Adjustable Support Simulations Edmond Lam 04 10 2017

Adjustable Support Simulations Edmond Lam 04. 10. 2017

Goals • Determine the range of adjustment before reaching yield strength • Investigate the effect of the thickness of the bars on the range of adjustment 04. 10. 2017 2

Simplification Top Plate • Top plate • Always bonded to the sleeve • -> suppress • Support • Additional mesh elements • Additional contact conditions (assumptions and convergence issues) • Test simulations reveal only very little deformation (1 E-8 m) • -> suppress 04. 10. 2017 Sleeve Horizontal Bar Vertical Bar Support 3

Top Plate Horizontal Bar Sleeve Vertical Bar Support Vertical Bar 04. 10. 2017 4

Contact Definition and Solution Method • Two contacts • Contact definition: no separation • Frictionless sliding allowed • But no gaps allowed between the surfaces • Algorithm • Augmented Lagrange • Penalty based -> require a good contact stiffness factor • Normal contact stiffness factor = 1 chosen after a sensitivity study 04. 10. 2017 5

Mesh and Convergence • Mesh • ~ 400’ 000 elements initially for the two bars and the sleeve • Adaptive mesh refinement enabled • ANSYS automatically refines the mesh where necessary after a run until the preset convergence criteria are reached • Convergence requirements • < 1% change in monitored values between two successive runs • Monitored values • Maximum equivalent stress in the two bars • Safety factor of the system and of the two bars • Time until convergence: ~ 20 minutes per case 04. 10. 2017 6

Cases Considered • For vertical bars of 4 different thickness • Only Load (228. 69 N – 3 supports for the weight) • Load + Displacement of the horizontal bar or vertical bar • 0. 5 mm, 0. 75 mm; 1. 25 mm; 1. 5 mm • Load + Simultaneous displacement of the horizontal and vertical bars • 0. 25 mm; 0. 75 mm; 1 mm 04. 10. 2017 7

Stresses of the Bars – Displacement of the Horizontal Bar Only Blue: Compression Red: Tension z x (exaggerated) 04. 10. 2017 8

Stresses of the Bars – Displacement of the Horizontal Bar Only Max Equivalent Stress of the Horizontal Bar (Pa) Max Equiv. Stress of the Horizontal Bar against X-Displacement of the Horizontal Bar 8 E+07 7 E+07 6 E+07 5 E+07 4 E+07 3 E+07 2 E+07 0. 0 E+00 2. 0 E-04 4. 0 E-04 6. 0 E-04 8. 0 E-04 1. 0 E-03 1. 2 E-03 1. 4 E-03 1. 6 E-03 X-Displacement of the Horizontal Bar (m) 04. 10. 2017 0. 5 mm Thicker Vertical Bar Original Thickness 0. 5 mm Thinner Vertical Bar 1 mm Thinner Vertical Bar Material: 30 Cr. Ni. Mo 8 Yield strength: 1. 034 E+09 Pa Ultimate strength: 1. 158 E+09 Pa 9

Stresses of the Bars – Displacement of the Horizontal Bar Only Max Equivalent Stress of the Vertical Bar (Pa) Max Equiv. Stress of the Vertical Bar against X-Displacement of the Horizontal Bar 9. 0 E+08 8. 0 E+08 7. 0 E+08 6. 0 E+08 5. 0 E+08 0. 5 mm Thicker Vertical Bar 4. 0 E+08 Original Thickness 3. 0 E+08 2. 0 E+08 1. 0 E+08 0. 0 E+00 2. 0 E-04 4. 0 E-04 6. 0 E-04 8. 0 E-04 1. 0 E-03 1. 2 E-03 1. 4 E-03 1. 6 E-03 X-Displacement of the Horizontal Bar (m) 04. 10. 2017 0. 5 mm Thinner Vertical Bar 1 mm Thinner Vertical Bar Material: 30 Cr. Ni. Mo 8 Yield strength: 1. 034 E+09 Pa Ultimate strength: 1. 158 E+09 Pa 10

Stresses of the Bars – Displacement of the Vertical Bar Only Blue: Compression Red: Tension z x (exaggerated) 04. 10. 2017 11

Stresses of the Bars – Displacement of the Vertical Bar Only Max Equivalent Stress of the Horizontal Bar (Pa) Max Equiv. Stress of the Horizontal Bar against Z-Displacement of the Vertical Bar 1. 2 E+09 1. 0 E+09 8. 0 E+08 6. 0 E+08 4. 0 E+08 2. 0 E+08 0. 0 E+00 2. 0 E-04 4. 0 E-04 6. 0 E-04 8. 0 E-04 1. 0 E-03 1. 2 E-03 1. 4 E-03 1. 6 E-03 Z-Displacement of the Vertical Bar (m) 04. 10. 2017 0. 5 mm Thicker Vertical Bar Original Thickness 0. 5 mm Thinner Vertical Bar 1 mm Thinner Vertical Bar Material: 30 Cr. Ni. Mo 8 Yield strength: 1. 034 E+09 Pa Ultimate strength: 1. 158 E+09 Pa 12

