passed the OEMA criteria for sta-tionary applications. The old crankshaft (13" x 11"), using the same analysis
) method, did not satisfy the OEMA criteria when the tangential effort (Tn) of the gas pressure, as listed by LLOYD2 references, was used. In February of
'984, LILCO project management requested more detailed calculations for the
) replacement crankshaft. This report serves to finalize the updated torsional calculation on the repla' cement crankshaft.
- 1.
- standard 'ractices for low and Mediaan Soeed Stationary Olesel and Gas
) ges.sinanitton, ate,aieginean.fam,ers4.,xiat-em.
- 2. *t.loyd's Register of Shtootng:* Guidance Notes on Torsional Vibration Charactart stics f Main and Avat1tery 011 Engines.1976.
Power are og incometerw inc. AC.1C64 SSS W Ave. Geoc, wt 53511 GCE/383-7C71
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Crankshaft Torsional Stress Calculations July 16, 1984 i
) for 8 L 17x21 Engine-Generator Set Page 2 l CCNSUL.TANTS EXECUTIVE supeWRY,
) 1. The replacement. crankshaft (13 x 12 ) is suitable for the intended ser-vice. The name plate rating of the engine is 3500 kw continuous at 450 rpm.
- 2. The replacement crankshaft satisfies the OEMA stationary engine crankshaft
) standard practica design criteria, which are:
- a. to insure that no harmful torsional virbratory stresses occur within five percent above and below the rated speed.
- b. for crankshaft made of conventional materials, torsional vibratory ,'
8
) conditions shall generally be considered safe when they induce a superimposed stress of less than 5000 PSI created by a single order of vibration or a superimposed stress of less than 7000 PSI creata '
by the sununation of the major orders of vibration.
- 3. The general method used in this report is based on:
) ~
- a. the conventional Holzer-table forced vibration method.
- b. the advanced hannonic synthesis method (modal sigerposition).
TORVAP, a coninon-domain torsional vibration analysis computer program, is employed. Program TORVAP R deals with natural frequency detennination forced virbration. TORVAP C deals with the harmonic synthesis methods to de-tennine the vibratory amplitudes and torques of masses and shafts that have
) been specified by the user. TORVAP program has built-in assumptions on magni-fier factor (a= function of damping) and on tangential gas pressure effort, based on user's input on horsepower, nm, and mechanical efficiency.
)
- 3. *I0rsional Tibration Analysit Pr"3qrane (TORVAP).* Cctreuter Aided Oesign.,
) Centre. *4eingley Ac4o. Camortdge, ut CH3 CHS. June 1975. Avat14 ale.
frQe Comsnare [nC., Anft AMor. ?tiCntqan.
Aower one Eg ntamecomes ec. Ac.1C64 SSS L.swton Ave. Sect. WI 53S11 8C8/382-7C71 h
J-e 3 A E I Crankshaft Torsional Stress Calculations for 8 L 17x21 Engine-Generator Set July 16,1984 Page 3 CCNSL.A.TANTS SUPNARY AND RECOPNEN0ATIONS 3
- 1. OEMA STATIONARY DIESEL STANDARD The TOI 13 x 12 replacement shaft meets DEMA crankshaft design objectives and criteria. The maximum single order torsional stress at rated load 3 (3500 kw) is at shaft section 9-10, close to the drive end. The maximum sum of orders torsional per TORVAP C is 5101 psi at shaft section between cylinders 5 and 3. All single order and sum of orders stresses are belcw ,
DEMA limits.
DEMA Limit TORVAP R TORVAP C Single Order 4.0 Order 4.0 Order 5000 psi 31% psi 3455 psi OEMA Limit TORVAP C TORVAP C
! Sus of Orders SRSS Sam of (6) 7000 psi 3763 psi 5101 psi l 2. ALLOWABLE SPEED RANGE There are no dangerous torsionals predicted in the speed range between 95%
and 105% of the synchronous speed at 450 rpm. The following results show that the highest torsional occurs at 95% rpm. 225 bmep. This is a lug-down condition. In this series of calculations, bmep is kept constant at i
225 psi, which is the rating.
h- Constant 225 Breo 1 I
Sum of Orders l Rom Sinole Order Shaft 6-7 Shaft 9-10 472.5 4010 psi 5490 psi 5673 psi 3
l 450.0 3455 psi 5101 psi 4900 psi 427.5 3071 psi 5627 psi 6232 psi power are Ermorgy ec- me. AC.TC64 SSS Lawton Ave. Geoc. WI S3511 SCS/362-7071
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3 p E I Cranxinaft Torsionai Stress Caicui.tions for 8 L 17x21 Engine-Generator Set auix 1e,1984 Page 4 CCNSULTANTS g 3. OVERLOAD CChSIDERATION The replacement crankshaft is safe at 3900 kw overload at 450 rpm, the maximum stress of single order is 3740 psi at shaft section 9-10, the TORVAP C sum of order torsional stress is 5401 psi at shaft section 6-7.
Single Order Sum of Orders SRSS Emeo Shaft 9-10 Shaft 6-7 Shaft 9-10 251 3740 psi 5401 psi 4030 psi ,
. l 3 Please see page I-2 for snaft section numbering system. f
- 4. SUITABILITY FOR USE Based on this detailed analysis, torsiograph data at Shoreham, and E .
guideline, the shaft is adequate for the intended generator service for tne SNPS. If this engine is a marine variable speed engine, the engine should have barred speed notice in the 410-430 rpm range for continuous operation.
D No barred speed notice is necessary for generator application.
- 5. CHECKING TEST DATA LILCO has requested FaAA and SWEC to obtain actual dynamic torsiograph data on the replacement shaft. This analysis checks within 14% with those I
test data. This reasonable amount of the discrepancy could be att. ..:ac to the following:
D a. Experimental error - 10% to 15% is considered acceptable.
- b. Tn assumption - PEI uses LLOY.0's Ta'ble as included in TORVAP software.
- c. Magnifier factor assumption - PEI uses built-in TORVAP software.
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3 P E I Cranashaft Tors 4enai Stress Caicuiations for 8 L 17x21 Engine-Generator Set Juix 18, 1984 Page 5 CCNSUL.TANTS
- 6. PREDICTION OF OYNAMIC TORSIONALS_
O TORVAP C is capable of: a) Prediction of the dynamic torsional stress vector of each mass and shaft section including amplitude and phase angle, b) Sumation of the torsionals of all modas.
The good correlation of TORVAP C dynamic results on free end amplitude and the dynamic torsiograch test record, taken by SWEC on January 8,1984. '-
demonstrated as follows. Twelve (12) order sum simulates even the c) I 9 details very well, l
TORVAP C Simulation On Free End Amolitude vs. Shaft Angle.
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.L 0.2 Se9/01, 4" Evaluation of Emergency Oiesel Generator Crankshafts at Shoreham and Grand Gulf 3 Nuclear Power Stations," Failure Analysis Associates, Palo Alto, California.
Maren 30,1984.
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J a p E I crankshaft Torsicaai seress caicuiations for 8 L 17x21 Engine-Generator Set auiy 16, 1984 Page 6 .
CCNSul.TANTS ,
METH005 0F CALCULATION ON NOMINAL TORSIONAL STRESS g
- 1. The analysis method is based on the vibration theory and experience 5 TORYAP', a Torsional Vibration Analysis Program, was used to check the following:
- a. The natural frequency and torsional stress of the engine generator 8 system for the first three modes, per TORYAP R program.
- b. significant orders at.the free .
The end amplitude of the crankshaft, sum of six per(6)ORYAP T C program.
- c. The shaft nominal torsional stress for all modes of 34x (6) .
significant orders, per TORYAP C program. ,,'
D Only results on those crank sections close to the drive end ar=
reported here.
- 2. The shaft nuntering system and mass-elasticity staulation data useo are shown in the following.
I cytteders Gear 1 2 3 4 5 6 7 8 F1p&sel Generator M M I
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47.9 47.9 47.9 47.9 $0.1 1100.0 2658.8 Imertia 6.4 49.2 47.9 47.9 1 2 3 4 1 6 7 8 C11 tneer 4 5 6 7 8 9 mass 1 2 3 0 00000000 10-11 '
17 14 44 14 67 74 8-9 9 10 Shaft f.?
K 18.1 M.1 M.1 H.1 H.1 M.1 H.1 H.1 16.9 p
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- 6.
- Torsional vibration Analysis Program (TCRVAP).* Coreuter Aided Cesign Centre. .ua dingley Road CAmridge. UK C33 CH8. June . 19 7s. ,
power are Eg ccameccre ec. A C. tC&4 555 Lawecys Ave. ,secc.wt53511 6C8/362-7071 e
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l Crankshaft Torsional Stress Calculations July 16,1984
~
for 8 L 17x21 Engine-Generator Set Page 7 ccNsut.TANTS RESULTS AND O!SCUSSION D
- 1. NATURAL FREQUENCY AND SYSTEM SIMULATION The natural frequency of the system is 2323.3 com for the first mode, 5575.2 cpm for the second mode, and 7000.4 com for the third mode. The results are almost the same as TDI and FaAA's calculations. PEI used the same inputs to simulate the mass-elasticity shaft system of the subject
- 13 x 12 shaft. The comparison is as follows.
Natural Frequency, Cpm .
Mode g TDI PEI FaAA First 2323.3 2323.3 2323.8 Second 5575.8 5575.2 5576.4 3
Third 7000.2 7000.4 7002.0 The resonant rpm of each order for each mode equals the natural frequency, 3
dividad by the order number. Only those orders with resonant frequene' around or lower than rated speed are investigated. For the first moc they arv 4.0 order resonance at 581 rpm and 5.5 order resonance at 422 e r .. .
The replacement (13 x 12) shaft has a 9'; higher first mode natural fre-quency than that of the old 13 x 11 shaft, as shown in the following:
PEI TDI Shaft Calculated Test 2323.3 cpm f 13 x 12 ---
) 2129.8 cpm 2146.0 cpm j 13 x 11
\
6 *Torstograon and Shaft Aseit tude Tests." Stone and Weester Engineering Corpora-tion for Long Island Lignting Coneany (LILCO).
power ene energy mcarnec.ones inc. Ac.1C64 555 L.swvton Ave. Geot wiS3511 sce/362 7071
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O O Crankshaft Torsional Stress Calculations July 16, 1984 I for 81.17x21 Engine-Generator Set Pa;e 8 :
CCNSt.A.TANTS
- 2. SINGt.E GRDER NOMINAL TORSIONAL STRESS O' The major order (4.0) causes torsional stress of 3146 to 3455 psi range, at shaft section, between cylinder 8 and flywheel, at the 225 bmep. The single order stress is increased 15% when the engine is running at 1055 rated RPM.
