Jackson M.J. Micro and Nanomanufacturing

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5. Mechanical Micromachining

5.1 Introduction

The development of microfludic devices in recent years such as

"lab-on-a-chip" has created a need to machine microscale features

that do not negatively interfere with fluid flow at that scale. Micro-

fluidic devices are classified as active or passive devices. Passive

microfluidics is a control topology in which the physical configura-

tion of the microfabricated system determines the functional charac-

teristics of the system with and without an external power source.

Passive microfluidics exploit various physical properties such as

shape, contact angle, and flow characteristics that achieve desired

functions. These devices function as pumps, valves, filters and reac-

tors.

They are classified as "BioMEMS devices" and include fluidic

sensors, micro-reactors, dispensers, valves, micro-pumps, flow

channels, filters, and separators, and biosensors. A review of micro-

fluidic principles is provided by Gravesen, Branebjerg, and Jensen

[1].

Owing to the principle of operation of BioMEMS devices, geo-

metric construction of microchannels requires micromachining tech-

niques to be highly accurate and to be able to machine engineering

materials in addition to traditional materials currently used in

BioMEMS devices.

5.2 Microfluidic Systems

Microfluidic devices require microscale channels to be machined

such that the dominant effects of passive microfluidic devices can be

192 Micro-and Nanomanufacturing

exploited. These effects are classified as: surface tension effects;

capillary force effects; Hagen-Poiseuille pressure drop effects; and

surface roughness effects to produce hydrophobic and hydrophilic

flows.

Passive micro-valves are traditionally made from a Si/Poly-

silicon based material in the form of check valves that are easy to

fabricate and can be integrated into a microfluidic system. The most

important dimension to be machined accurately is the diameter of

the microchannel because it determines the pressure drop across the

channel, and the pressure required to push fluid across an abrupt re-

striction. Conventional valves consist of valves with 45° taper ge-

ometry, 30° taper geometry, rounded valves and valves with restric-

tor channels. These valves are very easily machined but the pressure

drop across the valve requires external power sources to make the

fluid flow, or by using capillary suction so that an external power

source is no longer required. Novel types of mixing valves are

based on exploiting the "Coanda effect" that uses Taylor dispersion

of fluids to agitate and combine liquid flows by combinations of

dif-

fusion and convection mixing. These valves require a more sophis-

ticated way of machining in order to achieve the correct mixing of

the fluid. The construction of such valves is shown in Fig. 5.1 and

shows a complex set of channels that is used to mix fluids prior to

being dispensed using a fixed volume microdispenser that is com-

posed of fluid inlets and outlets, fixed volume reservoirs, passive

valves, and mixing chambers.

The development of mixing devices and their subsequent mi-

cromachining is only one part of the microfluidic device. Microflu-

idic devices are multiplexed with integrated microdispensers that are

systems that form "lab-on-chip" products. By definition these re-

quire a reservoir for holding fluids such that a dispersed volume is

dispensed using an air driving force that can be dispensed in a pro-

grammed ratio in the nanoliter range by using passive valves. The

challenges to machining these features are the generation of rough-

ness features on the microchannel that supports hydrophilic or hy-

drophobic effects. Control of microsurface roughness is best

achieved by mechanically machining using a high-speed milling

machine tool.

Mechanical Micromachining 193

Fluid 1

Coanda Effect

Fig. 5.1a. Mixing cell in a microfluidic channel incorporating a Coanda mixing

chamber and diffuser. The inset shows a simulation of the Coanda effect and its

mixing effect

Fig. 5.1b. The micromachined channel on the left shows the difficulties associ-

ated with micromachining this type of microfluidic chamber. The CFD simulation

to the right shows the mixing effect of this type of microfluidic channel

194 Micro-and Nanomanufacturing

The development of soft lithography has generated interest in the

manufacture of micro-and nanofluidic systems in which a "rubbery"

solid can be attached to a solid substrate to perform operations such

as controlling liquid flows, pumping fluids to act like syringes, and

controlling flows using a combination of

valves,

mixers, and separa-

tors.

