PSC Structural Analysis AEW20605A02
30‐12‐2011 TABLE OF CONTENTS
TABLE OF CONTENTS ....................................................................................................................... 2 1. 2. INTRODUCTION ............................................................................................................................... 4 1.1 Scope ....................................................................................................................................... 4 1.2 Reference Documents ............................................................................................................. 4 1.3 Defintions, Acronyms and Abreviations .................................................................................. 4 ANALYSIS DESCRIPTION ................................................................................................................... 5 2.1 Model ....................................................................................................................................... 5 3. MATERIALS ...................................................................................................................................... 7 4. LOADS AND BOUNDARY CONDITIONS ............................................................................................ 8 4.1 Safety Factors .......................................................................................................................... 8 4.2 Load Cases ............................................................................................................................... 8 4.3 Boundary Conditions ............................................................................................................... 9 4.3.1 CTR boundary conditions ................................................................................................. 9 4.3.2 PSC‐to‐CTR boundary conditions ................................................................................... 11 5. MATHEMATICAL MODEL (FEM) ..................................................................................................... 12 6. RESULTS ......................................................................................................................................... 14 6.1 Natural Frequencies .............................................................................................................. 14 6.2 Load Case 1 ............................................................................................................................ 17 6.2.1 Stresses .......................................................................................................................... 17 6.2.2 Displacements ............................................................................................................... 19 6.3 Load Case 2 ............................................................................................................................ 20 6.3.1 Stresses .......................................................................................................................... 20 6.3.2 Displacements ............................................................................................................... 22 6.4 Load Case 3 ............................................................................................................................ 23 6.4.1 Stresses .......................................................................................................................... 23 6.4.2 Displacements ............................................................................................................... 25 6.5 Load Case 4 ............................................................................................................................ 26 6.5.1 Stresses .......................................................................................................................... 26 6.5.2 Displacements ............................................................................................................... 28 6.6 Safety Margins ....................................................................................................................... 29 6.7 Bolted Joints .......................................................................................................................... 30 6.8 Fail Safe analysis .................................................................................................................... 33 Page 2 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 7. CONCLUSIONS ............................................................................................................................... 34 8. APPENDIX A: Bolts Verification Calculation ................................................................................... 35 8.1.1 Combined shear and tensile loads Safety margin ......................................................... 35 8.1.2 Actual Loads ................................................................................................................... 35 8.1.3 Allowable Loads ............................................................................................................. 36 8.1.4 Shear Safety margin ....................................................................................................... 36 8.1.5 Joint Separation Safety margin ...................................................................................... 37 Page 3 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 1.
