FINITE ELEMENT PREDICTIONS FOR A COLD SHEET METAL FORMING PROCESS USING TETRAHEDRAL MINI-ELEMENTS Min-Cheol Lee, Sang-Hyun Sim, Jae-Gun Eom, and Man-Soo Joun 1 Department of Mechanical Engineering, Gyeongsang National University Jinju, Republic of Korea 1 Contact Author Wan-Jin Chung * Product Design and Manufacturing Engineering, Seoul National University of Science and Technology Seoul, Republic of Korea * Presenter
20
Embed
FINITE ELEMENT PREDICTIONS FOR A COLD SHEET METAL FORMING ...msjoun.gnu.ac.kr/pub/2011-Papers/conference/2011... · FINITE ELEMENT PREDICTIONS FOR A COLD SHEET METAL FORMING PROCESS
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
FINITE ELEMENT PREDICTIONS FOR A COLD SHEET METAL FORMING PROCESS
USING TETRAHEDRAL MINI-ELEMENTS
Min-Cheol Lee, Sang-Hyun Sim, Jae-Gun Eom, and Man-Soo Joun 1
Department of Mechanical Engineering,
Gyeongsang National University
Jinju, Republic of Korea 1 Contact Author
Wan-Jin Chung*
Product Design and Manufacturing Engineering,
Seoul National University of Science and Technology
Seoul, Republic of Korea * Presenter
Sheet Forging
• Recently, industrial applications of sheet forging are increasing.
• The overall shape is made by sheet metal forming process ( stretching, drawing)
• In partial areas, forging is applied to get the detail shape which cannot be obtained by
conventional sheet metal forming process.
• Sharp corner, the drastic change of thickness can be achieved by using bulk metal forming
processes.
• Sheet forging is accompanied by three dimensional stress and deformation unlike
conventional sheet metal forming.
By Toyojima manufacturing co.
Background
• Sheet forging has the characteristics of both sheet metal forming and bulk
metal forming
• Simulation programs for specific process have been successfully used in
sheet metal forming and bulk metal forming
• However, the dedicated simulation programs for specific process show
limitations in simulation of sheet forging
• Thus, an appropriate simulation code for sheet forging is required.
Sheet
metal
forming
Bulk
metal
forming
Sheet forging
Elements for sheet forging simulation
• Shell element
– Widely used in most sheet metal forming simulation due to numerical efficiency
– Owing to geometrical and mechanical assumption, it shows distinctive limitations
when applied to plastic deformation in thickness direction.
– Cannot give reasonable answer to problems with sharp corner or drastic thickness
change even if the special shell element considering thickness stress is used
• Solid-shell element
– Express thickness stress nicely in the case that thickness change is moderate.
– However, still show limitations in sharp corner or drastic thickness change.
• Solid element
– No limitations in sharp corner or drastic thickness change due to no assumption in
geometrical and mechanical behavior
– Numerically inefficient due to the large number of element due to multi-layer mesh
systems to consider the bending in thickness direction.
– Use of bad quality elements with large aspect ratio due to small mesh size in
thickness direction may deteriorate the accuracy of the solution.
Sheet forging simulation using bulk metal forming simulator
• For successful simulation around the region with sharp corner or
drastic thickness change, bulk metal forming simulator should have
– Automatic mesh remeshing capability
– Solid element with good accuracy
• In this study, we used the bulk metal forming simulator, AFDEX 3D
with intelligent remeshing and MINI tetrahedral element.
• Bulk metal forming simulator should be also accurate in sheet metal
forming simulation for successful sheet forging simulation.
– Inherent boundary conditions in sheet metal forming should be treated
properly.
– accuracy by solid element should be competitive to the one by shell
element.
Adaptive remeshing - Considering contact boundary
contact boundary
Before remeshing After remeshing
Adaptive remeshing - Considering contact boundary
MINI Tetrahedral Element in AFDEX 3D
2
1 3
4
G
degree of pressure
degree of velocity
Developed by Arnold, Brezzi and Fortin.