The substrates can be silicon, but more robust materials such

as engineering materials require mechanical micromachining tech-

niques to generate the required profiles. Figure 5.2 shows the nature

of some complex shaped microfluidic systems. The figure shows a

stepped profile in the substrate so that liquid can flow on two levels.

A soft material such as polydimethylsiloxane (PDMS) is placed on

top of this network so that the fluid can be controlled and manipu-

lated to produce the right type of flow and concentration of chemi-

cals.

The nature of the complex topography of these channels is also

shown and can be machined from a variety of materials using mi-

cromilling tools.

Fig. 5.2. Microfluidic channel showing three-dimensional topographic profile that

is machined using micromilling tools. The branched network is also shown that

combines flows and mixes them as performed by adding colored dyes to a liquid

that produces a graded output of fluid

Mechanical Micromachining 195

The following section shows how micromilling can be used to

produce these features and to create microscale debris that can be re-

cycled by pressing in a mold to create powdered metal products with

extremely good engineering properties. The machining debris con-

tains nanocrystals produced during high strain rate machining of the

microfluidic channel.

5.3 Theory of Micromachining

5.3.1 Micromilling

As micro-and nanotechnology becomes increasingly important to the

needs of society, the need to create microfluidic devices in engineer-

ing materials becomes more apparent. High-speed milling has been

shown to provide a great deal of promise in creating microstructures

and in nanotexturing surfaces in engineering materials. Cutting tool

rotation is expected to reach

1,000,000

revolutions per minute (rpm)

compared with conventional cutting speeds of around 30,000 rpm.

Rotating the tool this quickly reduces cutting forces which produces

a higher quality of cut so that post-processing is not required.

Clearly, strain rates imparted to the workpiece at these speeds are

very high and this influences initial chip formation and chip removal

mechanisms. High strain rates imparted cause distinct chip forma-

tions in engineering materials to occur which are similarly observed

in other materials, most notably biological materials such as cancel-

lous bone. Certain soft metals such as aluminum do not machine

very well because the material adheres to the cutting tool. However,

high strain rates tend to overcome these limitations. During the last

five years MEMS and nanotechnology have promised to make avail-

able small-scale devices with the potential to improve our daily

lives.

To a certain extent this has been achieved but the market has

not realized its potential. Most products available are based on prod-

ucts used in the semiconductor industry, or in the form of sensors.

Manufacturing processes used in the production of these compo-

nents are limited by the material used. Hence, there are few produc-

196 Micro-and Nanomanufacturing

tion processes available for products requiring metals and other en-

gineering materials. One technique that shows much promise is ul-

tra high-speed milling, which has been shown to produce micro-and

nanoscale structures in the same way as a conventional machine tool

produces macroscale features. A special requirement of machining at

such small scales is the need to increase the rotational speed of the

cutting tool. The cutting speed of the cutting tool is given by the fol-

lowing equation assuming that the mass of the tool is concentrated at

radius, r:

= ro)

(5.1)

Where V is the cutting velocity (m/s), r is the cutting tool radius

(m) and

is the rotational speed in (radians/s). From this relation-

ship it can be seen that as the cutter diameter reduces in size to cre-

ate micro-and nanoscale features the rotational speed must dramati-

cally increase to compensate for the loss of cutting speed at the

micro-and nanoscale. At the present time, the fastest spindle com-

mercially available rotates around 360,000 rpm under load condi-

tions.

Research is being conducted to improve the performance of

these spindles where the initial aim is to reach

1,000,000

rpm [2].

Strain rates induced at these high speeds cause chip formation

mechanisms to be significantly different than at low speeds. Addi-

tionally, it is now possible to experiment at the extreme limits of the

fundamental principles of metal cutting at ultra high speed and at the

micro-and nanoscales using the conventional theories of metal cut-

ting.

Following the development of equations proposed by Shaw [3],

these expressions will be applied to a 6 flute end milling cutter with

a shank of diameter 1.59 mm, cutting diameter 700 |um, rotated at a

speed of 250,000 rpm or 26180 rad/s. The rake angle was a = 7°,

clearance angle 0=10° and the shear plane angle

= 24°. To illus-

trate the application of the established theories of metal cutting at

these scales, the metal used as an example was a hypoeutectoid AISI

4340 steel, and the horizontal force Fh was calculated using the

equation:

Mechanical Micromachining 197

=mrco

(5.2)

Where m is the tool mass (kg), and r is the tool radius (m).

Coef-

ficients of friction between different materials have been investi-

gated by Bowden and Tabor [4]. They discovered that when a

curved tungsten-carbide tool (WC) slides against a steel substrate the

coefficient of friction is in the range

JLI

= 0.4

—

0.6 under dry cutting

conditions, and between 0.1 and 0.2 under lubricated conditions.

Here, dry cutting conditions are used at high cutting speeds in order

to remove chips in an environmentally conscious manner that does

not use a lubricant that is harmful to the environment. Using the fol-

lowing equation,

(3 =

tan

-1

ju (5.3)

The friction angle P can then be determined under these condi-

tions.

It was found to be 30.96°. This is in excellent agreement with

Merchant and Zlatin's nomograph [3]. The vertical force F

can be

found using the relationship:

; ~

<5.4)

1 + juTan a

This was found to be 5.25 N. Again, referring to the Merchant

and Zlatin's [3] nomograph for the coefficient of friction, the value

can be independently predicted to be 5.33 N. The force per-

pendicular to the tool plane F is found to be:

F - F

Sina + F

Coscc (5.5)

F was determined as 6.66 N. The force normal to the tool plane

N is provided using the equation:

198 Micro-and Nanomanufacturing

N = F

Cosa-F

Sina (5.6)

Where

was found to be 11.1 N. The force perpendicular to the

shear plane F

can now be determined by,

Cos^>

- F

Sinj (5.7)

And was estimated to be 8.76 N. The force normal to the shear

plane N

is given by the equation:

Cos(f)

Sin<j)

(5.8)

Where N

is 9.61 N. Now the frictional force Ff

is:

Cosa

Sina (5.9)

Ff is approximately 6.66 N. It is possible to check this value with

Merchant and Zlatin's [3] nomograph for frictional force. However,

the values for Fh and F

are so small that the extreme limits of the

nomograph are reached so it is difficult to give an accurate value for

Ff it is certain this value is below ION which is in close agreement

with the calculated answer. The shear stress x is found using the fol-

lowing quotient:

r = ^- (5.10)

Which has a value of 1.8 GN/m

. The direct stress p is found by

applying the relationship,

-*- (5.11)

Mechanical Micromachining 199

a is found to be 1.95 GN/m . The chip thickness ratio, r, is given

by:

r =

—

(5.12)

Where t is the un-deformed chip thickness (or depth of cut) and

is the measured chip thickness. The milling experiment was con-

ducted at such a small scale that it was difficult to measure, t. There-

fore r was calculated using the equation:

r = ^ (5.13)

cosor + sinatan^

Which yields r = 0.425 and therefore t = 4.25

\xm.

This is in excel-

lent agreement with Merchant and Zlatin's [3] nomograph for shear

angles and the calculation can be made in confidence. Shear strain y

is found from

_ Cos a

Sin<f>Cos(<f>-a)

(

)

y was found to be 2.55, this can be independently verified from

Merchant and Zlatin's nomograph [3] for shear strain which yields a

value of 2.51.The cutting velocity V is found using:

= rco

(5.15)

Where JTis 9.1 m/s. The chip velocity is found from applying the

following equation:

200 Micro- and Nanomanufacturing

Sin

* (5.16)

Cos{c/)-a)

Where V

is equal to 3.9 m/s, this can also be found from

=rV (5.17)

The two results are in agreement with each other. The shear ve-

locity V

is given by:

(5.18)

Cos(</>

- a)

Where V

is calculated to be 9.5 m/s. V

can also be found from:

=yVSin</)

(5.19)

Again, the two results are in agreement with each other. The

strain rate y is given by:

VCoSOC

(5.20)

AyCos(<f>

- a)

Where Ay is the shear plane spacing and y is found to be 8333 x

}

. The feed rate is 1 mm/mii

and the feed per tooth d is given by,

10 s . The feed rate is 1 mm/min under experimental conditions

^- (5.21)

Nco