Metal cutting and high speed machining

METAL CUTTING AND

HIGH SPEED MACHINING

Edited by

D. Dudzinski

Universite de Metz

Metz, France

A. Molinari

Universite de Metz

Enim

Metz, France

and

H. Schulz

Technical University of Darmstadt

Darmstadt, Germany

Kluwer Academic I Plenum Publishers

New York, Boston, Dordrecht, London, Moscow

Library of Congress Cataloging-in-Publication Data

Metal cutting and high speed machining/edited by D. Dudzinski, A. Molinari, and H. Schulz.

p. cm.

Papers presented at the Third International Conference on Metal Cutting and High

Speed Machining, June 2001, Metz, France.

Includes bibliographical references and index.

ISBN 0-306-46725-9

I. Metal-cutting tools-Congresses. 2. Metal-work-Congresses. 3. High-speed

machining-Congresses. I. Dudzinski, D., 1952- II. Molinari, A., 1948- Ill. Schulz,

Herbert, 1936- IV. International Conference on Metal Cutting and High Speed

Machining (3rd: 2001: Metz, France)

TJll86 .M378 2002

671.5 '3-dc21

2001057982

Proceedings of the Third International Conference on Metal Cutting and High Speed Machining, held June

27-29, 2001, in Metz, France

ISBN 0-306-46725-9

©2002 Kluwer Academic I Plenum Publishers, New York

233 Spring Street, New York, New York 10013

http://www.wkap.nl/

1098765432

A C.l.P. record for this book is available from the Library of Congress

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No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any

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Printed in the United States of America

PREFACE

This book gives a coherent overview of recent developments in Metal Cutting and High

Speed Machining, presenting the latest research of international groups in theoretical and

experimental approaches in this field. Topics covered include: mechanics of cutting,

numerical models, chatter vibrations, machining processes (drilling, high speed milling,

grinding, hard turning), cutting tools and coatings, dry cutting, computer aided

manufacturing, numerical control and command, process monitoring and adaptive control,

machine tool (in particular the Parallel Kinematic Machines) and components (spindles and

linear motor feed drive). Special attention is made to industrial applications, to aeronautical

materials, for example. Various facets of metal cutting are developed to stimulate

interdisciplinary approach.

The book is constituted by a selection of papers presented at the Third International

Conference on Metal Cutting and High Speed Machining which was held in Metz, France, on

June 27-29, 2001. This conference brought together 360 scientists, researchers and engineers

from 31 countries; it promoted fertile discussions and exchange of ideas. The Conference is

co-organized by the Universite de Metz, Ecole Nationale d'Ingenieurs de Metz and the

Darmstadt Technische Universitat with a two years interval.

Progress in metal cutting needs a synergy between many disciplines among which

mechanics, of course, for the analysis and the design of the whole process, but in combination

with material science and physico-chemistry for elaborating new tools, coatings and new

work materials, tribology for the modelling of dynamic friction at the tool-chip interface,

computing for the development of efficient software simulating and optimizing the cutting

processes, applied mathematics for process monitoring and control. Interactions between

these disciplines are illustrated in this book.

The editors would like to express their appreciation to all the authors for their

contributions to this book. Special thanks are due to the members of the scientific committee

of the conference.

It is hoped that this book will provide to manufacturing engineers, researchers, and

students, information, help and a necessary interdisciplinary view to solve problems

encountered in machining processes and to-propose new ideas and applications in this field.

