Thermal Contact Conductance in Bolt Joints An expert

Thermal Contact Conductance in Bolt Joints

An expert is a man who has made all the mistakes which can be made, in a narrow field. 11/22/2020 Document reference 3

Summary § Theoretical Heat flow § Real Heat Flow § Theoretical Models § Semi-Empirical Model § Materials § Test Setup § Results § Discussion/Conclusion 11/22/2020 Document reference 4

Theoretical Heat flow Fourier Law of Heat Conduction 3 Dimensional Single Material Conduction Multilayer Conduction Unidimensional 11/22/2020 Document reference 5

Real Heat Flow Major Interface Parameters Affecting Conduction • Surface Roughness • Force • Temperature • Microhardness • Oxide Layers • Thermal Constriction/Dilatation 11/22/2020 Document reference 6

Theoretical Models Elastic: Fletcher and Gyorog Plastic: Modified CMY Model Rocca Mikic Model for Bolted Joints 11/22/2020 Document reference 7

Semi-Empirical Model Equivalent Fin Method (EFM) Not suited for significative thermal conductivity variations. 11/22/2020 Document reference 8

Empirical Model Based on Empirical Joint Design Rule of Thumb: Bolt Spacing for general construction should be at least 1, 5 D to the edge and 4 D between bolts. 1. 5 D 4 D 2 D 11/22/2020 Document reference 9

Empirical Model Step 1: Power Requirement Needed Step 2: Estimate Temperature at the Joint 11/22/2020 Document reference 10

Empirical Model Step 3: Select Type of Joint • Configuration (Parallel, Perpendicular, Inverted, etc…) Inverted Flow Radial Flow Perpendicular Parallel Direct Flow 11/22/2020 Document reference 11

Empirical Model Step 4: Select Bolt Size Step 5: Determine in Database Heat Transfer for Bolt Size, Material and Joint Temperature Step 6: Divide Database Heat Transfer by Power Requirement to determine number of Bolts Step 7: Validate Design 11/22/2020 Document reference 12

Materials 44. 01. 30 - ALUMINIUM 99, 5 % (EN AW-1050 A , state: H-24 half-hard) Tensile Strength Ultimate Strength Elongation at Break Hardness (Brinell) 75 MPa (min) 105 to 145 MPa 9% 38 BH (min) 44. 09. 56. B – COPPER (OXYGEN-FREE ELECTRONIC COPPER - Cu-OFE - EDMS 790780) Tensile Strength Ultimate Strength Elongation at Break Hardness (Brinell) 200 to 240 MPa 240 to 280 MPa 25% (min) 60 HBS (min) 44. 59. 32. A - STAINLESS STEEL (304 L LOW CARBON) – EN 10088 Tensile Strength Ultimate Strength Elongation at Break Hardness (Brinell) 11/22/2020 200 MPa 500 to 670 MPa 45% (min) 192 BH (max) Document reference 13

Test Setup Three access ports available. Two Wiring ports with 24 signal entries (One for the PT 100 probes) (24 used) (One for Electric Power) (16 Used, 8 available) Vaccum port can be modified to permit another 24 Signal entry Heaters Protected with MLI Cryostat Radiation Shield 11/22/2020 Document reference 14

Test Setup 11/22/2020 Document reference 15

Test Setup 11/22/2020 Document reference 16

Test Setup • All data presented for M 4 A 4 -70 Stainless Steel Bolt, (Torque 3 N m), unless otherwise referred. 11/22/2020 Document reference 17

Results: Cu-Cu M 4 A 4 -70 Stainless Steel Bolt, (Torque 3 N m) 330 Temperature [K] 280 • Very good linearity 230 • Delta T with visible difference 180 • Power transmitted (7 to 31 W) 130 80 0 50 100 150 200 250 300 Distance [mm] 11/22/2020 Document reference 18

