Metal cutting and high speed machining

Topics covered include: mechanics of cutting, numerical models, chatter vibrations, machining processes drilling, high speed milling, grinding, hard turning, cutting tools and coatings,

Tai ngay!!! Ban co the xoa dong chu nay!!!

METAL CUTTING AND

HIGH SPEED MACHINING

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)

©2002 Kluwer Academic I Plenum Publishers, New York

233 Spring Street, New York, New York 10013

http://www.wkap.nl/

1 0 9 8 7 6 5 4 3 2

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

All rights reserved

No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means , electronic, mechanical, photocopying, microfilming, recording, or otherwis , without written permission from the Publisher

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

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

AND CHIP FORMATION IN HIGH SPEED TURNING 31

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

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

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

PARAMETERS ON CHIP FORMATION PROCESS 91

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

vii

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 KTNEMATICS 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

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

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 1 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

FTNITE ELEMENT ANALYSIS 191 E.G Ng, S.L Soo, C Sage, R Dewes, and D Aspinwall

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

30 DEVELOPMENT OF CAM SYSTEM FOR HIGH SPEED MILLING 341

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

K Kase, and M Anzai

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

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

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

38 PARALLEL KINEMATIC MACHINES-DEVELOPMENT,

SOFTWARE METHODS AND EXPERIENCES 435

V Maier

MACHINE TOOL COMPONENTS

39 HIGH VOLUME CUTTING OF ALUMINIUM 445

H.Voll

THERMO-MECHANICAL-DYNAMIC BEHAVIORS OF MOTORIZED

MACHINE TOOL SPINDLES 455 C.-W Lin, J.F Tu, and J Kamman

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

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

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 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

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 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

only ensure that the number of atoms being considered is sufficiently large to yield accurate statistical averages Because the random error generally scales as N-112, where N is the number of samples, models that include about 103 atoms can be expected to produce results with about 3% statistical error, which is generally small relative to errors introduced by uncertainties in the potential-energy surface

Unlike Monte Carlo methods that adopt a statistical probabilistic approach, MD uses a deterministic approach that tracks the individual motion of each of the particles by solving the Hamiltonian equations of motion This process can be likened to the dynamic response of numerous nonlinear spring-mass systems under an applied load, velocity, or displacement conditions From this point of view, MD simulation is similar to other analyses that mechanical engineers routinely conduct, such as the investigation of vibrations of a mechanical system wherein a series of springless masses and massless springs are connected and the response of the system is investigated under a given external load

The time evolution of the ensemble is computed by integrating the equations of motion

in a discrete fashion using time steps, ~t, on the order 1 o-14s The method involves the calculation of the position and velocity of each individual atom at time t + ~t from a knowledge of its position and velocity at time t Such a classical treatment of the atomic interactions and the resulting dynamics in terms of potentials and the classical equations of motion is consistent (within certain limits) with the solution of the time-dependent Schrodinger's equation provided we are near the Bohr correspondence limit The actual solution of the equations of motion is accomplished by numerical integration that involves some approximations The resulting error, however, can be as small as desired within the memory and speed capabilities of the computing system

MD simulations are conducted through a series of time steps consisting of: (I) summation of the pairwise forces for each atom, (2) calculation of new velocities and displacements at each time step, and (3) determination of the new positions of the atoms For

an appreciation of the computational intensity involved in MD simulations, it may be noted that the number of differential equations to be solved is given by 6N, where N is the number

of atoms considered in the workpiece, which can vary from a few hundred to several thousand atoms The larger the number, the longer is the processing time Generally, 2 to 10 thousand atoms are considered in a simulation Thus, a 2000-atom model requires integration of 12,000 coupled, first-order differential equations of motion In most MD simulations of machining, the potential-energy function used is a summation of pairwise interactions with perhaps some three-body terms included The total number of pairwise terms in such a potential is given by N{N-1 )/2 Thus, for N = 2000, some 2 mill ion pairwise terms need to be calculated each time a derivative is evaluated Since two to four such evaluations must be done for every integration step, some 4-8 x 106 evaluations would be required for every trajectory Hence, the computation time increases very rapidly as the number of atoms considered increases However, the model must be "size-converged." That

is, the final results should not be sensitive to the inclusion of additional atoms in the model

To determine if a model is size-converged, preliminary empirical studies must be conducted

in which the sensitivity of the final results to the number of atoms included is determined

8 R KOMANDURI AND M RAFF

The optimum number is the smallest value ofN for which the final results are judged to be sufficiently insensitive to N

6 POTENTIAL ENERGY FUNCTIONS

Whenever a problem is treated on an atomic scale, there is a need for some knowledge

of the forces that exist between the atoms It is these forces that decide much of what we can observe of a natural phenomena In MD simulations, the interatomic bonding forces (both attractive and repulsive) are defined by an appropriate parameterized empirical potential-energy function