D. Dudzinski, A. Molinari and H. Schulz

v

CONTENTS

MECHANICS OF CUTTING

I. ON THE SIMULATION OF MACHINING AT THE A TOM JC SCALE .........

R. Komanduri and M.L. Raff

2. DYNAMICS IN HIGH SPEED MACHINING...... ............................................ 21

G. Warnecke and S. Siems

3. INFLUENCE OF MATERIAL PROPERTIES ON SURFACE INTEGRITY

AND CHIP FORMATION IN HIGH SPEED TURNING....................... 31

E. Brinksmeier, P. Mayr, T. Lubben, P. Pouteau, and P. Diersen

4. DETERMINATION OF FORCES IN HIGH SPEED MACHINING (HSM)

FROM MACHINING TESTS AND AV ARIABLE FLOW STRESS

MACHINING THEORY .............................. .. .............. ............................ 41

B. Kristyanto, P. Mathew, and J. A. Arsecularatne

5. THERMOMECHANICAL MODELLING OF CUTTING AND

EXPERIMENT AL VALIDATION .......... ................................................ 51

A. Moufki, A. Devillez, D. Dudzinski, and A. Molinari

6. INFLUENCE OF HEAT TREATMENT AND CUTTING PARAMETERS

ON CHIP FORMATION AND CUTTING FORCES .............................. 69

H. Schulz and A. Sahm

7. MEASUREMENT AND SIMULATION OF TEMPERATURE AND

STRAIN FIELDS IN ORTHOGONAL METAL CUTTING................... 79

Y.K. Potdar and A.T. Zehnder

NUMERICAL APPROACH OF CUTTING AND MACHINING

8. A PARAMETRIC STUDY OF THE EFFECTS OF CUTTING

PARAMETERS ON CHIP FORMATION PROCESS ............................ 91

M.R. Movahhedy, M.S. Gadala, and Y. Altintas

vii

viii CONTENTS

9. THREE-DIMENSIONAL FINITE-ELEMENT ANALYSIS

OF HIGH-SPEED MACHINING ............................................................. 107

J.F. Molinari

IO. PREDICTION OF CHIP MORPHOLOGY IN ORTHOGONAL

CUTTING BY MEANS OF A CUSTOMIZED

FINITE ELEMENT CODE................................. .. ..... ................... ..... ....... 119

E. Ceretti, L. Filice, and F. Micari

CHATTER VIBRATIONS

11 . KTN EMATICS AND DYNAMICS OF MILLING WITH ROUGHING

END MILLS ........ .......................................................................... ........ ... . 129

M.L. Campomanes

12. STUDY ON CHATTER VIBRATION IN RAMPING OF

SCULPTURED SURFACES.................................................................... 141

B.W. Ikua, H. Tanaka, F. Obata, and S. Sakamoto

13 . REGENERATIVE STABILITY ANALYSIS OF HIGHLY

INTERRUPTED MACHINTNG .. ................ .......... ................ ......... .......... 151

M.A. Davies, J.R. Pratt, B. Dutterer, and T.J. Bums

14. DETECTING CHATTER IN GRINDING .. ...... .. .. ........... .. ......... .. .. .. .. .... .... .. .. . 161

J. Gradisek, E. Govekar, I. Grabec, A. Baus, and F. Klocke

MACHINING PROCESSES

15. TOOL WEAR AND WORKPIECE SURFACE INTEGRITY WHEN

HIGH SPEED BALL NOSE END MILLING HARDENED AISI

Hl3 ............................ ........................................ ........... ............................. 171

D.A. Axinte and R.C. Dewes

16. THE EFFECT OF CUTTING ENVIRONMENT AND TOOL COATTNG

WHEN HIGH SPEED BALL NOSE END MILLING TITANIUM

ALLOY. ................................ .................. ............... ................................... 18 1

H. Niemann, E.G. Ng, H. Loftus, A. Sharman, R. Dewes, and D. Aspinwall

17. HIGH SPEED BALL NOSE END MILLING OF INCONEL 718 WITH

VARIABLE TOOL GEOMETRY- EXPERIMENTAL AND

FTNITE ELEMENT ANALYSIS. ............. ............ .................................... 191

E.G. Ng, S.L. Soo, C. Sage, R. Dewes, and D. Aspinwall

CONTENTS ix

18. INFLUENCE OF MACHINING CONDITIONS ON RESIDUAL

STRESSES: SOME EXAMPLES ON AERONAUTIC

MATERIALS ...... .. .. .. ........... ......... ........ .. .. .. .... ........ ... .. .. .. ....... .. .. .. ... .. .. . .. . 20 I