Results: Cu-Cu Extrapolated Temperature [K] Equation y = -0, 193 x + 130, 72 y = -0, 247 x + 145, 02 y = -0, 305 x + 160, 72 y = -0, 362 x + 176, 63 y = -0, 418 x + 191, 83 y = -0, 477 x + 207, 82 y = -0, 534 x + 223, 6 y = -0, 593 x + 239, 48 y = -0, 652 x + 255, 47 y = -0, 708 x + 270, 77 106, 6 114, 1 122, 6 131, 4 139, 6 148, 2 156, 9 165, 4 174, 0 182, 3 Equation Extrapolated Temperature [K] Delta T [K] Mean Joint Temperature [K] Heat Power [W] Conductance [W/K] h [W/K m 2] 104, 4 111, 4 119, 4 127, 5 135, 3 143, 4 152, 2 159, 9 168, 2 176, 2 2, 7 3, 2 3, 8 4, 3 4, 8 4, 7 5, 5 5, 7 6, 1 105, 5 112, 8 121, 0 129, 5 137, 4 145, 8 154, 5 162, 6 171, 1 179, 2 7, 1 9, 5 12, 0 14, 5 17, 1 19, 9 22, 6 25, 6 28, 2 31, 1 3, 2 3, 5 3, 7 3, 8 4, 0 4, 1 4, 8 4, 7 4, 9 5, 1 92420 101506 108232 109469 115404 120150 140242 135891 142781 148556 y = -0, 176 x + 126, 37 y = -0, 223 x + 139, 3 y = -0, 275 x + 153, 73 y = -0, 328 x + 168, 53 y = -0, 379 x + 182, 63 y = -0, 433 x + 197, 5 y = -0, 488 x + 213, 17 y = -0, 54 x + 227, 37 y = -0, 595 x + 242, 6 y = -0, 646 x + 256, 93 Heat vs Delta T 35 Temperature [K] 30 25 Power [W] Temperature vs Condutance R 2 = 0. 9988 20 15 10 5 0 0 5 10 15 20 25 30 35 40 Temperature [K] 11/22/2020 45 R 2 = 0. 96 200 180 160 140 120 100 80 60 40 20 0 80000 90000 100000 110000 120000 130000 140000 150000 160000 Heat transfer coefficient [W/K m 2] Document reference 19

Results: Cu-Cu Comparison between data obtained and a theoretical model. Plastic: Modified CMY Model 11/22/2020 Document reference 20

Results: Al-Al M 4 A 4 -70 Stainless Steel Bolt, (Torque 3 N m) 330 • Extraordinary linearity Temperature [K] 280 • Very small difference in extrapolated values 230 • Oxide layer might play a huge role in conductance at the joint 180 130 80 0 50 100 150 200 250 300 Distance [mm] 11/22/2020 Document reference 21

Results: Al-Al Equation Extrapolated Temperature [K] Delta T [K] Mean Joint Temperature [K] Heat Power [W] Conductance [W/K] h [W/K m 2] y = -0, 201 x + 130, 08 y = -0, 272 x + 147, 7 y = -0, 332 x + 163, 53 y = -0, 395 x + 180, 05 y = -0, 457 x + 196, 05 y = -0, 518 x + 212, 3 y = -0, 579 x + 228, 18 y = -0, 639 x + 244, 28 y = -0, 698 x + 260, 2 y = -0, 754 x + 275, 8 104, 955 113, 7 122, 03 130, 675 138, 925 147, 55 155, 805 164, 405 172, 95 181, 55 y = -0, 182 x + 127, 27 y = -0, 244 x + 143, 87 y = -0, 301 x + 159, 33 y = -0, 361 x + 175, 63 y = -0, 42 x + 191, 53 y = -0, 481 x + 208, 07 y = -0, 539 x + 223, 83 y = -0, 6 x + 240, 27 y = -0, 659 x + 256, 43 y = -0, 718 x + 272, 53 104, 52 113, 37 121, 705 130, 505 139, 03 147, 975 156, 455 165, 27 174, 075 182, 78 0, 435 0, 33 0, 325 0, 17 -0, 105 -0, 425 -0, 65 -0, 865 -1, 125 -1, 23 104, 7375 113, 535 121, 8675 130, 59 138, 9775 147, 7625 156, 13 164, 8375 173, 5125 182, 165 7, 06561 9, 48664 12, 04913 14, 48128 17, 14986 19, 8986 22, 55159 25, 6106 28, 18465 31, 08573 16, 24278161 28, 74739394 37, 07424615 85, 184 -163, 332 -46, 82023529 -34, 69475385 -29, 60763006 -25, 05302222 -25, 27295122 162427, 8161 287473, 9394 370742, 4615 851840 -1633320 -468202, 3529 -346947, 5385 -296076, 3006 -250530, 2222 -252729, 5122 R 2 = 0. 9977 40 35 30 25 20 15 10 5 0 Mean Temperature vs Condutance 200 0 5 10 15 Temperature [K] 11/22/2020 20 Temperature [K] Power [W] Power vs Delta T 150 100 50 0 0 500000 1000000 1500000 2000000 Heat transfer coefficient [W/K m 2] Document reference 22

Results: SS-SS Temperature [K] M 4 A 4 -70 Stainless Steel Bolt, (Torque 3 N m) 280 Poor linearity in the data obtained. 230 Experiment should be repeated. (Shield Deformation) 180 Huge temperature gradients with very small heat input. (0, 5 to 1, 5 W) 130 Very small difference in extrapolated values 80 0 50 100 150 200 250 300 Distance [mm] 11/22/2020 Document reference 23

