Jackson M.J. Micro and Nanomanufacturing

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Microgrinding 291

Grain bond

protrusion

Grain bond

protrusion

Displaced

material

Depth

of cut

Deep crack Conchoidal Maximum Workpiece

crack depth of cut

Fig. 6.23 Konig's model shows uneven protrusions out of the bond represent grain

depth of

cut.

Abrasive grain on the right side that protrudes slightly within critical

depth of cut region produces ductile streaks while on the left side grain protrudes

more than critical depth of cut region produces fracture and deep crack [75]

6.4.5 Aspheric Surface Generation

In recent years, there has been a dramatic advancement in the field

optics,

astronomy, and infrared applications. This led to an ever-

increasing demand for simple and complex aspheric smfaces which

produce better image quality vv^hen compared to that produced by

spherical lenses. An aspheric surface is generally defined as a sur-

face with a basic conic section form. To this basic conic section a

symmetrical deviation can also be superimposed and is given by a

symmetrical polynomial expression as follows [12]:

Z =

shapefactor x Jf

yJR''-{\^k)X'

r +

A^X

A^X"- +etc.

(6.3)

292 Micro- and Nanomanufacturing

Where X is the horizontal distance from the aspheric axis, Z is the

corresponding vertical distance or the vertical sag, shape = -1 for

convex; and = +1 for concave, where

R = radius of curvature, and

k - conic constant as given below:

k< -1 Hyperboloid

k--l Paraboloid

~I< k< 0Ellipsoid

k = 0 Sphere

k> 0 oblate ellipsoid.

The remaining terms in the above equation are the symmetrical

deviations from the basic conic form. The vertical sag of a spherical

surface and an aspheric surface with their basic equations and sym-

metrical deviation is shown in Fig. 6.24.

Manufacture of such aspherics has always been a challenge, es-

pecially on infrared window materials and metals. Therefore, manu-

facturers and researchers have put in a great deal of effort to system-

atically apply measurement science to design, manufacture, and

fabrication of highly precise devices to achieve low tolerances, bet-

ter surface finish, and low subsurface damage at reduced cost.

Currently, with the development of ultraprecision machine tools,

there have been reports of achieving all three desired aspects of pre-

cision aspheric. Single-point diamond turning is the principal ma-

chining method being used to machine extremely brittle materials

like silicon and germanium. However, efforts are in progress to ob-

tain the desired aspects of precision aspheric by diamond grinding.

The present work also explores the feasibility of obtaining subsur-

face damage free aspheric surface on single crystal silicon surfaces

[76].

Microgrinding 293

Fig. 6.24. Effects of sag creates a difference between aspheric and spherical sur-

faces as demonstrated by the use of

dial test indicator [76]

The principal use of aspheric lens designs is the reduction or

elimination of optical aberrations produced by looking through an

ophthalmic lens obliquely. We will begin our discussion of aspher-

ics by exploring some of these optical aberrations and their effects.

For ophthalmic lenses, a lens aberration occurs when rays of light

fail to come to a point focus at the ideal image position of the eye

(called the far point) as it rotates about its center.

294 Micro- and Nanomanufacturing

Oblique a&tlgmatism

Fig. 6.25. Rays of light from an object point strike the lens obliquely and are fo-

cused into two separate focal lines, instead of a single-point focus, resulting in

oblique astigmatism [76]

Astigmatic focusing error, which is illustrated in Fig. 6.25, re-

sults when rays of light from an object in the periphery strike the

lens obliquely. Two focal lines are produced from each single object

point. The dioptric difference between these two focal lines is

known as the astigmatic error of the lens.

Rays of light striking the tangential, or radial, plane of the lens

come to a line focus at the tangential focus. The resultant focal line

is perpendicular to the actual tangential plane. Rays striking the sag-

ittal, or equatorial, plane of the lens come to a line focus at the sagit-

tal focus. This focal line is perpendicular to the sagittal plane. Both

of these planes are shown in Fig. 6.26.

Coma is a distortion in image, wherein the focus and the magni-

fication are different for rays passing through various zones of the

optical system. It usually occurs when the incident rays are not par-

allel to optical axis and a ring shaped blur image is formed.

In refractive optics, chromatic aberration (lateral and longitudi-

nal) alters the image quality when the optical system has to operate

in a wide range of wavelengths. This is caused by the phenomenon

of dispersion (change of refractive index with wavelength), produc-

ing a variation in focal length with wavelength. Chromatic aberra-

tion increases the size of the blur in the image in direct proportion to

spectral range.

Microgrinding 295

Tangential

Plane /'

Axis of Symmetry.

SagittalPlanes Tangential Planes

Sagittal

Plane

Fig. 6.26. The sagittal (equatorial) and tangential (radial) planes of

lens [76]

The three types of aberrations cannot be eliminated simultane-

ously. Therefore any optical system needs a combination of several

lenses to get a better quality image. On the other hand, limitations on

system weight and overall manufacture costs demands a lesser num-

ber of

lenses.

Thus, a parabolic surface on silicon proves to be a bet-

ter choice for infrared application.

Traditional methods of generating aspheric surfaces on glass

have been time consuming [77]. A novel technique was developed

by Kapoor and Venkatesh that brought about heavy material re-

moval without affecting surface finish and profile [72]. This tech-

nique was extended to germanium and silicon using both metal

bonded and resinoid bonded wheels.

To remove material quickly and end up with the desired surface,

the contact area between the grinding tool and the workpiece should

be as large as possible. Since only spheres and toroids permit the

condition of full area contact, partial area contact, or line contact

will be the best alternative. The use of

machine with a rotating tool

suggests that the contact surface must be symmetrically rotational.

In general, the shape of the workpiece is not predictable. Hence, the

condition of the large contact area is put in jeopardy. Thus, the

method was chosen based on a long line contact between the tool

and the workpiece during the first step of rough grinding. During the

subsequent steps of polishing, the use of a flexible tool allows con-

formity between the workpiece and the tool, approaching the origi-

nal condition of

contact area.

Two cup-shaped identical size diamond-grinding wheels with

metallic (D20/30 MICL50M-1/4) and resinoid (SD240-R1OO B69-6

mm) bonding were used. The profile of the grinding edge is circular

in this case, but not restricted to this shape, thus, forming a toroid.

296 Micro- and Nanomanufacturing

The important feature is that the grinding surface shape is axially

symmetrical. It is now possible to program the tool path of this tool

on the CNC-machine such that it is in line (or arc) contact with the

workpiece as it cuts the desired shape on the glass [78].

To illustrate this, the grinding of a paraboloid is shown. The cup

tool can be thought of as consisting of a collection of circles whose

planes are perpendicular to the axis of rotation of the tool. When the

paraboloid is intersected by a plane, as shown in Fig. 6.27, the

common line is called an ellipse. When the task is to cut a concave

paraboloid, the tool must fit inside the paraboloid. Hence, the tool

must have a diameter smaller than the shortest radius found on the

ellipse of intersection of any plane intersecting the paraboloid. In the

case of a paraboloid, the shortest radius of curvature on the eclipse

of intersection is found when the plane contains the axis of symme-

try of the paraboloid.

Any circle at the outer side of

the

tool can be contained in one of

the planes intersecting the paraboloid. The angle that this plane

makes with the axis of the parabolid can be adjusted such that the

arc of the circle and that of the ellipse (Fig. 6.27) at d, differs in sag

height no more than a preset tolerance. This condition sets a certain

common arc length over which the difference in sag does not exceed

a certain value, say 0.5 |Lim. Subsequently the tool axis can be pro-

grammed to take a slightly different position relative to the axis of

rotation of the workpiece, as well as relative to the apex P, of the

paraboloid. The sequence is then repeated to form a neighbouring

zone of the one indicated in Fig. 6.27.

Two 5-axis vertical CNC machining centers (Fadal and Deckel)

are programmed to perform these sequences continuously, until the

paraboloid is completed. In this manner, a zone is ground during one

revolution. While in cutting with a point tool, in principle one line of

the paraboloid is cut it is, thus, clear that this method of grinding

with the nearest arc-contact can complete the same surface faster

than in the case of cutting with a point-tool.

