Qin Y. Micromanufacturing Engineering and Technology

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Production associated performance: yield, reli-

ability, scalabili ty, online/in-pro cess monitor-

ing/inspection ability, ease for integration into

process chains, dependence on skills/environ-

ment, impact on the environment, etc.;

Cost factors: all costing items including that for

auxiliary processes and equipment (e.g. that for

handling, assembly/packaging, cleaning, etc.).

Other Issues

Besides a series of activities such as economic

analysis, decision analysis, technological forecast-

ing, information monitoring, risk assessment,

market analysis, externalities/impact analysis,

etc., education and training are important for

the micro-manufacturing industry. These are

needed due largely to micro-manufacturing being

generally a knowl edge-intensive business.

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CHAPTER 1 Overview of Micro-Manufacturing 23

Micro-/Nano-Machining

through Mechanical Cutting

Xizhi Sun and Kai Cheng

INTRODUCTION

The emergence of miniature and micro-products

and components is increasingly demanding the

production of parts with dimensions in the range

of a few tens of nanometers to a few millimeters.

Micro-/nano-cutting is one of the key techno-

logies to enable the realization of micro-products,

while a great many micro-manufacturing pro-

cesses have been developed.

In this chapter, micro-/nano-cutting is defined

as the fabrication of miniature and micro-

components using geometrically defined cutter

edges. Typical micro-/nano-cutting operations

include micro-milling, micro-turning, micro-

drilling and micro-grinding.

Similarly to the conventional cutting opera-

tion, in micro-/nano-cutting the surface of the

workpiece is mechanically removed using tools,

but the depth of cut is normally at the level of a

micrometer or less. As the unit removal size

decreases, issues of tool cutting-edge geometry,

grain size and orientation, etc., considered to have

little or no influence at larger scales, becom e dom-

inant factors with strong influenc es on the result-

ing machining accuracy, surface integrity and

quality of the machined component [1]. In this

chapter, therefore, emphasis is placed on the

issues that prevail in micro-/nano-cutting, which

is essentially different from the conventional cut-

ting process. Furthermore, the chapter focuses on

the precision machines for micro-/nano-cutting

and the application of the process in various

fields.

FUNDAMENTALS OF THE MICRO-/

NANO-CUTTING PROCESS

While the mechanisms of c onventional cutting

are well established, micro-/nano-cutting

mechanics and the associated intricate issues

are less well understood. The depths of cut

involved are several orders of magnitude smaller

than those of conventional cutting, s o that it is

necessary to examine c losely the mi cro-/nano-

cutting process. Unlike conventional machining,

where shear and friction dominate, micro-/nano-

cutting may i nvolve significant sliding along the

flank face of the tool due to the elastic recovery

of the workpiece material. The effects of plow-

ing may also become important due to the large

effective negative rake angle resulting f rom the

tool edge radius. In addition, the sub-surface

plastic deformation and the partition of thermal

energies may also be quite different from those

of traditional cutting [2]. This section discusses

the fundamentals of t he micro-/nano-cutting

process.

Specific Energy and Cutting Force

Specific energy and cutting force are important

physical parameters for understanding cutting

CHAPTER

phenomena, as they clearly reflect the chip

removal process. As shown in Fig. 2-1 [3], the

specific energy generally increases with the

decreasing depth of cut, within the range from

10 nm to 20 mm. This is because the effective rake

angle will increase as the depth of cut decreases,

and the larger the rake angle the greater the spe-

cific energy. This phenomenon is often called the

‘size effect’.

Micro-/nano-cutting is also characterized by

the high ratio of the normal to the tangential

components of the cutting force, as shown in

Fig. 2-2 [3], that is, the resultant cutting force

becomes closer to the thrust direction when the

depth of cut becomes smaller. Since the depth of

cut is very small in micro-/nano-cutting, the

workpiece is mainly processed by the cutting

edge and compression will thus become domi-

nant in the deformation of the workpiece mate-

rial, which will result in larger friction force at

the tool/chip interface and consequently in a

greater cutting ratio. This indicates a transition

from the shearing-dominated process in conven-

tional cutting to a plowing-dominated process in

micro-/nano-cutting.

Minimum Chip Thickness and Chip

Formation

The definition of minimum chip thickness is the

minimum undeformed chip thickness below

which no chip can be formed stably.