4.0 Order Stress at 225 Bmeo O
BMEP RPM TORVAP C TORVAP R psi Saeed Stress Stress 225 472.5 4010 psi 3698 psi 225 450.0 3455 psi 3146 psi g {'
225 427.5 3071 psi ----
The figures compare favorably with DENA's allowable torsional s**
O of 5000 psi for a single order at rated as well as off speed c;
- Engine manufacturers customarily calculate the single order torsional stress caused by the first mode resonance. This is the TORVAP R program.
This first node, 4.0 order torsional stress is 101 smaller than that
- calculated per TORVAP C for all modes also shown above.
O Another significant order, the 5.5 order, increased dramatically from 1390 csi at rated to 3294 psi when the engine speed decreased to 427.5 rpm (95% of rated). The resonence 5.5 order torsional stress is 4793 ps,i at 422 rpm (93.7% of Iated speed). This resonance torsional stress is still below the OEMA single order limit of 5000 psi.
3 5.5 Order Stress at 225 Beeo TORVAP C BMEP RPM Stress, 225 472.5 898 psi O 225 450.0 1390 psi 225 427.5 3294 psi 225 422.0 4793 psi O : \
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- l Aower* end Ermegy ecomec.ones ec. AC.1C64 555 t.ewton Awe. Soot. SDS11 SCG/362-7071 e . , i.'
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-4J July 16, 1984 O Crankshaft Torsional Stress Calculations Page 9 for 8 L 17x21 Engine-Generator Set CCNSLA.TANTS
- 3. SUM 0F ORDERS NOMINAL TORSIONAL STRESS
,0 Two methods are used to calculate the sum of order torsional stress. The TORVAP C method which provides a true stan of orders for all modes. The other method is the " square root of sum of square" or SRSS method in con-junction with the TORVAP C calculation. TDI uses the SRSS method. These torsional stress values are compared in the following table.
Shaft 6-7 Shaft 9-10 Rating True Sum SRSS True Sum SRSS 225 bmep, 450 r 5101 psi 3375 psi 4900 psi 3763 psi
'O These figures compare favorably with the OEMA limit of 7000 psi for the sum of order torsional stress. For off-speed (95-105% rpm) fixed rack (constant 225 bmep) situation, the sum of order (true sum) torsional stress is calculated for those shaft sections from Section 5-6 up to :r..
drive end (Section 9-10). The comparison can be shown in the following graph. It seems that the highest stress occurs at 427.5 rpm, 225 bmep O . condition.
Torsional Stress Along the Crank Sections at 225 beep.
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4000 67 79 89 4 10
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power and E% reameccees cc. AC.1C84 555t.awcon Ave. Sooc. Wi S3S11 SCS/382 7071 i
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O o P E I Crankshaft Torsional Stress Calculations for 8 L 17x21 Engine-Generator Set July 16, 1984 Page 10 7
3 4. COMPARISON OF TORSIONAL RESULTS_
TORVAP C i's furnished to us by Comshare and is only capable of calculating the sum of any selected (6) orders. PEI designed a subroutine to combine This is (2) sets of TORVAP C outputs to get the (12) order sum figures.As the results accomplished to further improve the dynamic simulation.
show, the true sum of twelve (12) order provides a' marginally higher 3 nominal torsional stress level, and it does improve some of the dynamic details when the torsionals are plotted versus the shaft phase angle.
Comparison of Torsional Results l3 Amplitude f 1 Shaft No. Stress in psi l 5-6 6-7 7-8 8-9 9-10 Free e Item l
f -.44, 4a98 5101' 4941 4568 4900 0.56 ce9 TORVAP $ 6 .
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0.59 deg.
J-*J4 4982 6020 5493 5002 5238 TORVAP S 12 3512 3664 3763 0.39 deg.
SRSS of 5 6; 3187 3375 IO
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Torsional stress 56 is the sum of orders for 0.5,1.5, 2.5, 4.0, 4.5, and 5.5. 56 is the highest at shaft section 6-7 at rated condition.
3 Torsional stress S12 is the sum of orders for the above, plus 3.5, 5.0, 6.5, and 8.0. 512 is the highest at shaft section 6 .
At rated condition, the twelve (12) order sum gives 0.59 degree, 0.03 degree larger than that of (6) order. SRSS figures, on the other hand, are inherently lower by a substantial amount. They are included here to g check with the historical values used by the industry and that furnished i by TDI. .
PEI believes that the TORVAP C, used together with the PEI subroutine, is l
' the state of art torsional simulation program.
3 Aower em Erergy memcap ec. pC.TC6d SSS t.*wton Ave. Beos. WI 53511 eCS/3sa-7071 s'
O O July 16,1984 Crankshaft Torsional Stress Calculations for 8 L 17x21 Engine-Generator Set Page 11 i
5 .' COMPARISON OF FREE ENO AMPt.ITUDE There are now several sets of test and calculated data on free end amplitude taken on both the 13 x 11 and 13 x 12 replacement crankshafts at rated con-ditions. TOI's torstograph data shows three to five amplitudes of selected orders and the corresponding SRSS value. SWEC test report shows a full q
v array of the free end amplitudes, and its corresponding true sum results (0.69 degree). The experimental spread was 0.55 to 0.69 degree when several recordings were studied.
Originalf TDI Tests $WEC Test FaAA Calc [C TDI Test SWEC Test Date 1/8/84*l l
- I/8/84e 3/30/84* 5/19/84 9/28/83* j 12/12/75 l9/19/831 j 13 a12 13 a 11
~
I 0.5 0.10 0.06 0.07 0.07
- 1.5 0.17 0.21 0.17 0.18 0.14 0.21 l 2.5 0.12 0.12 0.13 0.14 0.11 0.15 .. .
0.07 Q 3.5 4.0 0.36 0.35 0.06 0.33 0.06 0.34 0.05 0.31 0.43 0.46 l 4.5 0.06 0.01 0.07 0.14 0.12 5.0 0.12 0.03 0.03 0.03 0.04 l 0.04
, 5.5 0.13 0.12 0.12 i 6.0 0.01 0.01 0.01 0.07 l E.5 0.01 0.01 e.05 0.'"
8.0 0.Gr
$25s 0.43 0.45 0.42 0.42 -
0.40 0.50 0.50 {
t True Sua 0.55 - 0.69 0.64 1 0.59
- Shoo Test for Gulf States $N-74038, overall ser meter
~ Shoo Test for E00K-ETElt. SM-74038 overall per meter l
Fo- the 13 x 11 shaft, the SWEC as well as TDI test data shows around 30 -
' 40% higher 4.0 order amplitude than that of 13 x 12 shaft. This indicates 1 that the 13 x 12 shaft stress level is indeed significantly reduced. For ,
the 13 x 12 shaft TORVAP C true sum amplitude checks well within the ex0eri mental spread of the SWEC test. In addition, TORVAP SRSS result checks within a few percent of the test data furnished by either TOI or SWEC.
i 4
- Evaluation of E:nergency Otesel Generator Crantsnafts at Shorenam and Grand Gulf Muc!eer Pomer Stations.* Failure Analysis Associates. Palo .
. Alto. Calt fornia. Maren 30. 1984 . . .
- 8. *Fleid Test of E:nergency Ofesel Generator 103.* Sereal and Mall.: Stone and weester Engineering Corocration. Figure 8-33. Feeruary. 1984.
- 9. *E:nergene/ Otesel Generator Crannsnaft Fatture Ineestigation therenam *
)
muclear Pomer Station.* Fatture Analysis Associates. Palo Alto. Califor.
nia. Octooer 31, 1943. +
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e fEUureP W efiSPgy rtCerPleCaories irsc. ps C. iced SSS Lauwton A Seunt. WI S$11 SCS/~3SS 7071 1
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e A E I Crankshaft Torsional Stress Calculations July 16, 1984 Page 12 for 8 L 17x21 Engine-Generator Set cess.A rm
- 6. SINGLE ORDER TORSIONAL STRESS ALONG THE CRANK SYSTEM _
TORVAP C is capable of calculating torsional stress for every shaft section, and for each significant siagle order input. For the major order (4.0) of an eight cylinder inline engine, the torsional stress increases as it approaches the first mode nodal point, which is located close to the flywheel end. For the subject shaft, both the 4.0 and 5.5 order torsionals are highest for shaft section 9-10. The 1.5 and 2.5 5 order torsionals are higher at shaft section 5-6, and decrease drasti-cally along the shaft section toward the flywheel end. Some integral orders, such as 1.0 and 2.0, on the other hand, provide additional " nodal" points along the shaft, as shown below. This figure substantiates the importance of using the modal superposition principle to predict shaft stress for all shaft sections. TORVAP R only deals with orders having a .
g first mode resonant frequency close to the rated engine speed considered. g' Stress Distribution For Individual Orders At Rated Conditions 3500 3"55 (PSI) o b
h 2500 -
h '( s, 1500 . NN Le 4 %, g
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power and Eg rent.cnes ec. AC.1C64 555 t awcon Ave. Geoc. wt 53511 BCG/362 7C71 h
) _
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_ , 1 3 July 16,1984 r
U l! ! Crankshaft Torsional Stress
" ' " Calculations ' '
r CONSU.TANTS !
) COMPARISON OF GAS PRESSURE TNIGENTIAL EFFORT Tn
- 7. i I
The TORVAP program has a built-in gas pressure tangential effort (Tn) data For this analysis, base software for each order, based on Lloyd's table.pm and mechanical efficienc
)
only horsepower, displacement,Several sets of in magnitudes used by TDI and FaAA to be input.
pared with Lloyd figures as follows: l Llovd T0! FaAA Source TDI 10 ,
19762 19836 1984 ,
) - Order 1973-749 k 11.0 88.5 155.9 0.5
- 95.4 106.9 1.0 90.1 129.5 112.3 1.5 19.0 74.5 122.7 2.0 -
20.2 62.0 71.7 77.0 2.5 51 . 2 51.4 ,
3.0 -
) 41.5 42.8 48.0
- 3. 5 16.7 4.0 13.3 32.7 27.7 ' 35.6 25.3 23.8 26.2
- 4. 5 9.9
) 5.0 7.3 19.2 17.4 14.7 12.8 15.5 5.5 5.7 ,
4.2 11.3 5.7 6.0
) 6.5 3.3 9.0 4.5 2.7 7.3 3.7
- 7. 0 2.2 5.9 3.1 7.5 o 4.7 2.5
) 8.0 1.9 _t 10.
