Machines and their design and production have fascinated mankind from the very beginnings of culture. The last decades have shown mechanical contraptions decreasing in size to almost invisible dimensions. The implementation of micromechanics has become not only a technological challenge, but also a necessity for a successful future development of whole industrial branches. Adequate design and replication techniques of micromechanical components as well as a deep knowledge of their properties are indispensable for further progress in this field. At

the same time the variety of materials used in micro system technology has increased significantly. Today not only silicon and polymers, but also metals and ceramics are of increasing interest for a large number of applications. In contrast to silicon and polymers, however, which can be structured by technologies well known from microelectronics, metals and ceramics require new forming and structuring techniques for dimensions in the sub millimeter range. In addition, mechanical properties of metallic and ceramic microparts are of special interest because they differ significantly from those measured in macroscopic dimensions.

It is because of these considerations that the German Research Council

(Deutsche Forschungsgemeinschaft, DFG) has decided to fund a collaborative research center (SFB 499) with approximately 2 million euros p.a. which tackles the problems arising when trying to design, produce and characterize advanced microstructures made of metals and ceramics. The two-volume book in hand presents the results of five years of research on micro engineering utilizing metallic and ceramic materials. It comprises the whole process chain from design and modeling of microcomponents along production preparation and two central replication techniques (micro powder injection molding and micro casting) to characterization and quality insurance, the scope encompassing both theoretical and experimental topics. The book is structured roughly according to the project groups which form SFB 499:

The first volume contains sections on design, tooling and replication techniques based on injection molding. The first section focuses on micro-component design including design environment, design flow, modeling and validation as well as on the modeling of micro powder injection molding (cf. chapters 1 to 3).

**V**

The second section on tooling describes preparatory steps for the production process. The production of mold inserts by micro milling, laser ablation, micro electro discharge machining and techniques based on lithography and electroforming is investigated, surface treatment methods using shot peening and ultrasonic energy are presented, and optimized mold materials for micro casting are identified (cf. chapters 4 to 9).

The third section on micro injection molding (chapters 10 to 12) is concerned with the production itself, focusing on the actual molding processes. Following an introductory chapter on general aspects of micro injection molding, micro injection molding of metals and ceramics including the challenging process steps of debinding and sintering (cf. chapters 11 and 12) are described. The second volume comprises three sections on replication techniques other than injection molding, on automation and on properties of the components produced.

The section on special replication techniques focuses on microcasting (chapter 13) and electroforming (chapter 14) of metals and on selected techniques for the manufacturing of ceramic microcomponents (chapter 15). The second section of volume 2 deals with automation and quality insurance and includes chapters on the automation of PIM, on assembly and on quality insurance and dimensional measuring techniques (chapters 16 to 18). The last section addresses the properties of metals and ceramics and of the components produced. Microstructure and mechanical properties including micromechanical testing under quasi-static and cyclic loading as well as tribology are investigated and numerical wear simulation is performed (cf. chapters 19 to 22). Working groups concerned with aspects touching all five project sections (e.g. on relationships between manufacturing processes) act as links between the projects.

Cooperation within SFB 499 is further enforced by concerted work on a demonstration device consisting of a micro-turbine and a sun-and-planet gearing. For a comprehensive treatment the chapters which directly deal with the research projects of SFB 499 are supplemented by several important research topics concerning micromechanical components (e.g. laser structuring, lithographic processes, electroforming, assembly) which are not part of the collaborative research center. In these cases guest authors have been asked to contribute. They come from Bremen University (Institut für angewandte Strahltechnik, BIAS), from

Braunschweig University (Institut für Werkzeugmaschinen und Fertigungstechnik, IWF) and several scientific institutes of Forschungszentrum Karlsruhe. By covering most aspects of the design, production, and properties of micromechanical components outside the silicon world, the authors hope to present a useful guide to students and readers looking for a comprehensive overview as a

starting point of in-depth research in this field. However, the detailed presentation of latest SFB 499 research results as well as contributions from literature should also be a source of new insights and inspiration for micro-engineering experts from research institutions and industry.

May 2005, Karlsruhe Detlef Löhe and Jürgen Haußelt, Volume Editors

Preface VI

We are proud to present the third and fourth volumes of Advanced Micro & Nanosystems

(AMN), entitled Microengineering of Metals and Ceramics.

Although microtechnology is often associated with semiconductor cleanroom

processes, this is by no means the only means of production available. The processes

we associate with traditional mechanical engineering mass production

have also been the focus of microtechnologists, with tremendous successes already

in place and a huge potential for further progress. Of course, every new

technology pairs the development of suitable materials with that of production

technology, and in the sub-millimeter range the challenges become immense.

Not only must raw materials be produced in particulate form fine enough to reproduce

the molds they are formed into, and molds need to be prepared at the

correct dimensions and surface quality, but new ideas are needed to make use

of machine parts produced in this manner, and new methods to assemble parts

into complete systems. In these two volumes you will find a comprehensive

treatment of a variety of challenges that arise in the process of producing microparts

from metals and ceramics, from materials, testing, production, computer

aided engineering all the way to assembly. We hope that these volumes will inspire

the transfer of these fascinating techniques not only to other research

groups, but also to industry and so broaden the range of items that can be successfully

miniaturized.

Covering recent advances from the world of micro and nanosystems, future

AMN issues will either focus on a particular subject, such as CMOS-MEMS and

the present twin topical volumes Microengineering of Metals and Ceramics, or be

a carefully chosen set of cutting-edge overview and review articles like the first

AMN volume on Enabling Techniques for MEMS and Nanodevices.

Looking ahead, we hope to welcome you back, dear reader, to the upcoming

fifth member of the AMN series, in which we take a close look at the fascinating

field of Micro Process Engineering. The articles will range from the fundamentals

and engineering over device conception and simulation to fabrication

strategies and techniques, and finally cover application and operational issues.

To cover such a wide spectrum, we are very glad to have the support of Dr. Nor-

VII

Foreword

Advanced Micro and Nanosystems Vol. 3. Microengineering of Metals and Ceramics.

Edited by H. Baltes, O. Brand, G. K. Fedder, C. Hierold, J. Korvink, O. Tabata

Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 3-527-31208-0

bert Kockmann from the University of Freiburg, Germany, who will edit this

volume.

Henry Baltes, Oliver Brand, Gary K. Fedder, Christofer Hierold, Jan G. Korvink,

and Osamu Tabata

Series Editors

May 2005

Zurich, Atlanta, Pittsburgh, Freiburg and Kyoto

Foreword VIII

Preface V

Foreword VII

List of Contributors XI

I Design

1 Design Environment and Design Flow 3

A. Albers, J. Marz

2 Modeling and Validation in Design 29

A. Albers, D. Metz

3 Modeling Micro PIM 51

D. Kauzlaric, A. Greiner, J. G. Korvink, M. Schulz, R. Heldele

II Tooling

4 Strategies for the Manufacture of Mold Inserts 87

J. Fleischer, C. Buchholz, J. Kotschenreuther

5 Micro End Milling of Hardened Steel 107

J. Schmidt, J. Kotschenreuther

6 3D Microstructuring of Mold Inserts by Laser-based Removal 131

A. Stephen, F. Vollertsen

7 Micro-EDM for Mold Inserts 161

J. Schmidt, M. Knoll, T. Masuzawa

IX

Contents

Advanced Micro and Nanosystems Vol. 3. Microengineering of Metals and Ceramics.

Edited by H. Baltes, O. Brand, G. K. Fedder, C. Hierold, J. Korvink, O. Tabata

Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 3-527-31208-0

8 Lithographic Fabrication of Mold Inserts 187

M. Guttmann, J. Schulz, V. Saile

9 Material States and Surface Conditioning for Mold Inserts 221

Ch. Horsch, V. Schulze, D. Löhe

III Replication Techniques – Microinjection Molding

10 Microinjection Molding – Principles and Challenges 253

R. Ruprecht, G. Finnah, V. Piotter

11 Micro Metal Injection Molding 289

V. Piotter, L. Merz, G. Örlygsson, S. Rath, R. Ruprecht, B. Zeep

12 Micro Ceramic Injection Molding 325

W. Bauer, J. Hausselt, L. Merz, M. Müller, G. Örlygsson, S. Rath

Subject Index XVII, end of the book

Contents X

XI

Advanced Micro and Nanosystems Vol. 3. Microengineering of Metals and Ceramics.

Edited by H. Baltes, O. Brand, G. K. Fedder, C. Hierold, J. Korvink, O. Tabata

Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 3-527-31208-0

Prof. A. Albers

Institut für Produktentwicklung

Universität Karlsruhe

Kaiserstrasse 12

76128 Karlsruhe

Germany

M. Auhorn

Institut für Werkstoffkunde I

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

K. Bade

Forschungszentrum Karlsruhe

Institut für Mikrostrukturtechnik

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

W. Bauer

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

G. Baumeister

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

T. Beck

Institut für Werkstoffkunde I

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

I. Behrens

Institut für Werkzeugmaschinen

und Betriebstechnik

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

H. von Both

Institut für Mikrosystemtechnik

Albert-Ludwigs-Universität Freiburg

Georges-Köhler-Allee 103

79110 Freiburg

Germany

C. Buchholz

Institut für Werkzeugmaschinen

und Betriebstechnik

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

M. Dauscher

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

List of Contributors

List of Contributors XII

G. Finnah

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

Prof. J. Fleischer

Institut für Werkzeugmaschinen

und Betriebstechnik

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

Prof. K.-H. zum Gahr

Institut für Werkstoffkunde II

Universität Karlsruhe

c/o Forschungszentrum Karlsruhe

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

A. Greiner

Institut für Mikrosystemtechnik

Albert-Ludwigs-Universität Freiburg

Georges-Köhler-Allee 10

379110 Freiburg

Germany

M. Guttmann

Forschungszentrum Karlsruhe

Institut für Mikrostrukturtechnik

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

Prof. J. Haußelt

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

V. Hegadekatte

Institut für Zuverlässigkeit

von Bauteilen und Systemen

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

R. Heldele

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

J. Herz

Institut für Werkstoffkunde II

Universität Karlsruhe

c/o Forschungszentrum Karlsruhe

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

Prof. J. Hesselbach

Institut für Werkzeugmaschinenund

Fertigungstechnik

Technische Universität

Braunschweig

Langer Kamp 19b

38106 Braunschweig

Germany

K. Heuer

Institut für Werkzeugmaschinen

und Fertigungstechnik

Technische Universität Braunschweig

Langer Kamp 19b

38106 Braunschweig

Germany

C. Horsch

Institut für Werkstoffkunde I

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

N. Huber

Institut für Materialforschung II

Forschungszentrum Karlsruhe

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

B. Kasanická

Institut für Werkstoffkunde I

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

List of Contributors XIII

D. Kauslaric

Institut für Mikrosystemtechnik

Albert-Ludwigs-Universität Freiburg

Georges-Köhler-Allee 103

79110 Freiburg

Germany

R. Knitter

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

M. Knoll

Institut für Werkzeugmaschinen

und Betriebstechnik

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

Prof. J. G. Korvink

Institut für Mikrosystemtechnik

Albert-Ludwigs-Universität Freiburg

Georges-Köhler-Allee 103

79110 Freiburg

Germany

J. Kotschenreuther

Institut für Werkzeugmaschinen

und Betriebstechnik

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

O. Kraft

Institut für Zuverlässigkeit

von Bauteilen und Systemen

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

Prof. D. Löhe

Institut für Werkstoffkunde I

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

J. Marz

Institut für Produktentwicklung

Universität Karlsruhe

Kaiserstrasse 12

76128 Karlsruhe

Germany

T. Masuzawa

Institute of Industrial Science

University of Tokyo

4-6-1 Komaba, Meguro-ku

Tokyo

Japan

L. Merz

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

D. Metz

Institut für Produktentwicklung

Universität Karlsruhe

Kaiserstrasse 12

76128 Karlsruhe

Germany

M. Müller

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

G. Örlygsson

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

V. Piotter

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

List of Contributors XIV

A. Raatz

Institut für Werkzeugmaschinen

und Fertigungstechnik

Technische Universität Braunschweig

Langer Kamp 19b

38106 Braunschweig

Germany

S. Rath

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

H.-J. Ritzhaupt-Kleissl

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

R. Ruprecht

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

Prof. V. Saile

Forschungszentrum Karlsruhe

Institut für Mikrostrukturtechnik

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

G. Schanz

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

Prof. J. Schmidt

Institut für Werkzeugmaschinen

und Betriebstechnik

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

J. Schneider

Institut für Werkstoffkunde II

Universität Karlsruhe

c/o Forschungszentrum Karlsruhe

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

J. Schulz

Forschungszentrum Karlsruhe

Institut für Mikrostrukturtechnik

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

M. Schulz

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

V. Schulze

Institut für Werkstoffkunde I

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

S. Soetebier

Institut für Werkzeugmaschinen

und Fertigungstechnik

Technische Universität Braunschweig

Langer Kamp 19b

38106 Braunschweig

Germany

A. Stephen

Bremer Institut für angewandte

Strahltechnik (BIAS)

Klagenfurter Str. 2

28359 Bremen

Germany

Prof. F. Vollertsen

Bremer Institut für angewandte

Strahltechnik (BIAS)

Klagenfurter Strasse 2

28359 Bremen

Germany

List of Contributors XV

H. Weule

Institut für Werkzeugmaschinen

und Betriebstechnik

Universität Karlsruhe

Kaiserstrasse 12

76131 Karlsruhe

Germany

J. Wrege

Institut für Werkzeugmaschinen

und Fertigungstechnik

Technische Universität Braunschweig

Langer Kamp 19b

38106 Braunschweig

Germany

B. Zeep

Forschungszentrum Karlsruhe

Institut für Materialforschung III

Hermann-von-Helmholtz-Platz 1

76344 Eggenstein-Leopoldshafen

Germany

I

Design

Advanced Micro and Nanosystems Vol. 3. Microengineering of Metals and Ceramics.

Edited by H. Baltes, O. Brand, G. K. Fedder, C. Hierold, J. Korvink, O. Tabata

Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 3-527-31208-0

Abstract

The design flow for primary-shaped microcomponents and microsystems is presented.

As a characteristic of microspecific design, the approach is predominantly

driven by technology. To integrate the relevant technological demands and restrictions

into the design synthesis for a realizable embodiment design in accordance

with the specified function, design rules are defined. These represent

mandatory instructions for the designer. To support the designer effectively the

design rules are provided within a computer-aided design environment. In addition

to an information portal, an embodiment design unit is built up on the basis

of the 3D CAD system Unigraphics, which includes an application for

knowledge-based engineering (KBE). The rule-based design methodology was

used for the development and design of a microplanetary gear.

Keywords

design environment; design flow; target system definition; operation system;

object system; design rule; knowledge-based engineering; methodological aid

1.1 Introduction 4

1.1.1 State-of-the-Art of Design Flows and Design Environments within

Microtechnology 4

1.1.2 Mechanical Microproduction 5

1.2 Design Flow 6

1.2.1 Specific Issues Within the Design of Microsystems 6

1.2.1.1 Dominance of Technologies 6

1.2.1.2 Surface-to-Volume Ratio 6

1.2.1.3 Dynamics 7

1.2.1.4 Standardization 7

1.2.1.5 Validation 7

1.2.1.6 Enhanced Material Spectrum 7

3

1

Design Environment and Design Flow

A. Albers, J. Marz, Institute of Product Development (IPEK),

University of Karlsruhe (TH), Germany

Advanced Micro and Nanosystems Vol. 3. Microengineering of Metals and Ceramics.

Edited by H. Baltes, O. Brand, G. K. Fedder, C. Hierold, J. Korvink, O. Tabata

Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 3-527-31208-0

1.2.1.7 Emphasis on Actuators 7

1.2.2 Microspecific Design Flow 7

1.3 Design Rules 9

1.3.1 Basics 9

1.3.1.1 Definition 9

1.3.1.2 Derivation of Design Rules 10

1.3.2 Design Rules Derived from Restrictions of Production

Technology 11

1.3.2.1 Design Rules for Mold Insert Manufacturing 13

1.3.2.2 Design Rules for Replication Techniques 14

1.4 Design Environment 18

1.4.1 Information Unit 20

1.4.2 Embodiment Design Unit 20

1.4.2.1 Preparing Elementary Rules for Computer-aided Design Rule

Check 21

1.4.2.2 Design Rule Check 24

1.5 Conclusion 27

1.6 References 27

1.1

Introduction

Microtechnology involves technologies for manufacturing and assembling predominantly

micromechanical, microelectrical, microfluidic and microoptical

components and systems with characteristic structures with the dimension of

microns. In doing so, microproduction technologies take on a key role, since

their process-specific parameters and boundary conditions determine the smallness

and attainable quality features of the components. Owing to the ongoing

progress in microtechnology and the increasing penetration of the market with

medium-sized and large-batch products, development steps preliminary and

subsequent to production are becoming more and more relevant for an effective

design in compliance with the requirements. Therefore, the designer needs to

be supported by a technological basic knowledge and know-how, regardless of

individual persons.

1.1.1

State-of-the-Art of Design Flows and Design Environments within Microtechnology

Microtechnologies include silicon microsystem technology, the LIGA process

and mechanical microproduction technology.

Silicon microsystem technology is the most widespread microtechnology

throughout the world. It is based on the process technology of integrated circuits

(ICs) and benefits from a comprehensive know-how from microelectronics.

Unlike in microelectronics, microtechnological products integrate active

1 Design Environment and Design Flow 4

and passive functional elements, which rely on at least two elementarily different

physical, chemical or biochemical effects and working principles. In addition

to sensors and information processing, particularly actuator functions are

performed. The predominantly 2.5-dimensional and sometimes three-dimensional

structures use silicon as substrate with its excellent mechanical properties.

Along with others, all these characteristics of silicon micromechanical systems

have required a specific design methodology ever since a critical level of

development from research into industry was reached. Different design process

models are known [1–3], which among other things integrate analytical and numerical

simulation tools. Silicon-based micromechanical products are developed

in an iterative sequence of synthesis and analysis steps. A specific difficulty lies

in the deviation between the designed target structure and the actual structure

after the optical lithography and etching process. Therefore, compensation

structures are introduced into the design and simulation environment, adjusting

the determined structure by dimensional add-on and auxiliary structures

[4–6]. Design rules are introduced as a methodological aid to represent this

technological information. Design rules have been used in microelectronics

since the early 1980s to enable very large-scale integrated (VLSI) circuits to be

synthesized automatically to the extent of nearly 100% [7]. Silicon microsystem

technology has now reached a high degree of development status. A lot of research

programs have led to design flow descriptions and collections of design

rules.

Like silicon microsystem technology, the LIGA process utilizes mask-based

process steps. The LIGA process approaches an obviously broader range of materials

and is characterized by extremely high aspect ratios with at the same

time the smallest lateral structure dimensions [8]. LIGA permits the manufacture

of mold inserts which can be used in replication techniques for large-batch

parts (Chapter 8). In addition to thermoplastics, also metallic and ceramic materials

are processed. To support the design and process, engineering design rules

are utilized which give – depending on the process sequence – instructions for

a design for manufacturing and for separating, manipulating and assembling

components [9]. Within different research programs, design environments for

computer-aided design of LIGA microstructures embedding design rules were

developed [10, 11]. The computer-aided design of LIGA microstructures still

shows a high demand. A standardized model for methodological design flow in

the LIGA process is lacking to date [12].

1.1.2

Mechanical Microproduction

To come up with a more cost-effective, medium-sized and large-batch suitable

process for manufacturing microsystems, the potential of miniaturizing mechanical

production technologies has been increasingly investigated in recent

years. Predominantly staged production process sequences for manufacturing

mold inserts by wear-resistant materials followed by a replication step show out-

1.1 Introduction 5

standing future prospects. Technologies such as micromilling and laser machining

are suitable for manufacturing complex three-dimensional free-form surfaces

(Chapters 5–7). By replication techniques such as micropowder injection

molding, high-strength microcomponents and microsystems from metallic and

ceramic materials can be produced in large quantities (Chapters 11 and 12).

When designing primary-shaped microparts with respect to function and

manufacturing, it is necessary to incorporate boundary conditions and restrictions

from process steps downstream to the product development into the design

activities as early as possible [20]. Thus, a design flow is introduced that

uses design rules to support the designer effectively with respect to functional,

geometric and capacitance demands. The process model and the method are

embedded in a knowledge-based design environment.

1.2

Design Flow

1.2.1

Specific Issues Within the Design of Microsystems

In contrast to the procedures and methods commonly applied in mechanical engineering

and precision engineering, product development of microtechnological

systems requires attention to the following issues.

1.2.1.1 Dominance of Technologies

Going beyond the basic rules and guidelines of embodiment design microtechnology

has a strong focus on parallelization of product and process development. Resulting

from the rapid advances in existing production processes and the appearance

of new technologies, the question of ‘how to manufacture’ becomes a conceptual

part of product development. Microproduction technologies, materials and

specific effects define the possible shape and function of new products.

1.2.1.2 Surface-to-Volume Ratio

Owing to the super-proportional rise in the surface-to-volume ratio in the range

of the characteristic and functional dimensions of microcomponents, the global

dimensions have a different ratio to local deviances. Higher level surface tolerances

in macroengineering have the same significance as notch form deviation

in microengineering. There is no longer a difference in magnitude between material

microstructures and work-piece dimensions. The numbers of crystals and

surface layers are relevant for the calculation of elastic properties.

1 Design Environment and Design Flow 6

1.2.1.3 Dynamics

As a consequence of their small volumes, microsystems have lower inertia.

They can be operated in higher ranges of frequency and show high dynamics.