In a simple pair potential, e.g Morse or Lennard-Jones potentials [20], only the direct interactions between atoms are considered and summed for a certain sphere with a radius that is usually equal to the spacing between four adjacent atoms They fully determine the total energy without considering any further cohesive terms that arise from the interaction with atoms fur away from the particle considered The atoms are regarded as mass points which have a central interaction with their nearest neighbors The interaction of any pair of atoms depends only on their spacing This implies that such potentials are principally radially symmetric and independent of the angular position of other atoms in the vicinity

A schematic diagram of a typical two-body interatomic potential is shown in Figure I It consists of an attractive part at large separations approaching a minimum in the region of the equilibrium separation, then becoming repulsive and increasing rapidly as r decreases further Because of many-body effects, theoretical models employing two-body potentials are somewhat approximate The description of an assembly of atoms by means of a sum of pair interactions is valid only under stringent conditions since the total energy of the system contains others terms due to n-atom interactions which are neglected in the second-order perturbation expansion In the case of a solid at equilibrium, therefore, care must be exercised in any calculation involving pair potential that the conditions of validity are fulfilled The accuracy of the results of such a calculation depends not only on the accuracy

of the chosen potential but also on the nature of the solid and on the situation to which the potential is applied

The question then is why use Pairwise Potentials? Frequently, pairwise interactions are used simply because a more accurate description of the solid would rapidly become too complicated for practical purposes These potentials are termed empirical although it is somewhat misleading to use the term "empirical." In fact, the present state of theoretical knowledge is such that such parameterized potentials often present a more realistic view of atomic interactions than potentials derived exclusively, and usually at great pain, from purely theoretical considerations that are themselves often approximate in nature Use of such complex interatomic potentials may lead only to inordinate computational time without actually providing significantly superior results

Empirical potentials are, in most cases, based on a simple analytical expression which may or may not be justified from theory, and which may contain one or more parameters adjusted to an experimental situation This is why the potentials are termed "empirical" The

ON THE SIMULATION OF MACHINING AT THE ATOMIC SCALE

Figure I Schematic of a typical two-body interatomic potential showing the variation of the potential energy and the

net force with interatomic separation •

10 R KOMANDURI AND L M RAFF

purpose is to facilitate the analytical treatment of problems at the atomistic level The availability of high-powered computers has enabled the use of more complex empirical potentials based on more widely varied experimental data Almost all forms of pairwise potentials are empirical, due to the approximations necessary to overcome the many-body problem involved in the interaction The validity of the function as well as the stability of the crystal for a given material are checked for various properties including cohesive energy, the Debye temperature, the lattice constant, the compressibility, and the elastic constants as well as the equation of state Of course, there are more complex interaction potentials developed beyond the pair potential, such as the embedded atom potential and Tersoff's potential [21-24] They should be considered where appropriate

7 BOUNDARY CONDITIONS

Two aspects should be considered in the formulation of adequate boundary conditions for MD simulations The first one is the size of the simulation box or the number of atoms under consideration It should be as small as possible to reduce the overall computational efforts (computation time, coding convenience, required RAM, etc.) At the same time, the simulation cell should be large enough to exclude the possibility that any kinetic disturbance can re-enter the block leading to an artificial perturbation of the lattice defects being investigated Furthermore, the box must be large enough to provide reliable statistics Second, a physically realistic coupling accounting for volume expansion, strain compatibility, and stress equilibrium between the surroundings and the simulation cell should be considered

8 VELOCITY RESET FUNCTION

Since plastic deformation in the primary shear zone and friction at the chip-tool interface is converted into heat, this has to be dissipated continuously In actual machining, much of this heat is carried away by the chip, the lubricant in addition to the tool and workmaterial It is essential that the effects upon the energy transfer within the solid that would be present for an extended lattice model, be included in the calculations This could,

of course, be accomplished by considering lattice models that contain large number of atoms, say, 106 atoms or more Such a procedure, however, is not computationally efficient The most efficient method for simulating the removal of the heat generated in machining is the use of velocity reset functions Velocity reset methods have been suggested by Agrawal et

al [25] and by Riley et al [26] The latter of these is the more general in that the procedure permits statistical fluctuations about the equilibrium temperature

ON THE SIMULATION OF MACHINING AT THE ATOMIC SCALE 11

9 APPLICATION TO MET AL CUTTING

MD Simulation can be used to address many machining problems at the nanoscale They include: 1 Mechanics of nanometric cutting of nonferrous materials, such as copper and aluminum, 2 Effect of various process parameters, such as, rake angle, edge radius, depth of cut on the cutting and thrust forces, the force ratio, and the specific energy, 3 Investigation of the nanometric cutting of workmaterials of known crystallographic

semiconductor materials, such as silicon The nature of deformation in the work material

ahead of the tool and subsurface deformation in the machined surface can be investigated at atomic level by this method The authors and their collaborators have conducted extensive studies on MD simulation of nanometric cutting of fee metals and silicon, tribology, and nonomechanical testing [27-36] In the following, the application of MD simulations to metal cutting will be briefly reviewed

9.1 Mechanics ofNanometric Cutting

The main difficulty in the experimental approach of nanometric cutting is that it is a

main advantage of the MD simulation is that it can be observed in situ Another advantage

of MD simulation is that it does not require an expensive ultraprecison machine tool located

in a controlled environment together with a trained person to operate it

In ultraprecision machining of nonferrous materials with a single-crystal diamond tool

on an extremely rigid, high-precision machine tool, the chip size is on the order of a few nanometers Therefore the mechanics of the process can be studied in detail using the MD simulation of the nanometric cutting [27) Different workmaterials whose interaction potentials are available can be studied under different processing conditions Use of animation techniques can provide a continuous sequence of the cutting process that often reveals important characteristics of the process that would otherwise go unnoticed

9.2 Effect of Process Parameters

The effect of various process parameters, such as the workmaterial under consideration, tool rake angle, edge radius, and depth of cut on the cutting forces, the force ratio, and the specific energy can be investigated using MD simulation with relative ease [27-30] The high cost of single-crystal diamond tools all but precludes their extensive use to cover a range ofrake angles, edge radii, etc Also, it is difficult to obtain precise geometry although experimental efforts are being made to obtain precision geometries This is particularly true

of the edge radius One may have to settle for what one gets it and determine it by established characterization techniques ln MD simulation, the effect of these parameters on the nature of chip formation, forces, force ratio, and specific energy can easily be determined and compared with the experimental results for verification Figures 2 and 3 show MD simulation plots of machining single crystal aluminum at various rake angles [27] and edge

well-12 R KOMANDURI AND L M RAFF

radii [28) Figure 4 shows the variation of the cutting and thrust forces, the force ratio, and the specific energy with rake angle [27) Also shown in the figure are experimental results

observed both in the simulations and the experimental results, although at much higher

materials free of defects, such as point, line, or area defects as well as the small size of the specimen considered

9.3 Crystal Orientation of the Workmaterial

The anisotropic behavior of single crystal materials in different orientations is well known How the crystal orientation and the direction of cutting affect the cutting process is again a difficult task by experimentation Single-crystal workmaterial are rather expensive and require extreme skill to orient them on the machine tool Again the analysis of the

measure forces (which are rather difficult to measure accurately), and try to relate the input

can be used advantageously to investigate the cutting process in different crystal orientations and directions of cutting Thus new insights not previously recognized by experimentation can now be obtained using these techniques [29,32) For example, Figure 5 shows MD simulation of machining single crystal aluminum in different orientations and cutting directions [29,32) One can clearly see the differences in the nature of deformation ahead of the tool, the dislocation generation and propagation depending on the crystal orientation and direction of cutting

9.4 Modeling of the Exit Failure in the Workmaterial

Burr formation in machining is commonly experienced and costly secondary burr

underlying reasons, and how to avoid or minimize burr formation are important

used to advantage to study the mechanics of the burr formation [34) Figure 6 shows a comparison of MD simulation of the exit failure [34) and optical micrograph of the exit

techniques should not be considered as the do-all and end-all of all problems They should

be considered as complimentary, each adding a piece to the jigsaw puzzle

ON THE SIMULATION OF MACHINING AT THE ATOMIC SCALE 13

Figures 2 MD simulation plots of machining single crystal aluminum at various rake angles [27] and edge radii [28]

(a) -75°, (b)-60°, (c)-45 °, (d) - 30 °, (e)-15 °, and (l) 0°

14 R KOMANDURI AND L M RAFF

Cut depth : 0.362 nm , Edge radius : 81 nm Cut depth: 1.448 nm, Edge radius ; 24 nm

Cut depth : 724 nm , Edge radius: 3 62 run Cut depth : 172 nm, Edge radius : 10 86 nm

Figures 3 MD simulation plots of machining of single crystal aluminum with tools of various edge radii

[28]

9.5 Nanometric Cutting of Silicon

Silicon is used extensively as a semiconductor material in the electronics and computer industry The single-crystal silicon wafers are polished and diced to required size for these applications Machining can play an important role in reducing costs and producing a superior product Attempts are currently being made to machine silicon using high negative

pressure, the structure of silicon can be transformed from a covalent cubic diamond structure

to a body-centered tetragonal crystal form resulting in considerable reduction in density

ON THE SIMULATION OF MACHINING AT THE ATOMIC SCALE 15 phenomenon in situ (35] Based on the simulation results, it appears that silicon may in fact change the crystal structure as evidenced by the significant densification of the workmaterial underneath the tool as well as in the chip under the conditions of cutting (Figure 7 (35]) ·

I _, _ ISi Crawford et al HI lCom8nd

Rake angle, degrees

Figure 4 Variation of the cutting and thrust forces, the force ratio, and the specific energy

with rake angle Data for the bottom figure is MD data [27)