INTRODUCTION 1.1
Scope Analyses have been made on the Splitters on the CTR box. Results are presented in this document. The natural frequencies, stresses and deformations generated due to the different load cases are calculated. 1.2
Reference Documents RD1 ‐ S‐SAR‐E‐BI‐A030‐A, “CTR Structural Design”. RD2 – NASA RP‐1228, “Fastener Design Manual”. 1.3
Defintions, Acronyms and Abreviations DOF – Degree of Freedom FF – Fitting Factor FS – Safety Factor FSU – Ultimate Safety Factor FSY – Yield Safety Factor FU – Uncertainty Factor MS – Safety Margin PSC – Power Splitter Combiner Page 4 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 2.
ANALYSIS DESCRIPTION 2.1
Model The analyzed model consists of 6 components, shown in the following figures. One CTR box with its cover and 2 Splitter boxes with their covers. Fig. 1: CTR box. Fig. 2: CTR cover. Page 5 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 Fig. 3: Splitter box without bolts, connectors and other electronic components. Fig. 4: Splitter cover. The Splitters are analyzed from the structural point of view, for this reason it is necessary to fulfill the natural frequencies requirements, and that the stresses generated in the structure, are within the established margins. Page 6 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 3.
MATERIALS All the components modeled in this analysis are made of Aluminium 6061‐T6. Aluminium 6061‐T6 mechanical and thermal properties are presented in the following table: Material
Aluminium 6061-T6/-T651
Density [kg/m3]
2700
Young Modulus [GPa]
68.9
Poisson ratio
0.33
Yield Stress [MPa]
276
Ultimate Stress [MPa]
310
Thermal Conductivity [W/m-K]
167
Coefficient of Thermal Expansion [m/m-K]
23.6 x 10-6
As seen in RD1, as internal non‐structural components were not included in the structural model, density was altered in order to replicate the mass of the complete part. Those supressed components are bolts, wires and connectors. Variation of mass due to differences between CAD and Abaqus models is also taken into account, as well as a 10% mass augmentation due to possible redesigns of the CTR. The material Density used in each component is calculated based on data from RD1 (section IV.I): Component
Original Mass [kg]
New Mass [kg]
New Density [kg/m3]
CTR box
3.478
6.735
4811
CTR cover
0.869
0.870
2700
PSC (splitter)
0.138
0.160
3108
In the case of the PSC, the difference in mass is due to internal components, which were supressed for this simulation. The “original mass” (0.138 kg) is the weight of the PSC box and cover alone, with the original aluminium density. The “new mass” (0.160 kg) is the actual total mass of the Splitter including all internal components. Thus, the density of the PSC box and cover was augmented to 3108 kg/m3. Page 7 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 4.
LOADS AND BOUNDARY CONDITIONS 4.1
Safety Factors Safety Factors are taken from RD1, section IV.III.1. Basic Safety Factors: The following chart establishes the mechanical safety factors for the design of the Service Platform structure at all assembly levels. 4.2
Load Cases Load Cases include acceleration and thermal loads. As seen in the following table, longitudinal acceleration load case is the critical one, while LC4 has the greater temperature change. The temperature differences in the load case 4 result from consider a CTR integration temperature to the structural panel which is between 17 to 23°C, and from the electronic temperature limits, which range from ‐40 to +50°C. The carbon fiber expansion coefficient is so low, so in these calculations will not be taken into account, and it will be the CTR who changes its dimensions with the temperature. Page 8 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 ΔT1 = Maximum absolute flight temp. – Integration temp. ΔT1 = +50°C‐17°C = 33°C ΔT2 = Minimum absolute flight temp. – Integration temp. ΔT2 = (‐40°C) ‐ 23°C = ‐ 63°C 4.3
Boundary Conditions 4.3.1 CTR boundary conditions Boundary conditions are applied on the fitting points 1 through 9. 4.3.1.1 Boundary conditions for Load cases 1, 2 and 3 Restrictions of DOFs at each fitting point are defined in the following table: 3
Page 9 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 Ref: X Restricted ‐ Free (*) Fitting number 7 restricts displacements in a perpendicular direction to the straight line that goes through the center of the fitting point 7 and the center of the hole in the fitting point 4. 4.3.1.2 Boundary conditions for Load case 4 For load case 4 (LC4) the fixture points are restrained in a different way than for the other load cases. In the center of the hole in the fixture point 4 in the CTR cover, a cylindrical coordinate system is created, the R axis is coincident with the X reference coordinate system axis, the θ axis is coincident with the Y axis in the reference coordinate system, and Z is coincident with Z in the reference coordinate system. The restrictions applied for the different fixation points are as follows: 1) Fitting points 1, 2, 5, 6, and 8, only take loads in the Z axis, with this restriction the moments about the R and θ axis are restricted. 2) Fitting point 4, takes loads in 2 axis, θ and Z, with this restriction the moments about the R and θ axis are restricted. 3) Fitting point 3, 7 and 9, restrains displacements only in the θ axis, but no moment on any axis. Page 10 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 4.3.2 PSC‐to‐CTR boundary conditions Each PSC is linked to the CTR by means of 4 bolts. Each of them is modelled as a wire element, linked by ridig couplings to the border of the hole, with the axial rotational DOF not restrained. Restrictions of DOFs at each fitting point are defined in the following table: Restrictions
Displacements
Fitting
1
2
3
4
Rotations
X
Y
Z
RX
RY
RZ
X
X
X
X
X
-
X
X
X
X
X
-
X
X
X
X
X
-
X
X
X
X
X
-
Page 11 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 5.
MATHEMATICAL MODEL (FEM) All components were meshed with linear tetrahedral elements of Coupled Temperature‐
Displacement type. The whole model has the following elements and nodes quantities: In detail, the splitters have the following mesh:
Page 12 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 Electronic components such as MTRs, PSUs and UCs are simulated as puntual masses distributed on the components fitting points. Their weights are: MTR = 5 x 0.850 kg PSU = 5 x 0.350 kg UC = 5 x 0.200 kg MTR1
MTR2
MTR3
MTR4
MTR5
PSU1
PSU5
UC1
PSU2
PSU3
UC2
UC3
PSU4
UC4
UC5
Page 13 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 6. RESULTS 6.1
Natural Frequencies Natural frequencies have been extracted in order to verify the imposed condition of at least 200 Hz for the first natural frequency. MODE 1 – 239.63 Hz MODE 2 – 281.97 Hz Page 14 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 MODE 3 – 317.16 Hz MODE 4 – 327.84 Hz Page 15 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 MODE 5 – 413.20 Hz MODE 6 – 455.29 Hz The condition of F1 > 200Hz is satisfied. Page 16 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 6.2
Load Case 1 Load case 1 (Ax = 15g, Ay = 6g, Az = 2g), with both temperatures (+15/‐16ºC). 6.2.1 Stresses Stresses [MPa] for LC1 are shown in the following figures. In case of the Splitters, only the one with greater stresses is shown. LOAD CASE 1 +15ºC Maximum stress: 59.0 MPa Page 17 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 LOAD CASE 1 ‐16ºC Maximum stress: 60.4 MPa Page 18 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 6.2.2 Displacements Displacements in mm for LC1 are shown: LOAD CASE 1 +15ºC LOAD CASE 1 ‐16ºC Page 19 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 6.3
Load Case 2 Load case 2 (Ax = 2g, Ay = 2g, Az = 2g), with both temperatures (+15/‐16ºC). 6.3.1 Stresses Stresses [MPa] for LC2 are shown in the following figures: LOAD CASE 2 +15ºC Maximum stress: 66.8 MPa Page 20 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 LOAD CASE 2 ‐16ºC Maximum stress: 71.4 MPa Page 21 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 6.3.2 Displacements Displacements in mm for LC2 are shown: LOAD CASE 2 +15ºC LOAD CASE 2 ‐16ºC Page 22 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 6.4
Load Case 3 Load case 3 (Ax = 2g, Ay = 6g, Az = 15g), with both temperatures (+15/‐16ºC). 6.4.1 Stresses Stresses [MPa] for LC3 are shown in the following figures: LOAD CASE 3 +15ºC Maximum stress: 61.6 MPa Page 23 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 LOAD CASE 3 ‐16ºC Maximum stress: 61.2 MPa Page 24 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 6.4.2 Displacements Displacements in mm for LC3 are shown: LOAD CASE 3 +15ºC LOAD CASE 3 ‐16ºC Page 25 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 6.5
Load Case 4 Load case 4 is only thermal, for both temperatures (+33/‐63ºC). 6.5.1 Stresses Stresses [MPa] for LC4 are shown in the following figures: LOAD CASE 4 +33ºC Maximum stress: 156.8 MPa Page 26 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 LOAD CASE 4 ‐63ºC Maximum stress: 299.2 MPa Page 27 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 6.5.2 Displacements Displacements in mm for LC4 are shown: LOAD CASE 4 +33ºC LOAD CASE 4 ‐63ºC Page 28 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 6.6
Safety Margins Safety margins for Splitters are calculated using the maximum stresses in each Load Case. Safety Margins are calculated in the following way: Yield Safety Margin σy