L. Guerville and J. Vigneau

19. SURFACE INTEGRITY IN FINISH HARD TURNING OF GEARS ............ 211

J. Rech, M. Lech, and J. Richon

20. WEAR TRENDS OF PCBN CUTTING TOOLS IN HARD TURNING ........ 221

T.G. Dawson and T.R. Kurfess

21 . AN ANALYTICAL STUDY ON THE ST ABILITY OF DRILLING

AND REAMING. .. ... .. .. ....... .................... ... ... ........................................... 233

J.A. Yang, V. Jaganathan, and R. Du

22. HIGH SPEED GRINDING: AN INDUSTRIAL STUDY OF

LUBRICATION PARAMETERS.................................................. .......... 251

A. Devillez., 0 . Sinot, P. Chevrier, and D. Dudzinski

23 . USE OF A HIGH SPEED MACHINING CENTRE FOR THE CBN AND

DIAMOND GRINDING OF NICKEL-BASED SUPERALLOYS ......... 267

J. Burrows, R. Dewes, and D. Aspinwall

CUTTING TOOLS AND COATINGS, DRY CUTTING

24. SHEAR LOCALISATION AND ITS CONSEQUENCE ON TOOL

WEAR IN HIGH SPEED MACHINING ............ .................................... . 277

S.V. Subramanian, H.O. Gekonde, G. Zhu, and X. Zhang

25. HSC-CUTTING OF LIGHTWEIGHT ALLOYS WITH CVD￾DIAMOND COATED TOOLS ............................... ......................... ...... .. 289