1.2.1.4 Standardization

Standards with regard to generic or product-specific dimensions do not exist for

the design of microcomponents and systems.

1.2.1.5 Validation

Mostly, either no equipment for the measurement and testing of microcomponents

is available at all or insurmountable physical obstacles occur (size of components,

essential accuracy of the measuring equipment). Design can, therefore,

only set requirements on what can be verified by means of measurement and

with the use of testing equipment.

Compared with silicon microsystem technology, the LIGA process and the mechanical

microproduction technologies show the following specific differences.

1.2.1.6 Enhanced Material Spectrum

Microsystem technologies with replication subprocesses possess an enhanced

material spectrum. Totally new applications arise from it, making it necessary

to characterize the materials with respect to their microstructures and properties.

This is an important input for product development.

1.2.1.7 Emphasis on Actuators

Since the LIGA process and mechanical microproduction technologies do not

rely on silicon as base material, there is enormous potential to develop actuators

using a multitude of effects. Integrated in a superior system or as an integrated

self-sufficient microsystem, actuators offer particularly energy and material interfaces

to the macroscopic world. A microspecific design methodology has to

be directed on methods and processes to calculate and design the relevant interface

machine elements.

1.2.2

Microspecific Design Flow

Each design process starts with a definition of the target system. The target system

definition is developed with the involvement of the customer and determines requirementsand

boundary conditions for the product that is to be developed(Fig. 1-1).

The target system definition helps to concretize the task and to clarify vague and

unexpressed demands on the object system – the subsequent microproduct – prior

to the beginning of the design. Along with the customer, a requirements list is

1.2 Design Flow 7

generated, which describes the target system by quantitative and assessed criteria.

To ensure that a fundamental criterion is not forgotten, checklists with main headings

exist for drawing up a requirements list [13, 14]. The requirements list represents

a dynamic document, which has to be examined continually with respect to

up-to-dateness and inconsistencies during the design process. Moreover, the risk

exists of specifying the task in an unchallenged or in an overextended way. An unchallenged

specification might lead to a product ahead of schedule but without

matching the real performance characteristics. On the other hand, an overextended

specification might limit the solution space in such a manner that no solution

could be developed [3]. For the target system definition of microelectronic circuits,

hardware description languages are standardized. The microsystem technology

of primary shaping concentrates on energy- and material-converting microsystems

with integrated information flow and with single functions from different

physical, chemical and biochemical domains, so no formal methods and target

system definition languages are available.

When conventionally developing products and systems of mechanical engineering

and precision engineering [13–16], a conceptional phase would follow,

in which basic partial solutions for functionally organized subsystems would be

developed and systematically combined to the optimum basic solution with consideration

of evaluation techniques. When developing microsystems, the

approach is ‘technology driven’. At the same time, the technology term describes

all of those scientific disciplines as a whole that contribute to the product development

process. This especially applies in production engineering and material

sciences. Among material sciences, also research on new or specifically formed

1 Design Environment and Design Flow 8

Fig. 1-1 Microspecific design flow

physical, chemical and biochemical effects has to be itemized. Effects are comprehended

as both those which are intentionally used to transfer the target system

into the object system by effects and active principles in order to fulfil a

function (e.g. shape memory effect) and those which inevitably result from phenomena

such as friction and wear.

Because of being driven by technology, parallelization of stages of conceptual

and embodiment design occurs, which exceeds different levels of abstraction.

While making conceptual decisions on system level related to function in a topdown

approach, simultaneously structural details conditional on technology are

being designed in a bottom-up way. In between, single components are preliminarily

drafted (basic design). These structural details can be entirely finalized and annotated

with all tolerance data and information relevant for production preparation.

Already during the subsequent design stage, a complete component can

be constituted in its final shape (detail design). The system comes to the stage

of basic design. Eventually the system itself is finalized and refined into a detailed

design documentation for transfer to production preparation. In doing so, the

approach constantly changes between the view on the complete system and the

smallest structural element (’meet-in-the-middle‘) [17], wherein the design space

is restricted for the designer through boundary conditions and restrictions of

the production processes. However, features that cannot be described as easily

as geometric quantities also have an influence. These are characteristics of the materials

themselves such as microstructure or mechanical properties and physical,

chemical or biochemical effects made accessible by them. The latter can develop

into disturbing effects when the dimensions become smaller, they can become

less important or even emerge and therefore open up completely new applications.

All of these ‘technological’ aspects therefore have to be integrated into the

microtechnological design of structures, components and systems [18].

Therefore, it is necessary to make the multi-technological knowledge from

the above-mentioned technologies directly available to the designer in the design

process. This is achieved via the methodological aid of design rules.

1.3

Design Rules

1.3.1

Basics

1.3.1.1 Definition

Design rules are instructions derived from technological restrictions which have

to be followed mandatorily for a realizable design.

Technologies embrace all processes and methods of production preparation,

production and material science including effects which are adjacent or subsequent

to the design process. Restrictions describe all boundary conditions, requirements

and constraints that influence the design embodiment of the prod-

1.3 Design Rules 9

uct with respect to the entire product life cycle. A realizable design is a design

that is completely specified in detail (CAD–CAM suitable 3D CAD model, drawings)

ready for production.

Owing to their mandatory character, design rules are an explicit part of the

conceptional and embodiment design activities. Disregarding the knowledge

about restrictions leads to a design that only inadequately fulfils the function or

is even not able to be manufactured, assembled, dimensionally characterized

and so on.

Design rules are mandatory instructions to be followed by the designer!

1.3.1.2 Derivation of Design Rules

Design rules begin by detecting potential influences that a technology could have

on the microtechnological design. The features and parameters of this technology

are quantifiably taken over in an extraction step. Then these properties will

be projected to existing and possible components and system structures and

marginal analyses of still realizable manufacturing sizes will be made, i.e. interpreted

relevant to design [19, 20].

Only a methodical trained product development engineer can carry out this

interpretation and raise technical facts via suitable query techniques (interviewing

techniques, e-mail query via special forms, so called ‘technology specification

sheets’; see, for example, Fig. 1-5). Now these ‘raw data’ need to be transformed

via creativity methods or with experimental knowledge into a methodical

knowledge that can be used by the designer. Knowledge from individual disciplines

– from the designer’s view this is data and information – is raised to a

higher level of knowledge and made available mono-disciplinarily, i.e. from the

designer’s point of view (Fig. 1-2).

According to a specially developed classification scheme, the interpretations

are formulated as generally applicable rules. The classification scheme that is

introduced here models itself on the technologies for mold insert production

and replication that are a part in the production process. The nomenclature is

as as shown in Fig. 1-3.

These different process steps are formulated separately for the further application

of the design rules in a knowledge-based design environment. It has to be

clearly determined to which type of part the geometric sizes refer. This is carried

out via a so-called rule class. It indicates for which type of part the rule

was formulated and to which manufacturing technologies and tools or materials

it applies. The letters ‘AA’ describe the type of part to which the rule refers, i.e.

‘mold insert’ or molded and sintered ‘model’. Then follows the information

about the production technique with a more detailed specification of tool group

and material group. When a rule is applied to different production techniques

or tool groups or material groups, the entries ‘xxx’ or ‘x’ are indicated. The rule

ends with a consecutive number for the respective rule composition.

Different rule sets exist for the mold insert manufacture and molding process

of parts explained above. However, they can be geometrically connected. Hence

1 Design Environment and Design Flow 10

the structure details of the mold insert that are influenced by the manufacturing

restrictions can also be found at the molded part, where the geometry sizes

scale around the sinter shrinking and complementary structures are developed.

The following section explains the design rules of the single technologies

(especially of process preparation and production) that are connected to process

chains for replication processes. A distinction is made between two large process

chains, ‘micropowder injection molding’ and ‘microcasting’.

1.3.2

Design Rules Derived from Restrictions of Production Technology

Design rules are a methodical aid for achieving a knowledge transfer from technological

facts (see, e.g., Fig. 1-5), especially from the operation system of production

technology to the operation system of product development. This is

demonstrated by the flow arrow in Fig. 1-4.

Fig. 1-4 demonstrates that not only are there indications regarding manufacturing

aspects passed on to the designer via guidelines for embodiment design

and rules, as in mechanical engineering or precision engineering, but that it is

also mandatory to employ the requirements and restrictions relevant to design

that are included in the design rules. Without the active design that includes

the knowledge facts in the rules, an effective and successful synthesis is not

possible in primary-shaping microtechnology.

1.3 Design Rules 11

Fig. 1-2 Knowledge transformation by interpretation relevant

to design

The rules used at present refer exclusively to the production process chains

for primary-shaped microcomponents. It has to be considered that most of the

time the model is created in the CAD and from there a negative form – the

mold insert – is generated. In the case of parametric CAD systems, the sinter

shrinkage can also be considered in this process and the mold insert can be designed

correspondingly larger. The manufacturing of the model is done in two

steps. First, the mold insert (negative) is manufactured. The technologies available

here are machining and abrasive processes (see Fig. 1-3 and Chapters 4–7).

The second step is the molding process of the model (positive) by means of

ceramic or metallic micropowder injection molding (Chapters 10–12) or microcasting

(Chapter 13).

To each of the two process steps different restrictions apply, e.g. it is not possible

to mill a cavity that is smaller than the milling cutter. Also, micropowder

injection molding requires a minimum wall thickness and a maximum flow

length. However, both parts are geometrically unambiguously connected, i.e. restrictions

of the mold insert manufacturing automatically apply also to the

molded part and vice versa. Here it has to be considered especially that the geometric

properties of both parts are not identical. First, the part is scaled during

the molding process because of the sinter shrinkage and then a negative is cre-

1 Design Environment and Design Flow 12

Fig. 1-3 Classification scheme for design rules

ated, so that, for example, a hole in the mold insert is converted into a cylinder

with a decreased height and diameter.

1.3.2.1 Design Rules for Mold Insert Manufacturing

Replication processes require as a first step the manufacture of a form – the

mold insert. To achieve the aim of a cost-effective, medium-sized and largebatch

production of microcomponents from metallic and ceramic material, abrasive

and machining processes of the mechanical microproduction are more advantageous

than processes based on lithography. For the majority of applications

in the Collaborative Research Centre 499, micromilling has been used for the

manufacturing of mold inserts so far.

Among others, micro end mill cutters are employed here in order to manufacture

2.5- and three-dimensional microstructures. Process-specific parameters that

have to be extracted are, for example, the body diameter of the tool and the length

of the milling cutter’s edge that is linked to it. If interpreted with relevance to design,

this implies that it is not possible to manufacture mold insert structures that

are smaller than the milling cutter diameter plus the milling cutter tolerance or

deeper than the maximum cutting depth. Owing to the circular cross section, vertical

inner edges are also impossible, i.e. all mold insert edges – equivalent to outer

edges of the final part – have to be provided with a minimal rounding radius.

1.3 Design Rules 13

Fig. 1-4 Flow of knowledge from production

technology (PT) to product development (PD)

by design rules

All these parameters and properties are collected in so-called technology specification

sheets and are interpreted with relevance to design (Fig. 1-5) [21].

In systematic scenarios, the determined technological facts are now projected

on to potential geometric structures or functional influences on the microparts.

The results are descriptions and mathematical connections that correlate machine

tool and tool parameters with design parameters. With the presentation

of the design rules, the designer is provided with abstract and descriptive, but

also concrete and computer-aided information about the same knowledge fact.

Fig. 1-6 shows a design rule for three-axis micromilling that applies both to the

end mill cutter and to the radius cutter.

Various other design rules exist in addition that name the technological restrictions

of three- and five-axis micromilling, and also rules for microelectrical

discharge machining and for laser machining.

1.3.2.2 Design Rules for Replication Techniques

The replication of microcomponents is done by micropowder injection molding

(PIM) and by microcasting. Micropowder injection molding as a replication

technique for microcomponents differentiates between metallic and ceramic injection

molding depending on the material to be molded. The PIM process

uses the mold inserts in order to mold the metallic or ceramic feedstock directly

into these molds.

The microcasting process is based on the lost-wax lost-mold technique, so as

a first step models have to be manufactured. These lost models, mainly made

from polymers, are mounted on a gate and feeding system made of wax. This

assembly is completely embedded in a ceramic slurry. After drying, the ceramic

is sintered, resulting in a ceramic mold with high mechanical strength. Simultaneously

during the burning process, the polymer model is molten and burnt

out. After the subsequent casting process, the metallic microcomponents can be

taken out of the lost mold.

Micropowder injection molding

Boundary conditions of the PIM process result from the necessity to attach runners

in a sufficient number and size to the part’s surface and to provide a surface for

the ejector pins contacting the molded part for removal. The maximum achievable

flow length and aspect ratios, and also sharp cross section transitions and cross

section bendings, limit the mold filling behavior and the molding process quality.

Especially the shrinkage of the material during sintering has to be considered.

Therefore, taking into account the sintering shrinkage, it is possible that smaller

structures may result compared with the dimensions of the mold insert, but shrinkage

tolerances of ±0.4% have to be considered at the same time (Fig. 1-7).

1 Design Environment and Design Flow 14

1.3 Design Rules 15

Fig. 1-5 Achievable manufacturing sizes in production preparation by means of three-axis micromilling

[21]

1 Design Environment and Design Flow 16

Fig. 1-6 KR_FE_MF3_x_001 – Minimum radius for vertical inner edges

1.3 Design Rules 17

Fig. 1-7 KR_MO_PIM_x_001 – Dimensional margin

Microcasting

To come to a design compatible with microcasting, several technological circumstances

have to be taken into account. Compared with micropowder injection

molding where the green compact and brown compact are intermediates on the

way to the final sintered microcomponent, in microcasting more and versatile

preparation and intermediate steps exist that influence the result. Depending

on the manufacturing process for the lost models, different concepts for casting-

compatible positioning of gates are necessary (model on substrate or single

injection-molded models with gate and feeding system). The attainable surface

roughness of the microcomponent is determined by the embedding mass employed

and ranges down to Ra=0.5 m for Stabilor G. In addition, the attainable

dimensional accuracy should be pointed out to the designer. By varying the expansion

ratio of the embedding mass, the dimensional accuracy is adjustable

within a few microns. In microcasting, small structures within a few 10 m in

wall thickness with at the same time high aspect ratios are processable. On falling

below a specific structural diameter, the filling pressure rises in a hyperbolic

manner, resulting in a more complicated form filling. This phenomenon is

expressed by the design rule in Fig. 1-8, which consequently has an influence

on the dimensional conception and the embodiment design (see Chapter 13)

[22, 23].

1.4

Design Environment

The filing of rules in a database is important for the applicability of the rules

for the designer and implementation in computer-based systems. The design

rules can be provided over an interactive knowledge portal and/or directly with

an application in 3D CAD.

The design environment is planned in a way that supports the designer with

respect to the product development phase in which the design is at that moment,

by means of the design rules that are correspondingly altered with the

abstraction level. In the early stages, the general comprehensive information

about the production processes and the material properties are the interesting

aspects. In the embodiment design phase, quantified values about realizable

manufacturing sizes have to be provided for a detailed design draft. Here, concrete

instructions are required that must be followed to realize a productioncompatible

and functional part design.

According to these different representation forms of the knowledge content of

design rules, the design environment itself has to be planned to be flexible and

application specific. Therefore, an information component, i.e. a web-based

interactive knowledge portal, and an embodiment design component that is

directly integrated into the CAD system as a working environment for the designer

were developed for the product development of primary-shaped microcomponents.

Both units access the same data of a database [24, 25].

1 Design Environment and Design Flow 18

1.4 Design Environment 19

Fig. 1-8 KR_MO_MIC_x_003: Minimum structure width

[22, 23]

1.4.1

Information Unit

A ‘design and methodology database’ (KoMeth), which supports the designer as

an interactive knowledge portal via different access possibilities with design

rules, serves as an information component. The access page offers different

selection fields that permit, according to the classification scheme (Fig. 1-3), the

search for rules for a specific manufacturing technology, for specific part types

or specific tools and materials. The rules that were found are displayed systematically

in a hit list according to their rule class and name. If the designer is already

familiar with the production process chain, a direct search over the list of

existing rule classes and names is also possible. When selecting a rule from the

hit list, an information page is displayed which shows the rule class, the numbering,

the rule name, a prosaic description, an algorithmic–mathematical formula

(if available) and sketches of geometric dimensions and illustrations of

real manufactured microstructures (Fig. 1-9).

In the course of product development, the abstraction level decreases and

more and more technological restrictions have to be considered. Especially at

the stage of realizing the embodiment design, the shape and dimensions of realizable

structure details are not easy to comprehend any longer. In addition to

the significance of errors and the inefficiency, these details deviate too much

from the original design work. Therefore, the so-called design rule checker was

established in mechanical engineering, microelectronics and mask-based microtechnology.

This approach is also used for rule-based embodiment design of primary-

shaped microcomponents.

1.4.2

Embodiment Design Unit

In addition to the presented qualitative and descriptive content, the knowledge

base of the database also includes concrete values of single manufacturing technologies

and knowledge about connecting these data with geometric characteristic

values in the form of rules. These are formulated separately because both

are independent of each other and subjected to permanent changes. The information

and parameter values are derived from the state of the microproduction

technologies and the material sciences. The rules are derived from the expertise

and the experience in the design process, process preparation and production,

and also from the part testing and material testing. Therefore, they are also subjected

to permanent development and completion. All information and knowledge

have to be saved independently of the CAD system. This offers the advantage

that the same information and knowledge data can be used for different

CAD systems and can be maintained without CAD.

1 Design Environment and Design Flow 20

1.4.2.1 Preparing Elementary Rules for Computer-aided Design Rule Check

With the application at hand, it has to be examined whether the designed geometry

can be manufactured by means of the production technologies and materials

selected. Therefore, the necessity to focus only on geometry is obvious, i.e.

on the individual surfaces and edges. As a result, a description by means of

boundary representation (B-rep) [26] has been chosen as the geometric model.

In addition, many common transfer formats for CAD data such as STEP [27] or

IGES support this description model.

1.4 Design Environment 21

Fig. 1-9 KoMeth – Design and methodology database

The task of a programmed algorithm is thus to derive geometric parameters

from the three-dimensional geometric model and connect them by means of

rules with the production technological parameter.

By adapting general rules to the special geometry and to the individual production

process, elementary rules are obtained. Consequently, they are not generally

applicable any longer, but describe concrete circumstances and can hence

be evaluated by the computer. As can be seen in Fig. 1-10, the preparation for

this is carried out in two parallel paths: the adaptation and concretization of the

rules and the determination of the geometric parameters.

Application- and process-specific adaptation of the design rules

The processing of the rules as provided by a database until the time when they

can be connected with the geometric parameters is carried out in three steps

(Fig. 1-10, left path):

1. The rules are loaded from a database into a list corresponding to their rule

code. Rules which are not appropriate according to the technology or the

tool/material are not considered.

1 Design Environment and Design Flow 22

Fig. 1-10 Preparing elementary rules from general design

rules and the geometry of the component

2. If a rule is defined for another type of machine element (model mold insert),

it is ‘translated’ by means of a transformation table. In doing so, certain

key words are replaced by others (e.g. inner diameter outer diameter)

3. In accordance with the applied production process chain, the production technological

data are loaded from a separate database, after which the respective

placeholders in the rules are replaced. If no equivalent for a placeholder can

be found in the database, the value ‘0’ is assumed.

Determination of the geometric parameters by means of the boundary

representation method

The evaluation of the geometry of the machine element is carried out in two

phases (Fig. 1-10, right path). First, all boundary representations from the database

of the CAD system need to be read, and second, the corresponding properties

of each representation are to be determined.

In the first phase:

1. a list of all solids of the machine element;

2. a list of all surfaces and edges of the solids from (1) are detected.

Geometric properties can be defined for solids, individual surfaces, two surfaces

or edges (Fig. 1-11). For the determination of a property, geometric information

about the individual boundary representations from the machine element

database is available, such as unit (normal) vectors, fulcrum, limiting or

proximate elements, etc. From this geometric information, simple geometric parameters

can be derived. Two surfaces, for example, are parallel when they have

identical unit normal vectors.

For other parameters, the calculation is more complicated, since there are various

influencing factors or interdependences. One example is the angle of an

edge, which is defined as the angle measured by the part between the adjacent

surfaces directly at the edge. For the determination of this quantity, the fact is

used that normal vectors are always indicated outwards from the volume solid

of the CAD.

In particular, the calculation runs through the following steps:

1. Determination of the adjacent surfaces.

2. Specifying a common point of the surface on the edge.

3. Determination of the unit normal vectors of two surfaces at this point.

4. Calculation of the angle between the unit normal vectors:

cos n1 n2

1.4 Design Environment 23

Fig. 1-11 Determination of the boundary elements and

their interrelations

5. Determination of the small angle between the surfaces:

180

6. Adjustment of nonparallel surfaces (0 180), if it is an inner edge

( 180) or an outer edge ( 180).

7. Check if one of the surfaces exceeds the common edge in the direction of the

other normal vector. This is possible by determining the turning point PE,1

on the surface F1 in the direction of the normal vector n2 of the other surface

F2. To obtain an obvious point, two further directions need to be defined. For

this the cross product n1 n2 and the first normal vector n1 are used. The

point PE,2 is determined analogously.

8. Adjustment if one of these two points is on the common edge of the surfaces;

if yes, then it is an outer edge, if not, it is an inner edge.

9. Calculation of the angle:

with an outer edge:

with an inner edge: 180

The detailed rules obtained by means of the steps listed above are now combined

with all applicable boundary representations and their geometric properties

in order to determine elementary rules. The latter consist only of numbers

and mathematical operations and can be evaluated by an appropriate commercially

available program [28, 29].

