ML20127K603
| ML20127K603 | |
| Person / Time | |
|---|---|
| Site: | River Bend  |
| Issue date: | 06/01/1985 |
| From: | Pischinger F FORSCHUNGSGESELLSCHAFT FUR ENERGIETECHNIK UND VERBREN |
| To: | |
| Shared Package | |
| ML20127K591 | List: |
| References | |
| NUDOCS 8506270505 | |
| Download: ML20127K603 (31) | |
Text
_ _ _ _ _ __ ___ ___ _
I FORSCHUNGSGESELLSCHAFT .
j FOR ENERGIETECHNIK UND VERBRENNUNGSMOTOREN MBH J0licher StraBe 342-352 5100 Aachen Tel. (02 41) 16 601 0 Telex 08 32301 l
l
! l l
Operational Safety of TDI DSR-48 Emergency l Diesel Generator Crankshafts at River Bend Station, Gulf State Utilities
(
)
June 1st,1985 Prof. Dr. Franz Pisch 8506270505 850612 PDR ADOCK 05000458 8 PDR
TABLE OF CONTENTS INTRODUCTION AND
SUMMARY
1.0 PRINCIPLES OF THE KRITZER-STAHL METHOD 2.0 CALCULATION OF CRANKSHAFT STRESS 2.1 Nominal Bending Stress Amplitude 2.2 Torsional Vibrations i 2.2.1 Operational Engine Data 2.2.2 Nominal Torsional Stress Amplitude 2.2.3 Equivalent Stress Amplitude 3.0 ENDURANCE LIMIT OF CRANKSHAFT 3.1 Calculated Endurance Limit 3.2 Fatigue Analysis 4.0 FACTOR OF SAFETY 5.0 COMPARISON OF FaAA AND FEV RESULTS
6.0 REFERENCES
4 INTRODUCTION AND
SUMMARY
The subject of this report is the operational adequacy of the crankshafts of the Transamerica Delaval Inc. (TDI)
DSR-48 engines Serial No. 74 039 (EG1A) and Serial No. 74 040 (EG1B) at the River Bend Station (RBS) for an electrical power output of 3130 kW at 450 rpm.
The installed 13-inch by 12-inch crankshafts are identified by TDI Part Number 03-310-05-AC and are forged and machined by Ellwood City Forge Corporation. The part numbers of the RBS crankshafts are the same as the part numbers of the crankshafts currently installed at the Shoreham Nuclear Power Station (SNPS) (1).
To define the adequacy of the crankshafts a conservative method is used which has been proven in industry practice.
This method also incorporates the experience with crank pin fillet fatigue damage identified in three 13-inch by 11-inch crankshafts previously installed in TDI DSR-48 engines at SNPS. Thereby, a high degree of reliability in determining the strength and stresses of the crankshaft is achieved. )
l By application of this proven conservative method, FEV concludes that the safety factor, s = 1.205, is completely l sufficient to assure the adequacy of the crankshaft for a l 1
output power of 3130 kW at 450 rpm. ;
l
1.0 PRINCIPLES OF THE KRITZER-STAHL METHOD To assess the adequacy of the crankshaft, a method commonly used by the german engine industry is applied. The Kritzer-Stahl method includes the calculation of the equivalent stress amplitude at the highest stressed location of the crankshaft by using stress concentration factors. This equivalent stress is compared with the endurance limit which, in a very conservative way, can be derived from standard material properties. In a more accurate way the endurance limit can be determined by crankshaft fatigue tests. Equivalent stress amplitude and endurance limit are then used to calculate the safety factor.
2.0 CALCULATION OF CRANKSHAFT STRESSES According to the Kritzer-Stahl method, the stresses in the pin fillet of the crankshaft are calculated as an equivalent stress amplitude using the maximum distortion energy theory:
- a. = V(s, &. )2 + 3(s, f. )2 h, : equivalent stress amplitude
[3,: notch effect factor for bending O'n, : nominal alternating bending stress amplitude
[3,: notch effect factor for torsion f,, : nominal alternating torsional stress amplitude Calculation of the nominal stresses necessitates the determination of the bending stresses in the plane of the throw and the torsional stresses due to the torsional vibrations of the crankshaft and generator system. The.value of the notch effect factor O introduces the influence of the geometric dimensions of the throw (particularly the highest stressed fillet radii), the stress gradient and the notch sensitivity of the material.