F. Klocke, R. Fritsch, and J. Grams

26. ENHANCED WEAR RESISTANCE AND TOOL DURABILITY

USING MAGNETIZATION.... ............................... ..................... ..... ...... . 301

M. El Mansori, K. Lafdi, and D. Paulmier

27. FUNCTIONALLY GRADED HARDMETAL SUBSTRATES FOR

COATED CUTTING TOOLS .................................................................. 311

J. Garcia, W. Lengauer, J. Vivas, K. Dreyer, H. van den Berg,

H.-W. Daub, and D. Kassel

28. INNER COOLING SYSTEMS-WEAR REDUCTION FOR DRY

CUTTING............................. .............................................. ...................... 319

E. Uhlmann and T. Frost

x CONTENTS

29. MIST COOLANT APPLICATIONS IN HIGH SPEED MACHINING OF

ADVANCED MATERIALS... ................................. ............. ........... ......... 329

M. Dumitrescu, M.A. Elbestawi, and T.I. El-Wardany

CAD/CAM/NC

30. DEVELOPMENT OF CAM SYSTEM FOR HIGH SPEED MILLING .......... 341

K. Morishige, T. Sakamoto, Y. Takeuchi, I. Takahashi,

K. Kase, and M. Anzai

31. AB-CAM: AN AGENT-BASED METHODOLOGY FOR THE

MANUFACTURE OF STEP COMPLIANT FEATURE BASED

COMPONENTS........................................................................................ 351

R.D. Allen, R.S.U. Rosso, Jr., and S.T. Newman

32. ASSESSMENT OF THE DESCRIPTION FORMAT OF TOOL

TRAJECTORIES IN 3-AXIS HSM: OF SCULPTURED

SURFACES ........................................ ...................................................... 363

E. Due, C. Lartigue, and S. Laporte

PROCESS MONITORING AND ADAPTIVE CONTROL

33 . TOOL CONDITION MONITORING USING TRANSITION FUZZY

PROBABILITY ............................................................ .... ................... ..... 375

R. Du, Y. Liu, Y. Xu, X. Li, Y.S. Wong, and G.S. Hong

34. TOOL WEAR MONITORING BY ON-LINE VIBRATION ANALYSIS

WITH WAVELET ALGORITHM........................................................... 393

G. Luo, D. Osypiw, and M. Irle

35. ADAPTIVE POWER FEEDBACK CONTROL IN CYLINDRICAL

TRAVERSE GRINDING ........... .............................................................. 407

K.A. Hekman, R.L. Hecker, and S.Y. Liang

MACHINE TOOL

36. A NEW MACHINE TOOL CONCEPT FOR ON SITE MAINTENANCE

OF LARGE METAL FORMING TOOLS: TRANSPORTABLE

MACHINING UNIT WITH HYBRID KINEMATIC STRUCTURE ...... 417

H.K. TOnshoff, H.-C. Mohring, G. Gunther, E. Lubbers, and A. Schmidt

37. THE DESIGN OF PARALLEL KINEMATIC MACHINE TOOLS

USING KINE TO ST A TIC PERFORMANCE CRITERIA....................... 425

F. Majou, P. Wenger, and D. Chablat

CONTENTS xi

38. PARALLEL KINEMATIC MACHINES-DEVELOPMENT,

SOFTWARE METHODS AND EXPERIENCES.................. .... ....... ....... 435

V. Maier

MACHINE TOOL COMPONENTS

39. HIGH VOLUME CUTTING OF ALUMINIUM......................................... ..... 445

H. Voll

40. EXPERIMENT AL STUDIES OF HIGH SPEED THERMO￾MECHANICAL-DYNAMIC BEHAVIORS OF MOTORIZED

MACHINE TOOL SPINDLES .......................... ................. ..................... 455

C.-W. Lin, J.F. Tu, and J. Kamman

41. ADVANTAGES IN APPLICATION OF LINEAR MOTOR MACHINES

IN DIE AND MOULD MANUFACTURING ... ................................ .. .... 465

E. Abele, H. Schulz, and B. Bork

42. ROBUST MOTION CONTROL FOR LINEAR MOTOR DRIVES ............... 475

D. Tong, A. Elfizy, and M.A. Elbestawi

AUTHOR INDEX.................. ......... ...................................... ... ........................ ..... 487

KEYWORDS INDEX ......... .............................. .. ...... .. ......... ....................... .......... 489

ON THE SIMULATION OF MACHINING

AT THE ATOMIC SCALE

Ranga Komanduri 1 and Lionel M. Raff 2

ABSTRACT

Molecular dynamics (MD) simulation is an extremely powerful technique for

investigating atomistic phenomenon. Almost all physical phenomena when considered at the

fundamental level can be attributed, directly or indirectly, to the forces acting between the

atoms that constitute the material. Atomic or molecular dynamics (MD) simulations are

playing an increasingly important role in the fields of materials science, physics, chemistry,

tribology, and engineering. This is because there is really no alternate approach to MD

simulation capable of handling such broad ranging problems at the required level of details,

namely, atomistic level. MD simulations are providing new data and exciting insights into

ultraprecision machining that cannot be obtained readily in any other way - theory or

experiment. In this paper, the principles of MD simulation, relative advantages and current

limitations of this technique, and the application of MD simulations in addressing a wide

range of machining problems will be presented.

l. INTRODUCTION

For a long time, miniaturization of products was limited essentially to one industry,

namely, the watch industry. Various components of a watch were fabricated mainly by

mechanical methods using minilathes, minidrilling machines, minimilling machines, and

1 Reg~ts Professor, Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater,

OK 74Q78, U. S. A, Phone: (405) 744-5900, Fax: (405) 744-7873, e-mail:ranga@ceat.okstate.edu 2 Regents Professor, Chemist!)' Department, Oklahoma State University, Stillwater, OK 74078, U. S. A

Metal Cutting and High Speed Machining, edited by

D. Dudzinski et al., Kluwer Academic/Plenum Publishers, 2002 1

2 R. KOMANDURI AND L M. RAFF

the like. Other applications of miniaturization include miniaturization of works of art, such

as paintings and production of miniaturized religious books, such as the Bible, the Koran,

the Bhagavath Geetha. However, these are people-oriented tasks rather than machine￾oriented tasks. Today, the machine-oriented tasks are changing and industry is moving

rapidly into micro- and nanotechnologies with unlimited opportunities and benefits to

society. With the development of rigid, ultraprecision machine tools and associated control

systems, it is becoming increasing possible to produce parts economically with very high

degree of accuracy (form accuracy in the submicrometer level) and surface finish on the

order of a few nanometers Ra. The advances made in this technology are being translated

into the design of more conventional machine tools with the result that both accuracy and

finish achievable, even with conventional machine tools, are improving rapidly, almost

following the famous Taniguchi Chart prepared in 1983 with predictions projected up to

Year 2000 [I). Whether it is producing parts by ultraprecision machining/grinding

technology, determining mechanical properties of materials for micro-electromechanical

systems (MEMS), analyzing friction at the atomic scale between the rider and disk in a

computer hard drive, or simulation of the nucleation and growth of diamond by low pressure

diamond synthesis, material behavior at the atomistic level is becoming more and more

pertinent in today's highly technology oriented society.