Figure 2-3 shows the chip formation with

respect to the chip thickness [4].InFig. 2-3(a),

where the uncut chip thickness, h, is smaller than

the minimum chip thickness, h

, only elastic

deformation results and no workpiece material

will be removed by the cutter. When the uncut

chip thickness approaches the minimum chip

thickness, as shown in Fig. 2-3(b), chips will be

formed due to the shearing of the workpiece.

However, since elastic deformation still exists,

the removed depth is generally smaller than the

desired depth. If the uncut chip thickness is larger

FIGURE 2-3 Schematic diagram of the effect of the minimum chip thickness.

FIGURE 2-1 Specific energy versus uncut chip thickness

for new and worn diamond tools.

FIGURE 2-2 Resultant force vector versus uncut chip

thickness at various rake angles.

CHAPTER 2 Micro-/Nano-Machining through Mechanical Cutting 25

than the minimum chip thickness, as shown in

Fig. 2-3(c), elastic deformation is significantly

reduced and results in the removal of the entire

depth of cut as a chip.

Due to this minimum chip thickness effect, the

micro-/nano-cutting process is affected by two

mechanisms: chip removal ( h > h

) and plowing/

rubbing ( h < h

). From a practical point of view,

the minimum chip thickness is a measure of the

extreme machining accuracy attainable because

the generated surface roughness is mainly attrib-

uted to the plowing/rubbing process when the

uncut chip thickness is less than the minimum chip

thickness. The extent of plowing/rubbing and the

nature of the micro-deformation during plow ing/

rubbing contribute significantly to increased cut-

ting forces, burr formation, and increased surface

roughness. Therefore, knowledge of the minimum

chip thickness is essential in the selection of

appropriate machining conditions [5]. Ikawa et

al. [6] obtained an undeformed thickness on the

order of a nanometer, as shown in Fig. 2-4,bya

well-defined diamond tool with an edge radius of

around 10 nm.

The minimum chip thickness depends on the

cutting edge radius, workpiece material and the

micro-cutting of steel, finding that the minimum

chip thickness is 20% and 30% of the cutting edge

radius for the pearlite and ferrite, respectively.

However, Shimada et al. [8] observed that the

minimum chip thickness can be around 5% of

the cutting edge radius for the cutting of copper

and aluminum, through molecular dynamics sim-

ulation.

Ductile Mode Cutting

The machining of brittle materials such as germa-

nium, silicon, and optical glasses at a large depth

of cut in conventional cutting has a tendency to

generate a rough surface and sub-surface crack-

ing. As a result, the machining of brittle materials

is normally achieved using conventional proces-

sing techniques such as polishing. However, intri-

cate features, the surface finish quality of the

workpiece produced, and a greater material

removal rate of processing demand an effective

means for the fabrication of brittle materials.

There is a transition in the material removal

mechanism of brittle materials, from brittle to

ductile, when the depth of cut decreases [9]. Based

on this feature, cutting in a ductile mode below

the critical depth of cut has been attempted with

the aim of obtaining a good surface finish and an

uncracked surface. Since the chip thickness in

micro-cutting can be of the order of the critical

depth of cut, micro-cutting can serve as a nov el

means of fabricat ing unique features with brittle

materials that are not achievable by polishing or

other techniques [1].

The results of many researches indicate that the

tool geometry and the cutting conditions are two

major factors affecting the value of the critical

depth of cut. It was found that the critical depth

FIGURE 2-4 SEM micrographs of chips generated from nanometric cutting; (a) thickness of chip 1 nm; (b) thickness of chip

30 nm.

26 CHAPTER 2 Micro-/Nano-Machining through Mechanical Cutting

of cut increases with the increase of the cutting

velocity and the negative rake angle [10,11].How-

ever, it is difficult to achieve ductile-mode cutting

with a greater feed rate, as shown in Fig. 2-5 [12].

Effect of Workpiec e-material Micro-

structure

The crystalline grain size of most workpiece mate-

rials is of the same order as the depth of cut in

micro-cutting, so that chip formation normally

takes place by the breaking up of the indivi-

dual grains of a polycrystalline material. Most

polycrystalline materials are thus treated as a

collection of grains with random orientation and

anisotropic properties [1]. The crystalline

graphic-orientation affects the chip formation,

the surface generation, and the variation of the

cutting forces [13]. There is a distinct difference

between micro-cutt ing and conventional cutting,

where the material can be treated as isotropic and

homogeneous. To et al. [14] obtained the eff ects

of the crystallographic orientation and the depth

of cut on the surface roughness by conducting the

diamond turning of single-crystal aluminum rods,

as illustrated in Fig. 2-6.