"Eiolvtton Of Emergency Of esel Generator Crantsnafts At Shorenas And Grand Gulf Nuclear Power Stations.* FaAA,Acril 19, 1984 Seoc. wt S3sti sos /3ea-7C71 -
Ac ** ere ew etar*wcerw m. Ac.9C64 SSS Le Ave.
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0 A'E I crankshaft Torsioaai Stress caicuiations for 8 L 17x21 Engine-Generator Set auiy 16,1984 Page 14
/
CCNSul.TANTS S This comparison shows the following:
- The set of Tn figures used by TDI in 1973-74 correspond to a very (
low imep (20 psi) level, as compared with those listed in Lloyd.
p
- Lloyd Tn figure for the 4.0 order is 10% higher than that used by
'd TDI in 1984, and is 8% lower than used by FaAA.
- Lloyd in figures for lower orders, especially those 0.5, 1.0, 1.5 and 2.5 orders are lower than those figures used by either TDI or FaAA. These lower Tn inputs could explain why TORVAP's sum of orders torsional results are somewhat lower than those of FaAA.
- O - Lloyd in figures for the 6.0, 6.5 and 8.0 orders are substantially i higher than those used by TDI. These higher Tn inputs explain why some of PEI's resonant critical stresses below rated rpm are sig-nificantly higher than those calculated by TOI.
O Lloyd Tn Table is based on many years of industrial experience on comercial engines running at a range of imep levels. The table is based on a representative comercial engine, and therefore, should be most acceptable for the purpose of predicting torsional stress levels for satisfying codes and design standards. The dynamic torsional amplf-tude predicted by using this set of representative Tn figures might not O exactly reproduce the dynamic test data of a particular engine in question. To reproduce the test data more exactly, a carefully measured indicator diagram is required.
Lloyd's Table does not take into account the difference of engine desian and operating parameters, such as:
3
- degrees of intercooling
- operating fuel-air ratio and turbo match
- injection timing
- machanical frictions, etc.
Power
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5 A E I Crankshaft Torsionai Stress Calculations for 8 L 17x21 Engine Generator Set July 16,1984 Page 15 CCNSut.TANTS
) 8. MAGNIFIER AND OAMPING FACTORS The magnifier assumption is built in the TORVAP software. It is a function-of the equilibrium amplitude G . The magnifier factor is a re-verse function to the damping factor. Most engine manufacturer's prefer to use their own test-proven damping relationship, in order to achieve a !
close check between the calculation and test results. Without this design
). and development background, PEI uses the TORVAP magnifier assumption as is.
l l
The comparison of TORVAP built-in magniffer factor and that used by TOI is ,
shown in the following table.
) COMPARISON OF MAGNIFIER FACTOR USED :
Order -TOI TORVAP %
4.0 16.6 17.3 8%
) 4.5 15.2 29.8 961 5.5 28.4 28.8 2%
6.5 28.3 32.0 145 8.0 28.5 27.0 -61 !
)
The comparison is reasonable for 4.0, 5.0, and 8.0 orders. The comparison is not good for the 4.5 order. This magnitude of difference will not alter the rated rpm torsional stress level, but it could alter substantially the offspeed torsional characteristics at those resonance speed ranges.
To ascertain more realistic damping characteristics of a specific engine, one must first run a variable speed run,perhaps at low bmep, and measure torsional amplitudes at free end throughout the speed range studied. Then, one would use a series of rational damping functions with damping coeffi-cients varied until the simulation checks with the test curve. After this test procedure, the damping coefficient can then be used in future simula-
) tion of the same engine design. TORVAP's magnifier factors range from 17.3 to 32.0, for those significant orders considered. These figures are quite in line with an average factor of 25, oftenly osed as a quick st.ess.
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Crankshaft Torsional Stress Calculations July 16,1984 for 8 L 17x21 Engine-Generator Set Page 16
, The effect of using (2) different sets of magnifier assumptions can be
) further demonstrated by (2) sets of calculated torsional amplitudes plotted versus rpm. The solid curve is per TORVAP R software. The dotted curve is taken from a TOI calculation using their own magnifier assumption.
Stress To psi - PEI Calculation per
} TOR'/AP R 21930 U
80C0 -TOI Calculatten 7000 - .
E000 . ,
)
- ? 100 i 5000 - Speed o
"A-4000 -
3000 -
2000 .
g 3m /g\-
1C00 A /- n W- -u
' z..
___/Y v v A '1 \Y *1\
w, -
wT Y' - , ,
q 200 250 300 350 4C0 450 500 550 600 r;m
)
The 4.0 order response is reasonably close despite the 15% difference in in and 8% difference in magnifier factor. This is the ma,jor order.
The large 4.5 order difference can be entirely attributed to the fact that
) TOI's magnifier factor is half that of TORVAP.
The $.5 order difference can be completely attributed to the 14% di"arewe in Tn The large 6 5 order difference can be entirely attributed to the Tn figures
) LLOYO's in is twice as much as that used by TOI.
The large 8.0 order 61fference can again be attributed to the fact that LLOYO's Tn is 90% higher than that used by TOI.
This discussion and analysis show the importance of having accurate Tn figures and magnifier factors when the entire dynamic response of the snaft
) is to te simulated, which is required for a variable speed application.
- In tne case of SNPS application, only, 450 rpm and its t 5 variation are needed for torsional scrutiny.
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- Set auiy 18, 1984 Page 17 CCNSL, t.TANTS
- 9. EFFECT OF NUMBER OF ORDERS USED IN THE CALC 1Jt.ATION
.o Two (2) sets of torsional stress at rated condition were obtained for com-parison. The (12) order sum dynamic results provided some 6-7's higher peak-to-peak amplitudes quite consistently when several traces were studied The details of dynamic amplitude at a specific phase angle, however, could vary up or down as shown below. PEI believes that (6) order true sum is quite adequate for most use. Twelve (12) order is only worthwhile when C- more exacting simulation of the dynamic response is desired.
(6) Order Sum Torsional Stress, Shaft 9-10, At Rated Condition
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.-3 APPENDIX Page 18 CCNSUI TANTS 3 -
TABt.E OF CONTENTS 13 Page I. TORVAP Program and Modi fi cati on . . . . . . . . . . . . . . . . . . . . . . . . I-1 II. Torsi onal S tress At 3900 KW , 450 RPM . . . . . . . . . . . . . . . . . . . . I; III. TORVAP Prog ram Inputs and Outputs . . . . . . . . . . . . . . . . . . . . . . 111-1 IV. Torsional Stress at Rated Condition for Second and Thi rd Modes pe r TORVAP R . . . IV-1 3
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APPEN0!X I TORVAP Program and Modification .
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Modification of TORVAP Program ...............................I1 Nominal Torsional Stress Calculations at Rated Condition ..... 1-10
) Nominal Torsional Stress Calculations at 225 beep 472.5 rys.... I.16 i
8 Nominal Torsional Stress Calculations at 225 beep 427.5 rpm... 1-22 .'.
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APPENDIX ! July 16, 1984 TORVAP Program and Modification .
Page I-1 .
CCNSU.TANTS
-, . : . . . . . - r . .
MODIFICATION OF TORVAP C PROGRAM g
The Torsional Vibration Analysis Program (TORVAP) is used throughout this report. The TORVAP software is available from Comshare Inc. , Ann Arbor, 9 Michigan.
The TORVAP program is made up of two parts. TORVAP R and TORVAP C. TORVAP R is used to give a general conception of the frequency response character-E istics of the entire system, to search the natural frequency and to deter- 8 mine the significant order and the stress caused by it. Most e.2gine 6tW-in the 1973-75 period use TORVAP R type of torsional analysis. As e D before TORVAP R program is virtually the comouterized version of the Holzer table - Dan Hartog - Ker Wilson classical torsional calculations.
TORVAP C is used to solve torsional differential equations of the entire B system for specified excitation torque, and to determine the torsional ;
amplitudes and stresses at any section'of the shaft. TORVAP C ha:.
optional built-in inputs and assumptions, including a Tn table at differenc b imep, based on Lloyd reference. TORVAP C calculates the sum of order results up to six (6) orders, for all modes. In order to enhance prediction of the dynamic behavior, PEC Consultants designed a sub-routine to add vectorally g the results of two (2) separate six (6) order programs. The dynamic free amplitude and torsional stress graphs are plotted, based on the sum of twelve (12) orders. Twelve (12) order results seem to provide slightly improved dynamic details than those based on six (6) order programs.
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^"'"ot* I TORVAP Program and Modification !
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Nominal Torsional Stress Calculations O
- 1. SYSTEM SIMULATION The simulation of the mass-elasticity system is the same as that used by FaAA and TDI. PEI Consultants agree with the mass-eiasticity figures, after examining several calculations and their close checks g with the test results on natural frequency of the shaft system. The j shaft system is represented below. i Shaft Numbering System and Mass-Elasticity Data Cylinders Gear 1 2 3 . 5 6 7 8 Flywheel Generator I n rn o (h
-.. ., o. , ... . . , ., , e.., , ,, .. .. M. ,
Cy t tster 4 . . O
- ]
1 2
3 5
1 g Ug g 00000000 theft 1-2 71 14 4-9 5-4 .7 7-8 t-9 9-10 K 5. 1 M.7 M.7 M.7 M.7 M.7 84.7 M.7 7...
O OOOOOOOO 1 O O Inertia (!) is the rotating mass inertia of the shaft in Ib ft sec .2 The values are furnished by TDI/FaAA Shaft stiffness data (X) in 10 .ft.lb/ 6 rad are furnished by TDI/FaAA.
D PEI spot-checked some' of the I & K figures. The TDI figures seemed reasonable.