Micro-electro-mechanical systems (MEMS), micro-opto-electro-mechanical systems

(MOEMS) are currently being developed for a myriad of applications ranging from

engineering to medical to biological applications. Recently, Japan had an interesting

research project on the development of an integrated microfactory where an entire factory

(accurate working machines) consisting ofN.C. machine tools, forming machines, assembly

equipment, and robots as well as the associated electronics and computational facilities all fit

in a brief case-on-wheels which can be transported to any place for show and tell [2]. The

demonstration part was the fabrication and assembly of a bearing within the accuracy

expected of such bearings (ABET l 0). Japan believes that in the future such systems will be

widely used in the fabrication ofmicromechanical components and devices.

2. ANALYSIS OF A PHYSICAL PHENOMENON

Traditionally there have been two approaches to scientific endeavor, namely, theoretical

analysis and experimentation. In general, the theoretical equations describing the

phenomenon are complex and difficult to solve analytically. Therefore, it is common

practice to make the equations tractable by invoking several underlying approximations and

assumptions. The validation of these assumptions, as well as the outcome of the theory, is

generally checked by experimentation. Thus, theory and experimentation compliment one

another and contribute toward a fundamental understanding of a given process or a physical

phenomenon.

With the advent of the computer age, a third approach, namely, simulation or numerical

analysis has been developed. This is principally because the laws governing many problems

in engineering and physical sciences are expressed mathematically by partial differential

ON THE SIMULATION OF MACHINING AT THE ATOMIC SCALE 3

equations, the direct solutions of which are possible only in limited cases. Numerical

methods, on the other hand, can solve complicated initial-value as well as boundary-value

problems by discretization of the independent variables (spacial and temporal) and the

transformation of the continuous derivatives into their discontinuous counterparts, i.e. their

finite difference quotients.

Numerical techniques began with the finite difference method (FDM), then extended to

the finite element method (FEM), and finally to atomic or molecular dynamics (MD)

simulations. While FDM and FEM methods are playing a significant role in addressing a

number of machining problems at the macroscale (or in a continuum), atomic-scale

simulations are providing new data and exciting insights into ultraprecision machining that

cannot be obtained readily in any other way - theory or experiment. The theorists consider

simulation as computer experimentation and the experimentalists consider simulation as

computer analysis. Still others consider MD methods as numerical simulations that lie

between analysis and experimentation. From this, it is clear that where MD simulations fit

depends entirely on the viewpoint of the investigator.

In this paper, the principles of MD simulation, the relative advantages and current

limitations of this technique, and its application to a range of machining problems will be

presented.

3. SIMULATION TECHNIQUES

Ashby [3] defined "simulation" as a study of the dynamic response of a modeled system

by subjecting the model to inputs that simulate real events. The model system may not

actually resemble the system under consideration; instead it can mimic it but adequately

describing the behavior and response of a real system. For example, Sir Lawrence Bragg

developed a "soap bubble" analogy to describe the behavior of a metal at high temperatures

simulating nucleation and growth of grains, formation of subgrains and their coalescence

into larger grains and even dislocation generation and propagation, although soap bubbles

have very little in common with metals.

Since the 1970's, continuum mechanics [FDM and FEM methods] approaches have

been applied to metal cutting problems [4-6). Here, the material is considered to be a

continuum neglecting the microconstituents (chemistry, crystal structure, lattice spacing,

grain size, second phase particles, etc.) of the work material or the tool, except through some

physical properties. The number of nodes and the distances between the nodes are selected

arbitrarily; a coarser mesh for gaining processing speed and a finer mesh for accuracy.

Similarly, the shapes of the elements are also selected arbitrarily, e.g. triangular, square, etc.

Also, the number of nodes is generally limited, perhaps to only a few hundred. This should

be kept in mind when comparing the number of atoms considered in MD simulation.

