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

Springback Springback

DD3IMP

DD3OSS

DD3TRIM



I. Introduction



IV. Example

V. Conclusions

CEMUC

OUTLOOK



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



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 }



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

n1 N1

n2 N2



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 itet

i

Filling the table STATUS (elements)

IF VOLUME (element) > 50 % THEN STATUS (elements) = {eliminate}

IF VOLUME (element) ≤ 50 % THEN STATUS (elements) = {keep}



TRIMMING ALGORITHM


Node projection scheme (correction type II)

π

Initial mesh Evaluation 1 Evaluation 2 / Type I

Final Mesh

A

A

Node adjustment in normal direction



TRIMMING ALGORITHM


Node projection scheme (correction type III)

π

Initial mesh Evaluation 1

Final Mesh

A

Evaluation 2 / Type I

A

Node adjustment in edge direction



TRIMMING ALGORITHM

Correction Stage

Animation of the trimming procedure:



TRIMMING ALGORITHM

Correction Stage

Trimming zone

π



TRIMMING ALGORITHM

Correction Stage

Pre-processing stage (elimination of elements)



TRIMMING ALGORITHM

Correction Stage

Correction stage (elimination of elements)



TRIMMING ALGORITHM

Correction Stage

Correction stage (adjusting nodes)



I. Introduction



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



I. Introduction



IV. Example

V. Conclusions

CEMUC

OUTLOOK



EXAMPLE

CEMUC Multi-step deep-drawing

Splitting ring test

Original cup Ring cut Ring split Ring Springback



I. Introduction



IV. Example

V. Conclusions

CEMUC

OUTLOOK



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

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

numerical simulation of multi-step deep-drawing processes-trimming 3d solid finite element meshes

Technology