1.4.2.2 Design Rule Check

The 3D CAD System Unigraphics for Knowledge Based Engineering (KBE)

For realizing the knowledge-based design environment, commercially available

system components are used to a great extent. Unigraphics (UG) V18 [30] is

employed as a CAD system as it offers the possibility of a full parametric design.

Furthermore, since version 17, a knowledge-based module (UG/Knowledge

Fusion) (UG/KF) and a programmable user interface (UG/Open API) have been

provided. The advantage of directly using a CAD system with an integrated

knowledge-based module is that no neutral interface formats are required. As a

result, costs and effort can be reduced and a loss of information (e.g. parametric

or attached attributes) due to several format conversions can be averted.

Indication of the production process chain with associated technological

specifications

Before it is possible to check the microcomponent, the designer needs to indicate

the production technologies used and the type of machine element of the

product model that is to be designed. For this purpose, in a pop-up window a

question on whether the mold insert or the model is involved and a question

concerning the techniques and tools planned for the production are displayed.

As a consequence, the corresponding rule classes can be derived.

1 Design Environment and Design Flow 24

Via the chosen rule classes, a database is addressed from which the applicable

design rules on an abstract level are read out. In a further step, the parameters

within the rules are replaced with concrete quantities from the production technologies,

e.g. by the tool diameter or the process tolerances.

A great advantage is that the production technological parameters are filed in

a separate database. Especially in the microdomain they change permanently as

there are always new process alternatives available or existing ones are improved.

The filing is carried out separately for the production preparation and

the production. In the production preparation not only the process but also the

tools are distinguished. For each of these any properties can be defined, which

are filed in a separate, connected database table. Hence new properties can be

introduced via the database only by means of modifications.

In a rule database all defined design rules are filed. They are contained in the

form of an explanatory text, which is also displayed in case of a rule infringement,

as well as in the form of an ‘IF – THEN – ELSE’ condition. The ‘IF’ part

is formulated as a mathematical equation with placeholders for production technological

and geometric parameters. If the described equation is correct, the

‘THEN’ part is carried out or, if not, the ‘ELSE’ part, which may be e.g. an automatic

correction.

Design Rule Check (DRC) process

The checking is to a great extent carried out by means of a C++ program, which

has been written exclusively for this task. In this program, the CAD data and

databases are read in and elementary rules are created. These elementary rules

are checked in the UG/KF module and rule infringements are presented in a

pop-up window.

In order to demonstrate functionality, a micromechanical component has

been defined, with the aid of which many production restrictions can be presented.

It is a short T-piece at which the web has been shortened slightly and

the vertical edges are rounded so that the mold insert can be manufactured by

micromilling. The mold insert is to be milled with an end mill cutter (diameter

200 m, length of cutting edge 400 m) on a three-axis micromilling unit. To

induce a rule infringement, the edges of the web are not rounded.

After the adjustment of the production technology and the type of machine

element, the checking is started and the result is later presented in a dialogue

box (Fig. 1-12 a). When an infringed rule is selected, the matching geometric

element is marked in the CAD model and additional information concerning

the rule is displayed. In this case (not rounded edge) also an automatic correction

is possible. If this is carried out for all four edges, the program does not

display an error message any longer (Fig. 1-12 b).

If the corrections are acceptable for the designer, drawings for the mold insert

and the model can be generated for production and quality assurance. Alternatively,

it might be possible to transfer the design data directly via a CAD–CAM

interface to the production preparation.

1.4 Design Environment 25

1 Design Environment and Design Flow 26

Fig. 1-12 (a) Interactive window with infringed rules; (b) manufacturable

part after automatic correction (rounded vertical

edges)

a)

b)

1.5

Conclusion

The approach presented here for the design of primary-shaped microcomponents

and microsystems was defined and validated by developing and designing

a microplanetary gear. Therefore, a tolerance concept for generic and gearing

tolerances was established and implemented in the gear unit. By manufacturing

and measuring single components of the gear, perceptions are iteratively integrated

to the tolerance concept. Subsequently, our Institute will introduce a

microgear test rig in order to test the components of microgears. The goal is to

obtain information regarding the transmission behavior of high-strength microcomponents

that are in contact within the system. In combination with the dimensional

measurement of single components, microsensitive features and

properties of microgears are deduced with consideration of their effects on function.

Moreover, the development of a new VDI guideline is being directed by

the Institute owing to its activities within the domain of microgears.

1.6 References 27

1.6

References

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1 Design Environment and Design Flow 28

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20 J. Marz, N. Burkardt, A. Albers, ‘Methodological

investigation of the product development

in microtechnology,’ in: Proceedings

of the 4th International Topical

Conference, European Society for the Precision

Engineering and Nanotechnologies

(EUSPEN); 2003, pp. 23–26.

21 A. Albers, J. A. Marz, N. Burkardt, in:

Design Methodology in MicroTechnology,

14th International Conference on Engineering

Design, ICED 03; 2003.

22 G. Baumeister, N. Holstein, V. Piotter, R.

Ruprecht, G. Schanz, M. Guttmann, F.

Winkler, A. Häfele, ‘Herstellung metallischer

Mikrobauteile unter Einsatz verlorener

Kunststoffformen’, Nachrichten

FZK 2002, 34, 198–209.

23 G. Baumeister, K. Mueller, R. Ruprecht,

J. Hausselt, ‘Production of metallic high

aspect ratio microstructures by microcasting’,

Microsyst. Technol. 2002, 8, 105–

108.

24 A. Albers, N. Burkardt, S. Hauser, J.

Marz, ,Prototyp einer wissensbasierten

Konstruktionsumgebung für den Entwurf

von Mikrobauteilen‘ Konstruktion

2005, 57, 76–81.

25 A. Albers, N. Burkardt, S. Hauser, J.

Marz, ‘Knowledge-based design environment

for primary shaped microparts’,

Microsyst. Technol. 2004, in press.

26 R. P. Cherian, P. S. Midha, L.N. Smith,

A. G. Pipe, ‘Knowledge based and adaptive

computational techniques for concurrent

design of powder metallurgy

parts’, Adv. Eng. Soft. 2001, 32, 455–465.

27 Geometric and Topological Representation;

DIN V EN V ISO 10303-42 (1994), 1994.

28 Maplesoft, Maple 9.5, http://www.maplesoft.

com/products/maple, September 2004.

29 The MathWorks, Matlab 7, http://

http://www.mathworks.com/products/matlab/

?BB=1, September 2004.

30 Unigraphics, CAD/CAM/CAE-System für

die durchgängige virtuelle Produktentwicklung

(VPD), http://www.ugsolutions.de/

products/unigraphics.shtml, 2002.

31 V. Piotter, T. Gietzelt, K. Müller, R. Ruprecht,

‘Herstellung von metallischen und

keramischen Bauteilen durch Pulverspritzgießen’,

in: Material- und Verfahrensentwicklung

für mikrotechnische Hochleistungsbauteile;

2001, pp. 59–64.

32 M. Weck (ed.), Mikromechanische Produktionstechnik,

DFG SPP 1012; Aachen:

Shaker, 2003.

Abstract

Microspecimens and microcomponents were modeled in order to analyze the

influence of the material anisotropy of the grains upon the stresses which develop

during loading. The limit of finite element analysis with isotropic material

models and the necessary consideration of the microstructure was investigated.

The influence of the number of grains in critical areas on the local stress was

analyzed. This has to be taken into account for a reliable dimensioning of microcomponents.

In a further step, the optimization of microcomponents was attempted

by means of an optimality criteria method, in order to minimize the

stresses at critical locations.

Keywords

finite element analysis; stress distribution; microstructure; grain orientation;

elastic anisotropy

2.1 Introduction 30

2.2 Modeling 30

2.2.1 Modeling of the Grain Structure 31

2.2.2 Modeling of the Microstructure 31

2.2.3 Modeling of the Single Grain Material 32

2.2.4 Mesh Generation 33

2.2.5 Microspecimens 34

2.2.6 Microcomponents 35

2.3 Simulation Results 35

2.3.1 Simulation of Microspecimens 36

2.3.1.1 Microbending Specimens 36

2.3.1.2 Microtensile Specimens 37

2.3.1.3 Microtensile Specimens Containing Pores 39

2.3.2 Microcomponents 42

29

2

Modeling and Validation in Design

A. Albers, D. Metz, Institute of Production Development (IPEK),

University of Karlsruhe (TH), Germany

Advanced Micro and Nanosystems Vol. 3. Microengineering of Metals and Ceramics.

Edited by H. Baltes, O. Brand, G. K. Fedder, C. Hierold, J. Korvink, O. Tabata

Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 3-527-31208-0

2.4 Structural Optimization of Microcomponents 44

2.4.1 Basic Principles of Shape Optimization 44

2.4.2 Modeling of the Shape Optimization 45

2.4.3 Results of the Shape Optimization 45

2.5 Conclusion 48

2.6 Outlook 49

2.7 Acknowledgment 49

2.8 References 49

2.1

Introduction

To reduce development times and development costs, a modern product development

process increasingly often employs numerical methods in order to replace

costly tests or at least to reduce their number. By means of the finite element

method and modern structure optimization tools, components and systems

are produced and tested virtually. Stresses are determined, dimensioning

is employed and variants are compared. In this way, long and expensive iterative

development processes can be shortened and the number of prototypes can be

reduced. Especially in the field of microtechnology, time- and cost-saving numerical

processes should be used owing to the major expense of the production

of prototypes. However, as in the dimensions of microtechnology effects occur

that can otherwise be neglected, the question is raised of whether common numerical

methods can be applied without any modifications. Therefore, this

chapter deals with the question of the reliable simulation of microcomponents

and the reliable transfer of macroscopic modeling to the micro range. Based on

these simulations, microcomponents and microsystems are optimized with regard

to the stresses that occur and reliable data for the dimensioning of microcomponents

are presented for the design engineer.

2.2

Modeling

In the Collaborative Research Center SFB 499, tests are carried out with specimens

(for microtensile and micro three-point bending tests, see Chapters 19

and 20) and with microcomponents and microsystems (see Chapter 1). In addition

to the experiments, numerical analyses are carried out in order to examine

the specific influences of the microstructure and to permit the dimensioning of

highly stressed microcomponents during design. Here it is necessary to model

the microspecimens and microcomponents with regard to their dimensions and

their ‘inner structure’, i.e. the grain structure.

2 Modeling and Validation in Design 30

2.2.1

Modeling of the Grain Structure

The microcomponents and the microspecimens are produced by powder injection

molding using the materials zirconia and 17-4PH (sintered steel) or by microcasting

of Stabilor G (gold-based dental alloy). The characteristic dimensions

of the examined components vary from 0.2 to 1 mm. The characteristic grain

size of the materials employed varies from about 0.5 to 1 m for ceramics and

from 20 to 50 m for metals.

The finite element method usually assumes isotropic material behavior. However,

anisotropic material behavior can also be taken into account when simulating

single crystals or compound materials. Apart from these and some other

cases, almost always quasi-isotropic material behavior can be assumed, as numerous

grains exist in the workpiece. The assumption of isotropic material behavior

is no longer justified when dealing with microcomponents that have only

a few grains in the relevant cross-section. In this case criteria must be established

for the relationship between microcomponent size and microstructural

parameters such as the grain size which allow the consideration of anisotropic

grain behavior [1, 2]. In order to investigate these questions, a model for polycrystalline

microstructures was developed.

2.2.2

Modeling of the Microstructure

For the modeling of polycrystals, some basic assumptions are applied:

The grains are large enough to describe them within the scope of continuum

mechanics.

The material behavior of the grains is described with a linear-elastic material

model.

The grains are assumed to be defect free, hence the material behavior is described

with the ideal single crystal parameters. (Since no single crystal data

are available for Stabilor G, they are approximated by single crystal data for

gold.)

Stochastic geometries are used for the modeling of irregular polycrystals. Owing

to its statistical properties, the Voronoi tessellation is suited to describe the

geometry of a polycrystal [3, 4]. The Voronoi tessellation is often used for the

generation of random grain structures, especially in material research.

A given number of points is taken as a starting point of the Voronoi tessellation.

These so-called generating points result from a process for describing a

random tessellation of a region [5, 6]. This point-generating process is chosen

in such a way that enables the Voronoi tessellation to describe the microstructure

of the polycrystals as realistically as possible, possessing also simple statistic

properties. A Voronoi tessellation is generally understood as a tessellation of

a region into convex polyhedrons, which do not overlap and consume the whole

2.2 Modeling 31

area. Fig. 2-1 shows a graph of a Voronoi tessellation. Owing to the properties

of a polycrystal, it is reasonable to use homogeneous and isotropic point processes,

such as the Poisson process [3, 5, 6]. Voronoi tessellations, which are

generated by a Hardcore Poisson process, are suitable for describing the grain

structure of a regular polycrystal [2, 3, 7]. In order to model the grain structure

of the materials as accurately as possible, micrographs are compared with the

numerically generated models (see Fig. 2-1). A good correspondence was

reached by variation of the Hardcore distance.

2.2.3

Modeling of the Single Grain Material

Two assumptions are made when modeling the three-dimensional material behavior

of a polycrystal:

The polycrystal is macroscopically isotropic, i.e. a preferred direction (texture)

of the crystallographic axes of the single grains does not exist.

The orientation of neighboring grains is interdependent.

The orientation of a crystal is usually described with the three Euler angles

, , and with 0 <2, 0 < and 0 <2 in crystallography [8].

The global coordinate system of the model is defined in a first step. The local

coordinate system is connected to the global coordinate system via rotations

around the three Euler angles. The three-dimensional material behavior of the

single crystal is given by the stiffness tensor regarding the local coordinate system.

A random orientation based on single crystal values is allocated to each

grain. Here, the Euler angles are used as random variables. Then the orientation

of each single grain is a random combination of these variables. An infinite

number of grains result in an isotropic polycrystal. In order to describe an al-

2 Modeling and Validation in Design 32

Fig. 2-1 Micrograph of a microspecimen of zirconia (see

Chapter 20) and Voronoi tessellation for mathematical description

most isotropic material, the Voronoi tessellation has to provide a sufficient

number of grains [1, 2].

Different material property files are used for the anisotropic FEM calculations

and their further statistical evaluation. Each material property file contains material

data for the grains and is based on the results of single crystal testing

combined with the random three-dimensional orientation of these crystals.

2.2.4

Mesh Generation

Owing to the large stress gradients that have to be expected owing to the discontinuity

in the material behavior of neighboring grains, it is necessary to

mesh the grains in a sufficiently accurate way. Based on the algorithm VorTess

[9] and the works of Weyer et al. [10], a rectangular, two-dimensional area with

a random grain structure is generated by means of a C program. Since an intact

grain structure is assumed, the meshes of neighboring grains have to be compatible

with each other. The meshing of the Voronoi tessellations is done in

MSC.Patran, because the Patran command language [11] provides an efficient

macro language that is suitable to mesh higher numbered grain models in a

compatible manner within finite time. The size of the finite elements is given

by the globular structure of the Voronoi tessellations. The largest value is determined

by the smallest edge of two neighboring grains in the whole model, because

at least one finite element has to describe this area of the grain. Owing to

the large fluctuations in the length of the grain boundaries, the smallest edge

often represents a reasonable value that should only be replaced by a lower value

in the case of models with extremely few grains. For more than 25 grains, a

finite element modeled microspecimen or microcomponent with grain structure

shows an essentially higher number of finite elements than a typical model

without represented grain structure.

In the finite element method, the number of finite elements has a significant

influence not only on the quality of the calculation, but also on the calculation

time. Owing to the large number of calculations necessary to deliver a reliable

statistical result, it is desirable to limit the number of finite elements to the

least necessary. Therefore, a different meshing strategy was applied for single

grains in order to reduce considerably the calculation time for the models with

grain numbers above 200. In the area of the grain boundaries, the size of the finite

elements in the model was determined by the smallest edge. However, the

size of the finite elements in the interior of the grains was substantially increased

and therefore the number of finite elements – and as a consequence

the calculation time – could be considerably reduced. Nevertheless, the accuracy

of the calculation could be maintained.

2.2 Modeling 33

2.2.5

Microspecimens

Simulation of grain structures usually employs the concept of a representative

volume element [12, 13]. Two different approaches on the micro and on the

macro levels are applied for describing the material behavior [14–16]. In doing

this, the following requirements have to be met: First, the micro level must be

sufficiently large, i.e. the considered area must provide a sufficient number of

microstructural details and can therefore be considered to be representative.

Second, the considered section must be sufficiently small that the stress gradients

existing on the macro scale are negligible and the material on the macro

level can be considered as homogeneous.

However, the dimensions of the microspecimens or microcomponents that

are treated in the Collaborative Research Center with their respective grain sizes

and also the stress gradients that occur do not always comply with the two requirements

described above.

As for microcomponents or microspecimens of ceramics (zirconia), sufficient

numbers of grains in critical cross-sections are even provided in the ‘worst case’,

i.e. the smallest part dimension 160160 m and largest grain size 0.3–1 m.

Here, (quasi-)isotropic material behavior can be assumed. This is not the case

for metals (17-4 PH, Stabilor G) with a grain size of 20–50 m. In order to guarantee

reliable modeling and simulation of the microspecimens or microcomponents,

the microstructure has to be modeled either directly in the microspecimens

and in the microcomponents or in the region of the component which is

of major interest.

Owing to an appropriate choice, the geometry of the Voronoi tessellations

could be directly used for the modeling of the microspecimens as microspecimens.

The upper part of Fig. 2-2 shows a micrograph of a microbending specimen

and the lower part shows a modeled microspecimen with 200 grains discretized

with 176000 finite elements, which are not visible here. By considering

2 Modeling and Validation in Design 34

Fig. 2-2 Micrograph of a metallic microbending specimen

with 200 m width (see Chapter 19) and modeled microspecimen

with 200 m width in MSC.Patran with 200 grains

the results given in Chapters 19 and 20, it was possible to model the mechanical

behavior of microspecimens two-dimensionally with regard to the grain distribution.

The comparison of micrographs of a metallic microbending or tensile specimens

showed good correspondence of the mathematical models with regard to

the specimen’s grain structures.

2.2.6

Microcomponents

The influence of the grain anisotropy in the case of complex geometries was

studied by the example of the ratio of critical cross-sections to the grain diameters

of sintered metals similar to those in the microspecimens. As shown in

Fig. 2-3, the tooth of a microplanetary wheel (see Chapter 1) was memorized

into a MSC.Patran database in which a Voronoi tessellation had been generated

previously. The contour of the part serves as a boundary. Unnecessary finite elements

of truncated and entire grains outside of the profile were removed. Then

the nodes were positioned on the circumferential edge of the model in order to

describe the profile exactly.

2.3

Simulation Results

The aims of the following calculations are to carry out fundamental examinations

of the influences of the grain anisotropy and to find the limits of the isotropic

modeling of different materials.

2.3 Simulation Results 35

Fig. 2-3 Tooth of a microplanetary

wheel with 33 grains and meshed grain

structure

Because of the small grain diameters of zirconia, from 0.3 to 1 m, and the

characteristic geometric dimensions of the microspecimens and microcomponents,

from 130 to 260 m, zirconia can be considered as quasi-isotropic. Since

zirconia shows a distinctive elastic anisotropy [16] and further miniaturization is

intended, the influences of the grain anisotropy and the limits of the isotropic

modeling are still to be analzyed. Therefore, the considered geometric dimensions

have to be decreased for zirconia compared with the models for metallic

materials. The specimen models with 10 grains in the cross-section have a 200-

m width for metallic materials and only a 10-m width for zirconia. The same

applies for the microcomponents.

In the following, the results always refer to the number of grains in critical

cross-sections. It should be kept in mind that this means different dimensions

for ceramic and metallic microspecimens or microcomponents. To establish the

influences of the grain anisotropy, the anisotropic results are standardized with

the isotropic results. HKS/Abaqus was used as finite element solver.

2.3.1

Simulation of Microspecimens

Micro three-point bending tests and microtensile tests were employed for the

determination of material values (see Chapters 19 and 20).

2.3.1.1 Microbending Specimens

Models for 10 different microbending specimens were generated two-dimensionally,

with a width to length ratio of 1: 5. The total number of grains ranged

from 10 to 250 and the number of grains in the critical cross-section from 1 to

9. The microbending simulation was carried out linear elastically with contact

and the seating and the die were modeled as rigid bodies. The travel of the die

was about 4% with respect to the width. The models were calculated for plane

stress with the materials zirconia, 17-4 PH and gold. The models with 5–9

grains in the width of the specimens describes the grain number for the metallic

specimens with 200 m width.

In order to examine the limits of conventional modeling and further simulation,

each model was first calculated isotropically, i.e. without considering the

grain structure. Then the single models were calculated with 50 different anisotropic

material property files, i.e. considering the grains. For the evaluation and

comparison of the results, the strain energy of each model was analyzed and

standardized with the isotropic result. Fig. 2-4 shows the deviations of the standardized

strain energy for microbending tests with 17-4 PH. Qualitatively similar

results were obtained for zirconia and gold.

At a nearly constant average value, the scatter of the strain energy decreases

with increasing number of grains, and the standard deviation thereby drops

continuously from 5.5 to 1.4%. The same analyses were carried out with zirconia

and gold. Here the results are qualitatively similar, but the deviation of the

2 Modeling and Validation in Design 36

strain energy in the case of zirconia is twice as large owing to the distinctive

material anisotropy. In the case of 17-4 PH and gold, it converges from initially

a 10% deviation to 2%, and in the case of zirconia from 20 to 10%.