Results: Al-Cu M 4 A 4 -70 Stainless Steel Bolt, (Torque 3 N m) Temperature 280 230 180 130 80 0 50 100 150 200 250 300 Distance 11/22/2020 Document reference 24

Results: Al-Cu Equation Extrapolated Temp 96, 795 101, 705 109, 205 116, 595 124, 23 131, 75 y = -0, 261 x + 129, 42 y = -0, 343 x + 144, 58 y = -0, 443 x + 164, 58 y = -0, 545 x + 184, 72 y = -0, 64 x + 204, 23 y = -0, 734 x + 223, 5 Equation y = -0, 126 x + 112, 5 y = -0, 16 x + 121, 77 y = -0, 208 x + 135, 23 y = -0, 255 x + 148, 43 y = -0, 304 x + 162, 17 y = -0, 353 x + 175, 97 Extrapolated Temp. 96, 75 101, 77 109, 23 116, 555 124, 17 131, 845 Delta T Heat Power Conductance h 0, 045 -0, 065 -0, 025 0, 04 0, 06 -0, 095 7, 06561 9, 48664 12, 04913 14, 48128 17, 14986 19, 8986 157, 0135556 -145, 9483077 -481, 9652 362, 032 285, 831 -209, 4589474 1570135, 556 -1459483, 077 -4819652 3620320 2858310 -2094589, 474 Delta T vs Power Variation of extrapolated Delta T insufficient 18 R 2 = 0. 9853 Heat Power 16 14 12 Same problem faced in Al-AL for the conductance 10 8 6 4 2 0 0 5 10 15 20 25 30 Cu-AL should also be evaluated Delta T 11/22/2020 Document reference 25

Discussion/Conclusion • Given the problems faced determining thermal conductivity effectively, it was chosen to develop an empirical approach that could avoid the problem. • An empirical approach is easy to use and understand but will require a complete database able to encompass all the majority of joint designs. • Further testing is required to evaluate the approach for Aluminum and Stainless Steel. • Results for Copper validate this approach, at least, for this material. 11/22/2020 Document reference 26

Discussion/Conclusion • Further testing: Reduce the overlap area of the contact joints. (See if it solves the problem with Al tests and SS 304. • Considerer a method to exact evaluating of the contact area. (I suggest dying liquid). • For the case considerer: M 4 bolt, the value of 50% tightening torque (2 Nm) plastified the plates materials in the case of Cu and Al. This can make it hard to develop a database in function of tightening torque. 11/22/2020 Document reference 27

Thank you for your attention 11/22/2020 Document reference 28

FAQ • • PT 100 Overlap Contact Area Plates Deformation Heating Elements PT 100 Fixation Radiation Shield Leak Testing 11/22/2020 Document reference 29

PT 100 Overlap Second degree equation for hot part, linear for cold part. (Copper OFE) 11/22/2020 Document reference 30

Contact Area 11/22/2020 Document reference 31

Contact Area 11/22/2020 Document reference 32

Plates Deformation 11/22/2020 Document reference 33

Heating Elements PTC heating element with self-regulation housed in a compact flat aluminum alloy construction, allowing heat transmission to thermal medium. This means that no thermal cut-out or thermostat is required. Technical Characteristics: Length 40 mm Width 35 mm Height Thermal Power 8. 5 mm 50 W Surface Temperature Voltage 100 º C 12 V ac - 24 V dc From practical testing it was determined that they cannot operate bellow ~130 K. Bellow this point the resistance of the heating element becomes to high to allow any current to flow, effectively stopping any electrical heat dissipation. 11/22/2020 Document reference 34

Wiring Copper OFE 200 mm length plate 10 mm from heater 10 mm from heat sink 50 mm x 50 mm overlap joint 0, 12 mm manganin wire Copper OFE 180 mm length plate 40 mm from heater 40 mm from heat sink 50 mm x 50 mm overlap joint 0, 22 mm copper wire Distance Probe Reading 0 1 92. 0 0 1 78. 7 25 2 91. 3 50 2 79. 6 50 3 88. 8 100 3 79. 1 100 4 84. 9 150 4 77. 9 125 5 83. 9 200 5 77. 3 150 6 82. 8 250 6 77. 5 11/22/2020 Document reference 35

PT 100 Fixation 11/22/2020 Document reference 36

PT 100 Fixation 11/22/2020 Document reference 37

Radiation Shield 11/22/2020 Document reference 38

Leak Testing 11/22/2020 Document reference 39