ML18044B048
| ML18044B048 | |
| Person / Time | |
|---|---|
| Site: | 05200046 |
| Issue date: | 07/31/2017 |
| From: | Hall G Korea Hydro & Nuclear Power Co, Ltd, Westinghouse |
| To: | Office of New Reactors |
| Shared Package | |
| ML18044B036 | List: |
| References | |
| MKD/NW-18-0027L APR1400-A-M-NR-14001-NP, Rev. 3, WCAP-17942-NP | |
| Download: ML18044B048 (29) | |
Text
Westinghouse Non-Proprieta1y Class 3 WCAP-1 7942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3 KHNP APR1400 Flywheel Integrity Report
@Westinghouse
Westinghouse Non-Proprieta1y Class 3 WCAP-17942-NP (APR1400-A-M-NR-14001-NP)
Revision 3 KHNP APR1400 Flywheel Integrity Report Gordon Z. Hall*
MRCDA - I, Engineering Services July 2017 Reviewer: Thomas E. Demers*
MRCDA - I, Engineering Se1vices Approved: Patrick Hill for Carl J. Gimbrone*, Manager MRCDA - I, Engineering Services
- Electronically approved records are authenticated in the electronic document management system.
Westinghouse Electric Company LLC 1000 Westinghouse Drive Cranbeny Township, PA 16066, USA
© 2017 Westinghouse Electric Company LLC All Rights Rese1ved
Westinghouse Non-Proprietary Class 3 ii ABSTRACT This repo1t demonstrates that the APRl400 reactor coolant pump (RCP) flywheel satisfies all of the RCP flywheel integiity criteria of the design specification [l ] and U.S . NRC Regulato1y Guide 1.14 [2]. The combination of shrink-fit and rotational stresses at n01mal pump operation speed and at overspeed are calculated and shown to be acceptable with respect to the prescribed criteria in [l , 2, and 8]. <}
The critical speeds for ductile and non-ductile fracture are computed and shown to be significantly gi*eater than two times n01mal speed as required by the Regulato1y Guide [2]. It is demonstrated that excessive defo1mation will not result from an overspeed condition.
WCAP-17942-NP (APR1400-A-M-NR-14001 -NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 iii TABLE OF CONTENTS ABSTRACT .................................................................................................................................................. ii LIST OF TABLES ....................................................................................................................................... iv LIST OF FIGURES ..................................................................................................................................... iv I BACKGROUND AND PURPOSE .............................................................................................. 1-1 2 REQUIREMENTS ........................................................................................................................ 2-1 2.1 LIMITS OF APPLICABILITY........................................................................................ 2-1 2.2 OPEN ITEMS .................................................................................................................. 2-1 2.3 DISCUSSION OF SIGNIFICANT ASSUMPTIONS ..................................................... 2-1 2.4 ACCEPTANCE CRITERIA ............................................................................................ 2-1 3 METHODOLGY .......................................................................................................................... 3-1 3.1 STRESSES AND RADIAL DISPLACEMENT DUE TO SHRINK FIT OF SECTIONS OF FLYWHEEL .............................................................................................................. 3-1 3.2 STRESSES AND RADIAL DISPLACEMENT DUE TO ROTATION OF FLYWHEEL3-2 3.3 STRESS INTENSITY FACTOR OF ASSUMED CRACK IN FLYWHEEL ................. 3-3 4 INPUT ........................................................................................................................................... 4-1 4.1 MATERIALS ................................................................................................................... 4-1 4.2 GEOMETRY ................................................................................................................... 4-1 4.3 ROTATIONAL SPEEDS PER THE DESIGN SPECIFICATION .................................. .4-2 5 EVALUATION ANDANALYSIS ................................................................................................ 5-1 5.1 SHRINK FIT REQUIREMENTS .................................................................................... 5-1 5.2 HUB-WHEEL ASSEMBLY SHRINK FIT CONTACT PRESSURE ............................. 5-1 5.3 HUB-WHEEL ASSEMBLY SHRINK FIT STRESSES .................................................. 5-2 5.4 ATTACH TO SHAFT SHRINK FIT CONTACT PRESSURE ....................................... 5-2 5.5 ATTACH TO SHAFT SHRINK FIT STRESSES ............................................................ 5-2 5.6 STRESSES DUE TO ROTATION AT 1,200 RPM .......................................................... 5-4
......................................................................................................................................... 5-6 5.7 STRESSES DUE TO ROTATION AT 125% OVER SPEED, 1,500 RPM ..................... 5-6 5.8 STRESS DUE TO ROTATION AT 1,800 RPM .............................................................. 5-6 5.9 JOINT RELEASE SPEED FOR PRESCRIBED SHRINK VALUES ............................. 5-7 5.10 CONSIDERATION OF MINIMUM SHRINK FIT......................................................... 5-7 5.1 1 EVALUATION OF STRESSES ...................................................................................... 5-8 5.12 CONSIDERATION OF SEISMIC EVENT ..................................................................... 5-8 5.13 STRESS INTENSITY FACTOR OF CRACK FOR OUTER WHEEL .......................... 5-8 5.14 EVALUATION OF INTEGRITY .................................................................................. 5-13 5.1 5 FATIGUE CRACK GROWTH ...................................................................................... 5-14 6 RESULTS AND CONCLUSIONS ............................................................................................... 6-1 7 REFERENCES ............................................................................................................................. 7-1 WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 iv LIST OF TABLES Table 5-1 : N 01mal and Critical Speed Comparison ................................................................................ 5-14 LIST OF FIGURES Figure 4-1 : APR1400 Flywheel Sketch [6] .............................................................................................. .4-2 Figure 5-1 : Standstill Stress due to Wheel Assembly Shrink Fit.. ............................................................ 5-2 Figure 5-2: Standstill Stress due to Shrink Fit onto Shaft......................................................................... 5-3 Figure 5-3: Total Stress at Standstill ......................................................................................................... 5-3 Figure 5-4: Stress due to Rotation at 1,200 RPM ..................................................................................... 5-4 Figure 5-5: Total Stress at 1,200 RPM ...................................................................................................... 5-5 Figure 5-6: Total Stress at Operation at 1,500 RPM ................................................................................. 5-6 Figure 5-7: Total Stresses at Joint Release Speed of 1,786 RPM ............................................................. 5-7 Figure 5-8: Polynomial Tangential Stress at Standstill ........................................................................... 5-10 Figure 5-9: Stress Intensity Factor versus Crack Length at Standstill .................................................... 5-10 Figure 5-1 0: Polynomial Tangential Stress at 1,200 RPM ...................................................................... 5-1 1 Figure 5-11: Stress Intensity Factor versus Crack Length at 1,200 RPM ............................................... 5-11 Figure 5-12: Polynomial Tangential Stress at 1,500 RPM ...................................................................... 5-12 Figure 5-13: Stress Intensity Factor versus Crack Length at 1,500 RPM ............................................... 5-12 Figure 5-1 6: Rotation Speed to Reach a K1c of 150 ksi-in112 .................................................................. 5-13 Figure 5-17: Change in Outer Wheel K1 from Standstill to No1mal Operation ...................................... 5-15 WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 1-1 1 BACKGROUND AND PURPOSE In suppo1t of the Design Ce1tification Application (DCA) of the APR1400 Advanced Light Water Reactor (ALWR) design, Korea Hydro & Nuclear Power (KHNP) requested Westinghouse to evaluate the integrity of the APRl400 RCP motor flywheel design. The subject matter of this repo1t is the flywheel integi*ity analyses pe1fo1med by Westinghouse to quantify the stiuctural integi*ity of the flywheel as well as the critical speeds of the flywheel under nonnal and off-nonnal operating conditions. Specifically, the objective of the analyses is to compute the sti*esses and critical speeds and to compare the results to criteria in the design specification [I] and U.S.
NRC Regulato1y Guide 1.14 [2].
Po1tions of this repo1t contain proprietary info1mation. Prop1ieta1y info1mation is identified and bracketed. For each of the bracketed sections, the reasons for the proprietary classification are provided using superscripted letters "a", "c", and "e". These letters stand for:
- a. The info1mation reveals the distinguishing aspects of a process or component, stlucture, tool, method, etc. The prevention of its use by Westinghouse's competitors, without license from Westinghouse, gives Westinghouse a competitive economic advantage.
- c. The info1mation, if used by a competitor, would reduce the competitor's expenditure of resources or improve the competitor's advantage in the design, manufacture, shipment, installation, assurance of quality, or licensing of a similar product.
- e. The info1mation reveals aspects of past, present, or fhture Westinghouse- or customer-fonded development plans and progi*ains of potential commercial value to Westinghouse.
Revision 1 conects wording in Section 5.11 in response to CAPAL 100377490. This conection has no impact on any of the evaluations, results, or conclusions in this repo1t. Revision 1 also details the critical speed for excessive defo1mation discussion in Section 6, item 9.
Revision 2 changes the Section 2.4, acceptance criterion I sti*ess limit to 1/3 Sy from 1/3 Su (Revisions O and 1) for total sti*ess in the flywheel at standstill and n01mal operating speed. The measured Sy is conservatively assumed to be 800 MPa or 116,030 psi. Preliminary measured Sy is 816 MPa per [9], and is pending on confi1mation by Siemens' material test repo1t.
Revision 3 updates all calculations per the updated design specification [1] which removed the previous standstill sti*ess in c1iterion 1, and the joint release speed and stress requirements in criterion 3 in previous revisions. The minimum specified yield sti*ength, Sy = 640 MPa (92,824 psi) is used instead of the prelimina1y measured Sy value repo1ted in [9]. Shrink fit dimensions are optimized to meet the n01mal operating sti*ess limit of 1/3 Sy. The previous revisions considered shlink fit reduction based on radial displacement delta of the shaft, hub and outer wheel as individual pieces. At the same time, the rotation ine1tia stress assumed the hub and outer wheel as one solid piece. This method resulted in a conservative total sti*ess. Revision 3 considers the shl*ink fit sti*ess at standstill, and combines the rotation ine1tia sti*ess with the shaft, hub and outer wheel as a single piece. Detail discussion is in Section 5.6. All affected calculation results are updated. The tenns "hoop sti*ess" and "tangential sti*ess" ai*e used interchangeably in this revision.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 2-1 2 REQUIREMENTS 2.1 LIMITS OF APPLICABILITY This repo1t is applicable to the KHNP APRl400 flywheel only.
2.2 OPEN ITEMS This rep01t contains no open items.
2.3 DISCUSSION OF SIGNIFICANT ASSUMPTIONS This repo1t contains no significant assumptions.
2.4 ACCEPTANCE CRITERIA The acceptance criteria in the specification [I] and the standard review plan (SRP) [8] include:
- 1. The total stress in the flywheel at nonnal operating speed does not exceed 1/3 of the minimum specified or measured yield strength (1/3 Sy) per [I and 8].
- 2. The total stress at design overspeed does not exceed 2/3 of the minimum specified or measured yield strength (2/3 Sy), where design overspeed is 125% of nonnal operating speed. +
The Regulato1y Guide acceptance criteria are established in [2] as:
- 3. Flywheel assembly should be designed to withstand n01mal conditions, anticipated transients, the design basis LOCA, and the safe shutdown eaithquake without loss of strnctural integrity.
- 4. The critical speed for ductile fracnire should be predicted.
- 5. The critical speed for non-ductile fracmre should be predicted.
- 6. The n01mal speed should be less than one-half of the lowest critical speeds.
- 8. The critical speed for excessive defonnation of the flywheel should be predicted.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 3-1 3 METHODOLGY This analysis calculates the stresses in the flywheel resulting from the shrink fit of the sections of the flywheel and the rotation of the flywheel at various speeds. Using these stresses, the integrity of the flywheel is evaluated by assuming a crack in the highest stressed location of the flywheel to assess if the cliteria of [l ] and [2] are satisfied.
3.1 STRESSES AND RADIAL DISPLACEMENT DUE TO SHRINK FIT OF SECTIONS OF FLYWHEEL The stresses due to shrink fit are dete1mined by the fo1mulae [3 , page 683].
The flywheel is constrncted by shrink fitting thr*ee pai1s. First, the outer wheel is shr*ink fitted to the hub. Next, the assembly of the outer wheel and hub is shrink fitted to the shaft. Then, the amount of shr*ink fit required to maintain contact between the outer wheel and the shaft is dete1mined by the relative radial displacement due to rotation at the maximum rotational speed.
The following definitions apply:
a = outside radius of outer wheel b= inner radius of outer wheel c = outer radius of the hub, nominally equal to b d = averaged inner radius of hub e = outer radius of the shaft, nominally equal to d The relationship between radial displacement of the inner radius and contact pressure for the outer wheel is expressed as:
Equation 1 [3]
In Equation 1:
a= outside radius of wheel b = inside radius of wheel P = contact pressure between outer wheel and hub E = Young's modulus v = Poisson ratio radial stress:
Equation 2 [3]
In Equation 2:
r = distance from center of wheel P = pressure on inner radius of wheel WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 3-2 tangential stress:
Equation 3 [3]
The relationship between the radial displacement of the outer radius and the contact pressure for the hub is expressed as:
Equation 4 [3]
In Equation 4:
c = outside radius of hub d = averaged inside radius of hub radial stress:
Equation 5 [3]
In Equation 5:
r = distance from center of wheel P = pressure on outer radius of hub tangential stress:
Equation 6 [3]
3.2 STRESSES AND RADIAL DISPLACEMENT DUE TO ROTATION OF FLYWHEEL The stresses and displacements due to rotation of a disk of unifo1m thickness are taken from [3 ,
page 746].
The change in the inner radius of the outer wheel due to rotation of "W" in radians/sec is expressed as:
llb = (1/4)(density/gravity)*W 2 *(b/E)* [(3 + v)a2 + (1 - v)b 2] Equation 7 [3]
The change in the outer radius of the hub due to rotation of "W" in radians/sec is expressed as:
llc = (1/4)(density/gravity)*W2 *(c/E)*[(l - v)c2 + (3 + v)d2] Equation 8 [3]
Equations 7 and 8 are used to calculate shrink fit values.
WCAP-1 7942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 3-3 The general fo1ms for tangential and radial stress due to rotation are:
St= (1/8)(density/gravity)*W2 *[(3 + v)*(R/+ R/ + R/ R/ lr2) - (1 + 3v)r2]
Sr= (1/8)*(3 + v)*(density/gravity) *W2 *[ R /+ R 2 - (Ro2R/!i2 )-12 ]
where, Riis inner radius; Ro is outer radius; "r" is the radial location of the stress.
The shaft, hub and outer wheel rotate as a solid piece until separation, therefore, Ri for whole assembly including the shaft is zero. The equations for tangential and radial stresses become:
St= (1/8)(density/gravity)*W2 *[(3 + v)*a2 - (1 + 3v)12 ] Equation 9 [3]
Sr= (1/8)*(3 + v)*(density/gravity) *W2 *(a2 - 12 ) Equation 10 [3]
3.3 STRESS INTENSITY FACTOR OF ASSUMED CRACK IN FLYWHEEL The stress intensity factor for an axial crack in a cylinder will be used to compute the effect of a crack in the outer wheel. The highest stress location is the inner radius of the outer wheel. The stress intensity factor fo1mula is taken from [4, Section C.5.5]. This fo1mula computes the stress intensity factor for a fomth order polynomial stress distribution for a longitudinal (axial) inside smface crack on a cylinder of infinite length. The tabular coefficients in [4] are listed up to a thickness to inside radius ratio (t/Ri) of 1.0.
[ St = SO+ S l (x/t) + S2(x/t) 2 + S3(x/t)3 + S4(x/t)4 Equation 11 Kr = [GOSO + G l S l (a/t) + G2S2(a/t)2 + G3S3(a/t)3 + G4S4(a/t)4]-f(na) Equation 12 In Equations 11 and 12:
St = tangential stress a = radial dimension of assumed crack t = distance between inner and outer radii of wheel x = distance from cracked edge WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 4-1 4 INPUT The units of dimensions and material prope1ties are given in metric units. The calculations are perfo1med in customary U.S. units. Some metlic units w ill be stated as reference values for compalison w ith other flywheel documentation.
The stress analysis in [6] is pe1fo1med in met1ic units. The results of the analysis in [6], when conve1ted to customa1y U.S. units, are slightly different than the results calculated herein (where the input values are conve1ted from metr*ic units).
4.1 MATERIALS The material selected for both parts of the flywheel is 26NiCrMoV14-5 [6]. This repo1t uses the stated prope1ties in [6]. The fracture toughness will be confirmed by direct test method per SRP
[8].
The modulus of elasticity (E) is 204,000 MPa or 29,587,956 psi.
The Ininimum Sy = 640 MPa, 1/3 Sy = 213 MPa or 30,941 psi; 2/3 Sy= 427 MPa or 61 ,883 psi.
The Ininimum tensile strength (Su) is 800 MPa or 116,030 psi. 0.7 Su= 560 MPa or 81,22 1 psi.
The n01mal operating temperature is conservatively assumed to be the environment condition, 49°C to 10°C, or 120°F to 50°F [l ].
The Ininimum fracttll'e toughness, K1c, at n01mal operating temperamre is at least 165 MPa-m 112 112 or 150 ksi-in [l ].
The density of the flywheel material is 7,850 kg/m 3 or 0.283 lbs/in3 .
4.2 GEOMETRY a, c, e WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 4-2
- - - - - - - - a- - - - - - - - - - - - 1 b =c I d=e -
Figure 4-1: APR1400 Flywheel Sketch [6]
4.3 ROTATIONAL SPEEDS PER THE DESIGN SPECIFICATION The speeds that are to be addressed include:
- n01mal operation at 1,200 RPM
?
- 125% ofno1mal operation = 1,500 RPM
- loss of shlink fit c}
- critical speed for ductile fracture
- critical speed for non-ductile fracture
- critical speed for excessive defo1mation WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-1 5 EVALUATION AND ANALYSIS 5.1 SHRINK FIT REQUIREMENTS The shrink fit is optimized based on the predicted separation speed of 1,680 RPM. The nonnal operation stress is confnmed to satisfy the criterion of 1/3 Sy with the optimized sluink fit. For this analysis, the manufacturing tolerances and smoothing tolerances listed below are assumed.
Note that the prescribed tolerance values are with respect to the diameter. The minimum manufacturing tolerances are zero; the smoothing tolerances were considered to be either positive or negative. The n01mal operating stress was confnmed to meet the 1/3 Sy criterion using the optimized slu*ink fit. Maximum tolerances will be used for stress and fracture calculations; minimum tolerances will be used for separation speed calculation only.
- Hub to outer wheel tolerance with respect to diameter o Manufacturing = [ r,c.e
] a, c, e o Smoothing = [1
- Hub to shaft tolerance with respect to diameter o Manufacturing = [
o Smoothing = [
- Hub to outer wheel slu*ink fit = 0.0123 inch
- Hub to shaft slu*ink fit = 0.0091inch The slu*ink fit is combined with the tolerance values to dete1mine the total interference for the stress and separation calculations.
The maximum tolerances produce the slu*ink fits that generate the highest stress:
- Hub to outer wheel slu*ink fit = 0.01386 inch.
- Hub to shaft slui nk fit is 0.01028 inch.
The minimum tolerances produce the slu*ink fits that generate the lowest separation speed:
- Hub to outer wheel slu*ink fit = 0.01195 inch.
- Hub to shaft slui nk fit is 0.00894 inch.
5.2 HUB-WHEEL ASSEMBLY SHRINK FIT CONTACT PRESSURE First, the outer wheel is slu*ink fitted on to the bub. The sluink fit contact pressure between the bub and the outer wheel is computed by combining Equation 1 and Equation 4. The sluink fit is:
Llb - LlC = 0.01386 inches This results in a contact pressure, P = 7,588 psi.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-2 5.3 HUB-WHEEL ASSEMBLY SHRINK FIT STRESSES The shrink fit stresses in the wheel assembly before attaching to the shaft are computed using Equations 2, 3, 5, and 6, and the contact pressure, P = 7,588 psi.
The stresses as a function of radial position are shown in Figure 5-1.
Shrink Fit Stress for Hub and Outer Wheel 15,000 10,000 5,000 "----
-- --*~--------- ---------
0 "iii C.
-5,000 ' ', . .,-
- f
~
-10,000
~ -15,000
-20,000
~'--
-25,000
-30,000
-35,000 0 10 20 30 40 Radial posit.ion, inches
- Tangential Stress - - - - Radial Stress Figure 5-1: Standstill Stress due to Wheel Assembly Shrink Fit 5.4 ATTACH TO SHAFT SHRINK FIT CONTACT PRESSURE The second sluink fit attaches the hub-wheel assembly to the shaft. The contact pressure due to the sluink of the wheel assembly onto the shaft is computed by combining Equation 1 for the wheel assembly and Equation 4 for the shaft:
Lld - Lle = 0.01028 inches This results in a contact pressure, P = 15,984 psi.
5.5 ATTACH TO SHAFT SHRINK FIT STRESSES The stresses due to the slu*ink fit onto the shaft computed by Equation 2, Equation 3, and the contact pressure P = 15,984 psi for the wheel assembly are shown in Figure 5-2. These stresses are added to the slu*ink fit stresses due to the assembly of the outer wheel and hub to be the total stresses at standstill, shown in Figure 5-3. As shown in Figure 5-2, the tangential stress (Si) from the second slu*ink fit is in tension, reducing the compressive S1 from the first slu*ink fit.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-3 Stress Due to Shrink Fit onto Shaft 30,000 25,000 20,000
'iii 15,000 10,000
' ~ ..........___
CL
.,,, 5,000
"'...cu 0 ___ . ..... ------* ----
~ -5,000
-10,000
-15,000 ,*
-20,000
-25,000 0 10 20 30 40 Radial position, Inch
- Tangential Stress - - - - Rad ial Stress Figure 5-2: Standstill Stress due to Shrink Fit onto Shaft Combined Shrinkfit Stress at Standstill 25,000 20,000
'iii 15,000 10,000 5,000
' '-....... ~-----
CL
- i 0 cu
~ -5,000 - ~
-10,000 ,,
-15,000 .. - ,
-20,000
-25,000 0 10 20 30 40 Radial Position, inches
- Tangential Stress - - - - Radial St ress Figure 5-3: Total Stress at Standstill The radial contact stress between the hub and the outer wheel is -15,0 12 psi.
The peak tangential (hoop) stress at the inside radius of the outer wheel is 18,524 psi.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-4 5.6 STRESSES DUE TO ROTATION AT 1,200 RPM The outer wheel, the hub and the shaft will rotate as a unit as long as there is a compressive radial stress at the boundaiy between the pa.its. The stress in the assembly due to rotation (Equations 9 and 10) will be combined with the shrink fit stress of the assembly . The rotation of the wheel assembly will reduce the contact stresses at the two shrink fit locations. This effect is captured by the rotation ine1tial radial stress calculated by Equation 10.
The tangential and radial stresses due to rotational ine1tia are dete1mined from Equations 9 and
+
10, respectively . The inner radius is zero as the shaft is solid. These stresses are plotted for a rotation of 1,200 RPM in Figure 5-4.
Stress due to Roation at 1200 RPM, (Eq. 9, 10) 8,000 7,000 6,000
~~ .._ .___
- 5,000 C.
- .....- ~
~ ... ~
- f 4,000 II ... ...
.b VI 3,000 *- ,,... -............
2,000 ... *,
1,000 '~
0
0 5 10 15 20 25 30 35 40 Radial Position, Inch
- Tangent ial Stress - - -
- Radial Stress Figure 5-4: Stress due to Rotation at 1,200 RPM The total stress dming operation at 1,200 RPM is the combination of the stress due to rotational ine1tia in Figme 5-4, and the stress due to shrink fit at standstill in Figure 5-3. The total stress is shown in Figme 5-5. This approach will result in a conse1v ative estimate of the hoop stress, as it directly combines the standstill shrink fit tensile stresses with the tensile stresses from the rotation ine1tia.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-5 Total Stress at Operation at 1200 RPM 35,000 30,000 25,000 20,000 "iii 15,000 1:1.
10,000
"'...CII
~ 5,000 0
.,..,. ~-~~~~---------------~-
-5,000 ____
-10,000
-15,000 0 5 10 15 20 25 30 35 40 Radial Position, inch
- - Tangential Stress - - - - Radial Stress Hub Total Stress at Operation at 1200 RPM 35,000 30,000 25,000 20,000
- 15,000 CL
- i 10,000 a,
- - Tangential Stress
~ 5,000
- - - - Radial Stress 0
-5,000
-10,000
-15,000 0 10 20 30 40 Radial Position, inch Figure 5-5: Total Stress at 1,200 RPM The total radial stress between the hub and the outer wheel is -8,232 psi.
The peak tangential stress at the inside radius of the outer wheel is 25,640 psi.
The peak tangential stress at the inside radius of the hub is -5,055 psi.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-6 5.7 STRESSES DUE TO ROTATION AT 125% OVER SPEED, 1,500 RPM Using the same procedure and equations as used in the previous section, the stresses at operation at 1,500 RPM are computed. These stresses are shown in Figure 5-6. The total stress is always in compression for the entirety of the hub for overspeed at 1,500 RPM.
Total Stress at Operation at 1500 RPM 35,000 30,000
'ill 25,000 20,000 l5,000 i
- f 10,000
-- - -Tangential Stress 5,000
......... ---- --------J_
0
-5,000
-- __, , -- - --- Radia l Stress
-10,000
-15,000 0 5 w ~ w ~ ~ ~ 40 Radial Po sition, Inch Hub Total Stress at Operation at 1500 RPM 35,000 I
30,000 25,000 20,000 I-
... 15,000
'ill I
- i 10,000
- - Tangential Stress i 5,000
- - -- Radial Stress 0
I
-5,000
-10,000
-15,000 0 5 10 15 20 25 30 35 40 Radial Position, inch Figure 5-6: Total Stress at Operation at 1,500 RPM The total radial stress between the hub and the outer wheel is -4,418 psi.
The peak tangential stress at the inside radius of the outer wheel is 29,644 psi.
5.8 STRESS DUE TO ROTATION AT 1,800 RPM Since the joint release limit of 150% nonnal operation speed and stress requirement were removed from the specification [1 ], the stress calculation at 1,800 RPM is no longer relevant.
WCAP-1 7942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-7 5.9 JOINT RELEASE SPEED FOR PRESCRIBED SHRINK VALUES The joint release speed is obtained by iterating the speed until either the contact pressure between the wheel assembly and the shaft is zero, or until the contact pressure between the hub and the outer wheel is zero. The joint between the hub and outer wheel becomes loose at 1,786 RPM for the shrink fit values with the maximum tolerances. This results in the worst stress condition. The total stresses including the rotational ine1tia stress for 1,786 RPM are shown in Figure 5-7.
Total Stress at Joint Release Speed 40,000 35,000 30,000 \
°[
QI 5i 25,000 20,000 15,000
~
~ ......
t-
- - - Tangential Stress
- - - - Radial St ress 10,000 5,000 , ,
,* ---- ~---. - ....
"'r-- ; .....
0 I '~
-5,000 -
0 5 10 15 20 25 30 35 40 Radia l Position, inch Figure 5-7: Total Stresses at Joint Release Speed of 1,786 RPM The total radial contact stress at the hub and the outer wheel interface is O psi.
The peak tangential stress at the inside radius of the outer wheel is 34,280 psi.
The joint release speed was also calculated for the minimum tolerance, i.e., zero manufactming tolerance and negative smoothing tolerance. The joint release speed is 1,662 RPM with the minimum tolerance.
5.10 CONSIDERATION OF MINIMUM SHRINK FIT The optimized shrink fit values are recommended for the flywheel.
calculation p1ior to revision 3 of this repo1t is no longer relevant.
Minimum shrink fit I WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-8 5.11 EVALUATION OF STRESSES Criterion 1: Total stress in the flywheel at nonnal operating speed shall not exceed 1/3 Sy. The total stress for this application is defined as the von Mises stress, which is
[1/-l(2)]*[(St - Sr)2 +(St'+ sr2)] 112.
The total von Mises stress at 1,200 RPM is 30,598 psi, which is less 1/3 than Sy = 30,941 psi.
Criterion 2: Total stress at design overspeed shall not exceed 2/3 Sy, where design overspeed is 125% of no1mal operating speed.
The maximum total von Mises stress at 125% of nonnal operation, 1,500 RPM = 32,081 psi, is less than 2/3 Sy = 61 ,883 psi.
+
5.12 CONSIDERATION OF SEISMIC EVENT The potential concern for seismic loads is a ve1tical (axial) force, which could exceed the friction resistance. (The friction resistance maintains the connection of the flywheel components.) The minimum friction forces at nonnal operation, the assumed staiting point for a seismic event, would occur for the case of the minimum original shrink fit. Horizontal seismic acceleration has a negligible effect on the shlink fit of the flywheel assembly.
The hub-wheel radial contact stress is -8,232 psi at 1,200 RPM.
The hub-shaft radial contact stress is -8,713 psi at 1,200 RPM.
Assuming a coefficient of friction of 0.2, the total axial resistance to ve1tical movement of the flywheel assembly relative to the shaft is 0.2 x 8,713 psi x thickness of the assembly x circumference of the shaft is 1,719,748 lbs.
The weight of the flywheel assembly is 23 ,174 lbs.
The ratio of the resistance friction force to the weight is the acceleration required to slip, A_slip = 1,719,748 / 23,174 = 74 times gravity. This is significantly above the seismic requirement of thl*ee times gravity specified in [1].
Similarly, the radial contact stress between the hub and the outer wheel is -8,232 psi. The resistance friction force is 2,310,018 lbs. The acceleration required to slip is 100 times gravity.
This is significantly above the seismic design requirement. Therefore, Criterion 3 is satisfied.
5.13 STRESS INTENSITY FACTOR OF CRACK FOR OUTER WHEEL The stress intensity factor as a function of crack depth is computed from the stresses computed in the previous sections of this repo1t. In all cases analyzed, the highest tensile stress is located on the inner radius of the outer wheel. The stress distiibution from this point toward the outer edge of the wheel can be represented by the fomth order Equation 11, and the sti*ess intensity factor, Kr due to this sti*ess is computed using Equation 12. The calculated Kr at standstill, 1,200 RPM, 1,500 RPM and 1,786 RPM are compared to Krc (150 ksi-in112) to ensure non-ductile fracnire does not occur. Critical speed for non-ductile fracrure is evaluated and discussed in Section 5.14.
Note that since the hub is always in compression, only the outer wheel needs to be evaluated.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-9 Outer Wheel Ki at Standstill The tangential stress is taken from Figure 5-3. The stress as a function of the flaw depth to thickness ratio is fit to a fomth order polynomial in Figure 5-8.
The radial extent of the outer wheel from the inner to outer radius is [ t' c.e. The stress, in Equation 11 fo1m, is:
St = SO+ Sl(x/t) + S2(x/t)2 + S3(x/t)3 + S4(x/t)4 St= 18,415 - 61 ,53 l(x/t) + 120,122 (x/t)2 - l 16,469(x/t)3 + 43 ,00 l (x/t)4 Outer wheel Kr from Equation 12 is shown in Figure 5-9:
Kr = [GOSO + G1Sl (a/t) + G2S2(a/t)2 + G3S3 (a/t)3 + G4S4(a/t)4]-/(1ta)
In the previous equation:
a = crack length in radial direction t = radial thickness of outer wheel WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-10 Tangential Stress at Standstill 25,000 I
20,000 15,000 ~
1::1.
,n 10,000
"'QI Ill
"- .______ y = 4300 lx4-116469x3 + 120122x2 - 615 l >< + 18415 r---. - -Hub Stress ii 5,000
- -Outer Wheel Stress
~
QI
~ 0 I - Poly. {Hub Stress)
{!
- Poly. (Outer Whee l Stress)
-5,000 I I
-10,000 =-9-k--3-7-8xL4 pJ..,%x4 8~""'5 >X~-469x-4-2' G3
-15,000 0.00 0 .20 0.40 0.60 0.80 1.00 Through-wall Ratio from Inside Rad ius, x/t Figure 5-8: Polynomial Tangential Stress at Standstill Kl at Standstill 70.0 I
60.0 N
-;:;- 40.0 50.0
_/" ~
--"~ /
V I
- - 30.0 I - Outer Wheel Kl X
/
20.0 II 10.0 II 0.0 - -
0 1 2 3 4 5 6 Crack Length from Inside Radius of Hub or Outer Wheel (Inch)
Figure 5-9: Stress Intensity Factor versus Crack Length at Standstill WCAP-17942-NP (APR1400-A-M-NR-14001 -NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5- 11 Kr at 1,200 RPM The tangential stress is taken from Figure 5-5. The stress as a function of through-wall ratio of hub or outer wheel is fit to a fomth order polynomial in Figure 5-10.
Tangential Stress at 1,200 RPM 30,000 25,000 20,000 CL
,,,- 15,000
"'f - -Hub Stress
~
10,000 - -outer Wheel Stress "iii C
--Poly. (Hub Stress) l>O 5,000 C
- - Poly. (Outer Wheel Stress)
~
0 0.f 1.
-5,000
-10,000 Through-wall Ratio from Inside Radius, x/t Figure 5-10: Polynomial Tangential Stress at 1,200 RPM Kl at 1,200 RPM 100.0 I i ---
90.0 80.0 70.0
./~
~
~
--- I I
I
=
- ~
60.0 50.0 I-
/
V - - I-I i;2' 40.0
/' - Outer wh eel Kl
(
30.0 I- - - I- - - I- -- -
I 20.0 I 10.0 0.0 -
0 0.5 1.5 2 2.5 3 3.5 4 4.5 s 5.5 6 Crack Length from Inside Radius of Hub or Outer Wheel (inch)
Figure 5-11: Stress Intensity Factor versus Crack Length at 1,200 RPM The outer wheel location is bounding at 1,200 RPM. For a 0.5-inch crack, K1 = 34.6 ksi-in 112 .
Therefore, K1c / K1 = 4.33, and there is no d sk of non-ductile fracture.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-12 Kr at 1,500 RPM The tangential stress is taken from Figure 5-6. The stress as a function of through-wall ratio of hub or outer wheel is fit to a fomth order polynomial in Figure 5-12.
Tangential Stress at 1,500 RPM 35,000 30,000 25,000 y = 43001x4 -116469x3 + 117005x2 - 645 3x+ 29535 20,000
';)I - Hub Stress C.
i 15,000 - outer Wheel Stress i - Poly. (Hub Stress) 10,000 - Poly. (Outer Wheel Stress) 5,000 L Th rough -wall Ratio from Inside Radius, x/t Figure 5-12: Polynomial Tangential Stress at 1,500 RPM Kl at 1,500 RPM 120.0 100 .0 80.0
~
C
- ... 60.0
- Outer Wheel Kl i:
40.0 20.0 0.0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Crack Length from Inside Radius of Hub or Outer Wheel (inch)
Figure 5-13: Stress Intensity Factor versus Crack Length at 1,500 RPM The outer wheel location remains bounding for 1,500 RPM. For a 0.5-inch crack, Kr = 40.2 ksi-in 112 . Therefore, Krc / Kr = 3. 73 , and there is no risk of non-ductile fracnire.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-13 5.14 EVALUATION OF INTEGRITY Crite1ion 4: The critical speed for ductile fracture should be predicted.
The critical speed for ductile fracture can be conservatively estimated by detennining the speed at which the maximum stress reached 0.7 times the ultimate stress. This criterion is consistent with ASME Code Section III, Alticle F-1330 [5].
Figure 5-7 shows that, at separation speed (1,786 RPM), the maximum tangential stress is 34,280 psi at the inside radius of the outer wheel.
Since the shlink fit stress is no longer present, the stress scales as the square of the rotation speed.
Therefore, the speed at which the stress reaches 0.7 Su (81,221 psi) is calculated as follow:
(1,786 RPM/:34,280 psi = (critical RPM/:81 ,221 psi The ductile fracture critical RPM = 2,748.
Crite1ion 5: The critical speed for non-ductile fracture should be predicted. To predict the critical speed for non-ductile fracture, a crack size must be hypothesized. For conservatism, a crack length of 0.50 inches is evaluated. The rotation speed to reach the minimum Krc of 150 ksi-in112 is plotted in Figure 5-14 as a fhnction of crack size.
The bounding critical speed for a crack length of 0.5 inches located at the inside radius of the outer wheel is 3,203 RPM.
Critical Speed for Non-ductile Fracture vs. Crack Size 3,500 I
3,000
\
'\.,
2,500
~ 2,000
- t: - Outer Wheel Critical Speed
~ 1,500 1,000 500 - -- -- - f-- -f- -
0 0 0.5 1.5 2.5 3 3.5 4.5 5.5 6 Crack Length from Inside Radius o f Hub or Outer Wheel, inch Figure 5-14: Rotation Speed to Reach a K1c of 150 ksi-in112 Criterion 6: The n01mal speed should be less than one-half of the lowest critical speeds.
shown in Table 5-1, this criterion is satisfied.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-14 Ta ble 5-1: N ormaI an d C ntica .. I S,peed C omparison Normal Operation Critical Speed/Joint Speed Critical Speed Speed/Critical Speed Separation Speed (RPM)
Ratio Ratio Ductile Fracture 2,748 0.44 < 0.5 Per Critedon 7 1.54 Non-ductile Fracnire 3,203 0.37 < 0.5 Per Critedon 7 1.79 Excessive Defo1mation 2,938 0.41 < 0.5 Per Critedon 7 1.65 N ote: Since critical speeds are gi*eater than the separation speed of 1,786 RPM, these critical speeds are only hypothetical, and could not occur in real life.
Crite1ion 7: The predicted LOCA overspeed should be less than the lowest cdtical speed.
The design overspeed is 125% of no1mal operation = 1,500 RPM. This is less than all critical speeds. This critedon is satisfied.
Crite1ion 8: The cdtical speed for excessive defonnation of the flywheel should be predicted.
The cdtical speed for excessive defo1mation can be conservatively estimated by dete1mining the speed at which the maximum stress reached the yield stress.
Figure 5-7 shows that, at separation speed of 1,786 RPM, the maximum tangential stress is 34,280 psi at the inside radius of the wheel. Since the shrink fit stress is no longer present, the stress scales as the square of the rotation speed. Therefore, the speed at which the stress reaches the yield stress (92,824 psi) is 2,938 RPM. Since this is greater than the joint separation speed, it is a hypothetical value that is impossible to be reached. Therefore, excessive defo1mation at overspeed conditions (i.e., 1,500 RPM) will not occur.
5.15 FATIGUE CRACK GROWTH The fatigue crack growth due to a life time of 6,000 cycles from standstill to nonnal operation can be predicted by the fatigue crack growth rates available in [5]. The delta Kr from standstill to nonnal operation is dete1mined by comparing the KI in Figure 5-9 and Figure 5-1 1. The delta KI for the outer wheel is shown in Figure 5-15.
Fatigue crack growth can be calculated using the generic carbon and low alloy fenitic steel growth rate in the ASME Section XI, FigureA-4300-1 in [5]:
da/dn = Co (~Kr)° In the previous equation:
Co = 1.99 x 10-io S S = 25.72 X (2.88-Rr3*07 n= -3.07 R = Kimin/K1max WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 5-15 A crack grows from 0.5 inches to 0.5032 inches in 6,000 lifetime cycles from standstill to n01mal operation. This is negligible growth.
Outer Wheel Delta K Standstill to Normal Operation 35.0 30.0
~ 25.0 t _,,,,. _,,,.,.
~
_.,,..... ~--- --- ~
.~ 20.0
'vi
- !.. /
/
~ 15.0
~
J!
o 10.0 -
/"
5.0 0.0 - -- -- -- -- -- --
0 1 2 3 4 5 6 Crack length, inch Figure 5-15: Change in Outer Wheel Kr from Standstill to Normal Operation Since the hub is always in compression, as shown in Figure 5-3 and Figure 5-5, the fatigue crack growth for the hub is negligible.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 6-1 6 RESULTS AND CONCLUSIONS This repo1t demonstrates that the APR1400 RCP flywheel satisfies all of the RCP flywheel integiity criteria of the design specification [1] and U.S . NRC Regulato1y Guide 1.14 [2]:
The acceptance criteria in the specification [ 1] include:
- 1. The total stress 30,598 psi at n01mal operating speed does not exceed 1/3 Sy of 30,941 psi.
This criterion is met.
of n01mal operating speed. This criterion is met. .
The Regulato1y Guide acceptance criteria are established in [2] as: +
- 3. Flywheel assembly is designed to withstand n01mal conditions, anticipated transients, the design basis loss of coolant accident (LOCA), and the safe shutdown eaithquake without loss of strnctural integi*ity.
- 4. The critical speed for ductile fracnire is 2,748 RPM.
- 5. The critical speed for non-ductile fracmre is 3,203 RPM.
- 6. The n01mal speed is less than one-half of the lowest critical speeds for fracnire. This criterion is met.
- 8. Excessive defo1mation can be conse1vatively defined as total stress reaching matelial yield strength, Sy. The shrink fit release speed is 1,786 RPM, with a maximum stress of 34,280 psi. This is much less than the Sy of 92,824 psi. The hypothetical speed at Sy is 2,938 RPM, which will not occur because the shrink fit will separate at 1,786 RPM. Additionally, the separation speed of 1,786 RPM is significantly greater than the LOCA overspeed of 1,500 RPM. Consistent with past practice [7], the excessive defonnation critelion is considered satisfied.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3
Westinghouse Non-Proprietary Class 3 7-1 7 REFERENCES I . KEPCO Design Specification, l 1A60-FS-DS485, Rev. 05, "Design Specification for Reactor Coolant Pump Motors," June 5, 2017.
- 2. US Nuclear Regulato1y Commission Regulat01y Guide 1.14, Rev. 1, "Reactor Coolant Pump Flywheel Integrity," August 1975.
- 3. Young, Wan en C. and Richard G. Budynas, "Roark's Fonnulas for Stress and Strain,"
Seventh Edition, McGraw-Hill Companies, Inc., New York, NY, 2002.
- 4. API 579-1/ASME FFS-1, "Fitness-For-Service," Annex C, "Compendium of Stress Intensity Factor Solutions," June 5, 2007.
- 5. ASME Boiler and Pressure Vessel Code,Section III, Division 1, Rules for Constrnction of Nuclear Facility Components, 2007 Edition with 2008 Addenda,Section XI, Appendix A 4300.
- 6. Siemens Doclllllent, 4D5 .0170.83-575711F, Rev. F, "Flywheel Calculation," May 30, 2011.
- 7. Westinghouse Repo1t, WCAP-15666-A, Rev. 1, "Extension of Reactor Coolant Pump Motor Flywheel Examination," October 2003.
- 8. U.S . Nuclear Regulato1y Commission Repo1t, NUREG-0800, "Standard Review Plan for the Review of Safety Analysis Repo1ts for Nuclear Power Plants: LWR Edition (NUREG-0800, Fo1merly Issued as NUREG-75/087)," Section 5.4.1.1, Rev. 3, "Pump Flywheel Integrity (PWR)," May 2010.
- 9. Westinghouse Letter, LTR-MRCDA-16-98-P, Rev. 0, "Westinghouse Responses to NRC RAI 503-8641 on the APR1400 RCP Flywheel Integiity," September 14, 2016.
WCAP-17942-NP (APR1400-A-M-NR-14001-NP) July 2017 Revision 3