By analyzing the stresses in microbending simulations a relatively large scatter

could be observed at the tensile side in the middle of the microspecimens of

up to 30% with zirconia and 22% for 17-4 PH and gold, in comparison with the

isotropic calculation. The increased stress always occurred when a grain with an

‘unfavorable’ orientation was in this area. If only a few grains are located in the

bearing cross-section, the dimensioning process has to consider this case. The

data lead to the estimation that for more than eight grains in the relevant crosssection,

quasi-isotropic conditions can be assumed for the metals considered.

Owing to the bending load stress gradients occur in the models. Therefore, the

influences of the grain anisotropy on the stresses of critical cross-sections or

critical areas cannot be described exactly.

2.3.1.2 Microtensile Specimens

Tensile tests were simulated for metals and for ceramics in order to elucidate

the influences of the grain anisotropy on the stresses.

The analysis of the microtensile test was similar to that of the microbending

test. Ten different micromodels of tensile specimens were generated two-dimensionally

with a width to length ratio of 1: 5. The number of grains ranged from

10 to 250 and the number of grains in the critical cross-section from 1 to 8.

The microtensile test was modeled linear elastically. The nodes at the lower end

of the specimen were kept at a fixed position and the nodes at the upper end

were charged with a force in the tensile direction. The models were calculated

2.3 Simulation Results 37

Fig. 2-4 Deviation of the strain energy in the microbending simulation

with a specimen made of 17-4 PH

for plane stress. Similarly to the bending models, a number of grains from 5 to

8 in the width of the specimens describes the metallic specimens with 200 m

width.

In order to examine the limits of the conventional modeling, each model was

first calculated isotropically, i.e. without considering the grain structure. Then

the single models were calculated anisotropically with 50 different material

property files.

Fig. 2-5 shows a modeled microtensile specimen with 70 grains, on the left

the isotropic calculation with a homogeneous state of stress, and in the middle

and on the right three anisotropic calculations.

Fig. 2-5 illustrates the inhomogeneous stress state due to grain anisotropy.

The stresses of the single grains show a clear dependence on their orientation.

For each calculation, another stress distribution can be observed in the model.

The calculations with different numbers of grains show similar results.

Furthermore, two different grain structures with 50 different anisotropic material

property files were calculated for each number of grains. Both models

show very similar results. The results are presented in Fig. 2-6, which shows

the scatter of the strain energy of 100 anisotropic calculations for the models

with different grain numbers with respect to the particular isotropic case.

It can be observed that the scatter of the strain energy decreases with increasing

number of grains in the models. A reduction in the deviation from the average

value is expected and would approach the isotropic limit for an infinite

2 Modeling and Validation in Design 38

Fig. 2-5 Left, homogeneous von Mises stress distribution in

the case of isotropic calculation; middle and right, inhomogeneous

von Mises stress distribution in the case of different

anisotropic calculations

number of grains in the model. The standard deviation of the strain energy

drops continuously with increasing number of grains from 9 to 1%. The scatter

of stresses and the strain energy in the case of zirconia is larger than for 17-4

PH or gold, but from a qualitative point of view similar results can be assumed

for these materials. Here the results allow the estimation that for more than

eight grains in the relevant cross-section, quasi-isotropic conditions can be assumed.

2.3.1.3 Microtensile Specimens Containing Pores

Material tests (see Chapter 19) showed pores as a possible failure initiation area

in the case of tensile loading. Therefore, the influence of the grain structure on

the stresses at pores was analyzed using further models, each with one pore at

a different position, set up on the basis of an existing two-dimensional model

for microtensile tests with 210 grains. The pore size was nearly half the diameter

of a grain, so that the pore always influenced several grains. Gold was used

as material, because pores sometimes occurred in Stabilor G microspecimens

made by microcasting. The models of the microtensile test pieces containing

pores were calculated with the same material property files as the respective

models without pores. Then their results were compared.

The resulting strain energies did not show significant differences for models

with or without a pore, because the influence of the pore was very local only.

However, in the area around the pore a noticeable stress increase vertical to the

tensile direction occurs (see Fig. 2-7). In Fig. 2-7 the four locations where the

highest stresses occured are labeled. In order to examine the influence of the

pore on the local stress, the respective stress maxima were compared with the

2.3 Simulation Results 39

Fig. 2-6 Scatter of strain energy with respect to the isotropic

value

stress values at the same position for the same model without pores. Owing to

the grain structure, it was not possible to determine a nominal stress value for

the cross-section without pores. Therefore, the stress increase can be understood

only in a limited manner as a notch factor.

Fig. 2-8 shows the scatter of the stress values at four locations of the anisotropic

calculation with respect to the stress value at the same locations without

pores. The two fluctuations on the left side apply to the left and right areas of

the pore on the edge; the deviations on the right side apply to the left and right

areas of the pore in the middle of the microtensile specimen. The two-dimensional

modeling of a pore can be interpreted like a hole in a flat bar for an analytical

calculation. The notch factor for an infinitely thick flat bar is then 3 [17].

The scatter shown in Fig. 2-8 is decisively influenced by the orientation and size

of the grains that directly surround the pore; the other grains only have a small

influence.

The orientations of the individual grains in the area of the pore were varied

specifically in order to explain the deviations of the stress increase. One materi-

2 Modeling and Validation in Design 40

Fig. 2-7 Position of the pores and simulation results, each for

an anisotropic calculation

al property file with a high increase factor and one with a low increase factor

for locations 1 and 3 were further examined. The orientation of the grains in

the area of the pore with the higher increase factor (here called material a) was

varied by the orientation of the same grains of the lower increase factor (here

called material b). Table 2-1 shows in the upper row the increase factor at location

3 of the model with the pore in the middle of the microtensile specimen.

The lower row displays the reduction of the increase factor at location 1 of the

pore at the edge of the microtensile specimen.

Table 2-1 clearly shows the approximation of the stress increase of material a

on material b due to the variation. The stress increase is significantly influenced

by the orientation of the adjacent grains. The remaining difference is caused by

the influence of the other neighboring grains. If they are also changed, the value

of material b is almost obtained.

The current simulations correlate well with the theoretical factor 3 of a cylindrical

through-thickness pore. However, no findings exist about the effects in

the direction perpendicular to the model. Therefore, further three-dimensional

simulations are necessary. Until this is implemented, a slight safety addition to

the dimensioning according to [17] should be employed.

2.3 Simulation Results 41

Fig. 2-8 Stress scatter at a pore

Table 2-1 Reduction of the stress increase factor due to variation

of the grain orientations

Material a Variation:

upper grain

Variation:

both grains

Material b

Location 3 3.16 3.06 2.84 2.65

Location 1 3.22 3.16 3.05 2.8

2.3.2

Microcomponents

Results obtained from microspecimens with simple geometries cannot be transferred

without further considerations to real components with a more complex

loading. For this reason, the influence of the grain structure on actual microcomponents

was also examined.

Five different models of a single tooth of a microplanetary wheel were generated

for the examinations. The grain number in the tooth varies from 17 to 97.

The single models provide 3–7 grains in the cross-section of the tooth root. The

model with 97 grains represents an upper limit. The modeling of a larger number

of grains in the tooth of the microplanetary wheel fails owing to the extent

of the modeling, which was done manually until now.

The calculations were performed with the materials 17-4 PH, zirconia and

gold. The models were calculated assuming plane stress. Similarly as in the

models of tensile and bending specimens, a number of grains between five and

seven describes the structure of gearwheels made of metals in the tooth root

cross-section. In order to reduce the calculation time, a direct force on the tooth

was used instead of a contact model. The lower edge of the models was fixed.

The examinations were standardized with the results of the isotropic case again.

The left side of Fig. 2-9 shows the isotropic calculation with a direct flux

through the tooth profile. In the middle an anisotropic calculation with a stress

maximum at the right tooth root is displayed. On the right an anisotropic calculation

with a decisive stress increase in the left tooth root is shown. The models

show similar results for all numbers of grains. In both anisotropic calculations

a grain with a low stiffness towards the force flux can be observed close to the

load application. However, since no critical location exists, this can be neglected.

The stress maxima in the anisotropic case preferably occur at the left tooth root,

2 Modeling and Validation in Design 42

Fig. 2-9 Calculation of a tooth of a microplanetary gearwheel

with a total of 33 grains and with five grains in the tooth root

cross-section for zirconia: on the left the isotropic calculation,

and in the middle and on the right the anisotropic calculations

but in one-third of the calculated cases, it occurred at the right tooth root also.

The stress maxima occurred in all areas of the tooth root, but preferably at grain

boundaries, as shown at the right tooth in Fig. 2-9. This can be explained by different

stiffnesses, depending on the orientation of the adjacent grains. The results

often show an almost direct flux of the stress through the tooth, similarly

to the isotropic calculation (see Fig. 2-9).

In the case of anisotropic material behavior, deviations of the stress values in

the tooth root are observed for different material property files. These deviations

and the behavior described above could be observed for all materials examined

(17-4 PH, zirconia and gold).

Solely the grain or grains directly located in the tooth root decisively influence

the stress value in this region. This could be demonstrated by specific variation

of the orientations of single grains in the tooth root. All materials show qualitatively

the same behavior, with the greatest scatter for zirconia and the smallest

for gold. Owing to the dependence of the stress values on the orientation of single

grains, it was not possible to obtain a convergence of the scatter of the stresses

relative to the isotropic case by increasing the grain number at the left tooth

root. The standard deviation was 20% for zirconia, 12% for 17-4 PH and 7% for

gold. The right tooth root showed a slight convergence of the standard deviation

from 20% to 16% for zirconia, from 16 to 12% for 17-4 PH and from 11 to 7%

for gold.

In the worst case, anisotropic calculations showed a large stress increase of

up to 80% with regard to the isotropic calculation. Owing to these extreme

stress increases, a factor of 1.8 has to be included with respect to the safe dimensioning

for microcomponents of zirconia with only a few grains in the

cross-section. For 17-4 PH and gold a factor of 1.4 is sufficient. The variation of

the orientation of single grains, corresponding to those of the calculations of

microtensile tests with pores, also showed the great relevance of the orientation

of the grain at the critical position. It has to be added that, owing to the two-dimensional

modeling, the influence of further grains in the third dimension

could not be considered, so that only one or two grains influenced the deviations.

However, there are more grains across the tooth width in the highly

stressed area, so that by an averaging over the grains in the tooth width, a reduction

of the deviation and therefore a reduction of the mentioned factors of

1.8 and 1.4, respectively, is probable. This is why a three-dimensionally modeled

grain structure of microplanetary wheels is examined.

It is desirable to reduce the large stresses in the tooth root already during the

design process. For this purpose, mechanical engineering employs numerical

optimization processes in order to decrease the stress at highly stressed areas in

workpieces by modifying the shape.

2.3 Simulation Results 43

2.4

Structural Optimization of Microcomponents

The examinations of microgearwheels clearly show the large stresses at the

most critical position for failure at the tooth root. If it were possible to reduce

this stress, a larger torque could be transmitted. For the optimization of components,

mechanical engineers employ optimality criteria methods, such as shape

optimization. The question is whether this method can be applied to microcomponents.

2.4.1

Basic Principles of Shape Optimization

The optimality criteria methods take advantage of the knowledge of the physics

and mechanics of the respective problem set. Theses will be postulated describing

the optimum.

A well-known and ascertained physical law relating to structural mechanics is

the fully stressed design [18]. An important mathematical optimality criterion is

the Karush–Kuhn–Tucker condition [19, 20], normally designed for convex optimization

purposes.

The theses of stress homogenization and stress minimization can also be considered

as optimality criteria [21]. Regarding the optimality criteria methods,

these criteria and the response behavior of modifications of the physical model

are implemented into a suitable algorithm. A convergence behavior is achieved

by the use of suitable redesign rules. The optimality criteria are particularly well

proven for shape and topology optimization where a large number of design

variables is required. It is important to note that the convergence rate is independent

of the number of design variables.

The optimization program used, TOSCA.shape, implements an optimality criteria

approach. A distribution of scalar values within a design area, the so-called

design response, are basically processed by the optimization algorithm. Depending

on the user-defined objective function, these values are minimized or maximized

by means of a homogenization within the design area. The shape change

induced by the optimizer, i.e. the variation of the finite element mesh, is managed

by displacing nodes. This leads to a decrease in the local surface curvature

in highly stressed regions. Typically, such scalar quantities are von Mises stresses

obtained from a static finite element analysis. The nodal displacement U

that is applied to a certain node by the optimizer is then calculated by means of

the following equation:

Un Fa b 1

where denotes a scalar calibration factor and F(a, b, ) is a function of the

scalar nodal design response a, used for optimization such as von Mises stress,

a reference value b and other parameters.

2 Modeling and Validation in Design 44

2.4.2

Modeling of the Shape Optimization

The finite element calculation of the microgearwheels is followed by a shape optimization.

A tooth of the microgear with two grains in the left tooth root was

chosen as a model for optimization. The surface nodes in the left tooth root

were determined as design area and as design response and their von Mises

stress values were determined. The objective function was stated as: minimize

the stress distribution within the design area.

Two boundary conditions were included in order to achieve reasonable results

in the calculation and with respect to the running ability of the gear and the

feasibility of production [22]. A mesh smoothing, i.e. the retightening of the surface

node that borders the design area and the prevention of shrinking of the

design area in order to achieve a continuous transition from design area to

tooth flank and to tooth base, respectively, was set up.

The iterative process ends when a user-defined stop condition is fulfilled. In

this case, the optimization was aborted after 15 iterations, when no substantial

difference could be determined any longer.

2.4.3

Results of the Shape Optimization

First, the model was optimized without consideration of the grain structure and

with isotropic material data. Then the same model was calculated and optimized

with 25 different anisotropic material property files. The left side of

Fig. 2-10 shows the different contours of the notch root for the isotropic material

and three anisotropic material property files (here denoted materials c, d and

e). The orientations of the individual grains in the root of the tooth were varied

specifically in order to explain the different contours after optimization. The orientations

of the grains in the tooth root from material c were varied by the orientation

of the same grains of material e. On the right side, the approximation

of the tooth root contour in the case of the variation of the grains’ orientation

in the tooth root is shown. As usual for shape optimization, small changes in

the contour have a distinctive effect on the stresses (see Figs. 2-10 and 2-11).

The results of the anisotropic material property files differ noticeably from

the result for the isotropic material. However, compared with the original models,

a reduction in the tooth root stress from 10 to 32% could be achieved for all

25 optimizations.

In order to demonstrate the influence of the orientation of the single grains,

the individual grain orientations in the tooth root were varied specifically. Material

c was varied by the orientation of the same grains of material e. For this

purpose, the orientation of the upper grain in the tooth root in material c was

replaced by the orientation of the grain of material e. Then, additionally, the orientation

of the upper grain was replaced. The difference in the geometry con-

2.4 Structural Optimization of Microcomponents 45

2 Modeling and Validation in Design 46

Fig. 2-10 Left, tooth contours after the optimization with different

material property files and right, convergence of the

tooth contour for the variation of the grain orientation and

renewed optimization

Fig. 2-11 Proportional deviation of the tooth root stress at the

optimized geometry with respect to to the non-optimized

tooth root

tours of the varied model can be explained by the influence of the remaining

surrounding grains (see Fig. 2-10).

After having clearly demonstrated the influence of grain anisotropy, the question

is how the geometry change affects the tooth root stress when other material

property files are used for calculation with the new geometry instead of those

used at optimization. This is relevant because in practice a large number of

components with very different grain structures will be molded by means of

one mold with a geometry defined after optimization. Therefore, the possibility

of optimizing the tooth root geometry in order to reduce the tooth root stress

should be proved. At least it should not lead to an increase in the tooth root

stress.

For this reason, the optimized tooth root that resulted from the calculation

with the isotropic material and, exemplarily, the optimized tooth roots of materials

c, d and e were calculated again with the remaining 25 material property

files. Fig. 2-11 shows the proportional deviation of the tooth root stress for each

material property file at the respective optimized model with respect to the original

model.

On average, a slight stress reduction of 1.5% was achieved for the model that

was optimized with the isotropic material. However, the individual results vary

between a reduction of 15% and an increase of 11.6%. The optimizations with

anisotropic material property files achieved an average stress increase of 0.5, 2.4

and 8.5%. For the individual simulations, the stress reductions ranged from

16.4 to 20.5% and were larger than those for the isotropic cases, but a larger

stress increase of 15–23.5% was also reached.

As the average values already showed, no substantial reduction in the tooth

root stress could be achieved by calculating the optimized geometries with other

material property files. However, for the dimensioning of microgearwheels, the

‘worst case’ has to be assumed and here all four optimized models showed a

substantial increase between 11.6 and 23.5%. It remains to note that the single

material property files lead to very different stress values for different geometries.

The following example demonstrates the difficulties of finding a general

optimized contour for the tooth root. For two anisotropic material property files

(here denoted as materials f and g), the different optimized geometries were recalculated.

In the case of the optimized geometries of the isotropic material, a

stress reduction of 6.6% for material f could be achieved but a stress increase of

5.2% for material g was obtained. In the case of the optimized geometries of

materials c, d and e, stress deviations of –11.9, 15 and 13.1% for material f and

of 14, –18.2 and 19.2% for material g were obtained, which means that these

two material property files behave differently. Consequently, the evaluation of

the results does not help in finding a general trend. As Fig. 2-11 demonstrates,

all optimized geometries show a stress increase in at least 50% of the new calculations

with other material property files. Owing to the inhomogeneous stress

distribution caused by the grain structure, a general loaction point where the

geometries could be varied in a way that would minimize the local stress increase

cannot be identified. Although it is possible to find an optimized solution

2.4 Structural Optimization of Microcomponents 47

for each case, it was not possible to find a global solution for the different grain

orientations. Therefore, the optimization of the tooth roots cannot be carried

out using this method.

2.5

Conclusion

Independent of the number of grains in the cross-section that are observed in

parts manufactured within the Collaborative Research Center, the limits of isotropic

modeling for different materials (zirconia, 17-4 PH and gold instead of

Stabilor G) were demonstrated. The microspecimens require at least eight

grains in the relevant cross-section to assume quasi-isotropic material behavior.

If a smaller number of grains is present in the critical cross-section, anisotropy

effects must be taken into account owing to their possible stress-increasing influence.

The examination of pores in microtensile specimens with few grains in

the cross-section showed a deviation of the stress increase depending on the orientation

of the surrounding grains. Results of further simulations have to be

implemented or the influence of additional stress increases have to be considered.

The demonstrator components do not deliver a limit value for the assumption

of quasi-isotropic material behavior by means of the examination results. The

stress deviation of the planetary gearwheel tooth simulation with seven grains

in the cross-section is, according to the material, up to 40% and is therefore too

large to be considered as quasi-isotropic. Here the dimensioning has to add an

additional safety factor.

With regard to the research activities in the Collaborative Research Center, zirconia,

owing to its small grain size, can be considered as a quasi-isotropic material

for the actual dimensions of the demonstrator components and microspecimens.

In the case of microcomponents of 17-4 PH and gold/Stabilor G, an additional

safety factor has to be included in order to account for the anisotropy of

the relatively small number of grains in the cross-section of the component.

The macroscopic approach of the fully stressed design was examined with regard

to its application to microcomponents with few grains. Owing to the inhomogeneous

stress distribution caused by the grain structure, it is not possible

to find an optimized tooth root geometry without a substantial stress increase

for individual grain configurations. Regarding the shape optimization, it remains

to say that the geometry changes are so small that they are smaller than

the tolerances of the present manufacturing processes (see Chapter 4). Therefore,

today the implementation of an optimized geometry is difficult to achieve.

2 Modeling and Validation in Design 48

2.6

Outlook

Current calculation models concentrate on the three-dimensional modeling of

grain structures in. This is the requirement for examining complex geometries

and stress states, e.g. caused by pores, in grain structures. At the same time,

further variation possibilities of the Poisson point process are developed by

means of variation of the Hardcore value in specific component areas, in order

to be able to account for changes in grain structures in different component

areas (e.g. middle/edge). To reduce the extensive manual work in the model of

microcomponents, solutions were found for the automated meshing of three-dimensional

models. The conversion into software and the calculation of three-dimensional

grain structures is in progress.

2.7

Acknowledgment

This research is financially supported by the German Research Foundation

(DFG) within the Collaborative Research Center (SFB) 499, ‘Development, Production

and Quality Assurance of Primary Shaped MicroComponents from Metallic

and Ceramic Materials’.

2.8 References 49

2.8

References

1 N. Wellerdick-Wojtasik, Theoretische

und experimentelle Untersuchungen

über die Fließflächenentwicklung bei

großer Scherdeformation; Dissertation,

VDI-Verlag, Vol. 18, Mechanik/Bruchmechanik

1997, 215.

2 S. Weyer, Mikromechanisches Modell

zur Ermittlung effektiver Materialeigenschaften

von geschädigten Polykristallen;

Dissertation, Universität Karlsruhe

(TH), 2001.

3 J. Osher, U. Lorz, Quantitative Gefügeanalyse

– Theoretische Grundlagen und Anwendungen.

Leipzig: Deutscher Verlag für

Grundstoffindustrie, 1994.

4 D. Stoyan, W. S. Kendall, J. Mecke, Stochastic

Geometry and Its Applications, 2nd

edn; Chichester: Wiley, 1995.

5 D. Stoyan, H. Stoyan, Fraktale Formen

Punktfelder; Berlin: Akademie-Verlag,

1992.

6 A. Okabe, B. Boots, K. Sugihara, Spatial

Tesselations – Concepts and Applications of

Voronoi Diagrams; New York: Wiley,

1992.

7 A. Fröhlich, Mikromechanisches Modell

zur Ermittlung effektiver Materialeigenschaften

von piezoelektrischen Polykristallen;

Dissertation, Universität Karlsruhe

(TH), 2001.