R KOMANDURI AND L M RAFF

18 R KOMANDURI AND L M RAFF

10 CONCLUDING REMARKS

The purpose of this paper is not to present original results but to share the underlying philosophy involved in all simulations It may be noted that FEM, FDM, and MD simulation are merely techniques and not solutions They play an important role in the fundamental understanding of the cutting process from continuum (or macro level) to atomistic level They should, therefore, be considered as complimentary rather than competing techniques Since FEM has been widely used, especially by civil and mechanical engineers, many take it for granted that FEM can be used for any problem and what it gives are the unquestionable results In other words, it is the solution to any problem Of course, FEM and FDM are powerful techniques but they have their own limitations Use of only a few hundred nodes or not paying much attention to its limitations does not seem to matter significantly for some researchers In contrast, due to lack of familiarity by the manufacturing community, they question the validity ofusing MD simulations as a simulation technique to address a wide range of physical problems Questions, such as the potential used, the number

of atoms considered, and the speeds used are always excuses for discouraging the use of MD simulations In sharp contrast, there seems to be no problem in considering a spring-mass-dashpot vibratory system under the influence of an external force when investigating mechanical vibrations Similar limitations in experimentation or simulation techniques again do not seem to bother these very researchers While there is no doubt that MD simulations, like the FEM and FDM, have limitations, they serve a useful purpose in niche areas where other techniques (including FEM and FDM) fail to provide critical information People working in the MD field are fully aware of the limitations of this technique and are paying increasing attention to overcoming some of these problems It is appropriate to state a comment made by a physicist regarding the choice of a potential and in support of

MD simulation in general and we paraphrase: "not recognizing the power of any of these techniques and not using it to our advantage is like throwing out the baby along with bath water."

In conclusion, it may be interesting to consider the following scenario Imagine that you are not an engineer, or a manufacturing specialist, or a tribologist Let us say that you have

no idea what a tensile test is, or how it is conducted, or what the results are Similarly, let us say that you have no idea what machining is, or what the mechanics of the process is Not being a tribologist you have only a limited knowledge, if any, about friction at the atomic scale On the other hand, let us say that you are a physicist who knows only molecular dynamics (MD) simulation Now imagine that you both set out to investigate and elucidate these phenomena Surprisingly you will both obtain results that are amazingly in full agreement in all cases with the interpretation of a research engineer, a manufacturing engineer, and a tribologist, as the case may be In other words, the physical phenomena are accurately represented by the result of the MD simulation Such is the power of the MD simulation technique

ON THE SIMULATION OF MACHINING AT THE ATOMIC SCALE 19

ACKNOWLEDGEMENTS

This project is sponsored by grants from the Manufacturing Processes and Machines Program (DMI-9523551) of the Division of the Design, Manufacture, and Industrial Innovation (DMII) and the Tribology and Surface Engineering Program (CMS-9414610) of the Division of Civil and Mechanical Structures of the National Science Foundation The author thanks Drs K Rajurkar, Delcie Durham, and Kesh Narayanan of DMII and Dr J Larsen Basse of the Tribology and Surface Engineering Program for their interest in and support of this work One of the authors (R K.) also thanks the A.H Nelson, Jr Endowed Chair in Engineering for financial assistance in the preparation of the manuscript Special thanks are due to the author's former graduate student, Dr N Chandrasekaran, for active collaboration without which none of this work would have been accomplished

REFERENCES

I N Taniguchi, Current status in, and future directions o( ultraprecision machining and ultrafine materials processing, Annals ofCIRP 32(2), 573-582, (1983)

2 - , Portable Machining Microfactory, Mechanical Engineering Laboratory, Tsukuba, Japan (1999)

3 M F Ashby, Physical modeling of materials problems, Materials Science and Technology , , 102 , (1992)

4 E Usui and T Shirakashi, Mechanics of machining - from descriptive to predictive theory, On the Art of Culling

Metals- 75 Years Later, ASME Publication PED 7 13-25 , (1982)

5 K Iwata, K Osakada and Y Terasaka, Process modeling of orthogonal cutting by the rigid-plastic finite element method, Trans ASME , J of Engg Mat and Tech., 106, 132-138, (Apr 984 )

6 J Carroll and J S Strenkowsk~ Finite element models of orthogonal cutting with application to single point diamond turning, Int J Mech Sci , 30(12), 899-920, (1988)

7 J Belak and I F Stowers, A molecular dynamics model of the orthogonal cutting process, Proc ASPE Annual

Con/, 76 , Rochester, NY ( 1990)

8 I F Stowers, J Belak, D A Lucca, R Komanduri , R L Rhorer, T Moriwaki, K Okuda, N lkawa, S Shimada,

H Tanaka, T A Dow, and J D Drescher, Molecular dynamics simulation of the chip forming process in single crystal copper and comparison with experimental data, Proc of the ASPE Annual Con/, I 00-103, ( 1991 )

9 J Belak, D B Boercker, and I F Stowers, Simulation of nanometer-scale deformation of metallic and ceramic surfaces, MRS Bulletin , 55-60 , (May 1993)

10 L M Raff; D A Thompson, The Classical approach to reactive scattering, in Chapter I Theory of Chemical

Reaction Dynamics , 3n1 Edition, Editor M Baer, CRC Press, 1-121 (1983)