Velocities and hydrostatic pressure are unknowns at real nodes
Velocities at the bubble node are condenced in the final equations
MINI tetrahedral element shows almost same accuracy in deformation
and stress distribution compared to hexahedral element.
Bend
ing p
rocess
Siz
ing p
rocess
Finite Element Ana. Des. 2009
Accuracy – Cold forging, rotor pole
Purpose
• In this study, conventional sheet metal forming is simulated by bulk metal
forming simulator using a multi-layer finite element mesh system.
– The accuracy of bulk metal forming simulator with linear tetrahedral MINI-
element is investigated.
– The influence of number of layers in a multi-layer finite element mesh system
on solutions of sheet metal forming simulations is also investigated.
Problem Definition
48
43
die
70
74
170
170
punch
blank
binder
die
punch
x
yz
x
⊙ Square-cup Deep Drawing Process
○ Blank : 150×150×0.78 mm
○ Flow Stress : 0.259566(0.007 ) MPa
workpiece
die
punch
binder
⊙ Quarter Mesh Model
○ NUMISHEET93 Benchmark Test
○ Binder Force : 19.6 kN, Binder is fixed away from die by 0.98 mm
○ Treatment of friction : the law of constant shear friction, with a shear factor of 0.02
○ No. of steps : 1,000
x
z
C B
A
DY
DX
Initial
blank
O
⊙ Definitions of Measured Draw-in
⊙ Finite element mesh system for the blank
Double-layer
Single-layer
To investigate the influence of he number of layers
⊙ Evolution of Deformed Shape and Effective Strain
100%
75%
50%
25%
0%
⊙ Final deformed shape and effective strain
Double-layer Single-layer
Comparison between Single-layer and Double-layer
x
z
C B
A
DY
DX
Initial
blank
O
DX, DY(mm) DD(mm)
Experiment results 27.95 15.36
Tetrahedral, Single-layer 27.61 13.85
Tetrahedral, Double-layer 26.50 13.15
Solid-shell (Xu et al.) 27.17 14.79
MTLFRM (shell) 28.90 16.20
LS-DYNA3D (shell) 30.03 16.43
PAM-STAMP (shell) 28.43 15.46
Comparison of the predictions with the
experimental results and other predictions by simulation.
⊙ Comparison of Draw-in
DX and DY were predicted well by both layers.
The difference in DD is mainly due to rigid-plastic assumption.
Distance from center(mm)
Th
ickn
ess
str
ain
0 20 40 60 80-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Experiment
Solid-shell (Xu et al.)
Tetrahedral, Single-layer
Tetrahedral, Double-layer
⊙ Comparison of Thickness Strain along OA line
Nice prediction of thickness strain in flange area
Double Peaks around punch corner observed in experiment
can be predicted by double-layer
The difference in the punch head is mainly due to rigid plastic assumption
# Elements 28185
# Nodes 9643
# Elements 13828
# Nodes 4790
(a) Deformation
# Elements 28185
# Nodes 9643
# Elements 13828
# Nodes 4790
(b) Effective strain
⊙ COMPARISON OF DEFORMATION AND EFFECTIVE STRAIN
BETWEEN FINE MESH AND COARSE MESH
DX, DY(mm) DD(mm)
Coarse Mesh 27.61 13.85
Fine Mesh 27.19 13.69
A sheet metal forming was simulated by bulk metal forming simulation program. A three-dimensional rigid-plastic finite element method with linear tetrahedral
MINI-elements was employed.
Multi-layer tetrahedral mesh systems were considered to represent bending deformation,
which is important in sheet metal forming.
Single- and double-layer mesh systems were investigated.
The application to the NUMISHEET93 benchmark. The resulting predictions were compared with experimental results and other predictions
found in the literature, and good agreement was noted.
The number of layers has little influence on the overall deformed shape.
The number of layers shows a non-negligible influence on plastic deformation near punch
corners with bending behavior.
The deformation around near-rigid region shows some deviations from experiment due to
rigid-plastic assumption.
The comparison indicates the feasibility of applying conventional bulk metal forming
simulators (with a little modification) to sheet metal forming process.