2.1 ' NOMINAL BENDING STRESS AMPLITUDE The bending moment along the crankshaft is calculated by using the continuous beam method. The determination of' the corresponding bending stresses (calculated by using the stress concentration factor) and a phase related superposition with the torsional stresses (shown in section 2.2) yields the following conclusions:
o The maximum. bending stress amplitude is about 50% of the maximum torsional stress amplitude o The maxima for torsional stresses and the maxima for bending stresses occur at different times during the cycle for all throws o The highest bending stresses and the highest torsional stresses occur at different locations in the fillet o The phase related superposition of torsional and bending stresses show that the maximum equivalent stress values are not increased at any throw by taking into account bending stresses
. These calculated results are supported by strain measurements at
- the crank pin fillet radii of the SNPS engines (4). Since the bending stresses have no effect on the maximum values of the
< m
equivalent stress, the equivalent stress amplitude may be calculated with the following formula:
- 6. = V3 (#, f,,)2 h, : equivalent stress amplitude ff,: notch effect factor for torsion
. A 7 n, : nominal alternating torsional stress amplitude 2.2 TORSIONAL VIBRATIONS The following sections present procedures used to obtain the engine operational data, nominal torsional stress amplitude and equivalent stress amplitude. Together these quantities describe the state of torsional vibration in the River Bend crankshaft.
Data for the SNPS crankshafts are presented for comparison.
1 2.2.1 OPERATIONAL ENGINE DATA A procedure based upon a large amount of experience with diesel engines of these sizes has been utilized in the determination of the cyclinder pressure curve. The following data represent input parameters:
o Mean indicated pressure o Peak firing pressure o Boost pressure o Compression ratio o Injection timing o Valve timing o Geometry of the engine
The mean indicated pressure was calculated from the power output and considers- the effects of friction losses. The boost pressure was measured in the intake manifold by RBS personnel.
The peak firing pressure was calculated from the measured values obtained by a Kiene mechanical pressure gage. Experience at SNPS has shown (by comparison with quartz transducer measurements) that the Kiene gage readings tend to overshoot the actual values most probably due to mechanical gage inertia. The Kiene gage data used in the RBS peak firing pressure calculation has been corrected by an overshoot ratio based upon SNPS experienco.
RBS Kiene gage measurements were only available for 3500 kW and 2607 kW output power levels.
Therefore, the peak firing pressure for 3130 kW was calculated by linear interpolation.
l The significant engine operational data are shown in Table 2 1.
A comparison of the calculated cylinder pressure curves for RBS and SNPS and the measured curve of SNPS are shown in Figure 2.1.
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2.2.2 NOMINAL TORSIONAL STRESS AMPLITUDE To calculate the torsional vibrations, the engine and the generator were described by a model consisting of masses of inertia, stiffnesses and damping rates (Figure 2.2). This model is adequate for an unrestrained forced and damped multimass vibration system. The acting force is given by the gas forces at the pistons and the masses of inertia from the pistons and the connecting rods (5). Table 2.2 shows the reduced data for the 11 mass system describing the crankshaft, flywheel and generator. These data are the same as those of the FaAA Report (1). However, they have also been independently recalculated by FEV based on information obtained from the crankshaft drawing.
The absolute and relative damping rates are functions of the kinetic energy of the vibration, the swept volume and the frictional losses in the engine. The appropriate factors for frictional losses were determined from FEV experience.
The solution of the 2nd order system of differential equations was performed by using Fourier analysis involving the decomposition of the periodic tangential forces into 24 harmonics (0,5th to 12th order). Table 2.3 shows the results of the Fourier analysis of the calculated cylinder pressure curve data for the RBS engines at 3130 kW output power and 450 rpm.
The first three fundamental modes of vibration are shown in Table 2.4.
Table 2.5 shows the nominal torsional stress amplitudes for the highest stressed throws for RBS (3130 kW) and for SNPS (3300 kW) at three different speeds. It can be seen that the highest stressed throw for nominal speed for both cases is at cylinder number 5/6.