11 W G Hoover Molecular Dynamics , Lecture Notes in Physics, Vol 258 , Springer-Verlag, Berlin, 1986

12 R Levine, R Bernstein, Molecular Reaction Dynamics and Chemical Reactivity, Oxford University Press, Oxford ( 1987)

13 J M Goodrellow, Molecular Dynamics : Application to Molecular Biology, CRC Press Inc ( 1990)

14 M Allen, J Tildesley, Computer Simulation of liquids, Oxford University Press, Oxford, U.K (1991)

15 I M Torrens, lnteratomic Potentials, Academic Press, NY (1972)

16 D.C Rapaport, The Art of Molecular Dynamics Simulation , Cambridge University Press, Cambridge, U.K (1995)

17 D Raabe, Computational Materials Science , Wiley-VCH, Weinheim, Germany ( 1998)

18 K Binder, D W Heermann, Monte Carlo Simulation in Statistical Physics : An Introduction , 3n1 Edition,

20 R KOMANDURI AND L M RAFF

21 B C Bolding and H C Anderson, Intearatomic potential for silicon clusters , crystals, and surfuces, Physical Review B , 41, 10568-10585 , (1990 )

22 J Tersoff, New empirical approach for the structure and energy of covalent systems , Physical Review B , 37 (12), 6991-6999 , (15 April 1988)

23 Brenner, D W and B J Garrison, Dissociative valence force field potential for silicon, Physical Review B , 34(2), 1304-1307 , (15 July 1986)

24 F H Stillinger and T.A Weber, Computer simulation of local order in Condensed phases of silicon, Physical Review B , 31(8) , 5262 - 5271 , (15 April 1985)

2 P.M Agarwal , L M Raff , and D L Thompson, Effect of the lattice model on the dynamics of dissociative chemisorption ofH2 on a Si (111) Surfilce, Suiface Science , 188 , 402 , ( 1988)

26 M E Riley, M E Coltran, and D J Diestler, A velocity reset method of simulating thermal motion and damping

in gas-solid collisions, J C hem Phys 88(9), 5934-5942 , (1 May 1988)

27 N Chandrasekaran, A Noori-Khajavi , L M Raft; and R Komanduri, A new method for MD simulation of nanometric cutting, Philosophical Maga z ine , 77( I), 7-26 , ( 1997)

28 R Komanduri, N Chandrasekaran, and L Raff, Effect of tool geometry in nanometric cutting: an MD simulation approach, Wear , 218 , 84-97 , (1998)

29 R Komanduri, N Chandrasekaran, and L M Raff, Orientation effects in nanometric cutting of single crystal materials: an MD simulation approach, Annals of C IRP , 48( 1 ) , (1999)

30 R Komanduri, N Chandrasekaran, and L M Raft; Some aspects of machining with negative rake tools simulating grinding: an MD simulation approach, Philosophi c al Magazine B , 79 ( 7) , 995 - 968 , (1999)

31 R Komanduri, N Chandrasekaran, and L M Raft; MD simulation of indentation and scratching of single crystal aluminum, Wear , 240 , 113 - 143 , (2000)

32 R Komanduri, N Chandrasekaran, and L M Raff, MD simulation of single crystal aluminum - effuct of crystal orientation and direction of cutting, Wear, 242 , 60-88 , (2000)

33 R Komanduri, N Chandrasekaran, and L M Raff, MD simulation of atomic scale friction , Physical Review B ,

40 A J Pekelharing , The exit railure in interrupted cutting, Annals of Cl RP , 2711 , 5 (1978)

41 Y Yan, M Yoshino , T Kuriagawa, T Shirakashi, K Syoji , and R Komanduri, On the ductile machining of silicon for micro electro-mechanical systems (MEMS), Opto-electronic, and optical application, Materials Science

&Engineering A , 297, 230-234 , (2001)

DYNAMICS IN HIGH SPEED MACHINING

G Warnecke and S Siems·

1 INTRODUCTION

The significance for High Speed Machining and especially High Speed Milling in production has increased since new machines and tools are able to apply high removal rates High Speed Machining enables the possibility to reduce process time on the one hand and to improve workpiece accuracy and workpiece surf.tee on the other hand High Speed Machining is mostly related to the application of high cutting speeds up to two or three times higher as in conventional cutting Due to short contact times between cutting edge engagements in high speed machining, material behavior of the workpiece at high deformation rates with occurring high gradients of deformation and temperature in workpiece and tool is not well known and cannot be described by means of conventional material Jaws Within the range of generally used cutting speeds, the cutting force decrease with increasing cutting speed At very high cutting speeds, however, the cutting force increases due to inertia forces The measurement of cutting forces at high cutting speeds is influenced by limitations of the measuring system To enable a reproducible measurement of the true cutting forces in milling operations, the system must be very stiff and a sensor with high resonance frequencies is required With a known system behavior, e g the transfer function, algorithms to calculate a signal which is not influenced by the system response, e.g resonance, can be used to increase the range of cutting speed where cutting forces can be measured

In milling, several cutting edges interact at a time with the workpiece leading to superposition of process effects In order to analyze the conditions in the cutting zone experiments were conducted with high cutting speed and short time contact without superposition of cutting edge engagements and process effects A force measurement system based on a three component piezoelectric force sensor with a high resonance frequency and an algorithm to calculate the real cutting forces were used In addition, acoustic emission was measured to analyze the dynamic behavior at higher frequencies

• G Warnecke, S Siems , Institute for Manuracturing Engineering and Production Management, University of Kaiserslautem , Kaiserslautern D-67653

Metal Cutting and High Speed Machining, edited by

D Dudzinski et al., Kluwer Academic/Plenum Publishers, 2002 21

22 G WARNECKE ANDS SIEMS

2 EXPERIMENT AL SETUP

The experimental set-up consists of a rotating single insert end mill tool and a

Tektroni x Real-Time

Digitizer RTD 710 A

Kistler 5007 feed

Figure 1 Experimental Set-up

In order to obtain single cutting edge engagements at high cutting speeds the feed of the linear motion table is in a crosswise direction to the tool, and has to be higher than the width of cut which occurs on the workpiece during the experiment The resulting surface

of the machined workpiece is easily accessible and the generated scratches in the

The chips generated during the process were embedded and polishes of the tudinal section were made These polishes were examined under a light microscope The workpiece materials have been 40 CrMnMo 7, C22, C45 and C60 steel The cutting conditions and mechanical properties of the examined workpiece materials are presented

longi-in Table l

Workl!iece material 40CrMnMo7 40CrMnMo7 C22 C45e C 60 Heat treatment Hardened hardened , tempered N N N

Hardness 641 HV 470HV 129HB 222HV 241 HB Tensile strength 1850 Mpa 1100 MPa 590MPa 720MPa 910 Mpa Elong after fracture 10% 21 % 16% 13% Cutting speeds [m/min] 400-1200 500-6000 500 - 6000 500 - 8000 500 - 6000

DYNAMICS IN HIGH SPEED MACHINING 23

A force-measuring system based on a Kistler 3-component force sensor is used to get information about the transferred energy in the cutting process For characterization of the dynamic process behavior, acoustic emission is measured using a wide band sensor

3 FORCE MEASUREMENT

In cutting experiments with the presented experimental set-up, the measured cutting forces have an impulse-like character Due to short-time cutting edge engagements, the measured cutting forces changes very quick and a high frequency range will be excited,

as can be seen when assuming a sinusoidal force signal (Figure 2.)

super-et al 1 and Herget2 the true force signal can be calculated when the transfer function of the measuring system is known The transfer function H(f) is defined as (Eq 1):

H(f)= Sy(f)

Where Sx(f) is the Fourier transform of the input x(t) and Sy(f) is the Fourier transform of the output y(t)

24 G WARNECKE ANDS SIEMS

If the transfer function H(f) and the output y(t) are known, the input x(t) can be

calculated using Eq (2)

x(t) = p [Sy(f)]

For the application of this measuring method, it is necessary to measure the transfer

function of the force measuring system The transfer function was measured by means of

an impulse hammer KISTLER 9722A500 with a load cell and a hard steel tip To reduce

the noise in a single measurement, the transfer function was calculated based on the

average of a series of 20 measurements according to Eq 3 with the Fourier transformed

input signal from the load cell (Sx) and the Fourier transformed output signal from the

force sensor (Sy)

a

Where Gxx = Sx"s; is the power spectrum of the input and Gyx = Sy"sx• is the cross

transfer function in cutting direction is shown in Figure 3

Figure 3 Transfer function of the force measuring system in cutting direction ,

shows the same peaks This means that these frequencies are not resonance frequencies of

the force sensor but of the clamping device and the analysis of forces with excitations up

DYNAMICS IN HIGH SPEED MACHINING 25

to this frequencies is possible The manufacturer of the force sensor indicates the resonance frequency of the force sensor as 30 kHz when it is uninstalled Figure 4 shows the original cutting force and calculated signals The original signal at 4500 m/min shows very strong vibrations which are successfully eliminated by the inverse filter algorithm The calculation of the original cutting force has limitations due to cross talk between all sensor inputs At cutting speeds higher then 5000 m/min the measured and calculated signals should not be used reliably for further investigations As a result it can be concluded that the dynamic characteristic of the cutting force measuring system can be increased to a higher level by applying an inverse filter algorithm

Figure 4 Original and calculated cutting force signals

As the force signal consists of a strongly increasing and decreasing part, the analyzed forces are the maximum forces To allow comparable results, the specific cutting forces were calculated dividing the cutting force by the undeformed chip section The measured specific forces are shown in Figure 5 For all kind of steels the forces decrease significantly with increasing cutting speed The higher the tensile strength of the workpiece material, the higher are the specific cutting forces at low cutting speeds After

a strong decrease of the specific cutting force, for example at the 40 CrMnMo 7, hardened and tempered, for a cutting speed ranging from 1500 m/min to 3500 m/min, the force is nearly constant or increased with further increasing cutting speed Due to limitations of the calculation algorithm it is not obvious if the increase of cutting forces with further increase of cutting speed takes place as described by Klocke et al 3• Inertia forces of the removed material in this cutting speed range are very low and cannot be responsible for the increase

G WARNECKE ANDS SIEMS

-tt-40 CrMnM o 7 , hardened and terlllered

+ -11 """"= -i C22

-+-C60

1000

cutting speed [m!min]