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0 July 16,1984 TORVAP Program and Modification Page I-3
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- 2. NATURAL F1EOUENCY l
Using the Holzer method to search the natural frequency of the system l
at a speed range of 1000 to 8000 cpa, the natural frequency is obtained as follows:
l l] Third Mode First Mode Second Mode 2323.3 cpm 5575.2 cpm 7000.4 cpm The first mode natural frequency, 2323.3 cps, is 5.2 times that of the -
l3 rated speed. The major order, 4.0, has it's resonance at 581 rps. !
The 13 x 12 shaft is affected by the 4.0, 4.5, 5.5, and 8.0 orders.
The second and third mode nstural frequencies are 12.4 and 15.6 t'-
that of the rated speed, respectively. These modes ar significant.
3 The natural frequencies of this replacement crankshaft are higher than the old 13 x 11 shaft, due to higher stiffness (K). The comparison is as follows.
13 x 12 Shaft 13 x 11 Shaft
) First mode Second made 2323.3 cpu 5575.2 cpu 2129.8 cpm 5455.4 cpm Third mode 7000.4 cpm 6495.2 cpm Shaft Stiffness (K) 84.7106 ft lb/ rad 71.210' ft lb/ rad Crankpin Diameter 12 inch 11 inch The shaft stiffness (K) of the replacement shaft is nearly 20%
g stronger than that of the old shaft, due to a 9% increase in the crankpin diameter, witA the main diameter remaining at 13 inches.
This higher K value contributes to two important improvements c. .
replacement shaft:
D - Increase the modulus or the strength of the shaft.
- Increase the natural frequency of the shaft by 9 % and thereby reduce the equilibrium amplitude by as much as 31%.
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- 3. FIRST fiODE H0t.ZER TABt.E O -- -
To sTm K as
- a Shaft ,
I g
.Fre, 0.00
'1 6.8 1.00 0.01 1-2 1 0 .01 1.01 0.01
.Q 49.2 0.99 0.05 2 1. 4 0.0a 2-3 0.06 3-4 O.11 1. 4 0.07 4 47.9 0.88 0.04 4-5 0.15 1. 4 0.10 5 47.9 0.78 0.04 ;
'O 5-6 0.1, 1.4 0.12 6 47.9 0.66 0.03 6-7 0.22 1. E 0.19 7 1 47.9 0.51- 0.03 7-8 1 0.25 1. M 0.17 8 47.9 0.34 0.02 .
8-9 0.26 1.a8 0.18 0 9 9-10 30 i o.i. 0.03 0.27 1.34 0.20 10 l100.0 -0.04 -0.04 11 2650.0 -0. 09- -0.23 Free 0.G3 O a = mass number Shaft = shaft nun 6er I = mass moment of inertia, Ib ft sec 2 g K = shaft stiffness,10 6ft lb/deg = K in rad divided by 57.3 a = rela ve vibration amplitude, assume 1 deg at mass 1 Ta = I ul .a = inertia torque,106 ft lb, calculated for at = 1 degree at a 1 6
O ITs = sunsnation of inertia torque,10 ft lb .
as = htia = relative angular vibration amplitude between '
masses, in degree Resul ts 4 max as = 0.20 degree at shaf t 9-10, when st = 1 degree max ETs = 270,000 ft lb at shaf t 9-10,when St = 1 degree pow =ra are Ew ncamtenes ec. AC.1C64 555 L.macori Ave. Geoc. wt 53511 6CS/362 7071
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July 16, 1984
)
TORYAP Program and Modification Page I-5 CONSUL.TANTS
- 4. RELATIVE AMPLITUDE FROM FIRST MODE HOLZER TABLE
) The relative torsional amplitudes S of each mass at first mode
- resonance frequency and the relative displacements as between masses are shown as follows.
Relative Amplitude 8 at Resonance, First Mode e i oo a.es ,,,,
o.se o.TS No.u '
No.n !
No.u
\ is
- n I I I 7 s' I E P 'i Relative Displacement Satmeen Massesas at Resonance, First Mode
)
o.ro 0.12 a.le o.o' / g o.as
. o.oi M Shaft' l.2
- 23 ' 34 45
- 54 " 67 " 74 89 " 9 10 16 67
)
The relative displacement (as ) curve shows that the maximum value of 0.20 is situated at shaft 9-10 between cylinder 8 (mass no. 9) and the flywheel . This maximum as location should correspond to the maximum
) re!ative stress caused by the major order of the first mode torsional vibration. *..,
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- 5. RELATIVE STRESS FROM FIRST MODE HOLIER TABLE l
.O The first mode natural frequency as previously stated is 2323.3 cpm. l The um of relative inertia torque, Ts, and relative torsional stress, l S, cm tabulated below for the resonance condition.
s ITs 5 m a shaft " #'"
V rad or nm
- 105 '**'D rad E
deg deg rad deg i 1.00 [
12 1 0.55 700 100 250 i 4 0.99
~
23 ' 4.47 575c0 800 1 2030 A 4 0.95 '
p
- V 34 8.13 104700 1460 37rm l
4 0.88 1 45 11.53 1 1484c0 2070 5250 5 0.18 56 14.54 1371c0 2620 6620 6 0.66 67 17.06 219600 3070 7770 J 0 . 51 t Q
I 19.01 3420
~
7-8 244800 1 8E60 4 0.34 g.g 20.33 261700 3660 9250 9 10 l 20.99 270200 37m 960 to -0.06 10-11 17 79 229100 Ira 3420 3 11 -0.09 ,
tTa = r(I.w 2s) in na wiien at = 1 rad, and in ft lb when 81 = 1 deg S = relative torsional stress = ITm/Z 3 I = crankpin section modulus = 5d3 /16, where d = 12", except when 4 = 16* for shaf t 10-11 Results !
l 2
IIs2 = effective inergia of system = 225.6 ft lb sec or G 305.8 kg m sec G = equilibrium amplitude factor = eo/Tn = 0.00085 ',g/ psi (1 deg per 1174 psi)
Maximum relative torsional stress at shaft 8-9 and 9-10 with relative g stresses of 9260 and 9560 psi / degree, respectively, for the first mode, t
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P E I APPENDIX I
. TOP.VAP Program and Modification July 16, 1984 CCNS t.nNy Page I.7
- 6. NOMINA. TORSIONAL STRESS AT RESONANCE AND SERVICE SPEED FOR FIRST 3 M00E. >ER TORYAP R PROGRAM The previous table shows that the maximum relative torsional stress occurs at shaft 9-10. These stress levels at the resonance speed (NC) and rated load speed (450 rpm) are calculated for all orders, 0.5 to 10.0, for the first mode, and are shown below.
S MEN AT 450 m ORDER NC NC/MS Z8 in e, Mr l Sr nf i Sr
.5 4647. 10.Jd 0.10 88.5 0.05 21.8 11010. l.01 $10.
1.0 2323. 5.16 0.15 95.4 0.05 21.7 11200. 1.04 133.
1.5 1549. 3.4 1.39 90.1 0.11 18.3 16690. 1.09 1117.
- 2.0 1162. 2.58 0.38 74.5 0.03 15.5 30760. 1.18 170.
3 2.07 1.39 62.0 0.07 20.1 14140. 1.31 920. 5
- 2. 5 929. ~"
3.0 774 1.72 0.15 51 .2 0.01 34.3 2830. 1.51 3.5 664 1.48 0.70 41.5 0.03 26.4 6240. 1.?-
4.0 581. 1.29 5.28 32.7 0.13 17.3 21930. 2.-
4.5 51 6. 1.15 0.70 25.3 0.02 29.8 4310. 4.13 4 2. .
5.0 465. 1.03 'O.15 19.2 0.00 47.3 1080. 15.30 350.
D .94 14.7 28.8 7.15 1191.
5.5 422. 1.39 0.Gt 4790.
6.0 387. .86 0.38 11.3 0.00 42.7 1470. 2.84 98.
6.5 357. .79 1.39 9.0 0.01 32.5 3330. 1.71 175.
7.0 332. .74- 0.15 7.3 0.00 50.3 430. 1.19 10.
7.5 310. .69 0.70 5.9 0.00 42.5 1450. 0.90 30.
8.0 290. .65- 5.28 4.7 0.02 27.4 5540. 0.71 144.
D 8.5 273. .61 0.70 3.9 0.00 47.5 1064. 0.58 13. l 9.0 258. .57 0.15 3.4 0.00 50.0 200. 0.49 ~
2 9.5 245. .54 1.39 3.1 0.00 42.6 1480. 0.2 10.0 232. .52 0.38 2.7 0.00 50.0 420. 0.36 , ..
p Where:
NC = critical speed of an order = 2323/ order .
MS = rated speed = 450 rpm ra = relative amplitude vector sum of all cylinders, in degree in = tangential effort of cylinder gas pressure from Lloyd, extrapo-lated to 250 inep, based on 225 beep and mech. eff. = 0.9 so = equilibrium amplitude of shaft 9-10 without magnification g = ef Tn tB , deg er = equilibrium amplitude factor from Holzer Table and engine data in degree Mr = 3.8 93 -4 , magnifier of resonance, only engine damping is considered b Mf = flank magnifier at service speed = ([1 - (h) 3 + (h) Mr Sr = 93 Mr S, torsional stress at resonant speed, psi Sf = eo Mf S, torsional stress at service speed, psi a
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TORVAP Program and Modification au'y 15 2$84 Page I-8 rm
- 7. NOMINAL TORSIONAL STRESS AT OVERSPEED CONDITION _
> The previous calculations were made at rated. An overspeed condition of 225 bmep and a 105% rated speed of 472.5 rpm was evaluated to consider the potential, but rare, over-shoot condition. Shaft section 9-10 is evaluated as follows:
)
ORDER NC MC/NS Es Tn og Mr Sr Nf 5f 0.5 4647. 9.83 0.70 88.5 0.05 22.0 10640. 1.01 51 0.
1.0 2323. 4.92 0.15 95.4 0.05 21.7 11140. 1.04 135. .
) 1.5 1549. 3.28 1.39 90.1 0.10 18.4 18190. 1.10 1127. 5 2.0 1162. 2.46 0.38 74.5 0 . 21 . 15.5 30850. 1.20 159. I 2.5 929. 1.9T 1.39 62.0 0.07 20.2 13780. 1.35 9d" 3.0 ~774 1.64 0.15 51.2 0.01 34.1 2880. 1.59 3.5 664 1.41 0.70 41.5 0.02 26.6 6090. 2.02 %.
4.0 581. 1.23 5.28 32.7 0.13 17.5 21360. 2.93 3698.
