Study on the Energy Absorption and the Local Buckling of the Expansion Tubes

Transcription

1 * Study on the Energy Absorption and the Local Buckling of the Expansion Tubes Kwanghyun Ahn * Jinsung Kim Hoon Huh School of Mechanical, Aerospace & System Engineering, Korea Advanced Institute of Science and Technology, Science town, Daejeon 3-71, Korea (Received / Accepted) Abstract : This paper deals with the local buckling characteristics and the energy absorption of the expansion tubes with the various dimensions of tubes and punch shapes The local buckling load and absorbed energy during the tube flaring process were discussed for each cases of tube and punch shapes by finite element analysis Absorbed energy of expansion tube is affected by the diameter and the wall thickness of tubes Punch angle and expansion ratio also affect to the energy absorption According to the buckling analysis, local buckling can occurs in some cases The absorbed energy of expansion tube significantly decreases when local buckling occurs For enhancement of energy absorption, it is important to predict local buckling load accurately In this study local buckling load is predicted by modification of equation Key words : Expansion tube( ), Energy absorption( ), Local buckling( ) 1 1) Device) (Light Collision Safety (Expansion Tube), 4 MJ 1,2) * ankh-1128@kaistackr

2 Table 1 Dimension of tube Parameter Range Thickness, t (mm) 1 t 3 Inner radius, r i (mm) 3 r i 46 Length, L (mm) 1 L 2 Friction coefficient, f 1 f FEM(Finete Element Method), FEM 3),,,, Fig 1 2 mm, 39 mm, 1 mm, 3 Table 1 Table 2 Table 2 Dimension of punch Parameter Range Punch angle, α 1 α 4 Expansion ratio, e(r p/r i) 12 e 1 Engineering stress (MPa) UTS = 9 MPa Yield = 43 MPa Engineering strain Fig 2 Engineering stress-strain curve of TWIP TWIP Fig 2 TWIP Fig 3 α=3, e=13, L=1 mm, r=39 mm 1 mm Fig 3 1, 1 mm 1 mm Fig 4 α=3, e=13, L=1 mm, t=2 mm Fig 1 Finite element model of tube and punch

3 t=3 mm t=2 mm t=2 mm t=1 mm t=1 mm L=1 L=12 L=1 L=17 L= Tube wall thickness (mm) Fig 3 Effect of tube wall thickness: Absorbed energy; Absorbed energy at punch stroke of 1 mm r=47 mm r=43 mm r=39 mm r=3 mm r=31 mm Tube length (mm) Fig Effect of tube length: Absorbed energy; Absorbed energy at punch stroke of 1 mm Fig α=3, e=13, r=39 mm, t=2 mm 222 Fig 6 Fig 7 t=2 mm, r=39 mm, L=1 mm Tube radius (mm) Fig 4 Effect of tube radius: Absorbed energy; Absorbed energy at punch stroke of 1 mm 23

4 1 1 α=6 o α=4 o α=3 o α=1 o e=1 e=14 e=13 e= Punch angle (degree) Fig 6 Effect of punch angle: Absorbed energy; Absorbed energy at punch stroke of 1 mm Expansion ratio Fig 7 Effect of expansion ratio: Absorbed energy; Absorbed energy at punch stroke of 1 mm Table 3 4 4) t=2 mm, r=39 mm, L=1 mm 1 Table σ σ α σ σ α α (1) σ σ α α Table 3 Four types of buckling behavior 4) Buckling Buckling Theory behavior load (kn) Elastic column buckling Euler formula Inelastic Tangent modulus column buckling formula Elastic local buckling Batdorf Inelastic local buckling equation 217 FEM result () 226 where α σ σ cr : buckling stress σ y : yield stress E : Young's modulus D : tube diameter (1) Table 4

5 Table 4 Dimension of tube Parameter Range Thickness, t (mm) 1 t 3 Radius, r (mm) 3 r Length, L (mm) 1 Friction coefficient, f (perfectly plastic) equation Stress (MPa) Stress strain curve of TWIP Average of stress distribution through thickness direction Strain Fig 9 Averaged stress distribution through thickness direction at the point that buckling occur Fig Tube wall thickness (mm) (perfectly plastic) equation Tube radius (mm) Fig 8 Local buckling load of expansion tubes using equation: buckling load wrt the tube wall thickness; buckling load wrt the tube radius Fig 8 Fig 1 (2) π ε (2) where σ ε (Ludwik model) ε : buckling strain Fig 11 Fig 11 2

6 (using averaged stress) equation Tube wall thickness (mm) (using averaged stress) equation Tube radius (mm) Fig 1 Local buckling load of expansion tubes using equation (2): buckling load wrt the tube wall thickness; bucklin load wrt the tube radius 32 Fig 11 Buckling strain wrt the tube wall thickness and tube radius Buckling load by equation (2) Bucklin load Punch angle (degree) Fig 12 Buckling load wrt the punch angle Fig 12 1 % 4 References 1) W M Choi, H S Jung, W H Yu, J S Ku and T S Kwon, "The basic study on the design of the light collision safety device", Proc KSR fall conference, pp26~31, 26 2) J S Kim, H Huh, J W Lee, T S Kwon, "Dynamic tensile characteristics of the steel sheets for a train", Proc KSAE spring conference, pp231~236, 27 3) Hibbit, Karlsson and Sorensen, User's Manual, John wiley & Sons, England, ) Bruce G Johnston, Guide to Stability Design Criteria for Metal Structures, Wiley-Interscience, pp261~329, 1976