Figure 5 Measured Cutting Forces of different machined steel types

4 CHIP FORMATION

To clarify the cutting zone conditions and the influence of dynamic effects during cutting, the chip formation mechanisms and its influence on the process dynamics in high speed machining is of particular importance Under special conditions, e g with further increase of cutting speed, chip formation is affected by deformation instabilities which indicate a transition from flow chips to serrated chips4• 5 • Apart from the cutting parameters, thermal and mechanical properties of the workpiece, e g its hardness and thermal conductivity, determine the chip formation mechanisms As a result of instabili-ties inhomogeneous deformation generates serrated chips

The material behavior of many workpiece materials, e g hardened steel or titanium alloys, leads to formation of serrated chips due to periodic brittle fracture6 or repetitive strain localization 7 This means that the deformation in the workpiece material concen-trates in narrow bands in the primary shear zone, where thermoplastic shear under nearly adiabatic conditions occurs4• As a result, the inhomogeneous deformation shear bands are generated periodically in the shear zone at a constant frequency called chip segmentation frequency The high deformations localized within small areas can be seen in Figure 6 where chips of different machined steel types with different chip formation mechanisms depending on the mechanical and thermal properties of the material are shown

The investigated 40 CrMnMo 7 steel shows a very strong segmentation for all cutting speeds and heat treatments The hardened 40 CrMnMo 7 steel has a very high hardness and therefore a low deformation ability With higher deformation ability for the hardened and tempered 40 CrMnMo 7 the chips show segmentation with a change of the structure in the shear bands A change of the chip formation mechanism from continuous chips to serrated chips in cutting.speeds ranging from 500 m/min to 6000 m/min can be

DYNAMICS IN HIGH SPEED MACHINING

·.; c = 5:5 00 mlmin 'i c = :50 0 m/min @ ·1 , = 1000 lll / 111111

Figure 6 Chip formation in machining different steel types ; (a) 40 CrMnMo 7 hardened and tempered , ( b )

40 CrMnMo 7 hardened , (c) C60 , (d) C45E

observed in machining the C60 steel which has a lower tensile strength and higher elongation after fracture Within the chosen cutting speed range, the workpiece materials C22 steel and C45e steel show basically different chip formation mechanism caused by their low mechanical properties At cutting speeds from 500 m/min to 8000 m/min segmentation cannot be observed, only continuous chips are generated For both steels a dependence of the structure, a decreasing curvature within the chip on cutting speed,

could be detected with variation of cutting speed The different chip formation nisms of the machined workpiece materials can be attributed to their different mechanical properties The change in the chip formation mechanism with increasing cutting speed is sometimes correlated with decreasing cutting forces (Figure 5.), but in the presented experimental investigations no correlation between chip formation mechanism and cut-ting forces can be found, because the materials with continuous chip formation (C22,

mecha-C45E) show a similar course as materials with chip segmentation (C60, 40 CrMnMo 7)

5 ACOUSTIC EMISSION

No further dynamic components, e g caused by the chip segmentation process, can

be detected with standard industrial force sensors caused by their dynamic limitations at higher frequencies In order to characterize the dynamic material behavior and as a result the chip formation process, acoustic emission is additionally measured using a wide band sensor with a frequency range of 250 kHz to 2 MHz A focus was put on the process of chip segmentation The chip segmentation frequency in high speed machining is signifi-cantly higher compared with conventional cutting due to the high cutting speed The frequency can be detected with suitable acoustic emission sensors8 if the chip segmen-tation is very intensive and the amplitude of the chip segmentation peak is higher than

28 G WARNECKE ANDS SIEMS

other peaks in the frequency spectrum This behavior can be observed at materials with a

very high hardness as the machined martensitic 40 CrMnMo 7 with a hardness of 640 HV

(Figure 7a) In the case of lower chip segmentation the frequency can often not be easily

identified, because the amplitudes are in the same range as the characteristic process

frequencies (Figure 7b) In order to examine the dependence of chip segmentation

frequency on cutting speed, experiments with variable cutting speed were conducted with

martensitic 40 CrMnMo 7 and the segmentation frequency was determined using the

measured acoustic emission signals as can be seen in Figure 7c

@Powerspedrum with strong segmentation

cutting speed [m/min]

Figure 7 (a) powerspectrum of AE-signal when machining 40 CrMnMo 7 hardened, cutting speed of

1200 m/min, (b) powerspectrum of AE-signal when machining 40 CrMnMo 7 hardened and tempered at a

cutting speed of2000 m/min, (c) chip segmentation frequency when machining 40 CrMnMo 7 hardened