) 4.5 516. 1.09 0.70 25.3 0.02 30.1 4210. 6.05 874.
5.0 465. 0.98 0.15 19.2 0.00 47.6 1060. 24.88 570.
~
5.5 422. 0.89 1.39 14.7 0.02 29.0 4690. 3.93 655.
6.0 387. 0.82 0.38 11.3 0.00 42.9 1440, 2.04 71.
6.5 357. 0.76 1.39 9.0 0.01 32.7 3260. 1.34 125. .
7.0 332. 0.70 0.15 7.3 0.00 50.0 420. 0.97 8. l
) 7.5 310. 0.66 0.70 5.9 0.00 43.2 1410. 0.75 26.
8.0 290. 0.62 5.28 4.7 0.02 27.6 5420. 0 .61 122.
8.5 273. 0.58 0.70 3.9 0.00 47.9 1040. 0.50 11.
9.0 258. 0.55 0.15 3.4 0.00 50.0 .200. 0.43 2.
9.5 245. 0.52- 1.39 3.1 0.00 42.9 1440. 0 .37 12.
10.0 232. 0.49 0.38 2.7 0.00 50.0 400. 0.32 3.
)
Comparing these data with those for the rated condition, the fourth order torsional stress is 17% higher than that at rated condition
) because NS of 472.5 rpm is closer to the resonance speed NC.
The second and third mede natural frequencies cause negligible shaft stress on shaft 9-10. The value of the 4.0 order is around 11 psi for the second mode, and 174 psi for the third mode at rated condition.
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TOR 7AP Program and Modification / Page I-9 0 *
- 8. TORSIONAL STRESS DISTRIBUTION (4.0 ORDER) ALONG THE SHAFT SYSTEM From the TORYAP C program, the nominal torsional stress at each shaft number can be calculated for all udes. The fourth order results are j tabulated as follows.
Mass vibration shaft T=tst gr. s g , 53,fg nass NO. II*IU E8I 8.41l6,no 441 @8. #1ps e #1 con 1 0.31 28.42 1-2 -0.00 28.42 131o 44 2-3 -0.01 28.45 16471 590 CT1. 2 3 0.30 25.42 g 3-4 -0.02 28.45 31 u 6 1112 g
~
, CTL 3 4 0.25 28.42 4-5 -0.03 28.44 45590 1812 C1L 4 5 0.Zs 28.42 5-4 -0.04 28.4a 58818 2"Jo CTL 5 6 0.21 23.41 g 6-7 -0.cs 23.43 70864 2!C6 CTL 6 7 0.16 28.40 7-8 -0.06 23.42 81487 2282 CTL 7 8 0.10 23.39 8-9 -0.05 25.40 90471 12"o CTL 8 9 0.o4 28.38 9-10 -0.07 25.3B 17855 3455
$ F.W. 10 -0.03 23.38 1o-11 -0.02 28.38 76694 1144 GZM 11 -0.Qs 28.38 The vibrations and twists in the table are represented by a cosine wave form and assume a positive rotation direction.
e (t) = e cos [n (wt - $,)]
ae (t) = as cos [n (at - 45 )]
n = the order of hamonics w = the angular rotation speed of ?)1e engine
~
8m and as = phase angle for mass and shaft, respectively, with respect to firf 5g TDC of the first cylinder.
b The maximum torsional stress caused by the 4.0 order Tn is 3455 psi for the sum of all modes. This is a'pproximately 97, higher than that caused by the first mode alone, (per TORVAP R).
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)
aus APPEN0!X ! July 16, 1984 j CCNSUL.TANTS TORVAP Program and Modification Page I-10
- 9. FREE END TORSIONAL AMPLITUDE AT RATED CONDITION
)
TORVAP C gives torsional amplitudes for each order and for the sum of' orders. Six (6) significant orders were selected for calculation. The square root of the sum of square (SRSS) amplitude was also calculated to compare with TOI data, as shown in the following' table.
) ' '
Order Amp 11tude G. degree de e O.5 0.07 37.4 1.5 0.14 83.5
) 2.5 0.11 22.0 5 4.0 0.31 28.4 4.5 0.07 21.1 5.5 0.12 60.9 SRSS 0.39 l
)
The dynamic free end torsional amplitude (true sum) for the six (6) selected orders is shown as follows.
sm.
) ..
- 3
'- i o g
-:A
-:i ,
3 n .:
-::i,,l e ..
,!E
.. ! i
) t. 3
~~ : I \ h
- = -...;.. ..; . [.......\...j. .
...q.;..j'.\
- .. 7
+-: g ,, ..i!> *
- tg ..
4a ;
\\
< =, : s . .I ,
- -: 'l ;l 'v \ . \l
' , . );
) -:
V g
4e.
,' , -- , T --l , ,- ,- ,
)
_ , . i The mean amplitude is 0.56 degree, based on a maximum 0.62 degree and a minimum -0.49 degree.
ACw.ava enes e% inmcmanes inc. AC.1C64 S S S W Ag e. Santac. WI S3S11 SCS/383-7C71
3 APPEN0!X !
July 16, 1984 CCNSt.M.TANTS TORVAP Program and Modification Page I-11
- 10. NCMINAL TORSIONAL STRESS FOR SHAFT 5-6 AT RATED CON 0! TION D
The shaft stress at rated condition is shown in the following table. Six (6) selected orders were used in this series of calculations. The SRSS torsional stress is also listed to compare with TDI data.
asa g D Order Stress, psi , g 0.5 674 484.6
- 1. 5 1718 219.2 2.5 1296 85.3 .,
D 4.0 2080 73.4 9 4.5 485 64.7 5.5 714 26.2 SRSS 3187 8 The dynamic stress ainplitude (true sum) for the six (6) selected orders is shown as follows.
l
- "mi . i
- ==
D :
- g
. ...)
e --i-.........,..........O............
! i 1
.m.am .
j l I
g _g ..r .
Fi ""FT"T" i .
_.._~*
i i i i
=
g The mean stress is 4498 psi, based on a maximum 3898 psi and a minimum
-5536 psi.
Aower= arc Ener gy eternecceae ec. A c.1C454 555 Lawecri Ave. Geoc. wt 53511 SCE/362 7C71 I
)
I 3-p E I APPENDIX I TORVAP Pmgram and Modification auw 16,1984 Page I-12 I
CONSULTANTS
- 11. ' NOMINAL TORSIONAL STRESS FOR SHAFT 6-7 AT RATED CON 0! TION
) -
The shaft stress at rated condition is shown in the following table. Six (6) selected orders were used in this series of calculations.
Phase Angle Order Stress, psi 9,. degree
)
0.5 261 350. 7 1.5 1604 204.8 2.5 1240 93.2 4.0 2506 73.4 4.5 , '439 60.4 .
) 5.5 858 27.9 's SRSS 3375
=
The dynamic stress amplitude (true sum) for the six (6) selected orders
) is shown as follows.
.E s
) . "*i
==.
=:i
.""* - . . . . . . .. ... ... .. . . . . . . . ... .. ...L
.?"'
~i
..: h{
)
==: [
- d I
~:
- 0
~: -
) *
=
ITTTTTTT7T9 -
- ..- .. ~ ,,
} The mean stress is 5101 psi, based on a' maximum 4634 psi and.a minimum
-5568 psi. ,
Ac*** end e% etnt.com ecc. A C. iC64-r SSS Lawton Ave. Geot. wt S3511 SCS/362-7071
) .
r
O q" E l APPEN0!X I Eii a July 16,1984 TORVAP Program and Modification Page I-13 .
g 12. NOMINAL TORSIONAL STRESS FOR SHAFT 7-8 AT RATED CONDITION The shaft stress at rated condition is shown in the following table. Six (6) selected orders were used in this series of calculations.
P e g Order Stress, pst g
0.5 882 350.2 1.5 978 204.8 2.5 814 93.4 -
O 4.0 2883 73.4 -
4.5 646 59.0 5 5.5 1098 28.2 SRSS 3512 O The dynamic stress amplf tude (true sim) for the six (6) selected orcers is shown as follows.
"; T T
=: -
O ":
==: q l :
. 1, 1 1 I
==l-.....j....{....... .. ..) . ,
t o **
1 U
"i ) Y
": i O ~~i V .
~~
T T T T T T~ T t- d 9,
.-=..=..==7-O The mean stress is 4941 psi, based on a maximum 4250 psi and a minimum
-5632 psi .
Aower and Emf ecamen m. AC.1C64 555 Lawton Ave. Soot. We S3511 ScW/36E-7071 O
. . . ~ , .. .
O o P E I TORVAP Program and Modification auix 16, 1984 Page I-14 CCNSULTANTS
- 13. NOMINAt. TORSIONAt. STRESS FOR SHAFT 8-9 AT RATED CONDITION O
The shaft stress at rated condition is s. wn in the following table. Six (6) selected orders were used in this series of calculations.
Phase Angle Order Stress, pst 95, degree 0.5 625 439.7 1.5 695 178.1 2.5 600 106.0 4.0 3200 73.4 G 4.5 609 62.5 g 5.5 1258 28.9 -
1 SRSS 3664 g The dynamic stress amplitude (true sum) for the six (6) selected orders is shown as follows.
e: =
e.
o ..: i
{1 l
-: 0 q
- l
- { (
,,.....4..,.r- .i -
r- T'
~
i s :. .
I Y
- ;.\ ,
- ~ i k l
==i k 0 0
~: "
' 'Y 'I "
Y D
== , , = = _ . '= _' .' _' _'~.
D The mean stress is 4568 psi, based on a maximum 4798. psi and a minimum
-4338 psi.
83ower em E% ccomet.or es cc. 83 C.1C64 STS Lawton Ave. Geoc. WI 53S11 SCG/362 7C71 g .
I O I 1
1 1
I APPENDIX I O Q Q l TORVAP Program and Modification
. July 16, 1984 Page I-15 CCNSUL.TANTS
- 14. NC,MINAL TORSIONAL STRESS FOR SHAFT 9-10 AT RATED CONDITION g
The shaft stress at rated condition is shown in the followin9 table. Six (6) selected orders were used in this series of calculations.
Order Stress, psi f3*,dg 0.5 4 399.5 1.5 85 204.2 2.5 199 94.4
4.0 3455 73.4 O 4.5 497 61.4
- 5.5 1390 28.4 SRSS 3763
. l g The dynamic stress amplitude (true sun) for the six'(S) selected orcers is shown as follows. .
l
~i f l 6 , g 1
": t
": /
=: . J.