MODELING THE MICRO-/

NANO-CUTTING PROCESS

In the past, extensive cutting tests were performed

to understand cutting mechanics and optimize

various cutting proces s variables. However, it is

difficult to investigate the micro- /nano-cutting

process solely by the experimental approach due

to the substantial cost of micro-tooling, the

required careful preparation of samples, and the

considerable amount of testing involved on

machine tools, which is both time consuming

and expensive. Furthermore, the in-process obser-

vation and accurate measurement of results are

also very challen ging.

The micro-/nano-cutting process is very

complex because of the size effect, elastic/plastic

deformation and fracture with high strain

rates, and varying material properties during

the process. Analytical modeling is thus con-

sidered extremely difficult at the current level of

FIGURE 2-6 The effects of the crystallographic

orientation and the depth of cut on the surface roughness.

FIGURE 2-5 Silicon surfaces machined at a cutting speed of 90 m/min and a depth of cut of 1 mm: (a) feed rate of 0.4 mm/

min (ductile-mode cutting); and (b) feed rate of 1 mm/min (brittle-mode cutting).

CHAPTER 2 Micro-/Nano-Machining through Mechanical Cutting 27

understanding of material beha vior. Most analyt-

ical-modeling efforts are based on kinematics

from empirical obs ervation combined with classi-

cal cutting models at the macro level. The appli-

cability and accuracy of these models are subject

to many limitations [1].

Although analytical models involve many

assumptions, the numerical modeling of micro-/

nano-cutting provides a powerful tool to assist

scientific understanding of the process. Using

numerical models, the effects of various cutting

conditions can be obtained easily and effectively

while undertaking less expensive experiments.

Finite element (FE) modeling and molecular

dynamics (MD) modeling are two popular numer-

ical modeling and simulation techniques for

micro-/nano-cutting. More recently, multi-scale

modeling methods based on combining FEM

and MD have emerged to overcome the disadvan-

tages of each method and to enable the simulation

of the cutting process more realistically.

In the following sub-sections, details of these

key modeling methods of micro-/nano-cutting are

discussed, with examples presented from pub-

lished research work.

FE Modeling

The FE method is based on the principle of con-

tinuum mechanics, in which materials are defined

as continuous structures and the effects of micro-

constituents such as crystal structure, grain size,

and inter-atomic distances are ignored. In an FE

model, only the value of the variables of nodes can

be obtained exactly: between the nodes, the values

of the variables are determined by interpolation

[15]. Hence, the number of nodes an d the dis-

tances between the nodes are selected based on

the required calculation accuracy.

The application of FE simulation to the cutting

process provides an effective means to understand

the mechanics and characteristics of the cutting

process. A typical FE cutting model is shown in

Fig. 2-7 [15], where the workpiece is fixed and the

tool is in motion. During cutting simulation,

the interaction of nodes between the interface of

the workpiece and the tool is transferred to other

nodes of the workpiece. The interactions between

nodes can be described by three kinds of finite-

element formulation: Lagrangian formulation,

which requires a remeshing algorithm or a chip-

separation criterion to form the chip; Eulerian

formulation, which needs a prior assumption of

a chip shap e; and arbitrary Lagrangian Eulerian

formulation. For the description of large plastic

deformation and large strain rate of a material

during the cutting process, the well-known

Johnson-Cock formulation is often used.

The application of the FE method in cutting has

been attracting a lot of research interest since the

1970s. Although micro-cutting could be signifi-

cantly different from conventional cutting, the

governing principles, e.g. plasticity a nd tool/chip

tribology, should remain but be heavily subject to

FIGURE 2-7 An illustration of an FEM cutting model.

28 CHAPTER 2 Micro-/Nano-Machining through Mechanical Cutting

the size effect [16]. According to these principles,

various aspect s in the micro-cutting process have

been investigated using the FE method, including:

1. Material removal and chip formation;

2. Effects of tooling geometry and process para-

meters;

3. Effects of material micro-structure;

4. Residual stress in micro-cutting.

MD Modeling

Molecular dynamics (MD) simulation is a well-

established methodology for detailed microscopic

modeling at the molecular scale. It is based upon a

model of the molecules of the matter or system

concerned, according to their atomic structure.