Stresses of the Bars – Displacement of the Vertical Bar Only Max Equivalent Stress of the Vertical Bar (Pa) Max Equiv. Stress of the Vertical Bar against Z-Displacement of the Vertical Bar 4. 0 E+08 3. 5 E+08 3. 0 E+08 2. 5 E+08 2. 0 E+08 1. 5 E+08 1. 0 E+08 5. 0 E+07 0. 0 E+00 2. 0 E-04 4. 0 E-04 6. 0 E-04 8. 0 E-04 1. 0 E-03 1. 2 E-03 1. 4 E-03 1. 6 E-03 Z-Displacement of the Vertical Bar (m) 04. 10. 2017 0. 5 mm Thicker Vertical Bar Original Thickness 0. 5 mm Thinner Vertical Bar 1 mm Thinner Vertical Bar Material: 30 Cr. Ni. Mo 8 Yield strength: 1. 034 E+09 Pa Ultimate strength: 1. 158 E+09 Pa 13

Stresses of the Bars – Simultaneous Displacement of Both Bars Blue: Compression Red: Tension z x (exaggerated) 04. 10. 2017 14

Stresses of the Bars – Simultaneous Displacement of Both Bars Max Equivalent Stress of the Horziontal Bar (Pa) Max Equiv. Stress of the Horizontal Bar against Simultaneous Displacements of Both Bars 9 E+08 8 E+08 7 E+08 6 E+08 5 E+08 0. 5 mm Thicker Vertical Bar 4 E+08 Original Thickness 0. 5 mm Thinner Vertical Bar 3 E+08 1 mm Thinner Vertical Bar 2 E+08 Material: 30 Cr. Ni. Mo 8 Yield strength: 1. 034 E+09 Pa Ultimate strength: 1. 158 E+09 Pa 1 E+08 0 E+00 04. 10. 2017 2. 0 E-04 4. 0 E-04 6. 0 E-04 8. 0 E-04 1. 0 E-03 Simultaneous Displacement of Both Bars (m) 1. 2 E-03 15

Stresses of the Bars – Simultaneous Displacement of Both Bars Max Equivalent Stress of the Vertical Bar (Pa) Max Equiv. Stress of the Vertical Bar against Simultaneous Displacements of Both Bars 9 E+08 8 E+08 7 E+08 6 E+08 5 E+08 0. 5 mm Thicker Vertical Bar 4 E+08 Original Thickness 0. 5 mm Thinner Vertical Bar 3 E+08 1 mm Thinner Vertical Bar 2 E+08 Material: 30 Cr. Ni. Mo 8 Yield strength: 1. 034 E+09 Pa Ultimate strength: 1. 158 E+09 Pa 1 E+08 0 E+00 04. 10. 2017 2. 0 E-04 4. 0 E-04 6. 0 E-04 8. 0 E-04 1. 0 E-03 Simultaneous Displacement of Both Bars (m) 1. 2 E-03 16

From extrapolation up to the yield strength: Vertical Bar Displacement range of the horizontal bar (only horizontal adjustment) Displacement range of the vertical bar (only vertical adjustment) Displacement range of both bars (simultaneous adjustment) 0. 5 mm thicker Up to 1. 82521 mm Up to 1. 40390 mm Up to 1. 35708 mm Original Up to 1. 95669 mm Up to 1. 58024 mm Up to 1. 41851 mm 0. 5 mm thinner Up to 2. 10496 mm Up to 1. 78631 mm Up to 1. 48287 mm 1 mm thinner Up to 2. 30213 mm Up to 1. 98169 mm Up to 1. 59089 mm A thinner vertical bar allows a wider displacement range while staying below the yield strength of the material. Note that the ranges reported are absolute limits. A margin should be allowed. Limitations not considered in the simulation: 1. Tilting and movement of the top surface of the sleeve -> reaction moment and force from the load 2. Force required to displace the bars cannot be estimated as the friction condition between the bars and the support are not known. 04. 10. 2017 17

Tendency for the Sleeve to Tilt – Z-Span z-span Because the reaction forces and moments from the load were not known, in the simulation no constraint was put on the surface except the weight of the load. Nevertheless this measure gives an idea of the tendency for the sleeve to tilt when the bars are displaced. z x 04. 10. 2017 18

Tendency for the Sleeve to Tilt – Displacement of the Horizontal Bar Only Z-Span against X-Displacement of the Horizontal Bar 1 E-04 9 E-05 8 E-05 Z-Span (m) 7 E-05 6 E-05 5 E-05 4 E-05 3 E-05 0. 5 mm Thicker Vertical Bar Original Thickness 0. 5 mm Thinner Vertical Bar 1 mm Thinner Vertical Bar 2 E-05 1 E-05 0 E+00 0. 0 E+00 2. 0 E-04 4. 0 E-04 6. 0 E-04 8. 0 E-04 1. 0 E-03 1. 2 E-03 1. 4 E-03 1. 6 E-03 X-Displacement of the Horizontal Bar (m) 04. 10. 2017 The tendency to tilt does not change with displacement of the horizontal bar. 19