""[....... ...L.j........ ..... .. ... .. .. . . j . . <. . .
s _ :. I
!l .
==== !
,i 1
=:
y \j, k [ (
e:
, ~: .
FTTTTTTTTT",
s == ..
D The mean stress is 4900 psi, based on a maximum 5017 psi and a minimum
-4783 psi.
power = are E% ntamme.ones ec. AQ.1C84 555 L awson Awe. Geoc. wi S3511 eCS/:362-7071
- I .
- 4
D E July 16,1984 TORVAP Program and Modification Page I-16 7
- 15. FREE END TORSIONAL AMPLITUDE AT 225 bmeo, 472.5 mm D TORVAP C gives torsional amplitudes for each order and the amplitude for the sum of orders. Six (6) significant orders were selected for calcula-ti on. The square root of the sum of square (SRSS) amplitude was also calculated to compare with TOI data, as shown in the following table.
E Order Amplitude 0, degree
'g"g A9*
0.5 0.07 37.4 1.5 0.14 83.5 2.5 0.12 21.4 '
D 4.0 0.37 28.6 ) 1 4.5 0.10 21.5 5.5 0.06 64.5
. SRSS 0.42 P
The dynamic free end torsional amplitude (true sun) for the six (6) selecte'd orders is stown as follows.
u-i f D ** : 6
== ; '
- t. *
- = if 0
.*= :t b
'~ b *]-'
i' -
a 4-
! lr .
- ' : b)
- =:
4..
- ! hj h
p
- =: V,
. F i T i T i TTTT-'i -
."" a. " "
"= =
I The mean amplitude is 0.59 degree, based on a maximum 0.62 degree and a minimum -0.55 degree.
Aower eno E% ecamecem ec. AQ.1C84 555 Lawton Ave. 4eot. WI 53511 6Ce/ 362-7C71 b
D l
I 3 APPEN0!X I A E I TORVAP Program and Modification au w 16. 1984 Page I-17 CCNSU'.TANTS D 16. NOMINAL TORSIONAL STRESS FOR SHAFT 5-6 AT 225 bmeo. 472.5 rem The shaft stress at 225 bmep, 472.5 rpm is shown in the following table.
Six (6) selected orders were used in this series of calculations.
D Order Stress, pst 9',
0.5 676 484.6 1.5 1729 219.2 2.5 1320 84.5 4.0 2466 73.6
- 4.5 684 64.0 .
5.5 333 24.8 )
SRSS 3442 The dynamic stress amplitude (true sum) for the six (6) selected orcers is shown as follows.
== .
3 ==: .
.. .. ==
""i l !\ l
==. ft n.: 'l O . ( !\ . 5'....}'...i.1......
== : ..
5 _-........;..7.................
==.! v man j'
"'" ! l )i
~; v aam . I! '
-i \]
l
) "'* :~ . - - -
iTi i i i . . .
..=,==_==,==_==
1
=
D The mean stress is 4816 psi. based on a maximum 4263 psi and a minimum 1
-5370 psi.
I A CWer* ere Eg ecamec.orw ec. AO.1C64 S S S L.a w sc e A ve. Geoc. wt53511 6CS/362 7071 e
)
APPENoix i
& l TORVAP Program and Modification JUIY 16. 1984 Page I.18 CCNSLA.TANTS
- 17. NOMINAL TORSIONAL STRESS FOR SHAFT 6-7 AT 225 bmeo, 472.5 rpm The shaft . stress at 225 tmp. 472.5 rpm is shown in the following table.
Six (6) selected orders were used in this series of calculations.
ase g Order Stress, psi p 0.5 261 350.8 1.5 1617 204.8 2.5 1269 93.3 4.0 2960 73.6 '
4.5 672 61.1 -
) 5.5 405 28.3 i SRSS 3698 The dynamic stress amplitude (true sim) for the six (6) selected' orders
) is shown as follows.
"i f
) ";
" :. j $
t
- i \ \', y
'j......j... ..>. ...\
}
~==il y..\ ')\'V Y. \,
- :I
- 1
\)I y
. 1 2h N' i
-j
- c-F"T"T h T T T T . . ~1
) The mean stress is 5490 psi. based on a maximum 5100 psi and a minimum
-5880 psi, oo . w am ecmcow ee. ac.$esd S$$ Lawton Ave. Boot. W S3511 SCS/363 7C71
) '
D APPEN0!X I D
A E I TORVAP Program and Modification auw is. 1984 Page I-19 C::NSutTANTS
- 18. NOMINAL TORSIONAL STRESS FOR SHAFT 7-8 AT 225 bmen, 472.5 rpm g
The shaft stress at 225 beep. 472.5 rpm is shown in the following table.
Six (6) selected orders were used in this series of calculations.
Order Stress, psi "h g
0.5 884 184.86 1.5 989 52.8 2.5 822 126.5 l 4.0 3388 65.6 '
B 4.5 901 90.0 5.5 595 201.6 I SRSS 3883 The dynamic stress amplitude (true sum) for the six (6) selected orders is shown as follows.
."'~ .; ..
- = =e
.. l i
> "l
-i n I \ )\ \
=":
1 1
I' ,
J)I g t'
I
= . . i l
}
-- i e i l
D -3 ! .I Ci t{l #
f .
-i \1 Ci : i.
P Ci V. ,
i i i i . . . . . i i
==
p .
The mean stress is 5212 psi, based on a maximum 4928 psi and a minic:um
-5496 psi.
acw. .no erw w ec.- .c.cr. ec. ac.tes4 .est con 4... e.oc. u samt t scenea 7c75 g
D
= APPENDIX I 3
d 5 July 16,1984 TORVAP Program and Modification Page I-20 g CONSULTANTS
- 19. NOMINAL TORSIONAL STRESS FOR SHAFT 8-9 AT 225 bmen, 472.5 rpm The shaft stress at 225 bmep, 472.5 rpm is shown in the following table.
B Six (6) selected orders were used in this series of calculations.
Phase Angle Order Stress, psi Os, degree 0.5 627 140.5 1.5 704 92.4 2.5 . 626 96.25
. 4.0 3740 65.6
- 4.5 888 78.75 19 8.0 5.5 730 D
SRSS 4073 The dynamic stress amplitude (true sum) for the six (6) selected orders y ,
is shown as follows.
- m. m, 1
" l
,";: I I- ==
I I 1 I. .!
> : A
"; N i
~*
-- i . . . . .L . . .. ...... ... ......t.. ...k.....{..
., I '
i e __.
.} \
~: 1
( i
- ".:: h 5
==: .
P !" ..
Fi "T-~.~ i Ti -
..,==_=__."1 6 . 6 a.. . . .
The mean stress is 5212 psi. based on a maximum 4928 psi and a minimum
' -5496 psi.
I Power
- end E% intameceae ec. PC.1CG4 555 L.awton Ave. Geoc. W153511 GCG/362 7071
O APPENDIX I -
O P E I TORVAP Program and Modification auir is. 1984 Page I-21 CCNSUL.TANTS
- 20. NOMINAL TORSIONAL STRESS FOR SHAFT 9-10 AT 225 beep, 472.5 rpm The shaft stress at 225 bmep. 472.5 rpm is shown in the following table.
o P' Six (6) selected orders were used in this series of calculations.
Phase Angle Order Stress, psi 95, degree Q'
O.5 5 399.6
- 1. 5 95 204.2 2.5 228 94.4 4.0 4010 73.6 I
4.5 732 61.9 '
5.5 838 29.1
=
l 0
SRSS 4168 The dynamic stress amplitude (true sum) for the six (6) selected orcan is shown as follows.
D -
"_ i ._
- 0
- ( 0 A
)i
-i h l' ,l 3 'l
- 1 ( i Z i .. ,
. . .i...1...,...., . .
l i l..i 7 i
t:i , j t
i l
3 . ].
^'" i \ k, \! Y ,
"" : 1 - y V '!
- =: 9 \j. ;
g ..
T* T i iT "T" . . T""T* *.
@ ,- . . . , = = , , -
g The mean stress is 5673 psi, based an a maximum 6243 psi and a minimum
-5104 psi.
Aower*areE % ete m c w cc. Ac.iC64 555 t.awecrs Ave. Geoc. WI 53511 8C41/362 7071 4
)
) TORVAP Program and tiodification July 16,1984 Page I-22
- 9. FREE END TOR $!0NAL AMPLITUDE AT 225 bmeo. 427.5 rom
) TORVAP C gives torsional amplitudes at 225 beep. 427.5 rps for each order and for the sum of orders. Six (6) significant orders were selected for l calculation. The square root of the sum of square (SASS) amplitude was also calculated to compare with T0! data, as shown in the following table.
)
- Order Amplitude 0, degree
'^
d 0.5 0.07 37.3 1.5 0.14 83.5
- 2.5 0.11 22.0 -
) 4.0 0.27 28.7 's' 4.5 0.05 21.6 5.5 0.33 51.1 SRSS 0.47
)
The dyr:amic free end torsional amplitude (true sum) for the six (6) selected orders is shown as follows.
- w. . . c e . u.
) s..; I $
q l i.. l @
i.. !
)
.e f ?\ ,,
.. -! _.I.
,... . .O
, r .i i ;
4
/\ .
lf
[i
! I \/
l [
'[
l ' if' V
l {V Vlj Qj y l
a
, '-. . l. -
~'
. ... . . _, ,.j._ ~.; .
- e. ;-
) The mean amplitude is 0.67 degree, based on a maximum 0.81 degree and a minimum -0.52 degree.
i 88ower* enes e% ccerces.ones ec. iso.1C64 SSS Lawton Awe. essoc. wt 53e11 eCe/383 7071
)
.: 'h
1 a
o e g APPENDIX I July 16,1884 Eiii u TORVAP Program and Modification Page I-23 CCNSULTI.NTS
- 10. NOMINAL TORSIONAL STRESS FOR SHAFT 5-6 AT 225 been. 427.5 rpm g
The shaft stress at 225 beep. 427.5 rpm is shown in the following table.
Six (6) selected orders were used in this series of calculations. The SRSS torsional stress is also listed to compare with TOI data.
