Microengineering of Metals and Ceramics

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).
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
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-
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
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
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
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
M. Auhorn
Institut für Werkstoffkunde I
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
K. Bade
Forschungszentrum Karlsruhe
Institut für Mikrostrukturtechnik
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
W. Bauer
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
G. Baumeister
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
T. Beck
Institut für Werkstoffkunde I
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
I. Behrens
Institut für Werkzeugmaschinen
und Betriebstechnik
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
H. von Both
Institut für Mikrosystemtechnik
Albert-Ludwigs-Universität Freiburg
Georges-Köhler-Allee 103
79110 Freiburg
C. Buchholz
Institut für Werkzeugmaschinen
und Betriebstechnik
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
M. Dauscher
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
List of Contributors
List of Contributors XII
G. Finnah
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
Prof. J. Fleischer
Institut für Werkzeugmaschinen
und Betriebstechnik
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
Prof. K.-H. zum Gahr
Institut für Werkstoffkunde II
Universität Karlsruhe
c/o Forschungszentrum Karlsruhe
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
A. Greiner
Institut für Mikrosystemtechnik
Albert-Ludwigs-Universität Freiburg
Georges-Köhler-Allee 10
379110 Freiburg
M. Guttmann
Forschungszentrum Karlsruhe
Institut für Mikrostrukturtechnik
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
Prof. J. Haußelt
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
V. Hegadekatte
Institut für Zuverlässigkeit
von Bauteilen und Systemen
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
R. Heldele
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
J. Herz
Institut für Werkstoffkunde II
Universität Karlsruhe
c/o Forschungszentrum Karlsruhe
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
Prof. J. Hesselbach
Institut für Werkzeugmaschinenund
Technische Universität
Langer Kamp 19b
38106 Braunschweig
K. Heuer
Institut für Werkzeugmaschinen
und Fertigungstechnik
Technische Universität Braunschweig
Langer Kamp 19b
38106 Braunschweig
C. Horsch
Institut für Werkstoffkunde I
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
N. Huber
Institut für Materialforschung II
Forschungszentrum Karlsruhe
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
B. Kasanická
Institut für Werkstoffkunde I
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
List of Contributors XIII
D. Kauslaric
Institut für Mikrosystemtechnik
Albert-Ludwigs-Universität Freiburg
Georges-Köhler-Allee 103
79110 Freiburg
R. Knitter
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
M. Knoll
Institut für Werkzeugmaschinen
und Betriebstechnik
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
Prof. J. G. Korvink
Institut für Mikrosystemtechnik
Albert-Ludwigs-Universität Freiburg
Georges-Köhler-Allee 103
79110 Freiburg
J. Kotschenreuther
Institut für Werkzeugmaschinen
und Betriebstechnik
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
O. Kraft
Institut für Zuverlässigkeit
von Bauteilen und Systemen
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
Prof. D. Löhe
Institut für Werkstoffkunde I
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
J. Marz
Institut für Produktentwicklung
Universität Karlsruhe
Kaiserstrasse 12
76128 Karlsruhe
T. Masuzawa
Institute of Industrial Science
University of Tokyo
4-6-1 Komaba, Meguro-ku
L. Merz
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
D. Metz
Institut für Produktentwicklung
Universität Karlsruhe
Kaiserstrasse 12
76128 Karlsruhe
M. Müller
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
G. Örlygsson
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
V. Piotter
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
List of Contributors XIV
A. Raatz
Institut für Werkzeugmaschinen
und Fertigungstechnik
Technische Universität Braunschweig
Langer Kamp 19b
38106 Braunschweig
S. Rath
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
H.-J. Ritzhaupt-Kleissl
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
R. Ruprecht
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
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
Prof. J. Schmidt
Institut für Werkzeugmaschinen
und Betriebstechnik
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
J. Schneider
Institut für Werkstoffkunde II
Universität Karlsruhe
c/o Forschungszentrum Karlsruhe
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
J. Schulz
Forschungszentrum Karlsruhe
Institut für Mikrostrukturtechnik
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
M. Schulz
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
V. Schulze
Institut für Werkstoffkunde I
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
S. Soetebier
Institut für Werkzeugmaschinen
und Fertigungstechnik
Technische Universität Braunschweig
Langer Kamp 19b
38106 Braunschweig
A. Stephen
Bremer Institut für angewandte
Strahltechnik (BIAS)
Klagenfurter Str. 2
28359 Bremen
Prof. F. Vollertsen
Bremer Institut für angewandte
Strahltechnik (BIAS)
Klagenfurter Strasse 2
28359 Bremen
List of Contributors XV
H. Weule
Institut für Werkzeugmaschinen
und Betriebstechnik
Universität Karlsruhe
Kaiserstrasse 12
76131 Karlsruhe
J. Wrege
Institut für Werkzeugmaschinen
und Fertigungstechnik
Technische Universität Braunschweig
Langer Kamp 19b
38106 Braunschweig
B. Zeep
Forschungszentrum Karlsruhe
Institut für Materialforschung III
Hermann-von-Helmholtz-Platz 1
76344 Eggenstein-Leopoldshafen
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
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.
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 Dominance of Technologies 6 Surface-to-Volume Ratio 6 Dynamics 7 Standardization 7 Validation 7 Enhanced Material Spectrum 7
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 Emphasis on Actuators 7
