Jackson M.J. Micro and Nanomanufacturing

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Mechanical Micromachining 221

5.5 Micromachining Tool Design

The accurate machining of microfluidic channels has created a re-

quirement for miniaturized machine tools referred to as meso ma-

chine tools (mMTs). The ability to machine pockets, slots, channels,

and contours of MEMS based devices, is dependent upon the ability

to spin a cutting tool at speeds in the range, 100-to-200 m/min. This

requires spindle speeds to be in excess of 500,000 revolutions per

minute using microscale cutting tools. Developments in the area of

micro-cutting tools, spindle design, and vibration dampening of

mMTs is being investigated by the author at Purdue University, and

developments in the area of process modeling, mechanistic model

development for multi-phase materials, molecular dynamics models

for chip formation in micromilling, and micro-drilling dynamics are

being conducted by Ehmann, DeVor, and Ni, at Northwestern Uni-

versity, and the Universities of Illinois and Michigan.

Conventional machine tool frames have been developed to

minimize vibrations and other sources of error during machining op-

erations. Most desktop conceptual machines are based on open-

frame models that provide easy access but the structural loop is

prone to Abbe errors. Figure 5.18 shows such a configuration.

Closed frame structures provide a better solution but the structure

is not optimized for developing desktop machine tools. A better so-

lution is afforded by the tetrahedral shape of structure that is com-

posed of six legs joined at spherical nodes, where the machining

zone is in the center of the frame. It has high stiffness and thermal

stability, and has viscous shear damping mechanisms built into the

legs of

the

structure. Damping of vibrations is afforded by means of

sliding bearing material applied to the self-centering spherical joint

(Fig. 5.19).

Several prototype mMTs have been built to explore the feasibil-

ity of using feed drives and spindle technologies. The two principal

feed drive technologies used include piezoelectric actuated systems

and voice-coil actuated systems. The first machines developed in-

clude those shown in Fig. 5.20 that use piezoelectric transducers that

operate similar to the inch-worm principle.

222 Micro- and Nanomanufacturing

Spindle

Tool

Workpiece

Fixture

X-Z table

Spindle

housinj

Faceplate

Carriage

Fig. 5.18. Illustration of the open frame structure

Mechanical Micromachining 223

Fig. 5.19. Schematic diagram of the tetrahedral structure developed by the Na-

tional Physical Laboratory, London

Open-loop machines have proven to be troublesome due to the

inability to maintain a constant velocity. The amount of pre-load on

the actuators produced wide variations in the velocity, and the ap-

plied loads caused velocities to change spuriously. Since actuators

are operated in the on/off mode, velocity was difficult to control and

adjust. Therefore, feedback control using LVDTs will provide a

greater level of control.

224 Micro- and Nanomanufacturing

Fig. 5.20. Piezoelectric-actuated mMTs. (a) Open-loop with mounted load cell

(University of Illinois at Urbana-Champaign); (b) Open-loop milling center (Uni-

versity of Michigan); and (c) closed-loop mMT (Northwestern University)

Voice coil actuated mMTs have been developed with a three-

axis voice coil stage, triaxial load cell, and triaxial accelerometer

again with a low speed air turbine spindle. Figure 5.21 shows the

general arrangement. All axes have a 1 micron resolution linear en-

coder and actuators apply a peak force of 42 N and 80 N for x and y-

axes,

respectively. Feed velocities range from 1 mm/s to 4 mm/s.

The principal author has developed a tetrahedral shaped mMT with

an ultra high-speed spindle (Fig. 5.5).

Mechanical Micromachining 225

Fig. 5.21. Voice-coil-actuated mMT (University of Illinois at Urbana-Champaign)

The design of high-speed spindles is of paramount importance

when one considers the size effect at the microscale. As discussed

elsewhere in this book, extremely high strain rates are required to

overcome the difficulties of removing material at the micro-and

nanoscales. High-pressure variations on the rotor causes the rotor to

fail and this severely limits the reliability and durability of the high-

speed spindles to support new developments in micro-and mesoscale

manufacturing technologies. Different designs of rotor are proposed

and optimum designs were chosen based on the lowest amount of

pressure variation on the surfaces of the rotor. Numerical simula-

tions of different rotor designs for different rotational speeds were

carried out using commercial computational fluid dynamics (CFD)

software package known as CFX. The results revealed that changes

in the rotor, inlet, and outlet geometries affect the pressure coeffi-

cient significantly.

226 Micro- and Nanomanufacturing

5.6 High Speed Air Turbine Spindles

Figure 5.22 shows a conventional high-speed air turbine spindle. To

drive a high-speed spindle a motor, or compressor, is integrated with

the spindle shaft. High-pressure compressed air enters into the hous-

ing of the spindle from the compressor via a standard pneumatic

connector.