Nonetheless, this analysis, along with others methods, have contributed significantly towards

a better understanding of the mechanics of the cutting process from one vantage point,

namely, computational.

4 R. KOMANDURI AND L. M. RAFF

In the late l 980's, MD simulation was introduced to model nanometric cutting as in

ultraprecision machining [7-9). Unlike in FEM, in MD simulations the nodes and the

distance between the nodes are selected not on an arbitrary basis but on the basis of more

fundamental units of the material, namely, centers of the atoms as the nodes and interatomic

distances as the distance between the nodes. Also, the shape of the crystal is dictated by the

crystal structure of the material and not arbitrary as in FEM. For example, the shape of the

crystal is fee or bee for cubic metals with the arrangement of the atoms depending on the

crystal orientation. Thus the process can be reduced to its fundamental units for analysis.

Also, MD techniques give higher temporal and spatial resolution of the cutting process than

is possible by a continuum mechanics approach. Typical scaling parameters in MD

simulation are the following: length scale : 10- 10 m (O. l run or 1 A); number of particles

involved: 103-106, and the time steps: 2-3 picoseconds (ps). Consequently, certain

phenomena that of necessity must be neglected in a continuum analysis can be effectively

investigated by MD simulation. However, since a large number of atoms constitute any

common material, one needs to consider the interactions of several thousands of atoms in

MD simulation of machining. Unfortunately, such a simulation requires significant memory

and fast processing times. It may be an interesting fact to note that an MD simulation of a

physical phenomenon may take several weeks of processing time (depending on the

complexity of the problem) for the description of the process lasting for less than a

nanosecond ! The number of atoms under consideration are, therefore, limited to a few

thousand and the speed of cutting to a very high value, typically, 100-500 mis, so that MD

processing time can be kept at a reasonable level, namely, a few hours to a maximum of a

few days. Of course, the results obtained and the physical understanding of the process can

more than justify the long processing times.

Since a large number of atoms constitute any common material, one needs to consider

the interactions of several thousands of atoms in a MD simulation of machining. Prior to the

1970's, such a task could be handled only by the so-called large mainframe computers of the

yester years with significant memory and fast processing times. Today, this is changing

rapidly with the availability of fast, inexpensive workstations with significant memory and

processing capabilities.

4. COMPUTER EXPERIMENTS

Computer experiments allow one to study complex systems and gain insight into their

behavior. They can also fill the gap between theory and experiment as some quantities or

behavior of a system may be difficult, if not impossible, to measure by experiment. What

distinguishes computer simulation from other forms of computation is the manner in which

the computer is used. Rather than serving as a fast number crunching machine, it serves as a

virtual laboratory in which a given physical system can be analyzed.

In real experiments, the process itself provides the basis for investigating the

relationship between the input and the output parameters. In other words, the physical

phenomenon is already in place in real experiments. In the computer experiments, the

ON THE SIMULATION OF MACHINING AT THE ATOMIC SCALE 5

physical phenomenon is absent and has to be introduced on some physical basis and

preferably in a mathematical form. This is done in the computer experiments in the form of

physical Jaws of nature, for example, Newton's laws of motion in MD simulations. The

potential-energy function operating between the atoms comprises an important part of the

input data. The accuracy of the potential data is limited by our current knowledge and

computational facilities. It cannot be stressed sufficiently that the results of computer

simulations, like those of any theoretical study, are only as good as the model. Consequently,

it is essential to investigate the sensitivity of the results to various aspects of the model. One

major uncertainty is the form of the interatomic potential, and very little significance may be

attached to the results of computer simulations that do not investigate their sensitivity to the

chosen potential. In general, the most interesting results from computer simulations are not

absolute numerical value for given quantities, but rather the comparative values of two or

more quantities. Provided that reasonable caution is exercised in interpreting the results of

computer simulations, there is no reason why these techniques should not be used with

considerable success to improve our understanding of the physical problems involving

atomic motions in crystals as in nanometric cutting.

Another point worth noting is that while a certain methodology has evolved over time

for the conduct of experimental work, the approaches taken by various researchers from

different disciplines in addressing problems using MD simulation are somewhat ad hoc. It is

hoped that due to rapid advances in this filed, a systematic methodology would evolve soon

in addressing a wide range of problems using MD simulation.