1.2.2 Microspecific Design Flow 7
1.3 Design Rules 9
1.3.1 Basics 9 Definition 9 Derivation of Design Rules 10
1.3.2 Design Rules Derived from Restrictions of Production
Technology 11 Design Rules for Mold Insert Manufacturing 13 Design Rules for Replication Techniques 14
1.4 Design Environment 18
1.4.1 Information Unit 20
1.4.2 Embodiment Design Unit 20 Preparing Elementary Rules for Computer-aided Design Rule
Check 21 Design Rule Check 24
1.5 Conclusion 27
1.6 References 27
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.
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
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].
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.
Design Flow
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. 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. 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 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. Standardization
Standards with regard to generic or product-specific dimensions do not exist for
the design of microcomponents and systems. 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. 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. 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.
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.
Design Rules
Basics 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! 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’.
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. 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. 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
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
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].
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]
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.
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 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:
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]. 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
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
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
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
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1 Design Environment and Design Flow 28
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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.
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.
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 Microbending Specimens 36 Microtensile Specimens 37 Microtensile Specimens Containing Pores 39
2.3.2 Microcomponents 42
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
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.
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
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.
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
 The material behavior of the grains is described with a linear-elastic material
 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
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.
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.
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
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.
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.
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
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.
Simulation of Microspecimens
Micro three-point bending tests and microtensile tests were employed for the
determination of material values (see Chapters 19 and 20). 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. 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
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. 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
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
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
both grains
Material b
Location 3 3.16 3.06 2.84 2.65
Location 1 3.22 3.16 3.05 2.8
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
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.
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
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
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.
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
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
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.
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
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.
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
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,
6 A. Okabe, B. Boots, K. Sugihara, Spatial
Tesselations – Concepts and Applications of
Voronoi Diagrams; New York: Wiley,
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,
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–
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,
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,
pp. 481–492.
21 E. Schnack, Ein Iterationsverfahren zur
Optimierung von Kerboberflächen, VDIForschungsheft
589; Düsseldorf: VDI-Verlag,
22 J. Marz, N. Burkardt, A. Albers, in: Conference
Proceedings EUSPEN; 2003, Vol. 1,
pp. 23–26.
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.
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
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 The Free Energy Approach for Many-body Dissipative Particle
Dynamics (MDPD) 60 Warren’s Approach for MDPD 63 EOS Measurement, Modeling Pressure, Specific Volume
and Temperature (pvT) 64
3.4.2 Fluid–Wall Interaction: the Contact Angle 67 Reflecting Boundary Conditions 68 Interactions for Reproduction of Wetting and Friction 69 Measurements of Contact Angle Between Molding Material
and Mold Insert 70
3.4.3 Viscosity Modeling and Measurement 72 The Parameters in DPD 72 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
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
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.
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
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
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:
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:
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.
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:

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
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)
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
  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
A convenient choice for the conservative force is [16]
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.
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
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.
Matching the Equation of State The Free Energy Approach for Many-body Dissipative Particle Dynamics
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 
3V ij
rij  f ij
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

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
ij 16
which, together with Equations (14) and (15), leads to
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 
and obtaining an expression for     /. For example, for the EOS
1  b  a2 19
of a van der Waals fluid, one finds

1  b  a 20
which leads to
1  bi  a  
1  bj  a
rij rijeij 21
One can see that, generally, the resulting forces are density-dependent manybody
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. 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
ij  Bi  jwCrijeij  B  0 22
with a different cutoff range rd  rc and
rd  2
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.
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. EOS Measurement, Modeling Pressure, Specific Volume and Temperature
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 
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 exp b4T  b5
for T  Ttrans 27
BT  b3s exp b4sT  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.
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 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 exp 
and both tangential components vt from a Gauss distribution centered at zero:
vt  2
2 exp 
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. 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. 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
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. 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
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
i  vi  ij  v
j  vj  ij 32
ij  vij  eij 33
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 
j2     j0 kjt k     34
where jt k is a shear wave oscillating, for example, in the y-direction along the
jt k i
i t exp ikxt
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. 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

d3 37
The wall shear stress
w can be calculated from the measured pressure loss p
across the die [62]:

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
kinematic viscosity [reduced units]
dissipation probability
0 0.2 0.4 0.6 0.8 1

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
0 a

 1n 40
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
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]
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]
20 40 60 80 100 120 140 160
The additional equation of motion for i is
i jji
vij  FD
ij  qD
 t  jji
vij  FR
ij  qR
ij   43
In [24], qD
ij is called ‘mesoscopic heat flow’ and is computed as follows:
ij  ij
Tj  w
Drij 44
Additionally, there is a ‘random heat flux’ [25] qR
ij with
ij  ijw
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:
2  w
D and 2
ij  2ij 46
Additionally, Equation (7) still holds and Equation (8) is replaced by
ij 47
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.
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
 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
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.
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
3 Modeling Micro PIM 82
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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
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.
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 Diamond Cutting Tools 90 Cemented Carbide Tools 90 Cutting of Steel as the Most Important Aim of Research 91 Microdrilling 93
4.3.2 Cutting with Geometrically Undefined Tool Edges 95 Microgrinding 95
4.4 Ablation Processes 98
4.4.1 Electrodischarge Machining (EDM) Processes 98 Introduction 98 General Functioning of the Process 98 Micro-EDM Processes 99 Workpiece Materials 99 Electrode Materials and Manufacturing 100
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 Introduction 100 General Functioning of the Process 101 Laser Beam Sources and Machining Methods 101 Laser Beam Machining/Structuring 102
4.5 Conclusions 103
4.6 References 104
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].
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.
Cutting Processes
Cutting with Geometrically Defined Cutting Edges 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. 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. 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. 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;
 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
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.
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.
Cutting with Geometrically Undefined Tool Edges 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])
Ablation Processes
Electrodischarge Machining (EDM) Processes 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]. 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. 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]. 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]. 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.
Laser Beam Machining (LBM) 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
4 Strategies for the Manufacture of Mold Inserts 100 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]. 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:
 boring and drilling;
 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
4.4 Ablation Processes 101 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]
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
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.
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
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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.
micromilling; micromolds; alternative tool production methods; hardened steel
5.1 Introduction 108
5.2 Micromilling 111
5.2.1 Tool 111 Tool Materials 111 Manufacturing Methods 114 Alternative Manufacturing Methods 114 Simulation 119
5.2.2 Work Piece 122
5.2.3 Process 122 Cutting Tools 123 Theoretical Considerations for the Cutting Force 123 Measurements of the Cutting Forces 123 Theoretical Considerations for Tool Deflection 123
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 Surface Quality 123 Burr Formation 125 Process capability 125 Manufacturing of Mold, Models and Test Structures
for Demonstrator Components and Wear Analyses 127
5.3 Conclusions 127
5.4 References 128

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