O Order Stress, psi deg 0.5 674 484.7 1.5 1711 219.3 2.5 1275 85.3
- O A.0 1813 73.8 N 4.5 394 66.0 5.5 2255 17.7 r
SRSS 3678 O The dynamic stress amplitude (true sum) for the six (6) selected orders is shown as follows.
l ?g ?g -
l I a D i .3 .
sn o 'Llicle.
l\ 1 ,
1.
l
- t. .
.B I t ,.
!.WJ1l.8'W'
- l6
{
1
.. . g i, . .
g
.j ,
.... t i \l I 1
I j l I O ; .) ,,
.. e.. .. g ,.,gg,.,, ,
.g. . .--...m..
O The mean stress is 5288 psi. based on a maximum 4194 psi and a minimum
-6381 psi.
i power em E% ccamecess ec. AO.1CS4 555 Lawcon Ave. Soot,wtS3511 GCE/.36a.7071 O
I E APPENDIX I ~
) I TORV4P Program and Modification July 16,1984 Page I-24 ccNsLATANTS
- 11. NOM! rial TORSIONAt. STRESS FOR SHAFT 6-7 AT 225 bmeo. 427.5 com
) The shaft stress at 225 beep, 427.5 rpm is shown in the fo1*owing table.
Six (6) selected orde.rs were used in this series of calculations.
Stress, psi N se Angle Order 93, degree 0.5 260 350.7 l l
1.5 1596 204.9 2.5 1217 93.3 4.0 2192 73.7 ,
4.5 322 60.7
) 5.5 2555 18.0
,8 SRSS 3941 The dynamic stress amplitude (true sum) for the six (6) selected orders
) is shown as follows.
... ; m.. .
- = .
> "i j '
... :' .... n
.i .. n .- I. . e .i
' \. ;i '. ."g, I
p!*
.: l I ;
.. c '
t * '.;
1 y
o , .. . I.t' ,
... ! , i
. .' ,8
. i l: .i* ; ., l
..1.t . .
l 4 ..
... . ! . 1 L
! 'l !'
) .... ! . . .
.. .:. i :. g ,.,Tf. ., ..,g. 4:. .. :4 The mean stress is 5627 psi, based on a maxic:um 4154 psi and a minimum
-7099 psi.
)
8ower om EM eter**etcess ec. AC.iC64 555 t.ewsm Ave. Eieoc. W 53511 SCS/362 7C79
)
I APPENDIX I s P E I' 70RVAP Program and Modification auis 16. 1984 Page I-25
^
CONSUt.TANTS
- 12. N0MINAl. TOR $!0NAL STRESS FOR SHAFT 7-8 AT 225 hmeo. 427.5 rem The shaft stress at 225 brnep. 427.5 rpm is shown in the following table.
Six (6) selected orders were used in this series of calculations.
Phase Angle Order Stress psi 9 . degree i
0.5 881 350.2 1.5 968 204.9 2.5 789 93.5 4.0 2532 73.7 ,
. 4.5 516 59.0 5.5 2908 18.5 SRSS 4179 The dynamic stress amplitude (true sum) for the six (6) selected orders.
is suwn as follows.
u . i '. .. . y; , ,,
I fu M
-_ t.l * ,
9 l
., r ,
u-
'} ,' *.\.) ." ** '
'd "
l *1
.: ; ..\.i . ..l .
i :i -
i
.. ..t l ., u \ ,, . , .. .-
' i i i. . ..
.t. . : .. . - .
\.
_ j . ,
t i s .
8 '" I ': .
b .u! ". e =
, i.:. J. J.g.,.5.g.. .
- w. .
The mean stress is 6120 psi, based on a maximum 4899 psi and a minimum 3 -7340 psi.
=
l .
power ene En eteet.cco ec. AQ.1C64 51.35 Lawton Awe. Becic, we 53511 6Ca/362-7C71 D
~W
{
E e 3 APPEN0!X I July 16. 1984
'J G u TORVAP Program and Modification Page I-26 l
! CCNSut.TM
- 13. $0MINAL TORSIONAL STRESS FOR $ HAFT 8-9 AT 225 bmep, 427.5 rem J
The shaft stress at 225 bmep. 427.5 rpm is shown in the following table.
Six (6) selected orders were used in this series of calculations.
Phase Angle Order Stress, psi O s degree 3
0.5 624 439.8 1.5 687 177.9 2.5 582 106.7 4.0 2826 73.6 -
J 4.5 475 63.4 5.5 3088 18.9 ?
SRSS 4352 3 The dynamic stress amplitude (true sum) for' the six (6) selected orders is shown as follows.
i....m . . . . . . . _
- m. -
m; s.s ;
! I \
. .. ; 3 1 e i
i I
\ {a \
\ il \
I sf 1
l i
( *\
- .-- - )
- f. \ '-
, ' {. c, , , ;, , ,
.! s' \ '
j '
i j, tg ):,
...s ! i T I \.
i*
\,j\ g(
s
- .u l b 'i ..
.. ... m. m.. .m . . . . .... .. .. m The mean stress is 5823 psi, based on a maximum 5531 psi and a minimum 9 -6115 psi.
Aower= enas Er'ergy ecamem ec. AC.1C64 555 t.awcen A=e. Geot. wt S3511 GCe/~362-7071 0
O J
' p [; g g! .PENDIX [
July 16, 1984 O ,
TCCVin cc. c. ;.'. i r.d P.-41 fi.= * ' -- . ort- I-27 i , CNSUL.TANTS ,
i
~ ~ -
.... .........----_-._....I --
- 14. NOMINAuTORSIONAl.' :.; Aff s Ft,k shAri 9-IC AT 24.3 t.:.w, 47. , . pm O The s aft stress at 225 beep, 427.5 rpm is shown in t' e following table.
Six (G) selected orders were used in this series of alculations.
Order Stress, psi $d58 A"d'
,, degree O
0.5 4 .t02.6 1.5 76 35.3 2.5 174 . :.
g
. 4.0 3071 *
' ! 4.5 306 ',
- c.
O 5.5 3294 13 I
i SRSS ; 4517
~ -_
The dynamic s'.ress amplitude (true sum) for the six (6) selected orders 3 ,
O i.si l li lt = 'l -
, t a.
2.~ '
i \. . ( ._,-........t...l.....,..
e
, \ \ '. . \ \ :!
j, i: ':
i .. . .
...!i , I :. !
{ e.I
.i ji ..
- .. il .
- j .- il g I
- $i '.- J .:n
.;.. . . .;.. y, 7., . g ,_.., j.. g.'_ .
.q.
1 I /
l The riean stress ;s o'232 , .1, based on a ;"aximum 6067 psi and a minimum I -6396 psi.
D
.. = . . . _ _ . _ . . _ . _ _ _ _ . . . _ . .
9:...- e n c xe .. vi:.r etc. < cc- ae icea ses . asa.7c71 E
1 v.
cw4 m '-
+==
-e
' p j
. p. m ' ~ , 4';
k'l',
I D -
l APP 90!X II July 16, l h ' i M
ter py . ww. , . - _
-j. -: .
3 Torsional Stress at 3900 XW Page D Torsional Stress At 3900 KW, 450 RPM . . . . . . . . - . . . . II-1 6
D -
- 9 4
- ww
- pgw- g
...-,.2..- ,4
- , m .
1 D -
I I
e D !
i W E% mm m AO.1084 '515t5 Lawcon Am asecye,w e q, ggg g g 3 4
t
)
APPENDIX II
) p E I auir 16, 1984 Page II-1 Torsionai Stress at 3900 KW CCNSLLTANTS TORSIONAt. STRESS AT 3900 KW, 450 RPM
) The overload condition of 3900 kw at 450 rpm is investigated and the results are tabulated as follows.
Shaft Torsional Strass, psi Free End ;
Order 5-6 6-7 7-8 8-9 9-10 Degree 4.0 744 287 973 690 5 0.08 ,
) 1.5 1866 1742 1061 753 93 0.15 2.5 1398 1340 879 653 215 I 0.12 4.0 2251 2713 3119 3463 3740 0.34 4.5 528 465 682 655 477 0.07
)
5.5 753 869 1109 1256 1405 0.12 SRSS 3450 3639 3777 3932 4030 0.42
) <
True Sum 4757 5401 5228 4883 5192 0.59-l In this case, fourth order Tn used is 35.0 psi corresponding to the 3900 kw,
) 251 bmeo or 280 imep condition. The maximum single order torsional stress is at shaft section 9-10, with an amplitude of 3740 psi, safely below the OEMA allowable of 5000 psi.
The maximum sum cf order SRSS figure is 4030 psi at shaft 9-10, and the m' ass -
sum of order true sum is 5401 psi at shaft 6-7. Both are based on TORVAP C six (6) order sunnation. They are again safely below the OEMA allowable of
) 7000 psi.
DEMA recommendation does not require calculation at overload condition. This is included here for our own reference only.
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.y O TORvAp program Inputs and outputs Page o TO RVAP Me thods . . . . . . . . . . . . . . . . . . . . . . III-1 .
Input Data for TORVAP and Output Requested . . . . . . . . III-1 Input Sheets Required for TORVAP Program . . . . . . . . . III-2
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TORVAP Program Inputs and Outputs July 16, 1984 CCNSUt.TANTs Page III-1 TORVAP Methods
) TORYAP (Torsional Vibration Analysis Program) is a computer program ifcensed from CAD Centre, U.K., and is available from Comshare, Inc., Ann Arbor, Michigan.
Program R provides Holzer natural frequency and determines the significant orders and stresses caused by f
)
Program C provides torque, stress and amplitude at each mass number, as well as sum of stress and amplitud6 for the six major orders evaluated.
TORYAP C is basically a modal supe: position method.
Input Data for TORVAP and Cutput Requested Bore = 17", stroke = 21", crankpin = 12" _ _.N a = mass nuiter I = mass moment of inertia,1b ft sec 2 Rated speed = 450 rps
) Limits = 1000 to 8000 cpe, for search natural frequency Exceder (orders to be studied) = 0.5, 1.0, 1.5, 2.0, 2.5, 3.5, 4.0, 4.5, 5.0, 5.5, 6.5, and 8.0 Engine cycle 4, banks 1 Full load, BHP /cyl = 611, rpm = 450, mech. eff. = 0.9 corresponding to inep = 250 pst
) Torque-speed constant = constant at 250 inep Gas tangential efforts reference Lloyd's Firing order = 2-5-8-4-9-6-3-7 given mass number corresponding to cylinder number 1-4-7-3-8-5-2-6 Stress limit = 5000 psi based on DEMA guidelines for single order torsional vibratory stress, 7000 psi for sum of orders.