The main limitations of the computer experiments are (a) limited observation time, (b)

finite system size, and (c) deviations in the potential-energy function used from the

description of an actual system.

5. MD SIMULATIONS

Atomic or molecular dynamics simulations are playing an increasingly important role in

materials science, physics, chemistry, and engineering. They offer a microscopic or, more

precisely, an atomistic view of physical phenomenon that cannot be obtained readily by

experiment. Predictions resulting from this atomic-level understanding are providing

increasingly accurate and useful information. Consequently, the field of atomistic simulation

is progressing rapidly as an indispensable tool, especially with the advent of fast,

inexpensive workstations. This trend can only continue with time, as the computers are

gaining speed, memory is increasing, and the cost decreasing all simultaneously. This

means that with the same effort one can simulate a system with a larger number of atoms or

integrate molecular-dynamics trajectories faster. Also, this field is evolving as a true

interdisciplinary activity with active participation by chemists, physicists, engineers,

tribologists, and material scientists.

Many detailed textbooks have been written on MD simulation [10-19] and should be

referred to for details. Here, aspects pertinent to the simulation of machining at nanoscale

are covered briefly.

6 R. KOMANDURI AND L. M. RAFF

Almost all physical phenomena, when considered at the basic elemental level, can be

attributed directly or indirectly to the forces acting between the atoms that constitute the

material. Basic concepts such as temperature and pressure, the strength and modulus of a

solid are intimately related to the forces between the atoms. For most purposes, the force

between two atoms is expressed in terms of derivatives of the potential-energy function.

These derivatives depend on the separation distances between the atoms. The potential

energy of a system having two or more molecules contains terms involving the vibration

frequency, relative orientation, and rotation of the molecules. When a large number of atoms

are held together by chemical bonding, they usually take the form of a regular lattice whose

structure is determined by the characteristics of the bonding. Many of the physical properties

ofa crystalline solid are intimately related to the type of bonding between the atoms.

Molecular dynamics simulations are generally separated into two distinct parts by

invoking the Born-Oppenheimer approximation. This approximation rests on the fact that,

due to large mass differences, the nuclei move slowly relative to electronic motion.

Consequently, it is possible to solve the quantum mechanical SchrOdinger equation for the

electronic energy in the electric field produced by stationary nuclei. In principle, the first

part of the MD simulation comprises repeated solution of the SchrOdinger equation at

different nuclear conformations to obtain a set of points, which when fitted to a suitably

chosen analytic function, constitutes the potential-energy surface for the system. In the

second part of the problem, the nuclear motion on this potential-energy surface is computed

for a given set of experimental conditions. Ideally, this calculation is executed quantum

mechanically.

In practice, MD simulations are usually further simplified. A typical workpiece in a

cutting experiment will contain on the order of I 023 to I 024 atoms or molecules. The solution

of the SchrOdinger equation, which would need to describe all the electrostatic interactions

between these atoms, is impossible to execute at the present time. In fact, if the number of

atoms present exceeds five, the problem of obtaining the potential-energy surface becomes

extremely difficult. For this reason, an empirical or semi-empirical approach is usually

adopted. This method involves the careful selection of parameterized functional forms based

on chemical and physical considerations. The parameters contained in these functions,

which describe stretching, bending, wagging, and dissociation motions of the atoms, are

then empirically adjusted to fit measured structural data, vibrational frequencies, the Debye

temperature, dissociation energies, and sublimation enthalpies for the crystal under

consideration.

The second part of the problem is also simplified by assuming that the masses of the

nuclei are sufficiently large that they obey the postulates of classical mechanics. In effect, it

is assumed that we are at the Bohr correspondence limit where quantum mechanics turns

into classical mechanics. This assumption permits us to replace the solution of the time￾dependent SchrOdinger equation with a much easier solution of the classical Hamiltonian

equations of motion. In addition, the number of atoms explicitly considered in the simulation

is generally reduced to several hundred or, at most, a few thousand. Since the experimentally

observable quantities are statistical averages over the ensemble of "" I 023 atoms, we need