1 S
I h
93 02 03 Oc Os 06 07 Os 09 Go i 033 0
O O O O O @ O O O e
C1 C2 C3 Cf. Cc; C6 C7 C8 Cg Co i
-D L .D D D D L .T 2 L 0ki ki ki ki ki ki ki ki ki ki NQ NQ NQ NQ NQ NQ N
.Q O
- Rotational mass of inertia 63 Cj : Stiffness Kaj : Damping coefficient, absolute damping rate Kji : Damping coefficient, relative damping rate j : Consecutive number Figure 2.2 Dynamic Model for Torsional Vibration Calculation
-~,e . - -
RBS SNPS 8 [kg m3 2 C [Nm/ rad) 8 [kg m] a C [Nm/ rad]
6 6 10 10 1 9,2 9,2 78,77 78,77 2 66,7 66,7 114,8 114,8 3 64,9 64,9 114,8 114,8 4 64,9 64,9 114,8 114,8 5 64,9 64,9 114,8 114,8 6 64,9 64,9 114,8 114,8 7 64,9 64,9 114,8 114,8 8 64,9 64,9 114,8 114,8 9 67,9 67,9 104,3 104,3 10 578,2 1491,5 419,9 375,3 11 6746,6 3593,4 e: rotational mass of inertia C: ro'cational stiffness Table 2.2: Comparison of Crankshaf t Reduction Data
f l
l l
n A 8 ## " psi]
l n n n n 0.5 3.90256 4.26893 5.78392 83.9466 1.0 2.10553 9.05973 9.30110 134.995 I 1.5 0.353077 7.17804 7.18672 104.307 .
2.0 -0.609062 -0.910697 1.10225 15.9979 l 1
2.5 -0.762219 4.86740 4.92672 71.5054 l l 3.0 -0.863256 1.46101 1.69698 24.6296 3.5 -1.00759 3.06477 3.22615 46.8236 l 4.0 -0.974064 2.06067 2.27929 33.0811 .
l 4.5 -0.841456 1.67027 1.87740 27.2482 3.0 -0.761378 1.27381 1.48401 21.5386 5.5 -0.673859 0.864746 1.09630 15.9115 6.0 -0.553287 0.586746 0.806473 11.7050 6.5 -0.462116 0.385605 0.601865 8.73535 7.0 -0.379106 0.213583 0.435131 6.31540 l 7.5 -0.279573 0.969344E-01 0.295901 4.29465 l 8.0 -0.205354 0.349093E-01 0.208300 3.02322 O.5 -0.153055 -0.164587E-01 0.153937 2.23421 9.0 -0.946335E-01 -0.511329E-01 0.107564 1.56116 9.5 -0.507813E-01 -0.566637E-01 0.760809E-01 1.10434 10.0 -0.265640E-01 -0.604512E-01 0.660306E-01 0.950354 10.5 -0.526966E-03 -0.618360E-01 0.618382E-01 0.897507 11.0 0.172898E-01 -0.482556E-01 0.512595E-01 0.743970 11.5 0.201030E-01 -0.373791E-01 0.424421E-01 0.615995 12.0 0.250662E-01 -0.321304E-01 0.407514E-01 0.591457 1
Harmonic coefficient T n = ilA y n +B' 2 8 n
j l
1 Table 2.3: Result of Fourier Analysis (RBS, Load 3130 KW at 450 rpm) i i
1 1
4 I
i u
1 RBS SNPS 1st 30,0 38,72 2nd 108,0 92,93 3rd 147,0 116,70 Table 2.4: Natural Modes of Vibration (Hzl
River Bend Station: i nt !""
Crank pin # 5/6 6/7 7/8 i
427.5 rpm 45.0 43.8 43.3 450 rpm 45.8 41.3 40.5 472.5 rpm 51.7 48.0 45.7 Shoreham NPS: i nt !""
Crank pin # 5/6 6/7 7/8 427.5 rpm 51.3 52.3 53.3 450 rpm 45.1 40.4 39.9 472.5 rpm 50.1 47.0 43.8 Table 2.5: Nominal Torsional Stress Amplitude i at 450, 427.5, 472.5 rpm nt These stresses are calculated for a load cor-responding to 3130 kW (River Bend), 3300 kW (Shoreham) at 450 rpm
l Table 2.6 shows the maximum nominal torsional stress amplitudes and the angular displacement amplitudes (b (0) at the free end of the crankshaft for 3130 kW output power at 450 rpm for RBS and for 3300 kW for SNPS. Figure 2.3 shows the dependence of both values on engine speed for the RBS crankshaft.
Verification of the 11-Mass Model was accomplished by repeating the calculations using a 19-mass model where each single throw was represented by two masses of inertia. Results indicate that throughout the crankshaft none of the calculated stresses were greater than those predicted by the initial 11-Mass Model.