Tendency for the Sleeve to Tilt – Displacement of the Vertical Bar Only Z-Span against Z-Displacement of the Vertical Bar 1 E-03 9 E-04 8 E-04 Z-Span (m) 7 E-04 6 E-04 5 E-04 4 E-04 3 E-04 0. 5 mm Thicker Vertical Bar Original Thickness 0. 5 mm Thinner Vertical Bar 1 mm Thinner Vertical Bar 2 E-04 1 E-04 0 E+00 0. 0 E+00 2. 0 E-04 4. 0 E-04 6. 0 E-04 8. 0 E-04 1. 0 E-03 1. 2 E-03 1. 4 E-03 1. 6 E-03 Z-Displacement of the Vertical Bar (m) 04. 10. 2017 The tendency to tilt increases with displacement of the vertical bar. 20

Tendency for the Sleeve to Tilt – Simultaneous Displacement of Both Bars Z-Span against Simultaneous Displacement of Both Bars 7 E-04 6 E-04 Z-Span (m) 5 E-04 4 E-04 0. 5 mm Thicker Vertical Bar Original Thickness 3 E-04 0. 5 mm Thinner Vertical Bar 2 E-04 1 mm Thinner Vertical Bar 1 E-04 The tendency to tilt increases with simultaneous displacement of both bars. 0 E+00 04. 10. 2017 2. 0 E-04 4. 0 E-04 6. 0 E-04 8. 0 E-04 1. 0 E-03 Simultaneous Displacement of Both Bars (m) 1. 2 E-03 21

Force Necessary to Produce Displacement – Displacement of the Horizontal Bar Only X-Force Necessary to Produce X-Displacement of the Horizontal Bar 180 160 X-Force Necessary (N) 140 120 100 80 60 40 20 0 0. 0 E+00 2. 0 E-04 4. 0 E-04 6. 0 E-04 8. 0 E-04 1. 0 E-03 1. 2 E-03 1. 4 E-03 1. 6 E-03 -20 X-Displacement of the Horizontal Bar (m) 04. 10. 2017 0. 5 mm Thicker Vertical Bar Original Thickness 0. 5 mm Thinner Vertical Bar 1 mm Thinner Vertical Bar Friction was not accounted for. 22

Force Necessary to Produce Displacement – Displacement of the Vertical Bar Only Z-Force Necessary to Produce Z-Displacement of the Vertical Bar 280 Z-Force Necessary (N) 270 260 250 240 0. 5 mm Thicker Vertical Bar Original Thickness 0. 5 mm Thinner Vertical Bar 1 mm Thinner Vertical Bar 230 220 0. 0 E+00 2. 0 E-04 4. 0 E-04 6. 0 E-04 8. 0 E-04 1. 0 E-03 1. 2 E-03 1. 4 E-03 1. 6 E-03 Z-Displacement of the Vertical Bar (m) 04. 10. 2017 Friction was not accounted for. 23

Force Necessary to Produce Displacement – Simultaneous Displacement of Both Bars X-Force Necessary to Produce Simultaneous Displacement of Both Bars 120 X-Force Necessary (N) 100 80 0. 5 mm Thicker Vertical Bar 60 Original Thickness 0. 5 mm Thinner Vertical Bar 40 1 mm Thinner Vertical Bar 20 0 0. 0 E+00 -20 04. 10. 2017 Friction was not accounted for. 2. 0 E-04 4. 0 E-04 6. 0 E-04 8. 0 E-04 1. 0 E-03 1. 2 E-03 Simultaneous Displacement of Both Bars (m) 24

Force Necessary to Produce Displacement – Simultaneous Displacement of Both Bars Z-Force Necessary to Produce Simultaneous Displacement of Both Bars 265 Z-Force Necessary (N) 260 255 250 0. 5 mm Thicker Vertical Bar 245 Original Thickness 0. 5 mm Thinner Vertical Bar 240 1 mm Thinner Vertical Bar 235 230 225 0. 0 E+00 04. 10. 2017 Friction was not accounted for. 2. 0 E-04 4. 0 E-04 6. 0 E-04 8. 0 E-04 1. 0 E-03 Simultaneous Displacement of Both Bars (m) 1. 2 E-03 25

1. Thinner vertical bars create lower stresses and increase the adjustment range. 2. Thinner vertical bars as well require smaller forces to perform adjustments. 3. Thinner vertical bars, however, makes the sleeve more likely to tilt – may need to take into consideration in actual application. 04. 10. 2017 26

Thank you. 04. 10. 2017 27