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 The implemented strategy of DD3TRIM consists firstly, to evaluate the elements that are to be eliminate/keep with the trimming and then adjust the remaining affected elements of the boundary to the desired trim geometry. This adjustment is done by node stretching technique for two different projection schemes with optimization of the final element shape at the boundary. Additionally, a splitting option is also introduced which allows, for instance, to open rings or other closed meshes. The implemented solutions were tested in the simulation of a multi-step deep-drawing benchmark test that consists on cutting a ring specimen from a drawn cup and then splitting it longitudinally along a radial plan. The process consists in a sequence of drawn, spring-back, trimming, splitting and final springback. All this steps were simulated with the DD3 family codes (DD3IMP, DD3OSS and DD3TRIM). In this example application problem, both algorithms (trimming and splitting) have show good reliability to treat the meshes during the multi-stage processes. http://www.ctresources.info/ccp/paper.html?id=3713

1. 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

2. 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

3. 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

4. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 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

5. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
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

6. 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

7. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 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

8. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 TRIMMING ALGORITHM
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 }

9. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 TRIMMING ALGORITHM
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

10. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 TRIMMING ALGORITHM
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}

11. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 TRIMMING ALGORITHM
CEMUC
 Correction Stage
 Node projection scheme (correction type II)
π
Initial mesh Evaluation 1 Evaluation 2 / Type I
Final Mesh
A
A
Node adjustment in normal direction

12. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 TRIMMING ALGORITHM
CEMUC
 Correction Stage
 Node projection scheme (correction type III)
π
Initial mesh Evaluation 1
Final Mesh
A
Evaluation 2 / Type I
A
Node adjustment in edge direction

13. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 TRIMMING ALGORITHM
 Correction Stage
 Animation of the trimming procedure:

14. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 TRIMMING ALGORITHM
 Correction Stage
 Trimming zone
π

15. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 TRIMMING ALGORITHM
 Correction Stage
 Pre-processing stage (elimination of elements)

16. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 TRIMMING ALGORITHM
 Correction Stage
 Correction stage (elimination of elements)

17. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 TRIMMING ALGORITHM
 Correction Stage
 Correction stage (adjusting nodes)

18. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 TRIMMING ALGORITHM
 Correction Stage
 Correction stage (adjusting nodes)

19. 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. Examples
V. Conclusions
CEMUC
 OUTLOOK

20. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 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

21. 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

22. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 EXAMPLE
CEMUC
 Multi-step deep-drawing
 Splitting ring test
Original cup Ring cut Ring split Ring Springback

23. 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

24. THE FOURTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
“Numerical Simulation of Multi-Step Deep-Drawing Processes: Trimming 3D Solid Finite Element Meshes”
 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

25. 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