 1 MS y = 

σ

FSY

FU

 max
where σy is the yield strenght; σmax is the maximum achieved stress; the FSY is 1.25; and the FU is 1.15. Ultimate Safety Margin 

σu
  1
MS u = 
σ

FSU

FU
 max

where σu is the ultimate strenght; σmax is the maximum achieved stress; the FSU is 1.4; and the FU is 1.15. The safety margins (MS) for the specified design loads shall be greater than 0.05. The following table shows the Safey Margins for each load case. Maximum stresses were extracted from the shown stress maps. Temperature
LOAD CASE 1
LOAD CASE 2
LOAD CASE 3
LOAD CASE 4
+15ºC
-16ºC
+15ºC
-16ºC
+15ºC
-16ºC
+33ºC
-63ºC
Actual Stress
[MPa]
47.58
50.75
47.58
50.74
47.57
50.83
104.67
168.31
Yield Stress
[MPa]
276
276
276
276
276
276
276
276
MSY
3.04
2.78
3.04
2.78
3.04
2.78
0.83
0.14
Ultimate Stress
[MPa]
310
310
310
310
310
310
310
310
MSU
3.05
2.79
3.05
2.79
3.05
2.79
0.84
0.14
Page 29 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 6.7
Bolted Joints Safety margins for the bolts linking the PSC modules to the CTR box are calculated extracting the nodal forces acting on the bolts in each Load Case. Shear, Joint separation and Combined shear‐tensile safety margins are calculated. All procedures are detailed in APPENDIX A. Extracted forces [N] and resulting safety margins are: SPL2
LOAD CASE 1
+15ºC
SPL1
RF1 [N]
SPL1
SPL2
SPL1
SPL2
Compose
Shear [N]
Bolt Safety
Margin
(NASA)
Bolt Safety
Margin
(shear)
Bolt Safety
Margin
(separation)
M4
-12.81
-13.40
-6.81
18.5
3,31
171,24
659,74
Bolt 12
M4
-4.72
-1.96
4.42
5.1
3,32
623,51
1017,93
Bolt 13
M4
-3.00
-0.52
1.45
3.0
3,32
1048,91
3096,90
Bolt 14
M4
-3.08
6.44
-2.21
7.1
3,32
446,24
2040,92
Bolt 21
M4
-5.01
-7.11
-2.48
8.7
3,32
366,12
1817,81
Bolt 22
M4
-3.28
-8.74
-0.32
9.3
3,33
340,99
14139,34
3,32
223,99
1531,75
3,32
717,89
1740,79
Bolt 23
M4
-11.38
8.47
-2.94
14.2
Bolt 24
M4
-3.93
-2.07
2.59
4.4
RF2 [N]
RF3 [N]
Compose
Shear [N]
Bolt Safety
Margin
(NASA)
Bolt Safety
Margin
(shear)
Bolt Safety
Margin
(separation)
Bolt 11
M4
-10.96
-3.34
-9.48
11.5
3,31
277,69
474,23
Bolt 12
M4
-5.07
2.86
6.81
5.8
3,31
547,50
660,70
Bolt 13
M4
-3.92
-8.67
3.95
9.5
3,32
334,50
1139,21
Bolt 14
M4
-3.66
-0.29
-4.43
3.7
3,32
868,60
1016,26
Bolt 21
M4
-4.06
-0.43
0.73
4.1
3,33
779,99
6175,07
Bolt 22
M4
-4.77
-4.06
-3.46
6.3
3,32
508,61
1298,78
Bolt 23
M4
-10.09
0.85
-6.30
10.1
3,32
314,23
713,99
Bolt 24
M4
-4.67
-5.80
5.89
7.4
3,32
427,76
763,98
RF1 [N]
LOAD CASE 2
+15ºC
RF3 [N]
Bolt 11
RF1 [N]
LOAD CASE 1
-16ºC
RF2 [N]
RF2 [N]
RF3 [N]
Compose
Shear [N]
Bolt Safety
Margin
(NASA)
Bolt Safety
Margin
(shear)
Bolt Safety
Margin
(separation)
Bolt 11
M4
-2.71
-10.19
-9.58
10.5
3,31
301,62
468,83
Bolt 12
M4
-2.10
-9.11
4.34
9.3
3,32
340,62
1035,42
Bolt 13
M4
0.68
-11.82
7.63
11.8
3,31
268,65
588,99
Bolt 14
M4
0.99
-3.50
-5.54
3.6
3,32
876,28
811,79
Bolt 21
M4
-3.58
-18.15
-6.47
18.5
3,32
171,58
695,27
Bolt 22
M4
-1.33
-8.45
1.09
8.6
3,33
372,20
4119,02
Bolt 23
M4
1.46
-4.14
4.41
4.4
3,32
726,05
1020,61
Bolt 24
M4
0.30
-3.88
-2.18
3.9
3,32
819,54
2064,38
