ML19114A302
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| Site: | 07103052 |
| Issue date: | 03/05/2019 |
| From: | Willems T TN Americas LLC, Orano USA |
| To: | Division of Spent Fuel Management |
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TN International CHAPTER 1 - APPENDIX 10 TN-MTR Names Signatures Date Prepared by T. WILLEMS Ref. DOS-18-011415-021-NPV Rev. 1.0 Form: PM04-3-MO-3 rev. 2 Page 1/20 NON PROPRIETARY VERSION JUSTIFICATION OF THE MECHANICAL STRENGTH OF PACKAGE MODEL SCREWED ASSEMBLIES UNDER ROUTINE TRANSPORT CONDITIONS TABLE OF CONTENTS
SUMMARY
- 1. INTRODUCTION
- 2. BASIC DATA
- 3. MECHANICAL ANALYSIS OF THE SCREWS
- 4. CONCLUSIONS
- 5. REFERENCES LIST OF TABLES
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 2/20 NON PROPRIETARY VERSION REVISION STATUS Revision Date Modifications Prepared by /
Checked by Old reference: DOS-16-00173678-113 1
N/A Document first issue. Revision number intentionally set to correspond to the source document revision number.
TWI / ALC New reference: DOS-18-011415-021 1.0 N/A New reference due to new document management system software.
TWI / ALC
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 3/20 NON PROPRIETARY VERSION
SUMMARY
This document presents the justification of the mechanical strength of package model screwed assemblies under routine transport conditions, specifically:
- lid to body attachment screws (item 150);
- cover to body attachment screws (item 151):
- orifice plugs to lid attachment screws (item 350)
Specific calculations are carried out for trunnion screws, as presented in section 1-3 in the safety analysis report.
Mechanical properties of materials at 120°C are selected to cover the maximum temperature of the cavity (shell) under normal transport conditions (see chapter 2).
The maximum axial force on the screws is calculated from the vertical acceleration under normal transport conditions. Moreover, for containment screws (lid screws and plug screws), the internal pressure and the force induced by the presence of seals are taken into account in the calculation of the maximum axial force.
The maximum axial force applied to each screw type is less than the minimum preload of screws due to the tightening torque. Thus, it is guaranteed that there will be no disengagement of clamped parts including parts of the containment, under routine transport conditions.
Von Mises stresses in screws and shear stresses in screw threads and tapped threads are less than allowable criteria. Differential expansion of screwed systems is taken into account.
Stresses due to pressure under the head are also below allowable criteria.
Therefore the mechanical strength of the lid, shock absorbing cover and plug screws is guaranteed under routine transport conditions.
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 4/20 NON PROPRIETARY VERSION
- 1. INTRODUCTION The purpose of this chapter is to justify the mechanical strength of the TN-MTR package model screwed assemblies under routine transport conditions.
Thus, stresses in the screws and the tapped threads are calculated and compared with the mechanical properties of materials. It is also checked that screwed assemblies do not disengage under forces resulting from routine transport conditions, in other words forces related to:
- a conservative maximum internal pressure of 7 bars (according to <3>);
- a vertical upwards acceleration equal to 2 g;
- temperature variations (differential expansion);
- compression of seals.
This chapter applies to the following screws:
- lid to body attachment screws (item 150), fitted with washers (item 153), screwed into the packaging flange (item 105);
- shock absorbing cover to body attachment screws (item 151), fitted with washers (item 152),
screwed into the packaging flange (item 105);
- orifice plug to lid attachment screws (item 350), screwed into the top disk of the lid (item 307).
Specific calculations are carried out for trunnion screws, as presented in section 1-3 in the safety analysis report.
- 2. BASIC DATA 2.1. Temperature considered Conservatively, the mechanical properties are considered at 120°C because this temperature upper-bounds the cavity temperature under normal transport conditions (NTC)
( according to chapter 2).
2.2. Packaging components The following table presents components of the packaging considered in the calculations in this chapter: the component with the screw tapped thread and the clamped part are specified for each screw type, with their items.
Screw type Tapped thread Clamped part Lid screws (150)
+ washers (153)
Flange (105)
Lid upper disk (307)
Shock absorbing cover screws (151)
+ washers (152)
Flange (105)
Screw support ring (722)
Plug screws (350)
Lid upper disk (307)
Plugs (330 and 333)
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 5/20 NON PROPRIETARY VERSION 2.3. Properties of materials 2.3.1. Screw materials The mechanical properties of screw materials used in this chapter are presented in the following table. They are taken from chapter 0.
Screw Lid screws Cover screws Plug screws Material Class 10.9 Yield stress Re at 20°C (MPa) 900 Ultimate strength Rm at 20°C (MPa) 1,000 Coefficient of thermal expansion 1
(/°C) 11.5 x 10-6 Youngs modulus (MPa) 212 000 According to Appendix B in <1>, there is no significant variation in the mechanical properties of screws for temperatures varying up to 150°C. Therefore the mechanical properties specified in this table are used for the temperature considered in this study (see section 2.1).
2.3.2. Material used for tapped threads and clamped parts The following table gives the mechanical properties of steels from which the tapped threads and clamped parts used in this chapter are made.
Packaging component Lid upper disk (307)
Flange (105)
Ring (722)
Plugs (330/333)
Steel Type K Type J Type A Type B Yield stress Re at 120°C (MPa) 430 216 146 353 Ultimate strength Rm at 120°C (MPa) 650 486 431 616 Coefficient of thermal expansion 2
(/°C) 16 x10-6 Youngs modulus (MPa) 200 000 These mechanical properties are interpolated linearly from the mechanical properties given in chapter 0.
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 6/20 NON PROPRIETARY VERSION 2.4. Tightening torques Tightening torques for the different screws are shown in the table below: These data are taken from Chapter 0.
Screw Tightening torque (N.m)
Lid screws 660 10%
Shock absorbing cover screws 660 10%
Plug screws 40 10%
2.5. Screw geometry The geometric properties of screws used in this chapter are given in table 1-10.1 and are taken from chapter 0 and <2>.
2.6. Criteria Criteria guaranteeing the mechanical strength of screws are determined from the mechanical properties of materials (see section 2.3) at the temperature defined in section 2.1.
The following criteria are considered for the different calculations performed in this study:
- Von Mises stresses in screws are compared with yield stresses of steels from which the screws considered are made;
- shear stresses in screw threads and tapped threads are compared with yield stresses of steels used for screws and threaded holes, multiplied by a factor 3
1 ;
- pressures under the head are compared with the value of 2
m e
R R
(see Appendix B in
<8>), for materials from which clamped parts are made.
All criteria used in this chapter are summarised in the following table:
Criterion (MPa)
Stress / Pressure Lid screws Cover screws Plug screws (Von Mises) 900 Shearing of threads Screw 520 Tapped threads 125 125 248 Pressure under head Clamped part 540 289 484
- 3. MECHANICAL ANALYSIS OF THE SCREWS 3.1. Loading conditions The loading conditions considered in this analysis of screwed assemblies are as follows:
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 7/20 NON PROPRIETARY VERSION 3.1.1. Pressure conditions The internal pressure of the packaging applies a force to the screws of the containment (lid screws and plug screws). The internal pressure used for the calculation corresponds conservatively to a pressure of 7 bars absolute, which is greater than the pressure reached under normal conditions of transport (see Chapter 3A).
The force in the screws due to this internal pressure is given by:
n PD F
p pressure 2
4
Where:
P: the internal pressure of the packaging (Pa), assumed equal to 7 x 105 Pa (7 bars according to <3>);
Dp: the average diameter of the seal delimiting the area to which the pressure is applied (internal seal, see table 1-10.2) (m);
n: the number of screws in the assembled part (n = 36 for the lid and n = 4 for the plugs).
Forces in the screws due to the internal pressure are given in the following table:
Screw Lid screws Plug screws Force Fpressure (kN) 17 1
3.1.2. Accelerations related to routine conditions of transport Accelerations due to braking, starting, turning and simple gravity create forces in the screws. These forces are related to the mass of components of the packaging and that of its content. According to <3>, the maximum acceleration in the upwards vertical direction is 2 g for routine transport conditions. This acceleration is conservative: the IMO directive <4> does not specify any upwards vertical acceleration. Considering the downwards acceleration due to gravity equal to 1 g, the selected vertical acceleration is 1 g upwards.
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 8/20 NON PROPRIETARY VERSION The force in the screws due to external accelerations applied to components is given by:
n g
M Facc
Where:
M: the mass of components held in place by the screws (kg);
- accelerations under routine conditions of transport (1 g);
g: acceleration due to gravity, (9.81 m/s²);
n, the number of screws for the assembled part.
The data used to calculate this force are given in Table 1-10.3.
Forces in the lid, shock absorbing cover and plug screws are given in the following table.
Screws Lid screws Cover screws Plug screws Force Facc (kN) 2 3
2 x 10-2 3.1.3. Forces induced by the presence of seals Lid seals (items 361 and 362) and plug seals (items 365 and 366) apply a force which opposes the tightening of the lid and plug screws.
The seal compression force is equal to:
j i
i i
seal Y
D n
F 1
)
(
Where:
Di: the mean reaction diameter of seal No. i (m);
Yi: the force per unit length compressing seal No. (N/m);
n: the number of screws for the assembled part.
Properties of lid and plug seals are given in table 1-10.2 (the dimensions are taken from chapter 0).
Forces due to seals applied to the screws are given in the following table:
Screws Lid screws Plug screws Force Fseal (kN) 5 3
3.1.4. Maximum axial force The maximum axial force applied to a screw is equal to the sum of the following forces:
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 9/20 NON PROPRIETARY VERSION the force due to the internal pressure in the packaging Fpressure (see section 3.1.1);
the force due to accelerations under routine transport conditions Facc (see section 3.1.2);
the force induced by the presence of seals Fseal (see section 3.1.3).
Thus, the maximum axial force in a screw is equal to:
seal acc pressure E
F F
F F
max The maximum axial force for each screw type is summarised in the following table:
Screws Lid screws Cover screws Plug screws Force FEmax (kN) 24 3
4 3.2. Preload in screws The minimum and maximum preloads in screws can be calculated as follows based on screw tightening torques (see section 2.4), (according to <2>):
)
583
,0
(
)
1(
16
,0
)
1(
2 0
mr d
p C
C F
Where:
- F0: preload force due to the tightening torque applied to the screw (N);
- C: the screw tightening torque (N.m);
C
- uncertainty on the screw tightening torque (%);
- : the coefficient of friction at the screw threads and under the screw head, 0742
,0
- the uncertainty on the coefficient of friction at the screw threads and under the screw head, 10 16
- p: the screw pitch (m);
- d2: the diameter at the flank of the screw thread (m), d2 = d - 0.6495 p;
- d: nominal screw diameter (m);
mr : average bearing radius under the head (m),
2 2
3 3
3 1
i e
i e
m d
d d
d r
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 10/20 NON PROPRIETARY VERSION
- de: outside diameter of the bearing surface under the screw head (m):
de = de screw for screws without washer; de = min (de screw ; de washer) for screws with washer;
- de screw: outside diameter of screw head (m);
- de washer: outside diameter of washer (m);
- di: inside diameter of the bearing surface under the screw head (m):
di = db for screws without washer; di = max (db ; di washer) for screws with washer (for screws with captive washer, di = db);
- db : diameter of the screw hole (m);
- di washer: inside diameter of washer (m);
The minimum and maximum preloads of the different screws due to the tightening torque are listed in the following table:
Screws Minimum preload due to the torque: F0 min (kN)
Maximum preload due to the torque: F0 max (kN)
Lid screws 161 258 Cover screws 118 189 Plug screws 24 38 It is checked that the minimum preload in screws due to the torque is more than the maximum axial force applied to the screws (see section 3.1.4). Therefore it is guaranteed that clamped parts will not disengage.
3.3. Expansion of materials Temperature conditions have an influence on screw preloads.
The force in a screw due to differential expansion is evaluated by the following formula (according to <5>):
2 2
1 1
1 1
1 2
1 2
1 A
E A
E A
E T
T F
Where:
F
- the force in the screw due to differential expansion between the screw and the clamped part (N);
- 2: the coefficient of thermal expansion of the material from which the clamped part is made (2 = 16 x 10--6 C-1);
- 1: the coefficient of thermal expansion of the material from which the screw is made (1 = 11.5 x 10--6 C-1);
- T2: the maximum temperature under routine transport conditions T2 = 120°C according to section 2.1);
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 11/20 NON PROPRIETARY VERSION
- T1: the ambient temperature at tightening, assumed to be equal to 20°C;
- E1: Young's modulus of the material from which the screw is made (E1 = 212 000 MPa);
- A1: the stress area of the screw(m²), A1 =
2 4
s d
- d: the stress diameter of the screw, ds = min (deq ; ddec);
- deq: equivalent screw diameter (m), deq =
2 3
2 d
d
- d3 the diameter at the root of the screw thread (m), d3 = d - 1.2268 p;
- ddec : the screw shank machined diameter ;
- E2: Young's modulus of the material from which the clamped part is made (E2 = 200 000 MPa);
- A2: bearing area between the screw head and the clamped part or the washer (m²),
A2 =
)
(
4 2
2 i
e d
d
- de outside diameter of the contact surface under the screw head (m):
- di inside diameter of the contact surface under the screw head (m):
The thickness of the washer is ignored in this calculation.
Forces due to differential expansion for the lid, shock absorbing cover and plug screws are given in the following table. The maximum preload of the screws is then calculated such that:
F F
F
max 0
max The results obtained for expansion of materials between 20°C and 120°C are presented in the table below:
Screws Differential expansion F120°C (kN)
Preload due to torque F0max (kN)
Maximum preload Fmax (kN)
Lid screws 26 258 283 Cover screws 57 189 246 Plug screws 4
38 42
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 12/20 NON PROPRIETARY VERSION 3.4. Maximum equivalent stress in the screws:
Maximum stresses in the packaging screws are calculated from the maximum preloads calculated in the previous section.
The maximum tensile stress in the screws is given by:
1 max max A
F
Where:
- Fmax: the maximum preload force (N), taking account of differential expansion between materials (see section 3.3);
- A1: stress area of the screw, 2
1 4
s d
A
(m²).
The maximum torsion stress is given by:
3 16 s
t d
C
Where:
- Ct: the maximum torsion in the screw (N.m),
)
583
,0 16
,0
(
2 min max d
p F
Ct
(according to <2>) ;
min
- the minimum coefficient of friction at the screw threads and under the screw head.
Thus, we obtain the maximum Von Mises equivalent stress:
2 2
max 3
VM The following table contains results for lid, shock absorbing cover and plug screws.
Stress (MPa)
Lid screws Cover screws Plug screws Tension max
577 242 500 Torsion 145 57 130 Von Mises VM
629 262 549 Criterion 900 Von Mises equivalent stresses in screws are less than the criteria defined in section 2.6:
therefore the mechanical strength of lid, shock absorbing cover and plug screws is guaranteed under routine transport conditions.
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 13/20 NON PROPRIETARY VERSION 3.5. Shear stresses in the threads:
The shear strength of screw threads and internal tapped threads is checked using the method described in reference <6>.
Shear stresses in threads are calculated as follows:
- In the tapped thread:
3 1
max C
C S
F t
- In the screw:
2 1
max C
C S
F vis
Where:
- Fmax: the maximum force in the screws (N), taking account of differential expansion between materials (see section 3.3);
- St: the stress area of tapped threads (m²),
L d
St
8 7
- Sscrew: the stress area of screw threads (m²),
L D
Ssrew 1
4 3
- L; the minimum contact length between screw threads and tapped threads (m);
- d: nominal screw diameter (m);
- D1: inside diameter of tapped threads (m), D1 = d1 = d - 1.0825 p;
- p: the screw pitch (m);
- C1: expansion factor for the nut. Since the tapped threads for lid, shock absorbing cover and plug screws are in thick walls, C1 = 1;
- C2: bending factor of screw threads. If 1
S R
, C2 = 0.897; otherwise, 4
3 2
2 9353
,0 057
,6 107 14 682 13 594
,5 s
s s
s R
R R
R C
- Rs: thread strength ratio, vscrew screw m
tapping tapping m
s S
R S
R R
- Rm tapping and Rm screw: the ultimate strengths of the tapped thread and the screw respectively;
- C3: bending factor of tapped threads. If 1
S R
, C3 = 0.897; otherwise, 3
2 3
296
,1 894
,2 769
,1 728
,0 s
s s
R R
R C
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 14/20 NON PROPRIETARY VERSION Shear stresses for screws and shells are given in the following table.
Stress (MPa)
Lid screws Cover screws Plug screws Screw stress 128 57 164 Screw criterion 520 Tapping stress 85 38 116 Tapping criterion 125 248 Shear stresses for screws and shells are less than allowable criteria (see section 2.6).
Therefore the mechanical strength of threads is guaranteed.
3.6. Pressures under the screw head If screws are not fitted with washers (case of plug screws), the pressure under the screw head is calculated as follows:
)
(
4 2
2 max i
e t
d d
F
Where:
- Fmax: the maximum preload in the screw (N), taking account of differential expansion between materials (see section 3.3);
- de: outside diameter of the bearing surface under the screw head;
- di: inside diameter of the bearing surface under the screw head.
For screws that are fitted with washers (case of lid and shock absorbing cover screws), the contact pressure between the washer and the clamped part is given by:
)
(
4 2
2 max i
washer e
c d
d F
Where:
- de washer: outside diameter of washer; c
- the contact pressure at the contact between the washer and the clamped part (lid or shock absorbing cover) (Pa);
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 15/20 NON PROPRIETARY VERSION The pressures under the screw head are presented in the following table:
Lid screws Cover screws Plug screws Contact pressure (MPa) 451 109 378 Criterion 540 289 484 Contact pressures are below the criteria defined in section 2.6. Therefore there will be no bearing of clamped parts.
- 4. CONCLUSIONS The maximum axial force applied to each screw type is less than the minimum preload of screws due to the tightening torque. Thus, it is guaranteed that there will be no disengagement of clamped parts including those of the containment, under routine transport conditions.
Von Mises stresses in screws and shear stresses in screw threads and threaded holes are less than allowable criteria. Differential expansion of screwed systems is taken into account.
Stresses due to pressure under the head are also below allowable criteria.
Therefore the mechanical strength of the lid, shock absorbing cover and plug screws is guaranteed under routine transport conditions.
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 16/20 NON PROPRIETARY VERSION
- 5. REFERENCES
<1> Standard ISO 898-1, 2013-Mechanical properties of carbon steel and alloyed steel attachment elements - Part 1: Screws, studs and threaded rods with specified quality classes
- coarse threads and fine threads;
<2> Standard E 25-030 - August 1984 -Attachment elements - screwed assemblies;
<3> Applicable IAEA regulations: see chapter 00;
<4> IMO/OIT/EEC-UNO directive for loading cargoes in transport equipment;
<5> Strength of Materials, S.P. TIMOSHENKO, Volume 1, Editions Dunod;
<6> <6> << Analysis and Design of Threaded Assemblies>> - E. M. Alexander - Society of Automotive Engineers, Inc - 1978 - No 770420
<7> Parker O-Ring Handbook, Catalog ORD 5700A/US, Parker Seals, 2001 Edition ;
<8> Standard NF E 25-030 December 2007 -Attachment elements - Screwed assemblies, Part 1: General design, calculation and erection rules.
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 17/20 NON PROPRIETARY VERSION LIST OF TABLES Table Description Pages 1-10.1 Geometric characteristics of packaging screws 1
1-10.2 Data concerning seals 1
1-10.3 Data required to calculate the force due to acceleration 1
TN International DOS-06-00032593-113 Rev. 1 Page 18/20 NON PROPRIETARY VERSION TABLE 1-10.1 GEOMETRIC PROPERTIES OF PACKAGING SCREWS Screws Lid screws Cover screws Plug screws Nominal diameter: d (mm) 30 42 12 Screw pitch: p (mm) 3.5 4.5 1.75 d1 (mm) 26.211 37.129 10.106 Thread flank diameter: d2 (mm) 27.727 39.077 10.863 Screw core diameter: d3 (mm) 25.706 36.479 9.853 Screw shank machined diameter:
ddec (mm) 25 36 Equivalent diameter: deq (mm) 26.716 37.778 10.358 Screw stress diameter: ds (mm) 25 36 10.358 Screw outside diameter: de screw (mm) 45 63 18 Washer outside diameter: de washer (mm) 45 70 Outside diameter of the bearing surface under the screw head: de (mm) 45 63 18 Inside diameter of the bearing surface under the screw head: di (mm) 35 45 13.5 Average radius under-head: rm (mm) 20.1 27.25 7.93 Minimum coverage: L (mm) (*)
40 55 12 Stress area: A1 (mm²)
490.9 1017.9 84.3 Contact area under screw head: A2 (mm²)
628.3 1526.8 111.3
(*) used conservatively
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 19/20 NON PROPRIETARY VERSION TABLE 1-10.2 DATA CONCERNING SEALS Seal Lid Plugs Inner seal Outer seal Inner seal Outer seal Inner diameter (mm) 1,055 1,093 81.93 111.14 Torus diameter (mm) 7.8 7.8 5
5 Average diameter (mm) 1,062.8 1,100.8 86.93 116.14 Compression force per unit length 28,000 (1) 18,000 (2)
According to chapter 0, the hardness of these EPDM seals is between 75 and 85 Shores.
According to section 2.4.2 in <7>, the hardness is usually expressed with a tolerance of +/- 5 Shores. Therefore a hardness of 80 Shores will be assumed for these seals. Furthermore, figures 2-4 to 2-8 in <7> show that the linear compression force increases with the torus diameter.
Thus, these forces in the above table are:
(1) obtained by extrapolation, for a torus diameter of 7.8 mm, of the linear compression forces in figures 2-7 and 2-8 in <7>, for a compression of 30% and a hardness of 80 Shores.
(2) taken conservatively considering the linear compression force in figure 2-7 in <7>, with a compression of 30% and a hardness of 80 Shores.
TN International DOS-18-011415-021-NPV Rev. 1.0 Page 20/20 NON PROPRIETARY VERSION TABLE 1-10.3 DATA REQUIRED TO CALCULATE THE FORCE DUE TO ACCELERATION Screws Lid screws Cover screws Plug screws Number of screws 36 6
4 Components held in place by the screws Lid + load Shock absorbing cover Plugs Mass of components held in place by the screws (kg) 2,700 + 2,800 = 5,500 1,650 7