Potential functions are used to describe the molec-

ular interactions, and the interatomic forces can

be derived from the differentiation of the potential

function. The motions of individual atoms are

usually assumed to be governed by Newton’s sec-

ond law. The numerical solutions to the motion

equations give the trajectories of the atoms, which

can be used to determine the macroscopic static

and dynamic characteristics of the system.

In the late 1980s, a research group in Lawrence

Livermore National Laboratory (LLNL) started

the MD simulation of the diamond turning of

single-crystal copper [17]. Since then, MD has

been successfully applied to a variety of phenom-

ena in micro-/nano-cutting.

A typical nanometric cutting MD model is

shown in Fig. 2-8 [6], which can be used to study

the cutting zone and cutting parameters in micro-/

nano-cutting.

The topics investigated by MD simulation are

as follows:

1. The effect of crystal orientation on surface

roughness;

2. Chip formation and the machined surface gen-

eration;

3. Minimum undeformed chip thickness in

nanometric cutting;

4. Cutting forces and cutting temperature;

5. Side flow and pile up phenomena in the cut-

ting process;

6. Surface integrity.

Although MD simulation has become a useful

tool in analyzing the nanometric machining pro-

cess, further research and development are

expected in the following areas:

1. Improvement of the model dimensions and

computational speed;

2. Establishing more accurate potential func-

tions for workpieces and cutting tools;

3. Developing a material model including de-

fects, such as vacancies, dislocations, grain

boundaries;

4. Tool wear simulation.

Multi-scale Modeling

Molecular dynamics (MD) simulation and the

finite-element (FE) method have been successfully

applied in the simulation of the machining pro-

cess. However , the two methods have their own

respective limitations. For example, MD simula-

tion can only cover the phenomena occurring at

nanometric scale because of the physical dimen-

sion, the computational cost and the scale, while

the FE method is suited to model meso- and

macro-scale machining and to simulate macro-

parameters such as the temperature in the cutting

zone, the stress/strain distribution and cutting

forces, etc. A natural approach to the simulati on

of multi-scale proces ses is to combine an MD

simulation for the critical regions within the

FIGURE 2-8 MD simulation model of the nanometric

cutting of single-crystal copper.

CHAPTER 2 Micro-/Nano-Machining through Mechanical Cutting 29

system with an FE method for continuum cover-

age of the remainder of the system. The hybrid

approach provides an atomistic description near

the interface and a continuum description deep

into the substrate, increasing the accessible

dimensional scales, and greatly reducing the

computational cost while increasing the modeling

accuracy and capacity.

Several multi-scale simulation methods have

been developed such as the FEAT method, the

quasi-continuum (QC) meth od, the MAAD

method, and the CGMD method. A remarkably

successful approach is the QC method proposed

by Tadmor et al. in 1996 [18].QCisawayof

simulating the macro-scale non-linear deforma-

tion of crystalline solids using MD. An integrat ed

MD-FE approach has been prop osed by the

authors for the multi-scale simulation of the

micro-/nano-cutting process with diamond tools

based on the QC method [19].

Figure 2-9 is a schematic diagram of the model

used for the multi-scale simulation of nanometric

cutting of single-crystal cop per [19]. It can be seen

that the mesh density becomes greater when pro-

ceeding upwards. At the top the interface meshes

disappear, and there are atoms instead of

mesh, entirely. The size of the work material is

0.2  0.1 mm, taking into account the transition

from nanometer to micrometer. The number of

atoms to be computed at the 50th step time is no

more than 20,000, which is much less compared

to 1.25  10

atoms included in the model for

MD simulation. This model is an embodiment

of the concept of multi-scale simulation for

micro-machining.

Figure 2-10 shows the simulation plots at the

first time step and the 50th time step, and the

corresponding atoms’ velocity contour line.

PRECISION MACHINES FOR

MICRO-/NANO-CUTTING

Ultra-precision Machine Tools

Ultra-precision machine tools play an important

role in the implementation of micro-/nano-cutting,

while they directly determine machining accuracy,

productivity, producibility and repeatability.

There have been great market demands for ultra-

precision machine tools which are capable of

FIGURE 2-9 Multi-scale model for nanometric cutting of

single-crystal copper.

FIGURE 2-10 Instantaneous diagram of copper’s cutting simulation by the multi-scale method: (a) at the first time step;

(b) at the 50th time step.

30 CHAPTER 2 Micro-/Nano-Machining through Mechanical Cutting