The reference shaft angle is assumed to be zero when the piston of
) cylinder 1 is at TDC, firing condition.
The output requested is:
) Maximum amplitude of single order at main mass 1 True sus amplitude at main mass 1 True sus torsional stress at shaft 5-6, 6-7, 7-8, 8-9, 9-10
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E I TORVAP Program Inputs and Outputs July 16, 1984 CCNSLA.TANTs Page III-2 Input Sheets Required for TORYAP Program
) 1: 1005 LOAD. 100% SPEED, L OY Tm, NON CYL MISFIRING (OATA) PEI'Y17*21612 INC NS 1 . t. 0 450 SPEED 2: TITLE 3: UNITS 2 2 (US INDUSTRIAL UNIT) 4: THETAREF ' MAIN' 1 450 450 . 10 5: RANGE ' SPEED' .
6: LIMITS 1000 . 7000 . 2 7: GENERATOR ' MAIN' 11 3 8: BRANCH ' MAIN' OESCRTFTTON 6.8 0. O. 1. 58.1E6 0. O. O. 12.
9: 1 ' GEAR' 12.
10: 2 'CYL l' 49.2 0. 50. 1. E4.7E6 0. O. O.
11: 47.9 0. 50. 1. E4.7E6 0. O. O. 12.
12: 3 'CYL 4 'CYL 3' 2' N 0. 50.1. E4.7E6 0. O. O. 12.
12.
13: 5 'CYL 4' 47.9 0. 50. 1. 44.7E6 0. O. O.
) 14: 6CYL 5' 47.9 0. 50. 1. E4.7E6 0. O. O.
E4.7E6 0. O. O.
12.
12.
15: 7 ' CYL 6' 7. i 0. 50. 1. 12.
16: 8 'CYL 7' N 0. 50. 1. E4.7E6 0. O. O.
17: 9 'CYL 8' N 0. 50. 1. 76.9E6 0. O. O. 12.
18: 10 'F.W.' 1100. O. O. 1. 276.7E6 0. O. O. 7 7 19: 11 ' GEN' 2650. O. O. 1. O. O. O. O. O.
h 20: EXCORDER 4.0 4.5 5.5 3.5 2.5 1.5 0.5 6.5 8.0 5.0 2.0 4.o 21: ENGINE CYE4 'CSA' 22: BORE 17.0 STROKE 21.0 BANKS 1 23: FULLLDXO 611. 450. 0.9 24: TORCUESPEED CONSTANT 'C' 25: HARN0NICS LLOYDS 'LLOYD' 2.* : EXCITATION
) 27: 2 'CYL l" O.0 0. O. O. 816.4 C.
0.
4.2 4.2 0.
0.
28: 3 'CYL 2' 540.0 0. O. O. 816.4 29: 4 'CYL 3' W 0. O. O. 816.4 0. 4.2 0.
0.
20: 5 'CYL 4' 90. O. O. O. 816.4 0. 4.2 31: 6 'CYL 5' 450. O. O. O. 816.4 0. 4.2 0.
32: 7 'CYL 6' 630. O. O. O. 816.4 C. 4.2 0.
) 33: 8 'CYL 7' W 0. 4. O. 816.4 0. 4.2 4.2 0.
0.
34: 9 'CYL 8' 360. O. O. O. 816.4 0.
35: LIMSTRESS M YE AUX '8' l 36: OUTPUT 37: MAXAW 'M.4TN' 1 38: SCANTORQUE ' MAIN' 5 ' MAIN' 6 't%IN' 7 ' MAIN' 8 ' MAIN' 9 39: SUMAMP ' MAIN' 1
) 40: SUMTORQUE ' MAIN' 8 41: SUMTORQUE ' MAIN' 9 42: SUMTORQUE ' MAIN' 7 43: SUxr0RQUE 'itAIN' 6 44: SUMTORQUE ' MAIN' 5 45: (ENO)
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) Torsional Stress at Rated Condition for Second and Third Modes per TORVAP R E3.9L
) Torsional Stress of Shaft 9-10 at 225 beep, for second Mode.IV-1 Torsional Stress of Shaft 9-10 at 225 beep, for Third Mode..IV-1 e~
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P E I Torsional Stress at Rated Condition for SeCond and Third Modes per TORVAP R Aaa adix tv July 16, 1984 i
CCNSULTANTS -Page IV-1 Torsional Stress of Shaft 9-10 at 225 bmeo, for SeCond Mode
) AT NC SPEED AT 225 base CADEA NC NC/'e5 Is in to Mr Sr Mr 5f 0.00 41.5 1826 1.00 sa 0.5 11150.5 24.78 1.51 88.5 5575.2 12.39 .25 95.4 0.02 29.5 5092 1.07 9 1.0 1.01 114 1.5 3718.S 8.26 3.79 90.1 0.01 32.8 3492
.70 74.5 0.08 19.3 18228 1.03 11
) 2.0 2.5 2787.6 2230.1 6.20 4.94 3.79
.25 62.0 51.2 0.01 0.01 34.1 39.8 2792 2076 1.04 1.06 81 4
3.0 1858.4 4.13
- 3. 5 1592.9 3.54 1.51 41.5 0.00 50.0 1030 1.09 22 4.0 1393.8 3.10 1.21 32.7 0.00 50.0 489 1.12 11 4.5 1238.9 2.75 1.51 25.3 0.00 50.0 628 1.15 14 5.0 1115.0 2.48 .25 19.2 0.00 50.0 90 1.19 2 5.5 1013.7 2.25 3.79 14.7 0.00 50.0 915 1.25 23 ,,
6.0 929.2 2.07 .70 11.3 0.00 50.0 130 1.31 3 88 50.0 1.38 16
) 6.5 7.0 457.7 796.5 1.91 1.77 3.79
.25 9.0
- 7. 3 0.00 0.00 50.0 56 3 30 f 47 1 7.5 143.4 1.65 1.51 5.9 0.00 50.0 147 1.58 5 8.0 696.9 1.55 1.21 4.7 0.00 5't.0 94 f.71 3 8.5 655.9 1.46 1.51 3.9 0.00 50.0 97 1.89 4 9.0 $19.5 1.38 .25 3. 4 0.00 50.0 14 2.12 1 9.5 586.9 1.30 3.79 3.1 0.00 50.0 191 2.43 9 10.0 557.5 1.24 .70 2.7 0.00 50.0 32 2.87 2
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Torsional Stress of Shaft 9-10 at 225 tseo, for TMrd Mode AT NC $ PEED AT 225 beso
} ORCER NC NC/3s Is in eg Mf Sf Mr l Se
.96 88.5 0.01 35.9 7460 1.00 208 0.5 14000.8 31.11 15.54 .86 95.4 0.23 15.0 101827 1.00 227 1.0 7000.4 18284 1.01 693 1.5 4666.9 10.37 3.10 90.1 0.02 26.5 1.39 9.6 387547 1.02 298 2.0 3500.2 7.78 2.52 74.5 0.02 29.2 13826 1.03 485 2.5 2900.2 6.22 3.10 62.0 0.07 20.1 42911 1.04 103
) 3.0 2333.5 5.19 .86 51.2 103
.96 41.5 0.00 43.4 4226 1.05 3.5 2000.1 4.45 174 1.97 32.7 0.01 38.2 6213 1.07 4.0 1750.1 3. 89 49.1 2916 1.09 65 4.5 1555.6 3.44 .96 25.3 0.00 0.00 50.0 2020 1.12 '45 5.0 1400.1 3.11 .86 19.2 0.00 41.9 4688 1.14 125 5.5 1272.3 2,83 3.10 14.7 82 2.52 11.3 0.00 47.2 3296 1.17 6.0 1166.7 2.59 1.21 83 1077.0 2.39 3.10 9.0 0.00 47.4 3256 6.5 50.0 766 1.25 19 7.0 1000.1 2.22 .86 7. 3 0.00 50.0 693 1.30 18
) 7.5 933.4 2.07 .96 5.9 4.7 0.00 0.00 50.0 1135 1.36 31 8.0 875.1 1.95 1.97 13 1.83 .96 3.9 0.00 50.0 460 1.43 8.5 823.6 1. 50 11 9.0 777.8 1.73 .86 3.4 0.00 50.0 359 0.00 50.0 1166 1.59 37 9.5 736.9 1.54 3.10 3.1 2.7 0.00 50.0 848 1.70 29 10.0 700.0 1.54 2.52
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Refe.ence List
)
- 1. " Standard Practices for Low and Medfian Speed Stationary Diesel and Gas Engines," Sixth Edition. Diesel Engine Manufacturers Association DEMA, 1972.
) 2. "Lloyd's Register of Shipping:" Guidanca Notes on Torsional . Vibration Characteristics of Main and Auxiliary 011 Engines,1976. ,'
- 3. " Torsional Vibration Analysis Program (TORVAP)," Computer Aided Design Centre Madingley Road, Castrid.;e, UK C33 OHB. June, 1975. Available from Comshare Inc., Ann Arbor, Michigan.
- D
) 4. " Evaluation of Emergency Diesel Generator Crankshafts at Shoreham and Grand Gulf Nuclear Power Stations," Failure Analysis, Associatas, Palo '
Alto, California. March 30. 1984. . ,
~
S. " Vibration Analysis for a Sound Generator-Set DesiM" Dr.11 .
Gee ,
7 September 19, 1978. . . . qp
- 6. " Torsional Vibration Analysis Program (TORVAP)," Caputer Aided Design Centre, Madingley Road, Cas6t.l 3 1975.
-e 9
- R-48,S/M
~6 .-7" Report ce CrinEfad Tur's' ' ~
TM . Inc. . Page 19r 74010/12 for LILCM RoTandT and attachment. April 4,1984.
)
- 8. " Field Test of Emergency Diesel Generator 103," Bercel and Hall, Str and Webster Engineering Corporation. Figure B-33. February,1984.
- 9. " Emergency Diesel Generator Crankshaft Failure Investigation Shoreham Nuclear Power Station," Failure Analysis Associates, Palo Alto, Califor-
) nia, October 31, 1983.
- 10. "Evalution Of Emergency Diesel Generator Crankshafts At Shoreham And Grand Gulf Nuclear Power Stations." FaAA, April 19, 1984. .
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