With the occurence of strong segmentation during machining the hardened

40 CrMnMo 7 steel, the chip segmentation frequency shows a linearly increasing trend as

cutting speed increases Primarily, this is due to more segmentation processes within a

fixed time period as cutting speed increases Secondly, the linear trend can be explained

by the constant distance in longitudinal chip direction of each segment with higher

cutting speed This is also a completely different behavior as observed in Aluminum9

where the distance between the segments is still increasing and the chip segmentation

frequency shows a degressive trend

DYNAMICS IN HIGH SPEED MACHINING 29

Another focus in measuring the acoustic emission was put on the calculation of the root-mean-square which is related to the energy transferred during cutting The RMS strongly depends on the machined material, because acoustic emission is based on elastic and plastic deformation behavior of the workpiece material and on friction effects Many investigations of the dependence of acoustic emission on friction or deformation mechanisms were performed10• 11 but still the casual relations are not clear The RMS values are calculated in the frequency domain because the applied sensor used had a frequency range from 250 kHz to 2000 kHz (Eq 4)

where X2 are the amplitudes in the frequency domain and fl and f2 specify the frequency range of the sensor The calculated RMS values for different steel types are presented in Figure 8 For nearly all materials, the RMS increases with increasing cutting speed Only the steel 40 CrMnMo 7; hardened and tempered, shows a maximum at 3500 m/min and after a short decrease the RMS is increasing again

By means of this model experiments each single contact between workpiece and tool can

30

be described in terms of time and place by cinematic considerations Different steel types

algorithm to calculate real cutting forces instead of a superposition of cutting forces and inertia forces were used to get information about the transferred energy in the cutting process A decisive decrease of the cutting forces was found which cannot be correlated with a change of the chip formation mechanism from continuous chips to serrated chips For the different materials, the chip formation mechanisms turned out to be different Continuous chips could only be observed using materials with low mechanical properties Due to the higher mechanical properties a change in the chip formation mechanism could

be observed The formation of serrated chips was decisively influenced by the cutting speed and the machined material During the examination, the frequency of chip segmentation was measured by means of acoustic emission Frequency of chip segmentation increased linear corresponding with increasing cutting speed

ACKNOWLEDGMENTS

This research project is supported by the German Research Foundation (Deutsche Forschungsgemeinschaft - DFG) in co-operation with the Institute of Production Engi-neering and Machine Tools and the Department of Physical Metallurgy (Materials Science), both at the University of Darmstadt

REFERENCES

S Miyaz.awa, Y Usui., Measurements of Transient Cutting Force by Means of Fourier Analyzer, Bulletin of

Mechanical Engineering laboratory , Mechanical Engineering Laboratory, Ibaraki, Japan, (1985)

2 T Herget, 1994, Simulation und Messung des zeitlichen Verlaujs von z.erspankrajtkomponenten beim Hochgeschwindigkeitsfriisen, Darmstlidter Forschungsberichte filr Konstruktion und Fertigung, Carl Hanser Verlag, MUnchen

3 F Klocke, S Hoppe, 1999, Experimentelle und nurnerische Untersuchungen zum Spanbildungsvorgang bei der Zerspanung mit geometrisch bestimmter Schneide mit hohen Schnittgeschwindigkeiten, in: Spanen metallischer Werkstoffe mil hohen Geschwindigkeiten, Kol/oquium des Schwerpunktprogramms der DFG

am 18 // 1999, Bonn, edited by H.K Tonshoffand F Hollmann (Hrsg.), pp 238-247

4 Z B Hou, R Komanduri., On a Thermomechanical Model of Shear Instability, Annals of the CIRP ,

7 M A Davies, T J Bums, C J Evans, On the Dynamics of Chip Formation in Machining Hard Metals,

Annals of the CIRP, Vol 46, pp25-30, (1997)

8 D Bahre, 1994, Proze)begleitende z.erspanbarkeitsanalyse beim Drehen von Stahl, Produktionstechnische

Berichte, PhD Dissertation, Vol 14, Universitat Kaiserslautem

9 S Siems, R Dollmeier, G Warnecke, Material Behaviour of Aluminium 7075 and AISI 1045 steel in High Speed Machining, Transactions of the North American Manufacturing Research Institution ofSME , Vol

INFLUENCE OF MATERIAL PROPERTIES ON SURFACE INTEGRITY AND CHIP FORMATION

IN HIGH SPEED TURNING

E Brinksmeier, P Mayr, T Lubben, P Pouteau, P Diersen*

1 INTRODUCTION

Due to their higher productivity and throughput, High Speed Cutting (HSC) nologies are commonly used in aerospace industry as weli as in die and mold manufac-turing for the machining of workpieces with high material removal rates For this reason, HSC technology is used mainly for milling of free formed surfaces [l] In addition to these applications, HSC technology has recently been used for cutting of rotationally symmetrical components like drilling and turning of shafts

tech-In contrast to milling processes, turning is a continuous cutting process that also leads to continuous chip removal during High-Speed-Turning (HST) processes [2] Therefore, it is of special interest to understand the chip formation mechanisms and the influence of HSC conditions on the workpiece quality in relation to the material proper-ties

• Ekkard Brinksmeier, Director and Head of the Division Manufilcturing Technologies at the Foundation Institute for Materials Science (IWT), Bremen, Germany Peter Mayr , Managing Director of the IWT and Head of the Division Materials Science Thomas Lilbben , Research Engineer at the IWT - Division Materials Science Philippe Pouteau , Research Engineer at the IWT - Division Materials Science Paul Diersen, Research Engineer at the !WT - Division Manufilcturing Technologies

Metal Cutting and High Sp e ed Ma c hinin g, e dited by