Microgrinding 297

zone

paraboloid

Fig. 6.27. Basic principle of grinding by zone [72]

The thermal imaging materials used were monocrystalline ger-

manium and silicon. Both blanks were polished after grinding. A

special aluminum tool was developed. A felt cloth was glued to the

spherical surface of this tool and a polishing paste of one-micron al-

pha alumina was applied to it during polishing. The same set-up was

used for polishing on the CNC machine.

T' = const.

^H^

-> " I

Fig 6.28. Aspheric surface generation process and schematic diagram showing

speed of the workpiece and the tool [79]

298 Micro- and Nanomanufacturing

The resinoid-bonded wheel was recommended by Tan [73] for

grinding both Ge and Si (Figure 6.28). Better surface roughness val-

ues were obtained with both wheels for Si. Si, however, was more

difficult to polish and a lighter pressure had to be applied to prevent

the felt from coming off. Thus, for the same time interval, Ge had a

much better surface finish. Polishing improved the form accuracy

with Ge, but not with Si. Both ductile and fracture modes of material

removal were observed with both Si and Ge[72]

Figure 6.29 shows some amount of ductile streaks on silicon and

Fig. 6.30 a massive amount of ductile streak on Ge. Better surface

roughness, form accuracy, and smoothness can be obtained with a 5-

axis CNC jig grinder, and also by dressing the grinding wheel for

ductile mode as suggested by Rusell [74]. The same type of work

has been conducted by Kapoor [72] who suggested that resinoid

bonded wheels give more ductile streaks than metal bonded wheels.

Fig. 6.29. Ductile streaks

obtained on Si during

aspheric generation [60].

Fig. 6.30. Formation of ductile streaks

on Ge during aspheric generation with

a resinoid-bonded diamond wheel. [60]

Microgrinding

299

6.5 Ultraprecision Grinding

6.5.1 Ultraprecision IVIachines and Development

Advancements

technology

now

make

possible

for

hard

and

brit-

tle materials

to be

machined

to a

very close tolerance. Ultraprecision

machining

has

been developed

and a new

machining concept called

ductile mode machining

has

been introduced. Using this machine

coupled with ductile mode theory, mirror finishes

can be

achieved

the

workpiece without

the

intervention

polishing [80,81].

ductile mode machining, feeds

and

depth

of cut

have

to be

very

small

the order

nm and

|Lim, respectively [82]. With

the ul-

traprecision machine set-up, full ductile mode machining

can be

achieved,

and

surface finish

mirror-like without subsequent proc-

ess like polishing [80,81].

Most

the ultraprecision machines available

in the

market

are

equipped with machining systems that adopt either single-point dia-

mond tools

multi-point abrasive (grinding) wheels. However,

some cases both machining systems

can be

incorporated into

one

machine

customer request

for

enabling both single

and

multi-

point abrasive machining operations. Figure

6.31

shows

typical

construction

both ultraprecision machines. According

Schulz

and Moriwaki

[84], an

ultraprecision machine

defined

as a ma-

chine that

has

machining systems with

the

following movement

ac-

curacies:

i. slide geometric accuracy

less

than 1

|Lim

ii.

spindle error motions of less than 50

iii.

control

and

feedback resolutions of less than 10

300 Micro- and Nanomanufacturing

Dia"Or:d tool

ALfSpmiJlc / Workpic-c

Rotational tabtc

Linear siz^t

J,, in car no tor

Linear

scale

Work Gpindle

MiCtO tool strvQ (Aerostatic bearing)

vVheei spincie

(Aerostatic bearing)

f .^ \ Column

V~V R. B.

Guideway

Fig. 6.31. A typical construction of (a) 2-axis an ultraprecision single-point dia-

mond turning machine [46], (b) 4-axis an ultraprecision diamond grinding ma-

chine (Courtesy Toshiba Machine Co, Ltd.)

With the above movement accuracies, it is expected that the ul-

traprecision machine will be able to generate the following work-

piece accuracies:

i. dimensional accuracy in the range of a few

micrometers

ii.

surface form accuracy in the range of lOOnm or

better

iii.

surface texture in the range of 5nm, or better

In order to satisfy the above requirements, the machine must ex-

hibit high degrees of thermal stability, stiffness, damping, and

smoothness of motion and must also be integrated with an ultrapre-

cision metrology system in the machine tool but isolated from the

response of the machine tool during machining [85]. There are at