Numerical Simulation of Multi-Step Deep-Drawing Processes-Trimming 3D Solid Finite Element Meshes

Numerical Simulation of
Multi-Step Deep-Drawing Processes:
Trimming 3D Solid Finite Element Meshes
A.J. Baptista*, J.L. Alves**, M.C. Oliveira*, D.M. Rodrigues*, L.F. Menezes*
* Department of Mechanical Engineering, University of Coimbra,
Polo II, 3030 Coimbra, PORTUGAL
** Department of Mechanical Engineering, University of Minho,
Campus de Azurém,4080-058,Guimarães, PORTUGAL
CENTRO DE ENGENHARIA MECÂNICA DA UNIVERSIDADE DE COIMBRA
THE SEVENTH INTERNATIONAL CONFERENCE ON
COMPUTATIONAL STRUCTURES TECHNOLOGY
&
THE FOURTH INTERNATIONAL CONFERENCE ON
ENGINEERING COMPUTATIONAL TECHNOLOGY
7-9 September 2004 Lisbon, PORTUGAL

THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
I. Introduction
II. Trimming algorithm
III. Splitting algorithm
IV. Example
V. Conclusions
CEMUC
 OUTLOOK

 INTRODUCTION
Nowadays reality
 Virtual Manufacturing
• Worldwide Market
• Demanding Customers
• Saturated Markets
• Competitors Aggressiveness
Actions to develop
• Reduce development time/costs
• Reduce production time/costs
• Improve production flexibility
• Increase quality
Main objective
Improve / Maintain Competitiveness
Promising solution
VIRTUAL MANUFACTURING
“Entire simulation of a product and all the processes involved in its fabrication”
CEMUC

Trimming
 INTRODUCTION
CEMUC
 Multi-step deep-drawing
 Development stage of Deep-drawing process (R&D Objective)
 Generic sequence of the deep-drawing process (That will be simulated)
Initial blank Deep-draw Final component
SpringbackSpringback
DD3IMP
DD3OSS
DD3TRIM

 TRIMMING ALGORITHM
CEMUC
 Global algorithm
GENERAL PROCEDURE TRIMMING
BEGIN
- Pre-Processing Stage -
o Characterization of the trimming surface and the correction type option
o Generate connectivity of Nodes, Edges and Faces
o Generate tables containing STATUS of nodes and elements
- Correction Stage -
DO [ for all the elements to be treated ]
o Calculate the volume of the affected element to be eliminated
o Apply correction type
 Project the affected nodes towards the trim surface
o Correct elements with pentahedral shapes
END DO
- Post-Processing Stage –
o Upgrade the coordinates and connectivity tables
END
D D 3 T R I M

CEMUC
 Pre-Processing Stage
 Connectivity of nodes, edges and faces of the 8 node “brick” element
1
3 4
2
5
7 8
6
F1
F6
F2
F3
F5
F6
A10
A11 A12
A1 A2
A3 A4
A5
A6
A7
A8
A9
 STATUS tables for nodes and elements
Element E1: {1,2,3,4,5,6,7,8}
Node Nn: {Ei,Eii,...}
Edge An: {Ni,Nii}
Face Fn: {Ni,Nii,Niii,Niv}
Elements (standard)
Nodes (8) - Ni
Edges (12) - Ai
Faces (6) - Fi
STATUS (nodes) = { keep; eliminate ; on surface }
STATUS (elements) = { to treat ; keep; eliminate }

CEMUC
 Pre-Processing Stage
 Filling the table STATUS (nodes)
 Filling the table STATUS (elements)
Evaluation of the inner product
Evaluation of the Euclidean distance
IF d(Ni , Surface) = 0 THEN STATUS (nodes) = {on surface}
IF n ni < 0 THEN STATUS (nodes) = {keep}
IF n ni > 0 THEN STATUS (nodes) = {eliminate}
IF SUM(STATUS (nodes) = {keep}) = 8 THEN STATUS (elements) = {keep}
IF SUM(STATUS (nodes) = {eliminate}) = 8 THEN STATUS (elements) = {eliminate}
IF SUM(STATUS (nodes) = {eliminate}) < 8 THEN STATUS (elements) = {to treat}
π
n
Trim zone
n1N1
n2 N2

CEMUC
 Correction Stage
 Run all elements with STATUS (elements) {to treat}
 Calculate the volume of the affected element to be eliminated:
 Decomposition of the hexahedron in 6 tetrahedrons
6
( )
1
eeV V i
tet
i
 

 Filling the table STATUS (elements)
IF VOLUME (element) > 50 % THEN STATUS (elements) = {eliminate}
IF VOLUME (element) ≤ 50 % THEN STATUS (elements) = {keep}

CEMUC
 Node projection scheme (correction type II)
π
Initial mesh Evaluation 1 Evaluation 2 / Type I
Final Mesh
A
A
Node adjustment in normal direction

CEMUC
 Node projection scheme (correction type III)
π
Initial mesh Evaluation 1
Final Mesh
A
Evaluation 2 / Type I
A
Node adjustment in edge direction

 Animation of the trimming procedure:

 Trimming zone
π

 Pre-processing stage (elimination of elements)

 Correction stage (elimination of elements)

 Correction stage (adjusting nodes)

I. Introduction
II. Trimming algorithm
III. Splitting algorithm
IV. Examples
V. Conclusions
CEMUC
 OUTLOOK

 SPLITTING ALGORITHM
CEMUC
 Global algorithm
GENERAL PROCEDURE SPLITTING
BEGIN
- Pre-Processing Stage -
o Characterization of the splitting surface
o Choice of correction type for the split elements
o Generate connectivity of Nodes, Edges and Faces
- Correction Stage - SIDE 1
o Generate tables containing STATUS of nodes and elements
CALL TRIMMING (only for element correction)
o Duplicate nodes in the splitting plane for the new elements created
o Create new elements to replace the split elements
- Correction Stage - SIDE 2
o Invert the normal orientation of the splitting plane
o Generate new tables containing STATUS of nodes and elements
CALL TRIMMING (only for element correction)
o Create new elements to replace the split elements
- Post-Processing Stage –
o Upgrade the coordinates and connectivity tables
END
D D 3 T R I M

 EXAMPLE
CEMUC
 Multi-step deep-drawing
 Splitting ring test
Original cup Ring cut Ring split Ring Springback

 CONCLUSIONS
CEMUC
 Conclusions
 On going work
 The developed algorithms of DD3TRIM prove to be robust and efficient to
to trim and split meshes
 Two kind of trim surfaces were implemented (plane and cylindrical)
 Three correction types are available to perform trims
 Implementation of generic trim surface (NURBS)
 Test several remapping strategies for the state variables transfer problem

Numerical Simulation of Multi-Step Deep-Drawing Processes-Trimming 3D Solid Finite Element Meshes

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