Page 30 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 SPL2
LOAD CASE 2
-16ºC
SPL1
RF1 [N]
SPL1
SPL2
SPL1
Bolt Safety
Margin
(NASA)
Bolt Safety
Margin
(shear)
Bolt Safety
Margin
(separation)
3,30
3641,12
366,75
6.73
4.9
3,31
645,67
668,03
-0.87
-0.13
-12.24
Bolt 12
M4
-2.45
-4.29
Bolt 13
M4
-0.25
-19.97
10.13
20.0
3,31
158,87
443,61
Bolt 14
M4
0.41
-10.23
-7.76
10.2
3,31
310,72
579,17
Bolt 21
M4
-2.63
-11.47
-3.26
11.8
3,32
270,17
1379,27
Bolt 22
M4
-2.83
-3.77
-2.05
4.7
3,32
676,79
2192,33
Bolt 23
M4
2.75
-11.77
1.05
12.1
3,33
263,18
4297,17
Bolt 24
M4
-0.44
-7.61
1.12
7.6
3,33
417,86
4016,14
M4
RF2 [N]
12.12
13.33
RF3 [N]
Compose
Shear [N]
Bolt Safety
Margin
(NASA)
Bolt Safety
Margin
(shear)
Bolt Safety
Margin
(separation)
-21.51
18.0
3,29
176,20
208,34
Bolt 12
M4
-5.13
-11.76
8.56
12.8
3,31
247,75
524,91
Bolt 13
M4
-8.72
-4.08
9.40
9.6
3,31
330,48
478,14
Bolt 14
M4
-1.41
-6.92
-20.06
7.1
3,29
450,69
223,53
Bolt 21
M4
-8.03
-0.77
1.65
8.1
3,32
394,74
2720,36
Bolt 22
M4
-1.84
4.30
-13.87
4.7
3,30
680,93
323,69
Bolt 23
M4
11.09
-17.06
-13.83
20.4
3,30
155,87
324,71
Bolt 24
M4
-4.37
4.09
2.44
6.0
3,32
532,69
1845,98
RF1 [N]
SPL2
Compose
Shear [N]
0.9
M4
Bolt 11
LOAD CASE 3
-16ºC
RF3 [N]
Bolt 11
RF1 [N]
LOAD CASE 3
+15ºC
RF2 [N]
RF2 [N]
Bolt Safety
Margin
(shear)
Bolt Safety
Margin
(separation)
116,19
185,30
10.95
8.8
3,31
359,87
410,30
11.89
15.6
3,30
203,95
377,60
-22.28
13.8
3,29
230,34
201,14
5.90
4.86
9.2
3,32
345,17
925,62
8.99
-17.01
9.6
3,30
332,05
263,65
-24.69
-17.19
27.6
3,29
114,59
261,02
5.74
5.1
3,32
622,38
783,60
13.97
Bolt 12
M4
-5.48
-6.94
Bolt 13
M4
-9.65
-12.23
Bolt 14
M4
-1.99
-13.65
Bolt 21
M4
-7.08
Bolt 22
M4
-3.34
Bolt 23
M4
12.38
-5.11
Bolt Safety
Margin
(NASA)
3,28
M4
M4
Compose
Shear [N]
27.2
Bolt 11
Bolt 24
RF3 [N]
23.39
0.36
-24.17
Page 31 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 SPL2
LOAD CASE 4
+33ºC
SPL1
RF1 [N]
SPL1
SPL2
RF3 [N]
Compose
Shear [N]
Bolt Safety
Margin
(NASA)
Bolt Safety
Margin
(shear)
Bolt Safety
Margin
(separation)
19.96
10.3
3,29
310,17
224,65
-6.18
-19.44
6.8
3,29
471,42
230,68
6.92
-19.67
6.9
3,29
459,74
227,87
8.49
19.15
8.7
3,29
364,46
234,08
-9.54
0.96
-23.22
9.6
3,28
331,94
192,96
5.53
-1.93
22.83
5.9
3,28
543,53
196,20
M4
-0.11
-7.17
23.66
7.2
3,28
444,17
189,29
M4
4.11
8.14
-23.28
9.1
3,28
349,05
192,41
Bolt 11
M4
-4.46
-9.24
Bolt 12
Bolt 13
M4
2.74
M4
-0.31
Bolt 14
M4
2.04
Bolt 21
M4
Bolt 22
M4
Bolt 23
Bolt 24
RF1 [N]
LOAD CASE 4
-63ºC
RF2 [N]
RF2 [N]
RF3 [N]
Compose
Shear [N]
Bolt Safety
Margin
(NASA)
Bolt Safety
Margin
(shear)
Bolt Safety
Margin
(separation)
Bolt 11
M4
8.52
17.63
-38.10
19.6
3,26
161,99
117,20
Bolt 12
M4
-5.22
11.80
37.10
12.9
3,26
246,46
120,36
Bolt 13
M4
0.59
-13.21
37.56
13.2
3,26
240,34
118,89
Bolt 14
M4
-3.89
-16.22
-36.57
16.7
3,26
190,43
122,14
Bolt 21
M4
18.21
-1.84
44.32
18.3
3,24
173,40
100,60
Bolt 22
M4
-10.57
3.69
-43.59
11.2
3,25
284,23
102,30
Bolt 23
M4
0.20
13.69
-45.18
13.7
3,24
232,18
98,67
Bolt 24
M4
-7.85
-15.54
44.45
17.4
3,24
182,36
100,31
Bolts are numbered in the following way: Page 32 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 6.8
Fail Safe analysis A fail‐safe analysis was performed in order to verify the bolted joints. The bolt with the most critical satefy margin was supressed from the simulation and forces were extracted again, in order to obtain the new safety margins. From the data shown in 6.7, the minimum safety margin is achieved for Bolt 23, Load Case 4 with ‐63ºC. Therefore, bolt 23 is supressed and simulation run again, obtaining the following results: SPL2
FAIL SAFE
LOAD CASE 4
-63ºC
SPL1
RF1 [N]
RF2 [N]
RF3 [N]
Compose
Shear [N]
Bolt Safety
Margin
(NASA)
Bolt Safety
Margin
(shear)
Bolt Safety
Margin
(separation)
17.67
-38.04
19.6
3,26
161,70
117,37
-5.22
11.79
37.05
12.9
3,26
246,59
120,54
0.58
-13.22
37.50
13.2
3,26
240,18
119,06
M4
-3.90
-16.23
-36.51
16.7
3,26
190,21
122,32
M4
10.42
-5.78
0.35
11.9
3,33
266,95
13013,14
Bolt 22
M4
-14.08
13.57
-0.52
19.6
3,33
162,28
8708,66
Bolt 23
M4
Bolt 24
M4
3.66
-7.79
0.17
8.6
3,33
369,88
26331,71
Bolt 11
M4
8.54
Bolt 12
M4
Bolt 13
M4
Bolt 14
Bolt 21
As it can be seen, the new safety margins are a bit higher. This is logical since, in a thermal load case, the suppression of a constraint generally relaxes the structure and diminishes the load on the remaining bolts. Page 33 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 7. CONCLUSIONS 
The Splitters are able to effectively withstand all applied Load Cases. 
Frequency requirements for the whole model are met (f >= 200 Hz). 
Material failure is not reached in any of the Load Cases (MS > 0). 
Maximum stresses are located in the elements where bolted joints are simulated. As their are modeled with rigid elements, results can be considered conservative. Nevertheless, all MS are satisfactory. 
Stresses for Load Cases 1, 2 and 3 on the Splitters are almost the same, since the mass of them is very small. The greater amount of stress is generated due to the thermal loads, which are the same for all 3 load cases. 
All bolted joints meet the required Safety Margin. Selected bolt size is M4, with a torque of 2.5 N.m. which is a typical value calculated assuming a limit of 60% of yield stress reached with the initial preload and typical steel to aluminium friction coefficients, for both head and thread contact areas. Page 34 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 8. APPENDIX A: Bolts Verification Calculation NASA's fastener design manual (RD2) was used in the estimation of allowable loads and safety margins for bolts. 8.1.1 Combined shear and tensile loads Safety margin Margin of safety for bolts, combining shear and tensile loads, is defined as: MS S,T =
1
 1 R + RT2
3
S
where RS =
Q S op
Actual shear load
=
Allowable shear load Q S allow
RT =
F T op
Actual tensile load
=
Allowable tensile load F T allow 8.1.2 Actual Loads 8.1.2.1 Shear loads Operation shear loads were obtained as shown in 9.1. 8.1.2.2 Tensile loads Total operation tensile loads for a bolt are calculated with the following formula:  kb
FTop = Fi * + 
 kb + kc