8 H. J. Bunge, Texture Analysis in Materials

Science; London: Butterworths, 1982.

9 H. Riesch-Oppermann, VorTess generation

of 2-D random Poisson–Voronoi

Mosaics as framework for the micromechanical

modelling of polycrystalline materials

– algorithm and subroutines description;

Forschungsbericht FZKA, 6325,

1999.

10 S. Weyer, A. Fröhlich, H. Riesch-Oppermann,

L. Cizelj, M. Kovac, Automatic finite

element meshing of planar Voronoi

2 Modeling and Validation in Design 50

tessellations. Eng. Fracture Mech. 2002,

69, 945–958.

11 MacNeal Schwendler Corporation,

MSC.Patran 2004, PCL Manuals; Santa

Ana, CA: MacNeal Schwendler. 2004.

12 R. Hill, Elastic properties of reinforced

solids: some theoretical principles. J.

Mech. Phys. Solids 1963, 11, 357–372.

13 Z. Hashin, Theory of mechanical behavior

of heterogeneous media. Appl. Mech.

Rev. 1964, 17, 1–9.

14 S. Weyer, A. Brückner-Foit, Versagensverhalten

keramischer Werkstoffe unter

Druckbeanspruchung. Jahresbericht 1999;

Karlsruhe: Institut für Keramik im

Maschinenbau, 1999.

15 S. Weyer, A. Brückner-Foit, A. Fröhlich,

Overall properties of ceramics subjected

to compressive loading. In: International

Conference on Engineering Ceramics and

Structures; Cocoa Beach, FL: American

Ceramic Society, 2000, pp. 101–107.

16 A. Fröhlich, S. Weyer, D. Metz, O. Müller,

A. Brückner-Foit, A. Albers, Investigations

on the reliability of FEA calculations

on the microscopic scale. In: Technical

Proceedings of the 2001 International

Conference on Computational Nanoscience,

Hilton Head Island, SC; 2001, pp. 161–

164.

17 FKM Richtlinie, Rechnerischer Festigkeitsnachweis

für Maschinenbauteile, 4., erweiterte

Ausgabe 2002; Frankfurt/Main:

VDMA Verlag, 2002.

18 H. Gallagher, C. Zienkiewicz, Optimum

Structural Design – Theory and Applications;

London: Wiley, 1973.

19 W. Karush, Minima of functions of several

variables with inequalities as side

conditions; MSc Thesis, Department of

Mathematics, University of Chicago,

1939.

20 H.W. Kuhn, A.W. Tucker, Nonlinear programming.

In: Proceedings of the Second

Berkeley Symposium on Mathematical Statistics

and Probability; Berkeley, CA: University

of California Press, 1951,

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21 E. Schnack, Ein Iterationsverfahren zur

Optimierung von Kerboberflächen, VDIForschungsheft

589; Düsseldorf: VDI-Verlag,

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22 J. Marz, N. Burkardt, A. Albers, in: Conference

Proceedings EUSPEN; 2003, Vol. 1,

pp. 23–26.

Abstract

Micro powder injection molding (Micro PIM) consists, in essence, of the same

process steps as its macroscopic counterpart (see Chapter 10). In order to obtain

a reliable and reproducible process flow suitable for mass production applications,

the process parameters must be identified. It turns out that the determination

of such process parameters by trial and error can be improved considerably,

as has been shown for the macroscopic process, by applying computer simulations

to predict the process result [1]. Commercially available simulation

programs for macroscopic modeling, however, seem to fail when it comes to

the prediction of the process in microscopic dimensions. The greater the complexity

of the mold geometry, the less reliable the predictions with conventional

simulation tools are [2]. A comparative study of different simulation tools can

be found in [3]. One of the common main drawbacks of all the programs is

their lack of standard rheological models for powder filled feedstocks. In fact,

most of the simulation tools use single-phase models for the description of the

feedstock. This does not allow for the prediction of, e.g., segregation effects. As

a consequence, there is a need for new approaches in this area. For the description

of the microscopic dynamics of fluid flow, molecular dynamics is one of

the most popular methods. It achieves very reliable fundamental results for

fluid behavior. When applied to geometries that extend above the nanometer

scale, the computational costs are so high that it is not possible to simulate an

injection molding process by this method in the foreseeable future. Dissipative

particle dynamics (DPD) is a particle method on the mesoscopic scale. Therefore,

it is a promising candidate to fill the gap between microscopic and continuum

methods. This chapter explains our efforts to apply DPD to the modeling

and simulation of Micro PIM and its verification by suitable laboratory experiments.

51

3

Modeling Micro PIM

D. Kauzlaric, A. Greiner, J. G. Korvink, Institute for Microsystemtechnology,

University of Freiburg, Germany

M. Schulz, R. Heldele, Institute for Material Research III (IMF III),

Forschungszentrum Karlsruhe, Germany

Advanced Micro and Nanosystems Vol. 3. Microengineering of Metals and Ceramics.

Edited by H. Baltes, O. Brand, G. K. Fedder, C. Hierold, J. Korvink, O. Tabata

Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 3-527-31208-0

Keywords

micro powder injection molding; computational fluid dynamics; dissipative particle

dynamics; simulation

3.1 Introduction 52

3.2 Flow Behavior of Polymers in Microchannels 54

3.3 Dissipative Particle Dynamics 57

3.4 Matching Macroscopic Parameters with DPD 59

3.4.1 Matching the Equation of State 60

3.4.1.1 The Free Energy Approach for Many-body Dissipative Particle

Dynamics (MDPD) 60

3.4.1.2 Warren’s Approach for MDPD 63

3.4.1.3 EOS Measurement, Modeling Pressure, Specific Volume

and Temperature (pvT) 64

3.4.2 Fluid–Wall Interaction: the Contact Angle 67

3.4.2.1 Reflecting Boundary Conditions 68

3.4.2.2 Interactions for Reproduction of Wetting and Friction 69

3.4.2.3 Measurements of Contact Angle Between Molding Material

and Mold Insert 70

3.4.3 Viscosity Modeling and Measurement 72

3.4.3.1 The Parameters in DPD 72

3.4.3.2 Shear Viscosity Measurements 74

3.4.4 Thermal Conductivity and Thermal Expansion, Measurement

and Modeling 76

3.5 Test Geometries 80

3.6 Conclusion 82

3.7 Acknowledgment 82

3.8 References 82

3.1

Introduction

The modeling and simulation of the behavior of materials in various applications

of modern microsystem technology is a challenging task. This is especially

the case for form-giving process simulation. In practice, high costs or restricted

possibilities in machine finishing require special care to be taken in the design

of the mold. Simulation tools emerging from theoretical modeling that ranges

from quantum physics of atomic-scale phenomena to continuum descriptions

of macroscopic behavior [4] and the system behavior, are still lacking engineering

tools to support the design processes in microsystem technology. In microsystems,

the presence of several orders of magnitude of length scales requires

the coupling of different tools appropriate for simulation at the respective spatial

scale. Given these boundary conditions for the design of microsystems, the

3 Modeling Micro PIM 52

use of advanced computer-aided design (CAD) tools promises a reduction in the

extent of physical testing necessary to prototype a device. Moreover, these

looked-for tools are the auxiliary means to reduce production costs for microsystems.

Activities to incorporate various physical models at different length scales

already exist (e.g. [5]), which show great promise for the solution of the given

task to simulate an entire process chain in microsystem technology.

The simulation of complex fluidic processes in a common framework with reasonable

computational effort – as is mandatory for its application in an engineering

design process – might be realized by superimposing particle dynamics on a

conventional computational fluid dynamics (CFD) simulation. Typically, the particle

dynamic simulation will be computationally more expensive than the CFD solver.

Moreover, the iterative procedure for fluid solvers, due to the non-linear nature

of the Navier–Stokes equations, will force the costly particle dynamics calculation

to be repeated in every iterative loop. To overcome this problem, it is desirable to

improve the coupling of the microscale simulation featuring noniterative and explicit

time marching to the continuum model acting on a much coarser length

scale and thus eventually leading to a feasible simulation process.

At the microscopic length scale, molecular dynamics (MD) represents an attractive

simulation technique for CFD. However, for length scales larger than

10 nm, a coarse graining of the molecular model is desirable owing to rising

computational costs. A very promising technique is DPD, first introduced by

Hoogerbrugge and Koelman in 1992 [6]. In essence, it is a treatment of the dynamics

of quasi-particles each representing small sets of the liquid’s molecules,

by stochastic differential equations in a fashion similar to a Langevin approach.

It combines features from MD and lattice gas methods (e.g. [7]). Since its first

introduction, this method has been applied to the simulation of a wide range of

phenomena, especially in the area of materials science. Many investigations

have been carried out in order to understand the capabilities of DPD as applied

to CFD problems [8–15].

DPD is a mesoscopic simulation method capable of ‘bridging the gap’ between

atomistic and mesoscopic simulation [16]. Its application range for different

simulation tasks includes mesoscopic dynamics of colloids [17], binary fluids

and the matching of macroscopic properties with DPD [18], domain growth and

phase separation in immiscible fluids [19] and the simulation of rheological

properties [20]. The last is a very important characteristic of this method and

augments its capability of predicting material properties, so necessary for microforming

processes.

Recently, DPD has experienced several improvements. Its algorithmic optimization

was a major focus, thereby making it a method appropriate for application

in the engineering field [21–23]. The inclusion of energy conservation in

the particle–particle interaction for the set of stochastic differential equations describing

a DPD model has been derived [24, 25]. This is an important extension

for heat flow applications. Recently, phase change models, built on the energyconserving

DPD models [26] for a solid–liquid phase transition, have been included.

Liquid–vapor coexistence, instead, cannot be modeled within a standard

3.1 Introduction 53

DPD approach unless one drops all the advantages of the method arising from

the use of larger time steps than are typical in MD [16]. Nevertheless, there are

several improvements that lead to a tolerable increase in computational costs,

that allow for modeling of liquid–vapor systems. The technical issues will be

considered in the following sections.

3.2

Flow Behavior of Polymers in Microchannels

Accompanied by the rapid development of microfabrication techniques, MEMS

technologies are now approaching a level where the standard macroscopic material

properties, such as Young’s modulus, tensile strength and Poisson’s ratio, cannot

be employed without restrictions at the microscopic level. This statement is

also true for fluid properties, which play a large role in microinjection molding.

Simulating the filling of microcavities with standard flow simulation packages

such as FLOW-3D and CFX4 have shown that the calculated flow front velocities

for water do not match the experimental data and differ by a factor of up to

70% [27]. This discrepancy between experimental and theoretical data can be explained

by various effects that occur in microdimensions. The large surface-tovolume

ratios result in strong influences from intermolecular interactions between

a fluid and a surface, e.g. surface tension effects, wall slip effects, viscous

effects (see Sections 3.4.2 and 3.4.3) and adhesion effects [28].

Most simulation tools designed for injection molding use the generalized

Hele–Shaw flow model for non-isothermal and non-Newtonian viscous fluids

[29]. This model does not take into account that, when the external characteristic

length (e.g. channel depth) becomes comparable to the internal characteristic

length (e.g. radius of gyration of a polymeric molecule), the long-range intermolecular

forces between the polymer chains and the molding surface begin to influence

rheological and capillary behavior significantly.

Various experimental observations have shown that the rheological behavior

of fluids near rigid surfaces is significantly altered compared with the bulk behavior

measured at a sufficient distance from surface walls [30–34]. It has been

shown, for example, that the viscosity near a channel wall is 50–80% higher

than in the bulk fluid.

The surface–fluid interactions are long-range intermolecular forces that cause

orientational effects. Based on that, Eringen and Okada [33] developed a nonlocal

continuum theory of viscous fluids with the following viscosity model:

b 1 c

Rg

D 2 1

Equation (1) describes the fluid viscosity , where b is the bulk viscosity, c is a

dimensionless constant, Rg is the radius of gyration for fluid molecules and D

3 Modeling Micro PIM 54

is the external characteristic length, e.g. the channel diameter. The gyration radius

Rg is defined as the root mean square of unperturbed random recoil of

polymeric molecules and depends strongly on the molecular weight of the polymer

[35].

If D and the radius of gyration are of the same order of magnitude, the viscosity

will rise significantly. Fig. 3-1 shows this relationship for a Newtonian

fluid based on the coefficients for polystyrene–cyclohexane [32], with c=19.5

and Rg=26 nm. A significant viscosity change near the surface wall can be observed.

Possibly this effect influences the filling of structural details during micro

powder injection molding.

The rheological data measured in macroscopic experiments and used in standard

simulation packages for injection molding are not completely suitable for

modeling the flow in microchannels.

The most common simulation tools for injection molding, MoldFlow and CMold,

both assume no-slip boundary conditions at the mold walls [36]. Various

theoretical studies [37–40] have attempted to describe the wall-slip phenomenon

with some success, although most of them are not properly derived from fundamental

physical principles. Yao and Kim [41] stated two possibilities as to why

slip can more easily occur in microchannels. The linkage of polymer chains

with each other can, on a basic mechanical level, be described with a spring–

damper system. If the channel size decreases, the number of springs across the

gap also decreases, and therefore the polymer melt appears to be more rigid, resulting

in wall slip. They also showed that an increased amount of pressure

drop is necessary to fill microchannels. The consequence is a higher pressure

on the fluid near the wall, which can lead to either a separation of grafting polymer

chains and the surface or disentanglement of grafting chains with bulk

chains, thus resulting in wall slip. In practice, this can lead to a plug flow in

microcavities with a nearly homogeneous flow velocity profile.

3.2 Flow Behavior of Polymers in Microchannels 55

Fig. 3-1 Rise of viscosity near solid surfaces predicted by Eringen and Okada [33]

This observation leads to another important fact for channels in microdimensions.

A significant effect when scaling a fluidic system into microdimensions

can be seen by looking at the Reynolds number:

Re

vD

2

where v is the fluid velocity, D the capillary diameter and the kinematic viscosity.

The Reynolds number relates the inertial forces to the frictional (viscous)

forces and will tend towards low numbers if the viscous forces dominate. It describes

the transition point between laminar (low Reynolds numbers) and turbulent

(high Reynolds numbers) flow. With small cavities in the micrometer

range and polymer viscosities high above 1 Pa s, it is safe to assume laminar

flow during Micro PIM for simple geometries (Re <<1).

The influence of surface tension and the resulting contact angle between

molding surface, ambient atmosphere and feedstock is yet another fact that today’s

simulating tools ignore. Some microdevices are based on the fact that with

decreased channel size, an appropriate fluid can fill a whole capillary system

without external pressure [42]. This is attributed to the capillary pressure as described

by the Washburn equation:

p

4S cos

d 3

where p is the equivalent pressure change at the front of a capillary flow, due

to the surface tension S, is the contact angle of the fluid with the capillary

wall and d is the diameter of a capillary with circular cross-section.

With the experimental data in Section 3.4.2, the influence of capillary pressure

on mold filling during Micro PIM can be estimated. The contact angle of

3 Modeling Micro PIM 56

Fig. 3-2 Calculated capillary pressure of a binder system on

molding surface with a contact angle of 36 and surface tension

of 23 mN m–1 at 160C

the binder-system on the molding surface at 160C is about =36 and the corresponding

surface tension S=23 mNm–1. The resulting pressure is illustrated

in Fig. 3-2. Typical filling pressures of several hundred MPa are used in PIM

so that the influence of wetting seems to be negligible [41]. In addition, it is

necessary to determine the compression ratio in the microcavities since the expected

pressure loss is likely to be high.

3.3

Dissipative Particle Dynamics

Continuum-based computational fluid dynamics (c-CFD) uses the available discretization

methods, such as Finite Elements, Control Volume or Finite Differences,

to treat numerically the partial differential equations of motion that describe

the hydrodynamic behavior of a fluid. The best known among these are

the Navier–Stokes equations.

In the DPD method, one discretizes the continuum fluid into small portions

as shown in Fig. 3-3. Usually, these portions are represented by point particles.

One might think of a DPD particle as a representation in terms of the center of

mass dynamics of a fluid portion. The positions and momenta of the particles

are updated in continuous phase space at discrete time steps. The updates are

computed by applying Newton’s second law for a particle of mass mi:

dri

dt

pi

mi

dpi

dt Fext

i ji

f ij 4

where ri and pi are the position and momentum vectors of particle i and Fext

i is

an external force field acting on each particle. f ij FD

ij FR

ij FC

ij is a net pair

force acting between two particles i and j, where FD

ij is a dissipative force, FR

ij is

a stochastic force and FC

ij is a conservative force.

Suitable forms for FD

ij and FR

ij , which fulfil the necessary condition of Galilean

invariance, are

FD

ij wDrijeij vijeij 5

3.3 Dissipative Particle Dynamics 57

Fig. 3-3 Schematic picture of a DPD discretization of the continuum

(from left to right) or a coarsening of the atomistic picture (from

right to left)

and

FR

ij ijwRrijeij 6

The vector eij =rij/rij is the unit vector pointing from particle j to particle i.

vij vi vj is the relative velocity between the particles. ij is a random number

with the properties ijt 0 and ijtklt

ikjl iljkt t

, where

ij 1 for i=j and ij 0 for i j, and x is the Dirac -function with

xdx 1. The scalar can be interpreted as a friction coefficient and is a

scalar noise amplitude. wDrij and wRrij are weight functions that determine

the range of the forces and their strengths as a function of the interparticle distance

rij. For rij rc, where rc is the cutoff distance, these functions vanish.

For a well-defined equilibrium temperature, detailed balance requires a fluctuation-

dissipation theorem for DPD to be fulfilled [43], which is

wDrij w2

Rrij 7

and

2kBT

m

2 8

where m is the mass of a particle, kB is the Boltzmann constant and T is the

equilibrium temperature. This means that the stochastic and dissipative forces

act together as a momentum-conserving thermostat. Usually, the weight functions

are chosen to be

wDrij w2

Rrij 1 rij

rc 2

rij rc

0 rij rc

9

A convenient choice for the conservative force is [16]

FC

ij awCrijeij 10

with a>0 representing a repulsion amplitude and wCrij wRrij.

For the numerical integration of Equation (4), the modified velocity Verlet algorithm

is used, as described in [16]. It takes into account that the dissipative

force depends on the velocities and vice versa. When using the alternative

Lowe–Andersen thermostat (see Section 3.4.3) later on, the standard velocity

Verlet algorithm known from MD is sufficient, since the thermalization is no

longer coupled to the force computation.

Because of the non-systematic coarse-graining procedure of DPD, quantities

such as length, time or energy lose their direct link to the corresponding quantities

of real fluids. For the DPD algorithm, this poses no fundamental problem,

since, as for MD, one can always compute using reduced units. This is what

3 Modeling Micro PIM 58

was done for all the DPD-based simulation results presented in this chapter. The

main difference from MD is that the direct conversion from reduced to real units

is lost. This has to be re-established by some additional empirical assumptions,

such as an agreement on how many MD atoms make up one DPD particle.

Additionally, the connection to real units can be re-established by matching

important properties of real fluids, such as the equation of state (EOS) or the

viscosity. How the matching was performed will be shown in more detail in the

following sections.

3.4

Matching Macroscopic Parameters with DPD

Both c-CFD and DPD need experimental thermodynamic and rheological data.

The most important information includes the EOS of the feedstock system, the

viscosity including its dependence on temperature and shear rate and the thermal

conductivity and heat capacity for the feedstock and the mold material. Additionally,

one should determine whether surface effects are relevant. This includes

measurements of the surface tension and of contact angles for feedstock

on mold material and binder on powder material.

There is a fundamental difference between c-CFD and DPD in the way in

which experimental data are used. For c-CFD, experimental datasets are input,

and they are used to set up material parameters for the underlying partial differential

equations through constitutive equations or look-up tables. In DPD, properties

of a fluid, such as the viscosity, are not specified directly, but emerge from

the underlying particle interactions of the model. In this case, the experimental

measurements are used to tune the interparticle interactions, until experiment

and simulation match.

Table 3-1 shows examples of phenomena that are well suited for modeling

with DPD. In order to reproduce these, detailed tuning of the parameters that

3.4 Matching Macroscopic Parameters with DPD 59

Table 3-1 Application fields of DPD and actions needed in order

to reproduce the phenomenon

Effect Challenge Solution

Flow Reproduce flow with particles DPD, interparticle forces as in

Equations (4), (5), (9) and (10)

Phase boundary Reproduce a flow front MDPD, interparticle forces depend

on density

Wetting and nonwetting Surface and interface energies Fluid–wall interaction forces

Heat conduction Transient thermal behavior including

boundary

Energy-conserving DPD

Mixing and segregation Reproduce multi-phase flow

with particles

Introduce discriminative particles

enter DPD must be performed. The following sections describe this matching

process for specific fluid properties. Section 3.4.1 deals with the reproduction of

the EOS. A discussion of static surface effects from an experimental and modeling

point of view follows in Section 3.4.2. Section 3.4.3 reports on experiments

and simulation for viscosity matching and Section 3.4.4 presents thermal experimental

results and gives a short overview of possibilities for reproducing the

correct thermal behavior in DPD.

3.4.1

Matching the Equation of State

3.4.1.1 The Free Energy Approach for Many-body Dissipative Particle Dynamics

(MDPD)

In DPD, the EOS can be ‘measured’, which means it can be computed. This is

done by fixing the temperature and density in a periodic system of particles and

by measuring the pressure. Several techniques exist for measuring the pressure

[16]. The virial expression for the pressure in three dimensions gives

p kBT

1

3V ij

rij f ij

11

where V is the volume of the simulated system and the sum indicates a sum

over all pairs of particles. The average is a time average over the time steps after

having reached equilibrium.