According to experience even the permanent misfiring of one cylinder has no detrimental effect on the crankshafts of in-line engines.
l I
l l
t
i RBS SNPS 3130 kW/450 rpm 3300 kW/450 rpm nominal torsional stress amplitude 45,8 45,1 2
T nt (N/mm ) Cyl. 5/6 angular displacement ~
0,73 0,69 amplitude $ (*)
i Table 2.6: Comparison of Torsional Vibration Characteristics c
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z O 4 0,4 30 i i e i , i e i i 400 450 500 Engine Speed [1/ min]
Figure 2.3: Nominal Torsional Stress at Different Engine Speeds, RBS A: 5 % Underspeed B: 450 rpm, Nominal Speed C: 455,5 rpm, 5th order critical Speed D: 5 % overspeed
2.2.3 EQUIVALENT STRESS AMPLITUDES The calculation of the notch effect factor $i is shown in Table 2.7. Since the 13-inch by 12-inch crankshafts at RBS have the same dimensions as the SNPS crankshafts (TDI Part No.
03-310-05-AC), the notch effect factor $t is the same.
Using the nominal stresses, the notch effect factor and the maximum distortion energy theory, the equivalent stress is
~
calculated. The values are shown in Table 2.8 for RBS and SNPS.
The nominal stresses and the angular displacement amplitude at the free end are also included, t
Calculation of Notch Effect Factor for Torsion 0, he : yk( U t- 1)+ 1 Un = 0,78 notch sensitivity of the crankshaft material at = 2,39 stress concentration factor
$, = 2,08 4 Calculation of Stress Concentration Factor at at : 2,14 -
g)(S) *9 2 IU) '
93 INI *94 (R) g) (S) = 0,93 : function of pin-to-main journal overlap g2 (B) =1 : function of web width g3 (W) = 1 : function of web thickness g4 (R) = 1,2 : function of fillet geometry at= 2,39 Table 2.7 Calculation of Notch Effect Factor for Torsion (6), (8), (9), (10) i i
l l
l 1
RBS SNPS 13" by 12" 13" by 12" 13" by 11" 3130 kW/450 rpm 3300 kW/450 rpm 3500 kW/450 rpm .
equivalent stress 166 163 270 anplitude O y[ N/mn 23 nominal torsional stress 45,8 45,1 71,2 anplitude t [N/mn* 3 angular displacement 0,73 0,69 0,92 anplitude 5(*)
- 2. 8 : Comparison of calculated Torsional stresses Table
~
3.0 ENDURANCE LIMIT FOR THE CRANKSHAFT A procedure for the calculation of an endurance limit for the RBS crankshafts is presented in the following sections. The calculation methodology includes various factors reflecting the geometric, material and processing parameters of an actual crankshaft. A factor of safety is developed by comparing this to the endurance limit experimentally determined by the failed SNPS crankshafts which were manufactured with similar design and materials.
3.1 CALCULATED ENDURANCE LIMIT Table 3 outlines the parameters used in determining the conser-vative endurance limit for the following crankshafts:
o 13-inch by 12-inch crankshaft of RBS o 13-inch by 12-inch crankshaft of SNPS o 13-inch by 11-inch crankshaft of SNPS It can be seen that the calculated endurance limit O'o of the RBS crankshaft differs by only 1,8% from the 13-inch by 11-inch crankshaft of SNPS. This change is due to small differences in the relative properties of the crankshafts. Influences on the properties affected by shot peening are not considered. Based upon the experience of FEV, the endurance limits shown in Table 3 are very conservative values.
3.2 FATIGUE ANALYSIS The experience with the three cracked or broken crankshafts at SNPS which exhibit approximately the same material properties and dimensions was drawn upon to determine an endurance limit 6mxp, The calculation is based on the following information.
o The number of cycles of the failed crankshafts is N = 4 -
106 cycles at 3500 kW and higher output power.
o The calculation of the equivalent stress amplitude of the 13-inch by 11-inch crankshaft at SNPS at 3500 kW yields 6 v11SNPS = 270 N/mm2 .
o An S-N curve of a crankshaft with about the same material and size is available. This curve is based on experience from a test bench and is shown in Figure 3 as a normalized function.
From the evaluation in Figure 3 the following conclusions can be drawn:
o The endurance limit of the 13-inch by 11-inch SNPS crankshaft is 6ogxp = 202.5 N/mm 2, o This experimental endurance limit GOEXP is 1.2 7 times the i
calculated endurance limit (section 3.1).
o The value of the experimental endurance limit 6 DEXP 18 within the usual range for crankshafts of this size (7).
i V
2-15-I 1
1 0,5-4 5$1 6 2 4 $ $1 7 2 AdEF g to 10 10 N (cycles) ,
Figure 3 Normalized S-N curve for total crankshaft fracture based on experimental investigations of original crankshafts with almost the same dimensions and the RBS crankshafts (from material properties as industry bench testing).