  Fe  FSU  FU 
where Fi* is the initial bolt load; kb is the spring constant of the bolt; kc is the spring constant of the clamped faces; FSU is the bolted joint safety factor (1.5); FU the uncertainty factor (1.15); and Fe the external load, obtained in 9.1. Initial bolt load, Fi*, is the torque load corrected by the torque precision factors. Fi * = Fi  tpf  tmf Torque load Fi is: Fi =
T
K D
where T is the fastener torque; D is the nominal diameter of the bolt; and K is the torque coefficient, resulting from the following formula:  d  tanψ + μ  secα
K= m 
+ 0.625 μC  2d  1  μ  tanψ  secα
where dm is the thread mean diameter, d is the thread outer diameter, Ψ is the thread helix angle, μ is the friction coefficient between threads, α is the thread angle and μC is the friction coefficient between bolthead and clamping surface. For each bolt type the following values are obtained: Torque coefficient
M3
M4
K
0.2108
0.2117
Page 35 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 A Torque precision factor (tpf) of 15% and a torque measurement precision factor (mpf) of 20% are assumed. Thus, the resulting initial bolt load equation is: Fi* =
T
 1.15  1.2  K D
Spring constants of the bolt (kb) and the clamped faces (kc) are: kb =
E b  Ab
L1
kc =
E c  Ac
e
where Eb is the elastic modulus of the bolt; Ab the resistant area of the bolt; and L1 the bolt length from bolt head to the thread. Ec is the elastic modulus of the clamped part; Ac is the gasket compression area, equivalent to 2.Ab; and e is the thickness of the gasket. 8.1.3 Allowable Loads 8.1.3.1 Shear loads Allowable shear load for a bolt is calculated with the following formula: Q Sallow =
σ Sult
 Ab FSU  FU
where σSult is the ultimate shear stress; and Ab is the resistant area of the bolt, calculated as: Ab =
π  d 2f
4
where df is the bolt thread inner diameter. 8.1.3.2 Tensile loads Allowable tensile load for a bolt is calculated with the following formula: FTallow = σ ult  Ab where σult is the ultimate tensile stress. With all these values, it is possible to calculate the previously shown safety margin of the bolt: MS Q , T =
1
−1
R + R2T
3
S
8.1.4 Shear Safety margin Shear safety margin is defined as: MS Q =
QSop
Actualshearload
1
 1=
 1=
1 Allowableshearload
QSallow
RS
All variables were already defined for the combined load safety margin calculation. Page 36 of 37 PSC Structural Analysis AEW20605A02
30‐12‐2011 8.1.5 Joint Separation Safety margin Joint separation Safety margin is calculated with the following formula: Tensile 
FTmax
1
Fe  FS
MS JS =
Compressive 
MS JS
F
= Cmax  1
Fe  FS
where Ft max is the maximum joint tensile load and FC max is the maximum joint compressive load, which are formulated as: F T max = F
*
i
( )
kb
k b+ k c
−1
F C max = F
*
i
( )
kc
k b+ k c
−1
Then, the safety margins formulas for joint separation are: Tensile  MS JS =
Fi *
 kb

 kb + kc
Compressive  MS JS =

  Fe  FS

Fi*
 kc

 kb + kc
1

  Fe  FS

1
Page 37 of 37