For a given choice of stochastic and dissipative forces producing a well-defined

equilibrium temperature T, the standard DPD model, as described above,

can be found to collapse to the following EOS [16]:

p kBT a2 12

where >0 is a constant and a>0 is the repulsion coefficient of the conservative

force defined in Equation (10). This shows that, for adjusting the EOS, the conservative

force is the only free parameter.

Now, the key question is whether this EOS fulfils our needs concerning the

simulation of Micro PIM. One requirement, which is definitely mandatory, is

the correct formation of a flow front, which means that we require the emergence

of an interface between the liquid and a sort of gas phase. From Equation

(12), it can immediately be seen that, for any temperature T, a single phase with

one equilibrium density will exist. Fig. 3-4 shows the consequences for a flow

simulation over a backward-facing-step geometry. The walls were modelled by

using Maxwellian reflection. This will be described in Section 3.4.2.

The snapshots show that, if liquid–vapor coexistence is not possible, no stable

flow front can be established and the DPD fluid behaves more like a gas. Particles

on a free surface spread away from it.

3 Modeling Micro PIM 60

It is obvious what has to be done in order to obtain liquid–vapor coexistence.

In MD, the simple Lennard–Jones potential can produce liquid–vapor coexistence

on an atomistic scale. One of the consequences of the coarse graining

procedure in DPD is the removal of the attractive part of the conservative force.

It should be clear that, at a free surface, such a potential leading to an interparticle

conservative force as given in Equation (10) is not able to attract particles

to the bulk of the fluid in a way that the surface remains stable.

Actually, it is possible to define purely repulsive interaction potentials which

can produce liquid–vapor coexistence by making the interaction range dependent

on density [44]. The intuitive solution is, of course, to add an attractive

force. Pagonabarraga and Frenkel [45] have developed a general procedure,

which starts out from the desired EOS that should be reproduced.

For this purpose, the free energy F of the system is expressed as a sum of the

individual free energies i of the DPD particles:

F i

i 13

where i is a local density approximation for particle i. The free energy is the

sum of a kinetic and an excess part. The variation of the excess part ex can be

taken to define the force acting on a particle by

Fi

rij

exj 14

3.4 Matching Macroscopic Parameters with DPD 61

Fig. 3-4 Flow of standard DPD fluid through a backward-facing step

The local density can be defined as

i j

wrij 15

where wrij can be chosen in a similar way as the weighting functions for the

forces are defined [see Equation (9)].

From Equation (4) and since random and dissipative forces may not contribute

to the pressure, the force is

Fi FC

i j

FC

ij 16

which, together with Equations (14) and (15), leads to

FC

ij

exi

i

exj

j

wrij

rij

eij 17

for the conservative pair interaction. Now, the correct conservative interaction

for our system can be determined by matching the desired equation of state to

the thermodynamic definition of the pressure:

p kBT 2

18

and obtaining an expression for /. For example, for the EOS

pvdW

kBT

1 b a2 19

of a van der Waals fluid, one finds

bkBT

1 b a 20

which leads to

FC

ij

bkBT

1 bi a

bkBT

1 bj a

w

rij rijeij 21

One can see that, generally, the resulting forces are density-dependent manybody

forces.

Trofimov et al. [46] determined that the computed EOS deviates slightly from

the desired one. An improvement was achieved by iteratively determining a ‘better’

local density approximation, which minimizes the difference between the

3 Modeling Micro PIM 62

average i and the global density n=N/V, where N is the total number of DPD

particles in the system and V the total volume.

3.4.1.2 Warren’s Approach for MDPD

Warren [47] directly modified the repulsion coefficient a of the original conservative

force from Equation (10), which consequently also changed the EOS. The

simple quadratic dependence on density was modified by making the repulsion

coefficient density dependent. More precisely, the force from Equation (10) was

made attractive by choosing a<0 and adding a repulsive many-body force of the

form

FC

ij Bi jwCrijeij B 0 22

with a different cutoff range rd rc and

wrij

15

2

r3

d

1

rij

rd 2

23

for the computation of the local densities of a 3D DPD fluid according to Equation

(15). For this computation, the same cutoff distance rd was used.

Results

In [47], the above was tested successfully for the static case of a pending droplet.

Here, the dynamic test case is investigated. One of the parameter sets from [47]

was taken (a=–40, B=40, rc=1, rd=0.75) and, for temperature adjustment, the

Lowe–Andersen thermostat [22] was used, instead of the dissipative and stochastic

forces described in Equations (5)–(7). This thermostat will be described in

detail in Section 3.4.3.

The step geometry of Fig. 3-4 was considered again, in order to test whether

stable flow fronts can be obtained in a dynamic non-equilibrium and non-stationary

situation. Fig. 3-5 shows that this feature was successfully achieved.

Two conclusions can already be drawn at this stage. First, since the flow front

emerges naturally from inter-particle interactions, DPD is a more natural flow

solver for fluids with free surfaces than standard c-CFD, where the flow front

has to be tracked in order to determine, for example, which viscosity has to be

assigned to a certain flow region.

Second, already this simple test case allows for a qualitative prediction of the

jetting effect, i.e. the free surface flow of the mold mass without contact with

the mold’s wall. In the example, this feature is clearly visible. It turns out that

halving the driving force reduces the jetting effect considerably. The effect never

disappears completely. Whether it leads to severe failures in the molded micropart

depends on the length and geometry of the remaining flow path. Reducing

3.4 Matching Macroscopic Parameters with DPD 63

the driving force to one-tenth of the original value leads to an arrest of the fluid

flow at a position only a few multiples of rc behind the inlet, i.e. in the narrow

part of the geometry. This means that short shots can already be observed.

The next step is to take the experimentally determined Tait parameters, to

find a polynomial approximation and to determine the corresponding conservative

DPD interactions from it following the procedure described above. Then,

the DPD-EOS has to be computed in order to test how well the original EOS

has been reproduced. If this test is successful, the DPD units can be synchronized

with the real units, based on this thermodynamic matching. A similar

synchronization can be performed based on a rheological matching, which

means on a matching of the viscous flow behavior (see Section 3.4.3).

It was pointed out in [47] that the gas phase is very dilute. This is reasonable,

since it represents the pure gas phase of the liquid material, which one would

only approximately obtain by equilibrating a droplet in high vacuum. In PIM

the material is also injected into vacuum, but not high vacuum. This means

that one has to check if additional DPD particles of a second species representing

the air have to be added to the simulation. However, their presence is definitely

less important than for macroscopic injection molding, where one typically

does not evacuate the mold.

3.4.1.3 EOS Measurement, Modeling Pressure, Specific Volume and Temperature

(pvT)

The interrelation between the state of matter data, i.e. pressure p, specific volume

v and temperature T, allows for the prediction of a material’s behavior under

injection molding conditions. Different methods exist for the determination

of the data for the isobaric pvT plot, where the specific volume v, i.e. the reciprocal

density, is plotted against temperature at constant pressure values. Material

properties such as compressibility and phase transformations are responsible

for non-linear characteristics of the diagrams. Depending on the method used

for determination, the pvT data can also serve for thermal expansion calculations

3 Modeling Micro PIM 64

Fig. 3-5 Flow of MDPD fluid over a backward-facing step

of the material during the filling phase or volumetric shrinkage calculations

during the packing phase of the injection molding cycle.

The state of matter diagram can be measured, for instance, with a high-pressure

capillary rheometer. A special nozzle is used to realize a closed system

filled with material. The pvT test is performed on cooling from the processing

temperature to well below the ejection temperature to avoid any decomposition

at this time. Typically the measurement starts from the molten state at normal

processing temperature since it is necessary to make sure that no voids are enclosed

in the molding material. Data are logged on a series of isothermal runs

while the pressure is raised to several hundred MPa for each isotherm. The

measurement of the specific volume is subsequently repeated during heating to

the maximum processing temperature, since decomposition at this time will

not further influence the data. A schematic plot of specific volume versus temperature

for both a crystalline and an amorphous material is shown in Fig. 3-6.

The pvT relationship is typically modeled using a modified two-domain Tait

equation [54–56]:

VT p V0T 1 C ln 1

p

BT 24

where V(T, p) is the specific volume at temperature T and pressure p, V0 is the specific

volume on the zero gage pressure isobar, C=0.0894 is a universal constant for

this model [57], B is the pressure sensitivity of the material. Two temperature domains,

one greater than the transition temperature Ttrans and one less than Ttrans,

are required to model the relationship because the thermodynamic properties of

polymers change at this temperature. Ttrans at zero gage pressure is denoted b5.

The specific volume obtained by extrapolating the zero-pressure isobar curve to

the transition temperature is denoted b1. This value is the same for both domains

when crossing the glass transition. When the material is semicrystalline, however,

3.4 Matching Macroscopic Parameters with DPD 65

Fig. 3-6 Typical transitions in pvT measurement, scheme of

determination of the Tait parameters for (a) amorphous and

(b) crystalline transitions

the transition due to crystallization is accompanied by an abrupt change in specific

volume, such that b1m, the melt specific volume at Ttrans on the zero-pressure isobar,

is greater than b1s. For each domain, the rate of change of specific volume with

temperature at zero pressure is measured by the respective b2 constants:

V0 b1m b2mT b5 for T Ttrans 25

V0 b1s b2sT b5 for T Ttrans 26

The remaining constants, b3 and b4, characterize the pressure sensitivity B of

the material:

BT b3m expb4T b5

for T Ttrans 27

BT b3s expb4sT b5

for T Ttrans 28

In particular, a positive b4 reflects a specific volume which becomes more pressure

sensitive with increasing temperature.

Typically, the binder for -PIM consists of more than one thermoplastic component

(see Chapter 11.2). Therefore, the pvT plot shows more than one transition

temperature. For the modeling and simulation of the molding step, the typically

observed domains are the solid state (at temperatures below the first

Ttrans1) and the state where all binder components are completely molten (above

Ttrans2). To validate a two-domain Tait equation for complex feedstock systems

in a c-CFD simulation tool, it is necessary to skip the temperature range between

the first and the last Ttrans where the material is only partly molten. The

value for b5 is then defined by the intersection of the curves based on the values

beyond the first Ttrans1 and above the highest Ttrans2 (see Fig. 3-7). Because of

3 Modeling Micro PIM 66

Fig. 3-7 Determination of the Tait parameter b5 for multiphase

compounds, idealized v,T diagram

this approximation, the cooling effects during the injection phase cannot be described

accurately by using the mentioned two-domain Tait model on multiphase

compounds. Therefore, considerations have to be made on extending the

model, applying it repeatedly or by developing a multi-phase model. In [57] and

[58] an extended non-equilibrium Tait model is described, introducing further

terms Vt(p,T) with additional parameters.

3.4.2

Fluid–Wall Interaction: the Contact Angle

In addition to fluid–fluid interactions, it is important to reproduce correctly the

fluid interaction with the mold wall. Computationally, three types of fluid–wall

interactions can be distinguished. First, there is simple mechanical interaction,

which means that the fluid is prevented from penetrating a certain region delimited

by a solid wall. Second, there is friction between the liquid and the wall.

This usually leads to the so-called no-slip condition at the wall, which means

that, directly at the wall, the parallel velocity components vanish. At high shear

rates, this no-slip condition is often violated. Third, in the microfluidic regime,

capillary effects can become relevant. It still has to be determined whether this

is also the case for -PIM.

Estimates for -PIM indicate that, for microstructures with diameters below

100 m, capillary effects become important [48]. These microscale surface effects

can either hinder or boost the flow, depending on the contact angle between

the feedstock and the mold material. On the other hand, in [41] it is argued

that surface tension, the driving force for the capillary effect, can be neglected

for polystyrene, with channel sizes over 1 m and for typical pressures

(several MPa to 200 MPa) applied in polymer injection molding.

The basis of their reasoning is the Washburn Equation (3). For the observed

fluid (polystyrene, S=0.033 N m–1), p is negligible compared with the applied

pressures during injection molding, for channel sizes down to less than 1 m.

As mentioned in Section 3.2, the possibility cannot be excluded that capillary effects

play a role in -PIM because of high pressure loss. In the following, some

possibilities for modeling these effects will be shown.

Similarly to the experimental domain, one can distinguish effects of fluid–

wall interaction in the modeling domain. In c-CFD, one usually defines a slip

or no-slip condition for hydrodynamics and a surface energy between liquid and

vapor and a contact angle between liquid and solid for hydrostatics.

In DPD, all fluid–wall models are dynamic in nature. Static properties are obtained

as solutions of equilibrated particle dynamics simulations. One can define

different kinds of reflection mechanisms for particles hitting a wall and, additionally,

interactions can be introduced between DPD particles and the wall.

Now, the chosen model and some possible alternatives for modeling the reflection

mechanism are shown, and then the introduction of additional interactions

is discussed.

3.4 Matching Macroscopic Parameters with DPD 67

3.4.2.1 Reflecting Boundary Conditions

For our simulations, including those described in Section 3.4.1, Maxwellian reflection

[49] was applied. This means that a particle hitting a wall is reflected

back into the system with a new velocity drawn from a Maxwell distribution.

This distribution corresponds to a temperature which is pre-defined for the

wall. Therefore, the wall acts as an additional thermostat. For a velocity vector v

in 3D, the new velocity can be obtained by drawing the perpendicular velocity

component vp from a Rayleigh distribution:

vp

m

kBTw

vp exp

mv2

p

2kBTw

29

and both tangential components vt from a Gauss distribution centered at zero:

vt 2

mkBTw1

2 exp

mv2

t

2kBTw 30

This boundary condition was used without any additional interactions. The effect

can be seen in Fig. 3-8. Here, results are presented for a simulation where

a gravitational force was added to the system, and which points perpendicularly

to the wall acting as a surface. The wall temperature and the fluid temperature

were both set to T=1. The droplet can be obtained, for instance, by starting

with a cuboid or cylindrical particle distribution which does not fill the whole

simulation domain. In our case, the droplet contains around 500 DPD particles.

A few additional DPD particles form the dilute gas phase.

Very strong de-wetting behavior can be observed, which is reasonable because

of the purely repulsive interaction. Additionally, it is interesting to observe that,

even for a wall temperature T 0, the contact angle is virtually unaltered.

3 Modeling Micro PIM 68

Fig. 3-8 Around 500 DPD particles forming a 3D droplet with

large contact angle. A gravitational force and a wall at the

bottom were included. The wall was modeled by Maxwellian

reflection only. Additionally, a vapor phase can be observed

Alternative, non-thermalizing reflection mechanisms are specular or bounceback

reflection [50]. Neither changes the de-wetting behavior because they still

produce purely repulsive fluid–wall interactions.

3.4.2.2 Interactions for Reproduction of Wetting and Friction

In order to obtain contact angles smaller than 90, it is necessary to introduce

attractive interactions between the fluid particles and the wall. A straightforward

method is the introduction of frozen particles at the wall [6]. The term ‘frozen’

denotes that these particles remain fixed at their initial positions, which means

that forces acting on them are ignored. However, the wall particles may exert a

force on the fluid particles.

Wetting behavior should be obtained if, for instance, the same MDPD interactions

are applied to the fluid–wall interaction, which were already used for the

fluid–fluid interaction in Section 3.4.1.

An example is shown in Fig. 3-9. Three stages of a spreading droplet on a surface

can be seen. The gravitational force is the same as before, and the wall has

been modeled by applying Maxwellian reflection and frozen wall particles with

a density of =6. The frozen wall particles, which are situated below the line,

are not shown. For this setup, even complete wetting has been achieved. This

enables us now to fix a desired contact angle between the two extremes of

Figs. 3-8 and 3-9 by adjusting the interaction forces between fluid and wall particles.

The thin film of DPD particles at the edge of the droplet, which can be

observed during wetting, is reminiscent of the well-known precursor film of real

spreading droplets (e.g. [51]).

3.4 Matching Macroscopic Parameters with DPD 69

Fig. 3-9 Around 500 DPD particles forming a 3D droplet which

shows complete wetting. As in Fig. 3-8, a gravitational force and a

wall at the bottom were included in the simulation. The wall was

modeled by Maxwellian reflection and frozen wall particles with density

=6. For the fluid–wall interactions, the same MDPD forces as

for the fluid–fluid interactions were applied

Alternatively to frozen wall particles, it is possible to obtain integral expressions

for the force exerted by the wall on a particle at a certain position. For infinitely

extended flat walls and standard DPD forces (see Section 3.3), these expressions

were derived in [50].

For arbitrary wall geometries, it is probably more convenient to compute the

force field from frozen wall particles, which can be removed afterwards. This saves

some computational time since the forces are computed only once and stored in a

look-up table for small cubic boxes in the interaction range of the walls. For

MDPD forces, this procedure is less straightforward, since the force from the wall

acting on the fluid particle also depends on the local density of the fluid particle

itself, which is not known beforehand. If the local density of wall particles should

also include contributions from the fluid particles, this is also only known at runtime.

The latter could be circumvented by defining an average density of the wall,

which hence is independent of the state of the fluid.

Whereas slip or no-slip conditions are explicitly defined in c-CFD, they

emerge indirectly from the fluid–wall interactions in DPD. Currently, the best

way to obtain no-slip conditions in DPD is the combination of specular reflection

with either integral or discrete fluid–wall interactions.

The question remains of whether it is really desirable to impose no-slip on

our system since, in this way, it is impossible to determine any transition from

no-slip to slip at a certain shear rate. Usually, one assumes no-slip in -PIM

modeling. However, since high shear stresses and velocities occur, this assumption

is highly questionable.

3.4.2.3 Measurements of Contact Angle Between Molding Material

and Mold Insert

For the characterization of contact angles, most measurements in practice are

performed with a sessile drop on a planar surface. In this case, the contact angle

of the polymeric binder on the solid surface is a measure for the intermolecular

interaction between these two materials. The methods used to determine

contact angles are not only crucial for the fabrication of compound materials.

During an injection cycle, the capillary pressure influences the filling of small

cavities. According to Equation (3), the pressure difference p in a thin capillary

depends on the surface tension S of the fluid, the contact angle between fluid

and capillary surface and the diameter d of the capillary. With decreasing component

dimensions, and thereby smaller structures in a molding insert, the capillary

pressure rises and lessens the necessary filling pressure. Both effects are

parameters which can be implemented in a simulation based on DPD.

Young derived an equation for sessile drops which specifies the equilibrium

of forces of surface and interfacial tensions SV, LV and SL that are linked together

by the contact angle:

LV cos SV SL 31

3 Modeling Micro PIM 70

The contact angle can be measured in the three-phase region (see Fig. 3-10)

consisting of the solid S, the applied liquid L and the ambient gas phase V.

One of the most widely used measuring methods for contact angles is based

on an optical contour analyzing system. The fluid drop rests on an exchangeable

planar surface in an optional furnace which controls the ambient temperature

and atmosphere. The contact angle can be measured manually with a goniometer

eyepiece or digitally with a video system combined with suitable software.

The final binder-powder compound that is used as the -PIM feedstock cannot

be measured with this method because of its high viscosity and inhomogeneous

melting behavior. However, the contact angle of a feedstock on a surface

is primarily defined by its fluent component and therefore the contact angle of

the binder should match that of the compound to a good approximation.

Fig. 3-11 shows, as an example, the contact angle of two different binder components

on a steel surface matching the mold insert material. However, the inhomogeneous

melt behavior of binder B causes large deviations. It is obvious

that both binder components spread on the solid material. This characteristic,

combined with a decreased binder viscosity at elevated temperatures, permits

improved feedstock fabrication.

3.4 Matching Macroscopic Parameters with DPD 71

Fig. 3-10 Contact angle at sessile drop in force equilibrium

Fig. 3-11 Contact angle of two different binder components on a steel surface.

Measured using a G10 Contact Angle Meter (DSA10) from Kruss AG

3.4.3

Viscosity Modeling and Measurement

Both experiment and DPD need a measurement setup to determine the transport

parameters, e.g. the viscosity. In DPD a viscosimeter is clearly an algorithm

that has to be added to the program code. From MD, these kind of measurements

are well known. By adjusting the parameters in DPD, the results from

experimental measurement have to be reproduced. Note that the adjustment of

the DPD parameters may not allow for the matching of all macroscopic variables

at once.

3.4.3.1 The Parameters in DPD

Once the EOS is adjusted by the conservative interactions, the rheological behavior,

which means the viscosity, can be fixed. Viscosity can be adjusted by

modifying the dissipative force. This can be seen from the transport properties,

which were derived for the limit t0 in [53] by solving a Fokker–Planck–

Boltzmann equation for DPD using the Chapman–Enskog method.

Since the stochastic force depends on the dissipative force according to Equation

(7), it is the thermostat that influences viscosity. This also means that, if

the range of viscosities that can be reached with the current thermostat is unsatisfactory,

another thermostat may be used without distorting the previously obtained

EOS.

In fact, one disadvantage of the thermostat, consisting of the dissipative and

stochastic forces described above, is the low Schmidt number (Sc) that it produces.

The Schmidt number is the ratio of the kinematic viscosity to the diffusion

coefficient, which is of the order of 1 for this thermostat. However, for liquids,

Sc should usually be larger, for instance around 1000 for water. Therefore,

it would be convenient if it were possible to increase the viscosity. This is also

useful if the DPD fluid should represent a relatively viscous PIM feedstock. Additionally,

this would increase the time-scale of the system.

Another disadvantage is the non-trivial integration of the emanating equations

of motion as already mentioned in Section 3.3. Both drawbacks can be

overcome by applying the Lowe–Andersen thermostat [22]. In this algorithm, it

is decided with a probability of t whether to thermalize the relative velocity

vij of a given pair of particles with a particle to particle separation rij <rc.

The value plays a similar role to the friction coefficient in Equation (5). By

construction of the algorithm, has an upper limit of 1/t or, conversely, there is

a minimum time of 1/ which is needed for complete thermalization of the system.

Therefore, larger friction coefficients not make sense. However, in practice,

the same limitation exists for the dissipative and random forces of the original

thermostat, since there exists an upper limit of the absolute value of a force acting

on a particle due to the limited accuracy of any integration algorithm.

The new relative velocity v

ij is drawn from a Maxwell distribution with variance

ij 2kBTm . Then, the new particle velocities become

3 Modeling Micro PIM 72

v

i vi ij v

j vj ij 32

where

ij

1

2

eijv

ij vij eij 33

Results

A rough comparison was made of the accessible viscosity ranges for the three

cases of standard DPD, MDPD with the original thermostat and MDPD with

the Lowe–Andersen thermostat. Each simulation was performed in a periodic

box with 1728 randomly arranged particles at a density of =5 and a temperature

of T=1. The time step was set to t=0.02. Note that, as already mentioned in Section

3.3, =5, T=1 and t=0.02 are all given in reduced dimensionless units.

The viscosity was computed via the transverse current correlation function

Ct k

1

j2 j0 kjt k 34

where jt k is a shear wave oscillating, for example, in the y-direction along the

x-axis:

jt k i

vy

i t expikxt

35

The kinematic viscosity can be obtained from the decay of the transverse current

correlation function [53]:

Ct k expk2t 36

For a measurable decay, the smallest k fitting in the periodic box was imposed

with a suitable amplitude as an initial condition on the system.

Standard DPD with the repulsive conservative force from Equation (10) and

a=40 reaches =0.31 for =3 (=4.5). If the conservative force is replaced by

the MDPD interactions also used in Section 3.4.1, the viscosity increases to

=1.31 for the same . Reducing to 0.5 (=0.125) results in =1.14, but with

a temperature deviation of roughly 20% from the desired value. This means

that the friction coefficient is too low for the thermostat to work properly. Increasing

to 9 (=40.5) gives =2.50. With the chosen time step, a further increase

produces numerical instabilities in the integration algorithm. Therefore,

the latter value can be seen as an upper limit for this thermostat at t=0.02.

For the Lowe–Andersen thermostat, the probability t was varied between

0.0625 and 1. The former means that, on average, 6.25% of the particle pairs

with rij <rc are thermalized, whereas in the latter case, every pair in the interac-

3.4 Matching Macroscopic Parameters with DPD 73

tion range is thermalized. Since the time step was kept constant at t=0.02, the

probability range corresponds to a range of =3.125–50. For all simulations,

the thermostat was able to keep the temperature constant at the desired value

T=1. The results are plotted in Fig. 3-12. It can be seen that the Lowe–Andersen

thermostat achieves viscosities between =3.02 and 17.27, which is indeed

larger than what is obtainable with the random and dissipative force.

3.4.3.2 Shear Viscosity Measurements

The viscosity was measured using a high-pressure capillary rheometer, as e.g.

sketched in Fig. 3-13. The piston of the rheometer presses the material at a constant

temperature and flow rate Q through a cylindrical die of known length l

and diameter d. The apparent shear rate on the wall of the tube is defined by

the equation

a

32Q

d3 37

The wall shear stress

w can be calculated from the measured pressure loss p

across the die [62]:

w

p

4

l

d

38

Therefore, the apparent shear viscosity a can be calculated from the measured

values of Q and p and from the geometric data for the die:

3 Modeling Micro PIM 74

Fig. 3-12 Kinematic viscosity of the MDPD fluid with Lowe–

Andersen thermostat plotted against the dissipation probability

t. All data points are averages over only 10 simulations.

This explains the large error especially for high dissipation

probabilities

kinematic viscosity [reduced units]

dissipation probability

25

20

15

10

5

0

0 0.2 0.4 0.6 0.8 1

a

w

a 39

The data from the viscosity measurements are fitted to the Cross model [63],

which handles both the Newtonian and the power law flow regimes found in

polymer rheology. The model treats viscosity as a function of temperature, shear

rate and pressure [Equation (40)]. Compared with other models in current use,

the constants of the Cross model have physical significance. The transition between

two regimes is characterized by the shear stress level at which shear thinning

starts. The slope of the power law curve is characterized by (1–n). The parameter

corresponds to the shear modulus and 0 is the viscosity in the region

where the Newtonian behavior predominates.

3.4 Matching Macroscopic Parameters with DPD 75

Fig. 3-13 Cross-section of a high-pressure capillary rheometer: 1,

test chamber; 2, test flow cylinder; 3, mass pressure probe; 4, full

circle capillary; 5, capillary uptake; 6, input for temperature probe;

7, capillary nut; 8, cap closure; 9, Pt100 temperature sensor; 10,

hexagonal screw; 11, band heater zone 3; 12, band heater zone 2;

13, band heater zone 1; 14, area heater zone 1; 15, pressure hole

However, as the bulk temperature approaches the solidification temperature,

this model underestimates the viscosity rise with decreasing temperature.

Therefore, the corresponding measurement standard ASTM D 3835 [64] requires

the Weissenberg–Rabinowitsch correction [60], which considers the difference

between apparent and actual shear rates, and the Bagley correction for the

entrance pressure loss:

T a p

0T p

1

0 a

1n 40

3.4.4

Thermal Conductivity and Thermal Expansion, Measurement and Modeling

Thermal conductivity is a quantity that describes the ability of a homogeneous

material to transfer heat by conduction. This quantity is a transport parameter

that enters a distributed parameter description of a material and does not directly

enter DPD. Nevertheless, it can be measured in DPD and therefore delivers

useful input for the material modeling and its accuracy within the DPD

approach. The same arguments hold true for thermal expansion.

For a solid material, the value of the thermal conductivity increases with temperature

and is normally almost independent of pressure changes. The thermal

conductivity can be calculated from the thermal diffusivity a if the density

and the specific heat capacity cp is known:

acp 41

The values of the density can be taken directly from the pvT plot by extrapolating

the specific volume to ambient pressure and calculating the reciprocal value

for each temperature (Fig. 3-14). The measurement of the specific heat capacity

is typically carried out by differential scanning calorimetry (DSC) using a sapphire

sample as reference (Fig. 3-15). The thermal diffusivity can be measured

precisely with the laser-flash method allowing for short measurement times

even at higher temperatures. The heating source and the temperature sensor

are coupled without contact, avoiding extensive preparation of the sample. A

short laser flash heats the top surface of the discoidal specimen (ca. 1 mm

thickness). Additionally, the whole assembly can be installed in a furnace to

measure the values of a at higher temperatures. The inserted heat spreads over

the specimen and warms the lower surface. The time-dependent temperature

distribution is given by the thermal diffusivity a. An infrared sensor detects the

warming and the measured signal is plotted. Mathematical analysis using numerical

models provides the thermal diffusivity and subsequently the thermal

conductivity can be calculated. However, since the thermal conductivity must be

experimentally determined by measuring the thermal diffusivity, the mass den-

3 Modeling Micro PIM 76

sity and the specific heat capacity as given in Equation (41), it might be useful

to reproduce these quantities by directly DPD.

In order to measure thermal expansion, a specimen is prepared and placed at

the bottom of the outer dilatometer tube with the inner one resting on the specimen.

The digital indicator, firmly attached to the outer tube, is in contact with

3.4 Matching Macroscopic Parameters with DPD 77

Fig. 3-14 Calculated thermal conductivity and measured specific

heat capacity of a -PIM feedstock material filled with 17-

4 PH powder (94 wt%) in the relevant molding temperature

range

the top of the inner die and indicates variations in the length of the specimen

with changes in temperature (see Fig. 3-16).

Temperature changes are efferted by a furnace in which the complete experiment

is performed. The thermal expansion coefficient is defined as [61]

L

LT 42

where L is the initial length of the specimen, T is the change in temperature

and L is the change in length. Measurements are performed on specimens cut

from molded parts in the direction of flow and transverse to it (Fig. 3-17).

The representation of the temperature as an internal variable of the DPD particles

requires the introduction of an additional degree of freedom. Using Español’s

notation [25], this degree of freedom i is introduced for each particle, representing

its internal energy, and, additionally, an entropy si si which is

needed for the definition of a ‘temperature’ Ti=(sii1 for each particle.

3 Modeling Micro PIM 78

Fig. 3-15 Temperature-dependent density change calculated

from pvT measurement of a -PIM Zirconia feedstock

Fig. 3-16 Tube dilatometer

density [g ·cm3]

temperature [C]

5.7

5.6

5.5

5.4

5.3

5.2

20 40 60 80 100 120 140 160

The additional equation of motion for i is

i jji

m

2

vij FD

ij qD

ij

m

2

2

ijw2

Rrij

1

t jji

m

2

vij FR

ij qR

ij 43

In [24], qD

ij is called ‘mesoscopic heat flow’ and is computed as follows:

qD

ij ij

1

Ti

1

Tj w

Drij 44

Additionally, there is a ‘random heat flux’ [25] qR

ij with

qR

ij ijw

Rrij

ij 45

ij can be interpreted as the thermal conductivity between two particles. It depends

on the particle energies of individual particle pairs and it is assumed that

ij =ji. The factor ij is a noise amplitude. Also, and from Equations (5)

and (6) now transform, in principle, to coefficients ij and ij for individual

pairs. w

D (rij) and w

R (rij are additional weight functions needed for the corresponding

changes of the particle energies.

ij is a second random number with

the same characteristics as for ij in Section 3.3. For simplicity, it is assumed

3.4 Matching Macroscopic Parameters with DPD 79

Fig. 3-17 Measured linear expansion coefficient of a commercially

available zirconia feedstock calculated from experimentally

determined thermal expansion data

here that all particles possess the same mass m. Otherwise, for the particle interactions,

a geometric mean would have to be calculated.

Again, the coefficients are not independent, but the following relations hold:

w

R

2 w

D and 2

ij 2ij 46

Additionally, Equation (7) still holds and Equation (8) is replaced by

ij

m

2kBTij

2

ij 47

with

T1

ij

1

2

1

Ti

1

Tj 48

representing a mean inverse temperature of two particles i and j. The thermal

conductivity as measured by experiment (Fig. 3-14) must be reproduced by the

coefficients entering Equations (44) and (45). Therefore, the respective measurement

of thermal conductivity has to be performed in DPD. We expect that the

Lowe–Andersen approach (see Section 3.4.3) is also applicable in this case.

3.5

Test Geometries

To verify our computational approach, test geometries for experimental verification

were developed. All molded parts consist of two identical specimens that

are connected in one layer rotated at 180. By placing the sprue in the middle

of the shape, identical component geometries along the melt flow path are obtained.

Multiple temperature and pressure sensors are positioned in the cavity

to characterize the state of the feedstock related to the position and to compare

it with simulation results. The different mold inserts serve for the evaluation of

the behavior of the feedstock. The test geometries were performed in double

cavities to realize the implementation of the instruments (Fig. 3-18). The mold

inserts shown serve as a compromise between minimal sensor diameter and

real microcavities. With respect to the sensor size (diameter 2.5 mm for pressure

sensor) and the required supplies it is currently not possible to create

smaller cavities without affecting the material flow by the sensors.

The different test geometries are designed for different purposes as follows:

Spiral: for investigation of the bulk factor in long cavities, i.e. ratio of flow

length to wall thickness.

Direction change: angle of 90 to investigate the temperature and pressure

drop and, as necessary, segregation at the corner.

3 Modeling Micro PIM 80

Injector: component with an obstacle behind the injection point to analyze

the material blending or transport connection after the barrier, characterization

of compression effects.

Diffusor: component with an obstacle at the end of the material flow to study

the filler content and the flow line problem and also characterization of decompression

effects.

Stair: part with steps to analyze the temperature and pressure changes in the

mold insert before and after steps.

Bending bar: the green compact and the sintered CIM part can be used directly

for the determination of solid-phase material properties.

Simulations with c-CFD programs have shown that most of the test cases cannot

be computed precisely enough to give valuable predictions for the process

parameters needed in Micro PIM [65]. Moreover, it is very difficult to incorporate

models for the description of particle flow in a continuum approach,

whereas in DPD the problem of a flow of solid particles in a liquid environment

is inherently accounted for.

3.5 Test Geometries 81

Fig. 3-18 CAD drawings of the specimen in the test geometries

tool. For a description of the geometry application, see

the text. The photograph shows the mold insert for the ‘spiral’

cavity with the connectors for heating and cooling

3.6

Conclusion

This chapter has reported investigations in modeling and simulation of Micro

PIM with a new fluid dynamic description using DPD. The individual parameters

that enter DPD modeling of this process have to be adjusted using different

specially designed experiments for the injection molding process. The most obvious

difference with respect to conventional approaches is that the parameters

measured in the experiment also have to be implemented as special measurement

experiments in the DPD, similarly to what is known from MD. The advantage

of DPD over c-CFD tools is that the computational effort for free surface

dynamics is lower and the modeling flexibility is larger. This is of particular

interest when two-phase flow comes into play, as is the case in Micro PIM. The

DPD model cannot replace a c-CFD modeling and simulation but it can help to

obtain more precise simulation results in regions where micro-features are relevant

and are, by their nature, not incorporated in a c-CFD simulation program.

This raises the question of proper handling of simulation regions with the respective

model and therefore their coupling, which is the subject of current investigations.

3.7

Acknowledgment

Financial support by the German Research Foundation (DFG) within the collaborative

research center SFB 499 Development, Production and Quality Assurance

of Primary Shaped Micro Components from Metallic and Ceramic Materials is gratefully

acknowledged.

3 Modeling Micro PIM 82

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II

Tooling

Advanced Micro and Nanosystems Vol. 3. Microengineering of Metals and Ceramics.

Edited by H. Baltes, O. Brand, G. K. Fedder, C. Hierold, J. Korvink, O. Tabata

Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 3-527-31208-0

Abstract

Among the most promising production technologies for producing microparts

in medium to high series are replication technologies, e.g. injection molding.

Replication processes are characterized by the injection of feedstock/material in

negative forms, the so-called cavities. To provide these cavities, different production

technologies such as cutting or material removal processes can be used.

This chapter presents the state of the art of special microproduction technologies

and points out strategies for fabricating micromolds and cavities.

Keywords

production technology; micromachining; micromold inserts

4.1 Introduction 88

4.2 Mold Inserts 88

4.3 Cutting Processes 90

4.3.1 Cutting with Geometrically Defined Cutting Edges 90

4.3.1.1 Diamond Cutting Tools 90

4.3.1.2 Cemented Carbide Tools 90

4.3.1.3 Cutting of Steel as the Most Important Aim of Research 91

4.3.1.4 Microdrilling 93

4.3.2 Cutting with Geometrically Undefined Tool Edges 95

4.3.2.1 Microgrinding 95

4.4 Ablation Processes 98

4.4.1 Electrodischarge Machining (EDM) Processes 98

4.4.1.1 Introduction 98

4.4.1.2 General Functioning of the Process 98

4.4.1.3 Micro-EDM Processes 99

4.4.1.4 Workpiece Materials 99

4.4.1.5 Electrode Materials and Manufacturing 100

87

4

Strategies for the Manufacture of Mold Inserts

J. Fleischer, C. Buchholz, J. Kotschenreuther, Institute of Production Science (wbk),

University of Karlsruhe (TH), Germany

Advanced Micro and Nanosystems Vol. 3. Microengineering of Metals and Ceramics.

Edited by H. Baltes, O. Brand, G. K. Fedder, C. Hierold, J. Korvink, O. Tabata

Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 3-527-31208-0

4.4.2 Laser Beam Machining (LBM) 100

4.4.2.1 Introduction 100

4.4.2.2 General Functioning of the Process 101

4.4.2.3 Laser Beam Sources and Machining Methods 101

4.4.2.4 Laser Beam Machining/Structuring 102

4.5 Conclusions 103

4.6 References 104

4.1

Introduction

Microtechnological approaches to miniaturization are based on processes transferred

from silicon technology. In particular, these are photolithography, processes

of depositing thin layers, etching techniques and the cost-efficient concepts

of batch manufacturing (see Chapter 8).

An evolutionary approach is offered by the processes of precision engineering

in which conventional methods of producing miniaturized components are

developed further. An example of this is the use of new methods of ultraprecision

machining for manufacturing the smallest components or structures. Mechanical

processes such as cutting, drilling and grinding and material removal

processes such as electrodischarge machining (EDM) or laser beam machining

(LBM) are used for the small and medium batch production of miniaturized

systems and microcomponents. These technologies can also be applied for

macroscopic components with microstructured functional elements. LBM is

especially suitable for applications demanding high precision for small-scale

manufacturing while excluding conventional methods. In combination with

electrochemical or electrodischarge processes or with milling, it is an ideal tool

for producing microstructures [1].

4.2

Mold Inserts

Micromolds place different demands on manufacturing methods. The most

commonly used methods are LIGA (lithography, electroplating and molding),

micromilling, EDM and LBM. LIGA is a process for producing microstructures

in a resist and then electroplating them. These structures are reproduced in a

metal, which can be used independently or as a tool for molding other materials.

In order to be able to find out which process is the most suitable for a certain

manufacturing task, a catalogue is being built which assigns certain design

features to a manufacturing process. The features that determine the manufacturing

method are:

hardness of the mold material;

quantities needed;

4 Strategies for the Manufacture of Mold Inserts 88

smallest structure size (embossed or engraved);

aspect ratio;

manufacturing time;

machining result (burr formation, surface quality);

electrical conductivity;

wall properties (steep, angled);

available budget;

complexity of geometry (2.5D or 3D).

Fig. 4-1 shows a micromold whose smallest feature is a 50 m radius at the

tooth tip. Hence the tool diameter needs to be 100 m or less. The workpiece

material is brass.

In this case, LIGA, micromilling, EDM and LBM are possible manufacturing

methods. However, milling would be the fastest process with sufficient accuracy.

With a mold aspect ratio exceeding three, a milling process cannot be chosen,

since tools of this length are not available. The same holds true for very hard

workpiece materials exceeding a hardness of 62 HRC or if very high geometric

accuracies are necessary.

Smallness, aspect ratio and accuracy are the benefits of the LIGA process;

costs and manufacturing time are the down side. Micromilling can only manufacture

materials up to approximately 62 HRC and so far is limited to a 100 m

tool diameter and an aspect ratio of 2 in the case of a 100 m tool. Satisfying

surface roughnesses of Rz0.3 m, short manufacturing times and a high degree

of freedom with five-axis milling are positive aspects of this process. EDM

can produce smaller structures than milling in harder materials and with very

high aspect ratios. It is a rather slow process, limited to electrically conductive

materials, and produces a slightly worse surface roughness than milling. LBM

4.2 Mold Inserts 89

Fig. 4-1 REM picture of a microgear mold (source: SFB 499)

can achieve small feature sizes (beam diameter 10 m), high aspect ratios in

almost any material in fairly short times and, in contrast to milling and EDM,

suffers no tool wear. However, surface roughness and flexibility of geometry are

among the disadvantages of this process.

4.3

Cutting Processes

4.3.1

Cutting with Geometrically Defined Cutting Edges

4.3.1.1 Diamond Cutting Tools

In ultraprecision machining, cutting tools of monocrystalline diamond are almost

exclusively used. Diamond has a very low friction coefficient and an excellent

thermal conductivity, which have a favorable effect on the cutting process.

The main advantages of this cutting material, however, are its great hardness

and the possibility of producing a cutting edge of almost atomic sharpness. The

production of extremely sharp cutting edges belongs to the most important

tasks which have to be fulfilled in microcutting. A cutting edge sharpness in

the sub-micrometer range allows the production of surfaces with roughnesses

of a few nanometers, providing them with an optical quality.

Materials used in diamond machining are aluminum, copper, brass, nickel–

silver and the so-called electroless nickel, an amorphous nickel–phosphorus alloy

allowing the production of a particularly good surface and low burr formation

with a comparatively high hardness. The group of ferrous products, especially

steels, is not yet suitable for diamond cutting. Owing to the high process

temperatures and the high affinity of carbon to iron, diamond is subject to a

graphitization process leading to exorbitant tool wear. There are developments

at various research facilities to solve these problems and to establish a method

which allows the cutting of steel with diamond tools. At present, the approach

of superimposing ultrasonic excitation on the tool movement or a preceding nitriding

process of the workpiece [2] seem to be the most promising approaches.

4.3.1.2 Cemented Carbide Tools

At present, the cutting process most commonly used and most extensively examined

is ultraprecision turning. This process is applied for the production of

molding tools made of non-ferrous metals for Fresnel lenses [3].

End milling is applied in tool and mold manufacture, and also in classical

precision engineering sectors such as the watch industry. This method allows

the production of complex geometries and even free-form surfaces.

As in conventional production technology, milling can be regarded as the

most flexible microcutting process. Single-tooth diamond disk milling cutters allow

the production of grooves similar to foil turning. This process is also called

4 Strategies for the Manufacture of Mold Inserts 90

fly-cutting. In contrast to foil turning, the grooves produced can be crossed one

or more times at suitable angles so that columnar or pyramidal structures are

manufactured (Fig. 4-2).

These structures are suitable as embossing dies and injection molding tools,

e.g. for optical lattice structures with typically 1–100 lines per mm. They are

used in diffraction optics and in light-guiding systems. Fly-cutting tools are

commercially available with minimum diameters around 100 m.

Diamond end milling cutters are commercially available with diameters down

to 300 m. These are usually straight-flute single-tooth milling cutters. For

negative structures, i.e. for the end milling of grooves, the minimum groove

width is limited by the tool diameter of 300 m.

4.3.1.3 Cutting of Steel as the Most Important Aim of Research

So far, microtechnology in general, but also microcutting, has been limited to

the structuring of silicon and non-ferrous metals such as electroless copper,

brass and plastics [5]. In the future, it will be of great importance to be able to

structure steel because of its material properties that reach from hard-brittle to

soft-ductile. Besides, silicon-based molds are not as wear-resistant as steel molds

when ceramic feedstock is employed.

Studies on the microcutting of steel have been performed particularly in Japan

and Germany since the mid-1990s, but are still within the scope of research.Wearresistant

mold inserts are a necessity for the economic efficiency of the molding

processes. However, the bending strength of the microstructures in the mold insert

in the case of high aspect ratios can also be very important for process safety,

and sometimes even for the applicability of the molding. In contrast to the ultraprecision

or microcutting of non-ferrous metals, diamond cannot be used for the

4.3 Cutting Processes 91

Fig. 4-2 Structures produced by fly-cutting (source: [4])

microcutting of steel. Here, cemented carbide milling cutters, widely used in conventional

machining, are of interest. Owing to the single grains which appear in

the form of micronotches at the cutting edge, sintered carbide tools are not suitable

for obtaining optical surface qualities comparable to those achieved with diamond

cutting. The comparably low price and the possibility of machining steels in

4 Strategies for the Manufacture of Mold Inserts 92

Fig. 4-3 Carbide end milling cutter by Magafor (source: wbk)

contrast to diamond tools, however, are the reasons for using sintered carbides as

cutting materials for microcutting tools.

The decisive feature for the tool to be suitable for microcutting is the formation

of a sufficiently sharp cutting edge. Since cemented carbide is a sintered

material with tungsten carbide grains as abrasive material bonded in a relatively

soft cobalt phase, the size of the tungsten carbide grains determines the achievable

cutting edge rounding (Fig. 4-3). Current grain sizes range from 0.5 to

1.0 m. Thus, cutting edge radii of a few micrometers can be realized.

Carbide end milling cutters are fairly commonly used in industry and are

available from several manufacturers, as coated and non-coated tools and with

diameters down to 0.1 mm. Tools in experimental stages reach diameters down

to 0.05 mm. Regarding microend milling of hard materials such as steel, however,

special attention has to be paid to process control and the bearing of the

machine tool to prevent the occurrence of stochastic tool ruptures or premature

wear. Furthermore, the process requires high cutting speeds. In addition, a

minimum feed per tooth is required to ensure material separation.

Fig. 4-4 shows a mold insert of a wheel rim for a microvehicle which was directly

milled in tool steel with a hardness 55 HRC. The surface roughness

achieved is Rz=0.3 m. The molded part has a reflecting surface and demonstrates

the capability of plastic injection molding.

4.3.1.4 Microdrilling

The geometries which can be produced by drilling are limited to cylindrical surfaces.

The conditions in the contact zone between the tool edge of the microdrill

and the workpiece are relatively complex. As the cutting speed along the major

cutting edge drops to zero in the drill center, the cutting in most tool areas does

not occur at an optimum speed with relatively high cutting forces [12]. In addition,

a considerable axial force is acting in the tool center caused by a chisel

edge which presses the workpiece material in the area of the major cutting

edges. Compared with conventional drills, microdrills have a larger ratio between

the core and tool diameter in order to increase the stability (see Fig. 4-5).

Generally, microdrilling tools are made of high-speed tool steel (HSS) or cemented

carbide. Commercially available microdrills have aspect ratios (l/d) of

4.3 Cutting Processes 93

Fig. 4-4 Steel mold insert (hardness 55 HRC, surface Rz=0.3 m) and molded

part (source: wbk)

15. To increase the wear resistance of the tools and thus extend the tool life,

microdrills are increasingly coated with refractory carbides or nitrides by PVD

or coated with diamond layers by CVD [5, 8, 13–18].

Industrial Application

Microdrilling is industrially used in the following fields:

nozzles for injection plants, valves, burners;

components for synthetic fiber production, spinning nozzles;

filters;

watch bearings and cases, bracelet links;

air bearings;

medical needles;

printed circuit boards (PCBs);

elements for fiber-optics.

4 Strategies for the Manufacture of Mold Inserts 94

Fig. 4-5 Drill parameters and tool coatings (source: [19–22])

In terms of quantity, microdrilling tools are mainly used in the mechanical

machining of PCBs. Their trend towards miniaturization and their requirements

with respect to drilling quality and production costs have accelerated the

development of microdrilling tools regarding precision, tool life and diameter

reduction.

At present, the smallest microdrilling tools have a diameter of 15 m.

Fig. 4-6 shows industrial applications of microdrilling. The left figures show

blind and through holes in PCBs. A hole in steel with a diameter of 19 m can

be seen at the top right. The bottom right picture shows a 30 m hole in a human

hair with a pushed-through 25 m thick wire.

Research

The development and optimization of specifications necessary for the drilling of

microholes in various classes of materials are a main focus of research. Furthermore,

theoretical and experimental examinations are carried out for optimizing

the microdrilling process.

4.3.2

Cutting with Geometrically Undefined Tool Edges

4.3.2.1 Microgrinding

Microgrinding allows the production of planar surfaces or grooves and of the

smallest components, such as miniature shafts or drills. Since the materials to

be ground are mostly semiconductor materials, glasses, ceramics or sintered

carbides, diamond grinding tools are primarily used. The most comprehensive

investigation results are available for the grinding processes which were developed

for the production of microelectronic components, especially for monocrystalline

silicon. In 1990, Tönshoff et al. published a compendium of mechanical

machining steps by geometrically undefined tool edges which are used for

the production of silicon wafers [25]. These include the processes of inside diameter

abrasive cutting (slicing), lapping by means of blades or wire, wire

grinding, surface grinding and dicing, which are necessary for the production

of wafers and singles chips and have been further developed by many researchers

since then [26–35].

A survey of the processes which are currently state of the art is given in

Fig. 4-7. The grinding wheels used for straight grooves may have very small tool

widths of 1–15 m.

A special type of grinding is the so-called dicing, by which wafers are divided

into single chips using grinding wheels with a typical width smaller than

100 m. An important field of application of this technology is the production

of read/write heads for magnetic film memories for which the machining of

thicker substrates of different ceramics is required. The further development of

and research on dicing aim to maximize the wafer or substrate surface, which

4.3 Cutting Processes 95

is available for chips or MEMS, by means of slots that are as narrow as possible

and have minimum chipping of the edges on the front and back sides of the

substrate and also to increase the output by high feed speeds [37–39]. As regards

the production of microstructured high-performance solar cells, the demands

are clearly higher with maximum chipping of edges of 2 m. Apart

from the further development of machine system and the tools, automated

quality control is of great importance.

A distinction is made between dicing, in which the cut is made completely

through the substrate into the carrier base, and scribing, in which the substrate

is not fully separated and grooves are produced [40]. An 80 m high and 5 m

wide and long web (aspect ratio 1: 16) was produced by Grundig on a high-duty

dicing machine using a resin-bonded dicing blade with diamond micrograin

4 Strategies for the Manufacture of Mold Inserts 96

Drilling in PCBs

Micro drilling in steel Drilling a hair

Fig. 4-6 Examples of microdrilling (source: [20, 23, 24])

according to: National Jet Company, USA

sizes of 3.5–3 m, a cutting width of 100 m, with a cutting speed of 85 m/s

and a feed of 120 mm/min (Fig. 4-8, left).

The high precision of the dicing technology was also demonstrated by Disco

Corporation [41] by microstructuring a human hair with a dicing blade having a

width of 5 m (Fig. 4-8, right).

As the demands on the cutting width are getting ever higher, where undesirable

chipping of edges occurs, ductile grinding with almost no chipping of edges in the

processes of dicing or profile grinding has also attracted interest [37, 44].

In addition to microstructures which can be produced by dicing, it is also possible

to produce structures using microabrasive pencils, hollow abrasive pencils

(diamond hollow drills) and peripheral grinding wheels. Here, a distinction has

to be made between three- and five-axis machining.

Abrasive pencils are applied in the watch industry and in precision engineering.

Additional application areas are, e.g., the mold, tool and model manufacture.

Since 1997, conventionally designed microabrasive pencils have been available

with a minimum diameter of down to 0.2 mm [45].

These microabrasive pencils can be used in various applications, which differ in

the contact surfaces between the tool and the workpiece. In the case of an almost

point-shaped contact, it was possible to grind free forms such as aspherical surfaces

in sintered carbide with a minimal radius of 0.25 mm [46]. By means of

a resin-bonded diamond abrasive pencil having a diameter of 0.25 mm and a grain

size of D=8–16 m, a surface roughness Ra=4 nm was produced.

Peripheral grinding wheels have also been used for the production of closed

microstructures. In 1999, Suzuki et al. demonstrated that it is possible to manufacture

molding tools in sintered carbide using profiled microgrinding wheels

by producing an example of a Fresnel lens structure [47].

4.3 Cutting Processes 97

Fig. 4-7 Survey of kinematics for microgrinding (source: [36])

4.4

Ablation Processes

4.4.1

Electrodischarge Machining (EDM) Processes

4.4.1.1 Introduction

The industrial utilization of the electrodischarge effect began in 1954. First,

minimum holes, e.g. injection nozzles, were produced on cavity-sinking EDM

machines. The first work concerning microelectrodischarge machining began in

1967–69 [48, 49]. The process became more interesting in the 1980s with the

propagation of silicon-based microelectromechanical systems (MEMS). At present

the main fields of application are holes for printer heads of inkjet printers,

spinning nozzles, injection nozzles, turbine blades, electron tube grids, tools for

punching of e.g. electronic components, microreactors, microtoothed wheels

and mold inserts for injection molding [50, 51].

4.4.1.2 General Functioning of the Process

According to DIN 8590, EDM, especially thermal removal by electric gas discharge

with the spark as energy carrier, belongs to material removal processes.

An electrically generated spark flashes over between the electrode and the workpiece.

This discharge has a material removal effect. A dielectric between the

electrode and the workpiece functions as an insulator. Another function is taking

up the removed particles and conveying them out of the machining area.

The sparks arising one after the other melt the electrode and the workpiece,

throw parts of them into the dielectric and leave a residue of the melt re-solidifying

on the material surface. The resulting roughened surface with many small

craters depends on the process parameters. By adopting suitable parameters,

4 Strategies for the Manufacture of Mold Inserts 98

Fig. 4-8 Test piece of ferrite (left; source: [42]) and microstructured

human hair (right; source: [43])

the removal of the undesired material from the electrode, which has the negative

contour of the form to be produced, can be kept much smaller than that of

the workpiece. With a multitude of removal pulses it is possible to remove a

large volume of material.

4.4.1.3 Micro-EDM Processes

The two most important variants of EDM are wire EDM and microcavity-sinking

EDM. In the former process, a wire is used to cut out a contour from the

workpiece and in the latter a cavity is produced by means of a negative form.

Since all sides of the electrodes can be used as a tool, it is possible to produce a

multitude of forms.

For the production of complex 3D geometries, among other methods EDM is

used. Here, the form is generated over several paths using mostly cylindrical rotating

electrodes [52–54], gradually removing up to 100 m thick layers from

the workpiece until the final depth is reached [55].

Typical accuracies which are currently achievable in micro-EDM are presented

in Table 4-1 [56, 57].

The smallest electrodes produced have a diameter of 4.3 m at a length of

50 m. Depending on the electrode diameter, today aspect ratios of the cavities

of 10–50 are reached. Sato et al. investigated holes of 15–300 m which found

application in inkjet nozzles of printers [58].

4.4.1.4 Workpiece Materials

Owing to its effective principle, the process allows workpieces to be machined

independently of their hardness and strength. A certain minimum of electrical

4.4 Ablation Processes 99

Table 4-1 Achievable workpiece accuracies

Parameter Wire EDM Micro cavity-sinking EDM

Form deviation (m) ±1 ±2

Positional deviation (m) <±1 <±1

Median roughness, Ra (m) 0.1–0.2 0.2–0.3

Mean roughness depth, Rz (m) 0.5–2.5 1–5

Minimum structure width (m):

Webs 20–40 20–40

Grooves 50–60 20–40

Maximum aspect ratio:

Webs 20–30 15–25

Grooves 60–80 10–25

Holes 10–25

Internal radius (m) 20 10

Smallest electrode dimensions (m) 30 10

conductivity is needed, however, in order to permit EDM. Related research studies

were carried out by Reynaerts and co-workers [59–61] and Masaki et al. [62].

4.4.1.5 Electrode Materials and Manufacturing

Die-sinking EDM

In conventional EDM, copper and graphite are primarily used. Because of its

high price, tungsten–copper is preferably used for low-wear machining, in particular

for filigree structures and for the machining of carbide. Silver–tungsten

and tungsten carbide are also used as electrode materials [63, 64].

For drilling up to a diameter of 0.1 mm, it is possible to use tube electrodes,

allowing higher removal rates and aspect ratios to be achieved owing to the inner

flushing. Electrodes with diameters below 100 m are currently available as

solid material only. The smallest available rod electrodes of sintered carbide currently

have a diameter of 50 m. If smaller electrodes are needed, these have to

be self-produced.

Alternative methods of producing electrodes are the LIGA process, conventional

cutting, ultraprecision machining and hot pressing [63, 65].

Wire EDM

Wire EDM places special demands on the electrode. Because of the running-off

electrode, the wear at the wire is of secondary importance. When using thin

wires (diameter 20–100 m), attention has to be paid that the tensile strength of

the wires is not exceeded. This risk can be reduced by the thermal process.

Therefore, mainly tungsten wires are used which have a tensile strength of

about 2500 N/mm2 [66]. Chapter 7 gives further information about the EDM

process and process applications.

4.4.2

Laser Beam Machining (LBM)

4.4.2.1 Introduction

The first realization of a functioning laser was successfully achieved by Maiman

in the USA in 1960. This first laser set-up consisted of a rod-shaped ruby body

which was excited by a flashlight [67]. Although this laser type is no longer important

today, it was the impetus for the technological development of the current

laser systems and applications. Development will continue to be rapid in

the coming years, particularly since utilizing innovative technologies is becoming

more and more important in material machining owing to increasing competitive

pressures.

4 Strategies for the Manufacture of Mold Inserts 100

4.4.2.2 General Functioning of the Process

LBM is based on the impact of high-energy electromagnetic radiation on a

workpiece. For this purpose, the radiation is directed in a defined way on the

surface of the workpiece and formed to a desired power density and distribution

by optical means. The absorption of the radiation in the workpiece or at its surface

results in the desired influence on the material; in other words, the energetic

effect on the material occurs thermally. The laser beam ‘tool’ is not subject

to wear and has high flexibility. Depending on the intensity and the qualities of

the material, there are different interaction processes which are used for the design

of the method. Depending on the laser beam source, there are different

machining mechanisms. With CO2 and solid-state lasers, it is possible to use

two different mechanisms depending on the process control. In laser beam

melting machining, the material is transferred to a liquid phase through the energy

input of the laser and then blown off the machining spot by means of a

gas flow. This method is superior because of high removal rates for medium

surface qualities.

With higher beam intensities, the material is directly vaporized, resulting in

finer structures with better surface accuracies, but reduced removal rates. In the

above-mentioned laser types or mechanisms, the laser beam can be guided on

to the workpiece surface either by a scanner or directly by an optic. In excimer

lasers the material removal is generated by electron band transitions and a

mask projection process is used for beam formation [67–69].

4.4.2.3 Laser Beam Sources and Machining Methods

For laser beam machining, mostly pulsed laser beam sources are used, the machining

being possible for the whole spectrum of materials (metals, plastics,

ceramics). Common pulsed laser systems for material removal are listed in Table

4-2 [1].

Laser beam machining is applicable in the following fields:

lithography;

boring and drilling;

labeling;

engraving;

caving;

structuring;

removal of surface layers/cleaning.

Especially in tool and mold manufacture, the laser is increasingly used as a

machining tool because it is very flexible and independent of the mechanical

properties of the material, such as hardness or strength. Therefore, it is possible

to machine materials which are difficult to cut in addition to small structures.

Two main fields of laser application for tool manufacture are described in the

following.

4.4 Ablation Processes 101

4.4.2.4 Laser Beam Machining/Structuring

The first plants for LBM, in which a CO2 laser beam source was used [70, 71],

were introduced at the end of the 1980s. Since the CO2 laser beam could only

be guided to the machining spot via large-scale mirror systems and optics, the

workpiece geometries to be machined were very limited and the plants very inflexible.

In the process of laser caving, the material is removed layer by layer

through the effect of the laser beam. A characteristic feature is pulsed operation

with which it is possible to achieve energy densities of up to 1000 W/cm2 with

very short pulse times. In the case of materials that are difficult to machine,

this leads to sublimation removal without thermal effects on the adjacent material.

At present, it is basically possible to produce structures down to a size of

10 m. Depending on the laser beam sources used and the machine design, the

plants that are currently on the market allow the production of structures up to

a size of 100 m with an aspect ratio of 1: 10. The accuracy currently is

0.03 mm, which is not sufficient for micromachining. Hence there is still a

need for the further development of laser beam sources for micromachining.

Moreover, the surface machined by a laser needs a further finishing to remove

residues of the removed material [72].

Fig. 4-9 shows a component produced by laser caving [73].

Depth engraving is a commercialized process in tool and mold manufacture

which above all is used for the production of inscriptions. In this process also

the power density of the laser beam is so high that the material vaporizes within

a few nanoseconds during the machining. The surface and burr quality obtained

by laser depth engraving can be compared with the results obtained by

EDM. With steel, removal rates of more than 10 mm3/min can be reached [72].

4 Strategies for the Manufacture of Mold Inserts 102

Table 4-2 Laser systems and parameters for laser beam machining [1]

Laser

system

Pulse

energy

Max.

power

Repetition

rate

Wavelength

Pulse

length

Nd:YAG laser 70 J 300 W 1–300 Hz 1064 nm 0.1–20 ms

Diode-pumped qualityswitched

Nd:YLF laser

135 J 6 W 0.5–50 kHz 1074 nm 25 ns

Diode pumped Nd:YAG

laser

1 mJ 0.5 W 1–500 Hz 1064 nm 30–50 ps

520 J 532 nm

280 J 355 nm

100 J 266 nm

Titanium sapphire laser 200 mJ 2 W 10 Hz 780 nm 150 fs

390 nm

TEA CO2 laser 0.18–50 J 5 kW 30 kHz 10.6 m 6Js

Excimer laser 10 J 1 kW 1–300 Hz 308 nm 10–30 ns

248 nm

193 nm

157 nm

Apart from flexibility and speed, the laser engraving process stands out with respect

to zero wear when compared with conventional methods such as EDM or

high-speed milling. More detailed information regarding the laser ablation process

can be found in Chapter 6.

4.5

Conclusions

As described above, different production technologies can be employed for the

manufacture of micromolds and cavities. The processes of cutting and material

removal are suitable to meet the requirements especially for molds within replication

technologies with abrasive material (e.g. powder-injection molding). In

nearly all cases of manufacturing, EDM and LBM are possible processes to

achieve microstructures in hard material. For structures with aspect ratios ❤

and hardness of workpiece materials <62 HRC, cutting processes can also be

used. The selection of the appropriate process technology with respect to manufacturable

part features must be very specific. Therefore, a catalogue is being

built up which assigns certain design features to a manufacturing process (see

Chapter 18).

4.5 Conclusions 103

Fig. 4-9 Microstructured part and typical laser caving parameters

[73]: 1–5 m material removal; Rz<6 m

(Ra=1.3 m); maximum removal rate, 10 mm3/min; material,

steel; laser, Q-switched Nd:YAG; maximum machining

depth, 10 mm

4 Strategies for the Manufacture of Mold Inserts 104

4.6

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Abstract

Miniaturization of devices and components is one of the main trends in technology.

Microfluidic, micromechanic, microoptical and microelectronic devices

are combined with microsystems, leading to new products. For a major breakthrough

in microtechnology, economical processing is of vital importance. At

present, most manufacturing processes are adapted from the semiconductor industry,

which is economical only for large lots. Furthermore, these usually lithographic

processes strongly restrict the design geometry. Microcutting has the

potential to overcome these problems and to offer new fields of application to

microtechnology. New developments of microcutting of steel are presented here

in general in addition to research results obtained by Project B2 ‘Microcutting’

of the Collaborative Research Center 499.

Keywords

micromilling; micromolds; alternative tool production methods; hardened steel

5.1 Introduction 108

5.2 Micromilling 111

5.2.1 Tool 111

5.2.1.1 Tool Materials 111

5.2.1.2 Manufacturing Methods 114

5.2.1.3 Alternative Manufacturing Methods 114

5.2.1.4 Simulation 119

5.2.2 Work Piece 122

5.2.3 Process 122

5.2.3.1 Cutting Tools 123

5.2.3.2 Theoretical Considerations for the Cutting Force 123

5.2.3.3 Measurements of the Cutting Forces 123

5.2.3.4 Theoretical Considerations for Tool Deflection 123

107

5

Micro End Milling of Hardened Steel

J. Schmidt, J. Kotschenreuther, Institute of Production Science (wbk),

University of Karlsruhe (TH), Germany

Advanced Micro and Nanosystems Vol. 3. Microengineering of Metals and Ceramics.

Edited by H. Baltes, O. Brand, G. K. Fedder, C. Hierold, J. Korvink, O. Tabata

Copyright © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

ISBN: 3-527-31208-0

5.2.3.5 Surface Quality 123

5.2.3.6 Burr Formation 125

5.2.3.7 Process capability 125

5.2.3.8 Manufacturing of Mold, Models and Test Structures

for Demonstrator Components and Wear Analyses 127

5.3 Conclusions 127

5.4 References 128

5.1

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