Definition:
6 Y= : stress amplitude ratio (SAR), the ratio g
DEXP of the equivalent stress amplitude (fatigue stress) to the value of endurance limit.
Determination of the endurance limit
= 1.326 : SAR for crankshafts of the type of the Y3 SNPS 13-inch by 11-inch crankshafts at N
=4 -
10 6 cycles
Figure 3 continued:
c = 203.7 N/mm 8 : Calculated endurance limit of the failed DEXP SNPS crankshafts
- v U
DEXP" Y1 2 of the 8 = 270 N/mm : Equivalent stress amplitude failed SNPS crankshafts cDEXP of endurance limit from experience
- Ratio S2* o D
to the calculated value of endurance limit (CD" 2 " l' : 5.dditional safety factor These results confirm that the calculation procedure to determine endurance limits which was used in this analysis is very conservative. In this case, the calculated endurance limit contains an additional safety factor of 1.227. Therefore, FEV concludes that a reliable assessment of the crankshaft can be obtained by using the experimental endurance limit which includes the effects of actual engine operation.
4.0 FACTOR OF SAFETY The equivalent stress amplitudes as well as the calculated and experimental endurance limits are shown in Table 4. The safety factors can be calculated as shown in Table 4 using the experimentally determined additional safety factor inherent in the conservative values.
The safety factor for 3130 kW and 450 rpm at RBS of S = 1.205 is within the range of the safety requirements (S = 1,15.. 1,30) that are normally considered adequate by the german engine manufacturers. The draft rules of CIMAC require a minimum safety factor of only 1,15 for calculations which do not use experimental crankshaft data. The fact that there are experimental results available in this' case allows FEV to conclude that the safety factor is completely adequate for the crankshafts at RBS.
5.0 COMPARISON OF FaAA AND FEV RESULTS A comparison of the most important data concerning the adequacy of the RBS crankshafts at 3130 kW output power and 450 rpm is shown in Table 5. The following conclusions are drawn:
o The stress values computed by FaAA and FEV are in excellent A A agreement ( 7ntsis,av , 9)i o FaAA cites a higher endurance limit than FEV o FaAA calculates a higher safety factor than FEV The differences between the FaAA and FEV values are explained by different S-N curves. FaAA relies on an S-N curve of a laboratory probe specimen for the given material. FEV uses an experimentally determined S-N curve for actual crankshafts, which contains known conservative features.
l
FaAA FEV Nominal Torsional stress 46,94 45,8 Amplitude tntS/6 [N/mm j a ',
Equivalent Stress 164,7 166 Amplitude 6 [ N/mm* ]
Angular Displacement 0,7 0,73 4(*)
Endurance Limit 227 200 D
Exp Safety Factor 1,39 1,205 S
Table 5: Comparison of FaAA and FEV Results for RBS at 3130 kW/450 rpm
a
6.0 REFERENCES
(1) : Failure Analysis Associates, Palo Alto, California Evaluation of DSR-48 Emergency Diesel Generator Crankshafts at River Bend Station; 85-5-10 (2) : American Bureau of Shipping Report on Castings or Forgings; #640; #635 (3): Ellwood City Forge Company Report of Tests of Crankshaft; 5-15-80 (4): Stone & Webster Engineering Corporation Field Test of Emergency Diesel Generator 103; B1-1160037-1 (5): Mass, M./Klier, M.
Die Verbrennungskraftmaschine Bd. 2 Krnfte, Momente und deren Ausgleich in der Verbrennungskraftmaschine, Springer Verlag 1981 (6): Thum, A./Buchmann, W.
Dauerfestigkeit und Konstruktion, VDI-Verlag 1932 (7): Forschungsvereinigung Verbrennungskraftmaschinen e.V.
Kurbelwellen III Studie Uber den Einfluss der Baugr6be auf die l
_ ~ - . _-, _.
Dauerfestigkeit von Kurbelwellen Zeuner, M., Heft 199 (1976)
(8): Kritzer, R.
Mechanik, Beanspruchung und Dauerbruchsicherheit der Kurbelwellen schnellaufender Dieselmotoren Konstruktion 13/11, 12 (1961)
(9): Stahl, G.
Der Einfluss der Form auf die Spannung in Kurbelwellen Konstruktion 10/1 (1958)
(10): Hasselgruber, M./Knoch, W.
Zur Berechnung der Formzahlen von Kurbelwellen MTZ 21/8 (1960)
I
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