(a)

Fig. 5.22. Conventional high-speed air turbine spindle: (a) expanded view; (b)

view of rotor; and (c) view of spindle where rotor body is located showing exhaust

port where air is directed to vanes of the rotor in (b)

The compressed air enters the housing through the shaft and ro-

tates the rotor of the spindle. The cutting tool, which is attached to

the center of the rotor, rotates with the speed of the rotor and ma-

chines the workpiece more quickly than conventional spindles. The

rotor is supported by an air bearing, which provides stability to the

rotor and also transmits the necessary torque. In the present chapter,

various designs of rotor for different rotational speeds are proposed

and to check the validity of their performance, fluid analysis of ro-

tors has been undertaken using a proprietary software package. Pres-

sure coefficients on the rotors were calculated and compared for

dif-

ferent designs of rotor to determine the optimum design of the rotor.

The pressure coefficient is defined as the difference between the

highest and the lowest pressure on the surface of the rotor, which is

normalized by the imposed inlet pressure. The pressure coefficient

determines the pressure exerted by high-speed compressed air on the

rotor and for the optimum design of the rotor, the pressure coeffi-

cient should be as low as possible as large values of pressure coeffi-

cient indicate that high pressure variations may cause a severe im-

balance of the load on the rotor.

Mechanical Micromachining 227

5.6.1 Fluid Flow Analysis

Fluid analysis of different designs of high-speed rotor was carried

out using the commercial CFD software, CFX

5.5.1.

With the devel-

opment and use of

CFD,

it is possible to examine and predict the ro-

tor's performance and to optimize the geometry prior to the con-

struction of a prototype. In the present section, the design of the

rotor governed by its fluid domain is described by the governing

equations of fluid flow. The boundary conditions for the numerical

solution are described.

5.6.2 Assumptions in the CFD Approach

The following assumptions were considered for the numerical solu-

tion of high-speed spindles using the CFD approach:

(1) The rotor's rotational speed depends on the pressure of the

compressed air, entering from the compressor. But the nu-

merical simulation was carried out by considering a decoup-

led system, i.e., for a given pressure (60 psi) of the air, the

rotating speed of the rotor has been assumed to have a con-

stant value such as half-a-million rpm, one million rpm, etc.

This means that the current study deals only with fluids prob-

lem, not the fluid-structure problem.

(2) Steady-state simulation was assumed for all numerical simu-

lations.

5.6.3 CFD Geometry Model

Typical rotor geometry is shown in Fig. 5.23. The bearing compo-

nent of the high-speed spindle was omitted in the CFD model, as the

pressure distribution across the rotor is the key objective. The outer

diameter of the rotor is 0.3 inches (7.6 mm), inner diameter of the

228 Micro- and Nanomanufacturing

rotor is 0.092 inches (2.34 mm), the height along the z-direction is

0.1445 inches (3.6 mm) and the angle between the rotor blades is

Fig. 5.23. Modeled rotor shown in Fig. 5.11 [2]

A cylindrical housing with a diameter of 0.31 inches (7.8 mm)

was modeled around the rotor with a height along the z-direction of

0.1735 inches (4.4 mm) so that the rotor could rotate freely inside

the housing. The spindle is driven by compressed air. Three inlets,

with a diameter of 0.055 inches (1.4 mm), that make an angle of 120

degrees with each other, were created around the housing. The inlets

were created at an angle of 45 with the z-axis of the rotor, so that

the air can directly impinge on the rotor blades, thus the torque and

the angular speed of the rotor could be varied. An outlet for the air

was created at the center of the housing. Three inlets and cylindrical

housing are shown in Fig. 5.24.

Mechanical Micromachining 229

inlet

Inlet

iut

Inlet

Fig. 5.24. Front view of the geometry considered for numerical solution with three

inlets and housing [2]

5.6.4 Fluid Models

Air was considered to be a compressible, viscous ideal gas, with a

molar mass of 0.03 kg/mol, dynamic viscosity of 1.725E-05, specific

heat capacity of 1003.8 J/kg.K, and a thermal conductivity of

0.02428 W/m.K. The flow in the high-speed spindle is seen as com-

pletely turbulent. Turbulence is described by the k-e turbulent model,

in which k is the turbulent kinetic energy and s is the turbulent eddy

dissipation. A total energy heat transfer model was considered as the

kinetic energy effects are important in the model.

230 Micro- and Nanomanufacturing

5.6.5 Boundary Conditions

The following boundary conditions were applied to the model:

(1) Opening boundary condition with a static pressure of 60 psi

and static temperature of 293 K at three inlets;

(2) Opening boundary condition with a static pressure of 0

(zero) and static temperature of 293 K at the outlet;

(3) A no-slip (moving) wall boundary condition on the rotor. A

constant angular speed of the rotor was also specified;

(4) A no-slip (stationary) wall boundary condition on the hous-

ing surfaces and inlet surfaces.

5.6.6 Governing Equations

The governing equations of three-dimensional fluid flow

were represented as:

Continuity Equation,

d{pU

)

dX;

(5.45)

Momentum Equation,

djpufjj)

L+

euj

dxj dx

dxj

eff

dxj

eff

Where repeated indices imply summation from 1 to 3, p is the

density, Ui are the cartesian velocity components, P is the pressure,

Xi are the coordinate axes, and (Jeff is the effective viscosity, which

is defined as: