REVIEW Micro-machiningrsta.royalsocietypublishing.org/content/roypta/370/1973/3973.full.pdf · Review. Micro-machining 3975 physical chemical mechanical cutting reactive ion etching

Phil. Trans. R. Soc. A (2012) 370, 3973–3992doi:10.1098/rsta.2011.0056

REVIEW

Micro-machiningBY EKKARD BRINKSMEIER* AND WERNER PREUSS

Laboratory for Precision Machining, University of Bremen, Bremen, Germany

Manipulating bulk material at the atomic level is considered to be the domain ofphysics, chemistry and nanotechnology. However, precision engineering, especially micro-machining, has become a powerful tool for controlling the surface properties andsub-surface integrity of the optical, electronic and mechanical functional parts in a regimewhere continuum mechanics is left behind and the quantum nature of matter comes intoplay. The surprising subtlety of micro-machining results from the extraordinary precisionof tools, machines and controls expanding into the nanometre range—a hundred timesmore precise than the wavelength of light. In this paper, we will outline the developmentof precision engineering, highlight modern achievements of ultra-precision machining anddiscuss the necessity of a deeper physical understanding of micro-machining.

Keywords: micro-machining; diamond machining; ultra-precision grinding; polishing

1. Introduction

Scientists study the world as it is; engineers create the world that has never been.

(Theodore von Kármán)

When engineers ‘try to make things that do not exist in nature’ [1, p. 1], theyapply ‘scientific principles to design or develop structures, machines, apparatusor manufacturing processes . . . all as respects an intended function, economicsof operation and safety to life and property’ [2]. What engineers had in theirtool boxes in the nineteenth century and during the first half of the twentiethcentury was mainly classical mechanics, electrodynamics and thermodynamics.Even when it became evident that all the mechanical, chemical and electronicproperties of matter are a consequence of the structure and dynamics of theatoms making up the world around us, described by quantum laws, it was notnecessary for engineers to understand quantum physics, because they were notdealing with individual atoms but with lumps of them, 1020 or so at once, forwhich the classical laws were all they needed. By the mid-twentieth century,this picture began to change. The invention of the transistor and the laser gavebirth to microelectronics and optoelectronics, which lie at the heart of modern*Author for correspondence ([email protected]).

One contribution of 16 to a Discussion Meeting Issue ‘Ultra-precision engineering: from physics tomanufacturing’.

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3974 E. Brinksmeier and W. Preuss

Table 1. Range of operation and achievable surface quality of nano-, micro- and macro-machining processes.

nano-machining micro-machining macro-machining

size of machined area 1–105 mm2 1–105 mm2 1–105 cm2

volume removal in onemachining step

from 10−3 to 102 mm3 from 10−3 to 102 mm3 from 10−3 to 102 cm3

material removal rate from 10−5 to 1 mm3 s−1 from 10−5 to 1 mm3 s−1 from 10−5 to 1 cm3 s−1

relative figure error from 10−5 to 10−3 from 10−7 to 10−5 from 10−5 to 10−3

surface roughness (Sa) 1–102 Å 1–102 nm from 10−1 to 10 mm

communication. Without a basic knowledge of quantum mechanics, an electricalor optical engineer working in these fields would be helpless. What about precisionengineering, micro-machining in particular? Are we hitting the atom yet?

2. Micro-machining processes

The term ‘micro-machining’ refers to a machining process by which small(‘microscopic’) bits of material are removed in order to achieve a high geometricalaccuracy that otherwise is unattainable. Because the amount of material removedlocally in a micro-machining process is rather small and removal rates oftenare very low (table 1), micro-machining is particularly suited for manufacturingof micro-structures and micro-parts. If a micro-machining process is set up formachining of large workpieces, this is attempted because extremely tight figureand roughness tolerances can be met. Depending on the accuracy achieved,these applications are traditionally referred to as ‘precision machining’ or ‘ultra-precision machining’. When the amount of material removed becomes increasinglysmall, the transition to nano-machining is made, which is an important branch ofnanotechnology [3]. Electron beam lithography and X-ray lithography combinedwith chemical etching, electroplating and moulding (LIGA) are the enablingtechnologies for the fabrication of microelectronics and microsystems [4].

Micro-machining processes can be classified according to the physical natureof the removal process into physical, chemical and mechanical (figure 1). Whilephysical and chemical machining are limited to specific applications, mechanicalmachining is almost universal and has a long tradition. This is because a hugeclass of engineering materials (metals, semiconductors, ceramics, optical glassesand plastics) can be processed and a large variety of surfaces with optical,electronic or mechanical functions can be generated. Mechanical micro-machiningis further subdivided into cutting and abrasive machining, with the lattercomprising precision grinding and polishing and the former being dominated bydiamond turning and milling.

The goal of micro-machining is to achieve the required accuracy in one singlemachining step without being forced to iterate slowly converging machining andtesting cycles. Thus, all parameters that affect the accuracy of the process mustbe identified and controlled as much as is needed for reliably reaching giventolerances. When this is accomplished, the process is called ‘deterministic’. Notall micro-machining processes are deterministic with respect to a set of given

Phil. Trans. R. Soc. A (2012)



Review. Micro-machining 3975

physical

chemical

mechanical

cutting

reactive ion etching

laser beam machining

ion beam machining

electrochemical machining

diamond turning

diamond milling

polishing

precision grindingabrasive machining

Figure 1. Classification of micro-machining processes.

tolerances. By pushing the frontier of indeterminism towards tighter tolerances,the precision engineer is struggling with countless and delicate causes and effectsirrelevant to macro-machining. In the following sections, we will focus on thosemicro-machining processes that are most advanced and closest to the asymptoticlimit of machining accuracy imposed by the atomic structure of matter.

3. Diamond machining

Diamond turning and milling have evolved into fast and reliable techniques forgenerating complex optical surfaces that cannot be produced economically in anyother way, or cannot be created in any other way at all. Products that requirediamond machining for the fabrication of at least one of their components areall around us, such as a computer mouse, a DVD player, a pocket camera, amobile phone, a barcode scanner, reflective tape or a contact lens. All thesecomponents are mass produced by injection or compression moulding or, in thecase of glass lenses, by hot isostatic pressing, relying on the quality of diamond-turned metal moulds [5]. Diamond-machined optical components are neededfor projection systems, displays, laser scanners, sensors, scientific instruments,medical and defence equipment, laser beam guiding, illumination systems andmany more. These products exhibit a multitude of different surfaces rangingfrom rotational symmetric aspheres to freeform and structured surfaces withFresnel or prismatic elements (table 2). The surface finish obtained by diamondmachining is between 1 and 10 nm Sa, depending on machining conditions andon material properties; the achieved figure accuracy ranges between 0.1 and 1 mmpeak-to-valley, depending on the size and shape of the workpiece.

How has diamond machining reached the precision and flexibility that isavailable today?

There are two key elements that have enabled the evolution of mechanicalmachining towards higher accuracy:

— control of the accuracy of the machine, and— control of the accuracy of the tool.





Table 2. Diamond-machined optical elements and precision parts exhibiting different typesof surfaces.

symmetrical surfaces freeform surfaces structured surfaces

moulds for plastic lenses non-telecentric imaging systems automotive lightingIR optics head-up displays lens arraysUV optics LED lighting systems prism arraysCO2-laser mirrors range finders phase platesophthalmic lenses F-theta lenses Fresnel lensesscanner polygons flat panel backlight units lab-on-a-chip

Error movements of slides and spindles can only be measured and compensatedif they are repeatable [6]. Hence, random error movements of machine elements(e.g. asynchronous spindle run-out; bending of slides under varying loads) must beminimized, i.e. the mechanical accuracy and stability of the machine and machinecomponents must be optimized in the first place. Initially, mechanical accuracyis achieved using self-reversal techniques and geometrically stable materials suchas cast iron or granite [7]. Once accurate machines have been built along suchprinciples, they can be employed for producing more accurate components (suchas journal bearings for ultra-precise air-bearing spindles, which are machined onultra-precision lathes). In turn, ultra-precision components (such as air-bearingspindles) can be used for creating ultra-precise tools. Monocrystalline diamondsare used for two reasons: (i) single crystals can be ground and polished yieldingextremely sharp and flawless edges with radii less than 75 nm [8] and (ii) wear ofthe cutting edge is almost negligible when cutting non-ferrous metals and selectedplastics and semiconductors. The anisotropy of the abrasive wear of diamond [9]must be observed in tool design, because tool life also depends on the hardnessof the tool’s rake face.

Evans [10] and Marsilius [11] summarized the milestones in the evolution ofdiamond machining as follows.

In the 1960s:

— Systematic investigation of error sources of machine movements; errormotion of linear slides less than 0.5 mm over 300 mm.

— Development of high-precision air-bearing spindles; axial and radial run-out less than 50 nm.

In the 1970s:

— Encoder feedback for position control less than 100 nm.— Grinding and polishing of diamond tools with well-defined geometry;

fabrication of radius tools with cutting edge waviness less than 1 mm.

In the 1980s:

— Beginning of commercialization of diamond machining.— Introduction of laser interferometers for position control; resolution less

than 10 nm.





Table 3. Evolution of commercially available diamond machining equipment [11].

1980s 2000s

machine base cast iron or granite granite or epoxy graniteslide ways air bearing or rolling bearing oil hydrostatic bearingaxis drives lead screw and servo motor linear motorspindle bearing porous graphite or orifice orifice or groove compensatedspindle drive belt drive direct brushless DC motorspindle feedback none encoder (resolution 0.1 arcsec)positioning laser interferometer (resolution 6 nm) glass scale (resolution 0.6 nm)controller commercial CNC PC-based controllers

— Implementation of computer numerical controls.— Mechanical and chemical polishing of radius tools with controlled waviness

less than 0.1 mm.

In the 1990s:

— Introduction of glass scales with electronic interpolation for positioncontrol; resolution less than 1 nm.

— Introduction of oil hydrostatic bearings for linear slides; error motion lessthan 0.15 mm over 300 mm.

— Introduction of multi-axis machines for freeform machining.— Introduction of PC-based controls.— Improved environmental control by air-conditioning of machine housings.

In the 2000s:

— Introduction of fast tool servo (FTS) and slow slide servo (SSS) turning.— Introduction of linear motors for driving linear slides.— Customized software for freeform machining.— Development of ion beam polishing of diamond tools for shaping of non-

circular cutting edges.

The progress made within 25 years of machine development is summarizedin table 3.

Many specialized ultra-precision machines have been constructed which surpassthe accuracy of commercially available equipment. The large optics diamondturning machine built at the Lawrence Livermore National Laboratories (figure2) with a contouring accuracy less than 0.1 mm over 812.8 mm is supposed to bethe most precise machine in the world [12]. Other special purpose machines havebeen built for diamond turning of large mirrors up to 2032 mm diameter [13],Fresnel lenses up to 1950 mm diameter, precision drums up to 2000 mm in length[11] and mandrels for the production of Wolter mirrors for X-ray telescopes [14].

The progress made in the development of tools and equipment is reflected byan improvement in the achievable surface roughness and figure accuracy, but evenmore by the tremendous increase in complexity of accessible surface shapes. Whilein the 1970s and 1980s diamond turning had been welcomed as a cost-effective





Figure 2. Schematic of the vertical axis large optics diamond turning machine (courtesy of LLNL).

technique for generating rotationally symmetric aspherical surfaces (figure 3), ithas become possible today to create freeform shapes and structured surfaces, evenin combination. Increasing complexity is associated with a loss of symmetry of thesurface and hence with an increase in the number of degrees of freedom needed formoving a tool past a surface, i.e. an increase in the number of controllable machineaxes. For diamond machining, the challenge is twofold. First, it is not easy tomaintain stiffness and contouring accuracy (which has now become volumetricaccuracy) when adding more axes to a machine. Second, owing to the nature of thecutting tool (which is a polished single crystal diamond), only a very few cuttingoperations can be realized (compared with conventional multi-axis machining),which are essentially limited to single edge circumferential milling (fly-cutting)and ball-end milling, the latter being used if small radii of curvature make fly-cutting impractical. On the other hand, because cutting edges are extremely sharp(less than 50 nm edge roundness), the surface finish does not depend on cuttingspeed, so that, in contrast to conventional machining, milling operations maybe substituted by scraping or chiselling, and turning operations may be sloweddown, allowing for adjusting the tool’s position by an additional linear axis incorrespondence with the angular position of the workpiece. This technique iscalled SSS turning, if the third axis is a major axis of the machine, or FTSturning, if the tool is driven by a voice coil or a piezo actuator. Because themoving mass is smaller in FTS turning, accelerations may be higher, but strokesare much smaller than in SSS turning.

An example of a freeform surface generated by raster milling on a state-of-the-art three-axis ultra-precision machine is shown in figure 4. A figure error lessthan 0.3 mm peak-to-valley and a surface roughness Sa less than 4 nm is withintoday’s standard. It is worth mentioning that machining of freeform surfaces inoptical quality would not be possible without fast computer numerical controls,because the rate at which slide positions have to be updated during machining isof the order of 103 commands per second.





Figure 3. Diamond turning of an electroless nickel-plated hyperbolic mirror for a LIDAR system.

50 mm

Figure 4. Electroless nickel-plated mould for an F-theta lens. Non-rotationally symmetric surfacecreated by raster milling on a three-axis ultra-precision machine.





50 µm10 µm

(a) (b)

Figure 5. (a) A white-light interferometric image and (b) a schematic of a hologram diamond turnedinto a copper–nickel–zinc substrate with a nanometre stroke ultra-fast tool servo system [17].

100 µm 100 µm

(a) (b)

Figure 6. Scanning electron microscope images of retro-reflective prisms. (a) Triangular cornercubes created by intersecting three systems of V-grooves with an included angle of 70.53◦.(b) Hexagonal corner cubes created by micro-chiselling [18].

The FTS concept was originally conceived for increasing the accuracy of anultra-precision lathe [15] and was applied later for non-circular turning of asphereswith a small deviation from rotational symmetry [16]. Recently, Brinksmeieret al. [17] presented a 350 nm stroke FTS operating at frequencies up to 10kHz, which can be used for the generation of holograms (figure 5). Anotherexample illustrating the progress that has been made in micro-structuring ofoptical surfaces by diamond machining is shown in figure 6. For a long time itwas believed that hexagonal corner cube prisms, which offer a 100 per cent yield ofretro-reflected light, would be impossible to generate by diamond machiningowing to alternating convex and concave corners. Instead, it was thought thatonly triangular prisms could be machined, which are all convex, by intersectingthree systems of V-grooves fly-cut into a metal substrate. However, Flucke et al.[18] have demonstrated that hexagonal prisms can be cut out by a micro-chisellingprocess with dedicated diamond tools and a genuine cutting strategy.





300

150

(nm

)

40

30

(µm) 20

10 1020

3040

material: electroless nickeltool nose radius: re = 0.76 mmfeed per revolution: f = 4.8 µmlubricant: mineral oilroughness: Ra = 3.4 nm

(µm)

Figure 7. A scanning force microscope image of a diamond-turned electroless nickel surface. Theroughness is limited by the height of the feed marks [19].

Despite this impressive record of achievements, we may ask whether there arelimitations to the achievable precision in diamond machining and how far we areaway from natural or practical limits. In an attempt to answer this question,let us first examine what we mean by precision of machining. The quality ofa machined surface is best analysed by looking at the deviation between themachined and the ideal surface as represented in the (two-dimensional) spatialfrequency spectrum. Spatial frequencies below approximately 1 mm−1 are usuallyreferred to as figure errors. Figure errors are caused by the imperfections of themachine’s geometry, Abbe errors and positioning errors owing to errors pertainingto the metrology frame. The machine’s geometry is susceptible to temperaturegradients and temperature changes, thus temperature control is imperative.Depending on the kinematics of the machining operation, imperfections ofthe geometry of the diamond tool may also contribute to the figure error.But, even if geometrical errors could be eliminated completely, there wouldbe figure errors caused by misalignment of the tool and the workpiece and bydistortions induced by mounting stresses. Spatial frequencies between 1 mm−1

and 10 mm−1 are referred to as waviness. Waviness may also be caused byerror movements of the slides, but usually results from long-term oscillationsof the machining system such as varying oil or air pressure, thermal or electricaloscillations, mechanical oscillations excited by periodic or sudden accelerations orby imbalance of spindle rotation. Spatial frequencies larger than approximately10 mm−1 make up surface roughness. Chatter and vibrations caused by oscillatingcutting forces and/or insufficient balancing are the main causes for textures andsuperstructures observed on diamond-machined surfaces. Once these have beeneliminated, surface roughness is determined by machining parameters and by theresponse of the workpiece material to cutting (cf. figures 7 and 8). At this level,the sharpness and microscopic perfection of the cutting edge come into play, andhence tool wear.

As is evident from the foregoing discussion, the accuracy of diamond machiningdepends on a multitude of factors and is the target of the combined effortsof production engineers and precision engineers [20]. But at no point in thisdiscussion have we left the domain of classical physics; there is no need to consideratomic physics. With the exception of tool wear.





0.15

–0.10

0

89.2

80.8

(µm

)

0.05

0

–0.05

0 12.3 24.7 37.0 49.3(µm)

3.84 µm

31 nm

61.7

0

profile

(µm

)

(µm) (µm

)Figure 8. A scanning force microscope image of a diamond-turned OFHC copper surface. The

roughness is limited by the elastic recovery of the individual grains [19].

H

not diamond turnable

diamond turnableLi

Be

Na

KTi V Cr Mn Fe Co Ni Cu Zn

Cd

Au

AgPd

PtIrOs

RhRuTc

Re

Ge

Sn

PbTiHg

Ga

In

Al Si

B C N O F Ne

He

ArClSP

As Se Br Kr

Xe

RnAtPoBi

ITeSbRb

Cs

Fr Ra Ac

8 µm

15 µm

6 m 3 µm

6 µm

cutting distance

30 km

La HfBa

Sr Y ZrNb Mo

WTa

ScCa

Mg

Figure 9. Scanning force microscope images of the cutting edge of a diamond tool after cutting(left) iron and (right) copper.

We remain puzzled by the fact that there are certain materials that leavethe diamond cutting edge virtually untouched even after long distances of cut(considered to be ‘diamond turnable’), and others that cause substantial toolwear, sometimes at a rate which deserves the term ‘catastrophic’ (figure 9). Thisobservation cannot be explained only by differences in the mechanical propertiesof the materials such as hardness and fracture toughness. A search through the





Figure 10. Precision grinding of a tungsten carbide mould with a fine-grained diamond wheel(courtesy of Moore Nanotechnology Systems).

periodic table suggests the presence of a chemical component in diamond toolwear, as has been pointed out by Paul et al. [21]. The reduction in diamond toolwear achieved by ultrasonic vibration cutting [22], in which the contact betweenthe cutting edge and the workpiece material is interrupted periodically at a highfrequency, also points in this direction. Another strong indication of chemicallyinduced wear is Brinksmeier’s & Gläbe’s [23] discovery that nitrided steel canbe diamond-turned without appreciable tool wear while untreated steel cannot.Thus, there is an urgent need for a better understanding of the wear mechanism ofdiamond, i.e. the development of microscopic wear models that take into accountthe chemical aspects of wear.

4. Ultra-precision grinding

Although the evolution of diamond machining has not yet reached its final stage,the main concern today is an improvement in productivity rather than an increasein flexibility and accuracy. In ultra-precision grinding, the situation is different[24]. In fact, similar ultra-precision machining equipment is used for precisiongrinding, but the ideal grinding tool has not yet been invented.

The surprising finding that grinding of brittle materials can produce opticallysmooth surfaces without sub-surface damage is explained by the phenomenon ofductile-to-brittle transition. A material is supposed to behave brittlely, if thereis no apparent plastic deformation before cracking. However, on the nanometrescale, even brittle materials behave plastically as long as the potential energyincrease in the volume subject to indentation is not sufficient to initiate cracks.Hence, ductile-mode grinding of brittle materials is possible, provided the uncutchip thickness is smaller than a critical thickness at which crack formation setsin [25]. The challenge in ductile-mode grinding of brittle materials is to maintainthis condition at least in a small zone around the deepest point of cutting that willbecome the new surface generated in the grinding process. Because the critical





metal bonded wheel

specific grindingfluid for ELID

negativeelectrode (–Ve)brush (+Ve)

coolant

feed

workpiece

chuck

Figure 11. The principle of electrolytic in-process dressing (courtesy of RIKEN).

uncut chip thickness of most brittle materials is less than 200 nm [26], it is evidentthat ductile-mode grinding can only be achieved with ultra-precision machines(figure 10) and grinding wheels exhibiting an excellent roundness, because anyprotruding grain will initiate cracks. Roundness requirements for ductile-modegrinding cannot be met by wheels with an average grain size larger thanapproximately 15 mm because of the variance of the statistical height distributionof the abrasive grains, even if perfectly dressed. Fine-grained diamond wheels,however, wear quickly and must frequently be reconditioned to re-establishroundness while shrinking in diameter. This is the dilemma of precision ductile-mode grinding: if the wheel is reconditioned, the depth of cut will change in anunpredictable way, leading to figure errors; if the wheel is not reconditioned, itwill cease to work in ductile mode because roundness is lost.

The first breakthrough in the development of ductile-mode grinding was madeby Ohmori & Nakagawa [27], who invented electrolytic in-process dressing (ELID)of metal-bonded grinding wheels. Continual in-process dressing is made possibleby electrolysis of the metallic bond of the wheel (figure 11). The dressing processcontinues at a constant rate because of the formation of an oxide layer onthe surface of the grinding wheel. This technique, which has been adaptedto different grinding kinematics, has enabled ductile-mode grinding of glasses,ceramics and metals, yielding optical surfaces with excellent roughness and sub-surface integrity. However, the ELID process is not predictable as much as wouldbe necessary to compensate for changes in the geometry of the grinding wheel;hence, it is difficult to meet figure tolerances [28].

Another approach to escape the dilemma of ductile-mode grinding has beenproposed by Zhao et al. [29]. Wear of the grinding wheel could be reduced toan acceptable level if coarse-grained wheels with an average grain size largerthan 100 mm could be employed. In order to meet the roundness requirementsof ductile-mode grinding, the abrasive layer of the wheel is ground or polisheduntil the grain surfaces appear to be aligned on a common cylindrical ortoroidal envelope surface (figure 12). Zhao et al. demonstrated that ductile-mode grinding of optical glasses with ‘engineered wheels’ of this kind is possible.Moreover, a large volume of material can be removed before any wear is detected,which essentially is grain wear; no cleavage or breakage of individual grains





original wheelperipheral envelope

before truing

metal bond

peripheral wheelenvelope after

truing 100 µmflattened diamondgrain top surfaces

after truing

(a) (b)

Figure 12. Truing of coarse-grained diamond wheels within the abrasive layer. (a) The principleof preparing a common envelope surface. (b) A scanning electron microscope image of the wheeltopography obtained by truing.

hydrostatic pressure: phyd = 0 MPa workpiece material:

surface orientation:

scratch direction:

tool rake angle: g = –45°

cutting speed:

pressure medium:mineral oil

{111}-plane

<221>-plane

vc= 0.4 m s–1

single-crystal silicon

hydrostatic pressure: phyd = 200 MPa

scratch direction 100 µm

Figure 13. Crack formation in silicon observed in plunge-cut experiments with a negative rakediamond tool with and without applying hydrostatic pressure [31].

is observed. However, before ductile-mode grinding with engineered coarse-grained wheels can be investigated in detail, a suitable dressing technology mustbe developed.

The idea of using engineered wheels might have an even larger potential forductile-mode grinding. As is well known in fracture mechanics, the brittle-to-ductile transition of brittle solids depends on compressive stress and temperature.The critical uncut chip thickness is not a material constant but depends ontemperature and stress conditions, which can be manipulated by adjusting cuttingparameters. Thus, ductile-mode diamond turning of silicon and germanium canbe achieved by using diamond tools with a negative rake angle [30] becausecompressive stresses are induced in the cutting zone, which decreases theprobability of crack formation. A similar observation was made by Brinksmeieret al. [31] in plunge-cut experiments with silicon subjected to compressive stress ina pressurized oil environment (figure 13) leading to hydrostatic pressure aroundthe cutting edge. The question arises how engineered wheels could be designed





to increase the critical uncut chip thickness in the cutting zone. Unfortunately,there is a lack of microscopic models of crack formation that are needed to makeductile-mode grinding more predictable.

5. Polishing

Polishing is the oldest and most delicate technique for smoothing and figuringof surfaces. There are a multitude of different polishing processes: mechanicalpolishing with different kinds of abrasives and polishing tools, chemical polishing,etching and combinations thereof; there is polishing with fluid jets and with laser,electron, atom or ion beams; there are polishing processes assisted by vibration,by pressure or by heating; with simple or with very sophisticated kinematics; andthere are transitions and overlapping with related processes such as lapping andhoning. Moreover, there is almost no material that could not be polished withone or the other of these techniques. So why is polishing not the rule rather thanthe exception in micro-machining?

The answer, of course, is that the majority of polishing processes are notdeterministic. If polishing is used not only for improving surface roughness andfor removing sub-surface damage but also for surface figuring, the figure actuallyobtained by the polishing process is in most cases unpredictable. Hence, thesurface has to be measured and corrected locally by additional polishing stepswith the risk of introducing new errors. For polishing to become a deterministicprocess, the material removal function must be known and must be controlledduring the process. However, the removal function is affected by a large numberof variables: some may be known but difficult to control; others may not haveeven been identified. Moreover, material removal functions can only be predictedif the material removal mechanisms are understood. Research in this field isan interdisciplinary task involving solid-state physics, surface chemistry andtribology [32].

As long as theory fails to unveil the microscopic origin of the materialremoval function, it still may be obtained from measurement [33]. When thisis accomplished, deterministic material removal depends on the stability ofthe process. Argon ion beam polishing is a fairly stable process that is usedfor finishing telescope mirrors and correcting residual errors of mechanicallypolished or diamond-turned optics [34]. Another example is magneto-rheologicalfinishing (MRF) developed at the University of Rochester [35]. The processrelies on an abrasive fluid jet whose profile and viscosity can be controlledby a magnetic field, because ferromagnetic particles are dispersed in the fluid.Thus, the material removal function can be adjusted and is kept constant bythe continual renewal of abrasives carried with the fluid (figure 14). The MRFprocess is the first deterministic polishing process that has been commercializedand is employed for the production of aspherical lenses, moulds and mirrorsin industry.

6. Towards the physics of micro-machining

As has become evident in the preceding sections, there are a couple of openquestions in micro-machining that require an analysis of the dynamics of





Figure 14. Magneto-rheological finishing of an aspheric calcium fluoride lens (courtesy ofQED Technologies).

machining at the atomic level. In diamond machining, we would like to knowhow we can diamond-turn steel and other iron-based metals. An explanation ofthe phenomenon of ‘catastrophic’ tool wear observed in experiments (figure 9)has been proposed by Paul et al. [21], who have pointed out the catalytic role ofunpaired 3d electrons of the iron atom. But the details of the wear process are notwell understood. What kind of reaction takes place? What are the reaction rates?On what parameters do they depend? In ductile grinding of brittle materials, wewould like to know how cracks are propagating and how crack formation can beavoided. How should engineered wheels be engineered? Even at the beginning ofthe twenty-first century, mechanical and chemo-mechanical polishing is but littlemore than black magic, because tribology and surface chemistry are exceedinglycomplex and difficult to analyse at the atomic level—both theoretically andexperimentally.

The situation here is similar to problems in molecular biology. Given thesequence of amino acids in a protein, how will it fold and acquire its biologicalfunction? In both situations, we are faced with the problem of understandingNature on the meso-scale. While the system is too big to predict its propertiesstarting with the basic laws of quantum mechanics, we also cannot infer itsbehaviour from the laws of classical mechanics because the system is toosmall. To deal with such complex systems, the method of molecular dynamicshas been developed, which is a numerical simulation of the motion of all theatoms of the system based on a compromise between quantum and classicaldynamics. The method is widely used for modelling of proteins and otherbiomolecules, as well as in materials science. However, tribology, crack formationand chemical wear are big challenges for molecular dynamics simulations, notonly because the electronic structure of the atoms, which is responsible for theformation of chemical bonds, should be taken into account but also because ofthe long time scales involved compared with applications in biochemistry andmaterials science.





50 300

300 300

300

350400

450 400

350

50

100

100

diamond tool

–1000

0

0

(Å)

(Å)

(Å)

(Å)

10–10

100

simulated cutting speed: 100 m s–1

–100 0 100

(K)

(a)

(b)

monocrystallinecopper

diamond tool700750650

550

Figure 15. Molecular dynamics simulation of orthogonal micro-cutting of monocrystalline copper.(a) Snapshot after a cutting time of 200 ps. (b) Temperature distribution in the cutting zone [38].

The first attempts at studying abrasive material removal with moleculardynamics simulations were made in the early 1990s [36], in which the interactionof neighbouring atoms was approximated by a simple pair potential neglecting theelectronic structure of the atoms. Since then, simulations of cutting processes haveadvanced from two-dimensional (with a few hundred atoms) to three-dimensional(with hundreds of thousands of atoms), and from picoseconds to nanosecondsof simulated cutting time. Although still far away from time and length scalesthat can be realized in cutting experiments, the pair potential approach andsubsequent refinements could reproduce characteristic features of micro-cuttingprocesses: chip formation, formation of dislocations and slide planes, the increasein specific cutting forces with decreasing depth of cut (‘size-effect’), and wear ofcutting edges [37]. By averaging the potential and kinetic energies of the modelatoms, it has become possible to estimate stresses and temperatures in the cuttingzone close to the cutting edge which are inaccessible to measurements (figure 15).

The molecular dynamics approach to micro-machining has often beencriticized. It has been argued that there is no way of verifying the results ofthe simulations by experiment. Hence, it is difficult to judge the errors caused bynumerical integration and limited time resolution, by incorrect potential energysurfaces and by approximations made in the model. Pictures and movies of cuttingprocesses derived from such simulations could at best give a qualitative impressionPhil. Trans. R. Soc. A (2012)




sp3 sp2 sp

Figure 16. Molecular dynamics simulation of diamond polishing with a pairing of two {110} facessliding along the 〈100〉 direction with a speed of 30 ms−1 and a pressure of 10 GPa. The edgeof a diamond grain moving from left to right is piling up atoms of the amorphous layer createdby polishing. Carbon atoms are coloured according to bond hybridization. Terminating hydrogenatoms are shown in blue [39].

of what is going on in the real world. Moreover, molecular dynamics hardlyprovided any new insight into the dynamics of micro-machining, nor has it beenvery helpful for tailoring tools or designing machining processes.

The harshest criticism, however, comes from those scientists who believe thatunderstanding of a complex system cannot be achieved by mimicking the motionof atoms in a computer rather than by discovering patterns of cause and effectand identifying those mechanisms that lead to the emergence of the characteristicproperties of the system. From an epistemological point of view, a computersimulation of a complex system, even if perfectly correct, is no more satisfyingthan a proof of a mathematical theorem generated by a computer program insteadof being obtained through logical reasoning. The difference between empiricismand understanding is the ability to control. Computer algorithms create anoutput from a given input. But only if we understand the inner mechanismsof a system can we manipulate it and design conditions that lead to a desiredoutput or behaviour.

However, this is not the full story. If molecular dynamics simulations becomesufficiently accurate and trustworthy, they could be considered as a virtual four-dimensional microscope with atomic resolution, with which virtual experimentscould be carried out that cannot be performed with any existing equipmentin the laboratory. We could make observations, change the experimentalconditions and identify mechanisms as well as we can do in real experiments.Of course, the test of any model derived from real or virtual experiments is areal experiment.





Recently, Pastewka et al. [39] demonstrated that molecular dynamicssimulations can contribute to an understanding of micro-machining processes,if the breaking and formation of chemical bonds is taken into account. Theprocess studied by the authors was the polishing of diamond with diamond grainsfor various surface pairings. The simulation revealed that during polishing anamorphous interface layer is formed (figure 16). Because carbon atoms disruptedfrom the lattice undergo a transition from sp3 to sp2 or sp bond hybridization,they can form strong bonds with atoms sitting at the surface of the lattice,eventually pulling them into the growing amorphous layer. Thus, the surfaceactivation by amorphous carbon atoms is the key for understanding the polishingprocess. The simulation also revealed the microscopic origin of the well-knownanisotropy of the polishing rate, because the probability for disruption of latticeatoms strongly depends on the orientation of the diamond lattice with respectto the polishing direction. Thus, it was possible to identify the underlyingmechanism that explains the macroscopic behaviour of the tribological system.It is hoped that microscopic wear models which include phase transitions andchemical reactions at the tribological interfaces, obtained by molecular dynamicssimulations, will make an important contribution to the basic understanding ofmicro-machining processes in the future.

7. Conclusion

What comes next in micro-machining? In the history of technology, often anurgent need has triggered invention. Sometimes—as in the case of the laser,or, looking back in history, of the steam engine—an invention has triggereda revolution. Today, it is difficult to imagine an invention that revolutionizedprecision machining. (Almost unnoticed, the advance of the computer did so twodecades ago.) Of course, the demands of the optics and microelectronics industrieswill continue to exert pressure to improve the quality, efficiency and reliabilityof diamond machining processes. Perhaps spatial mid-frequency errors couldbe controlled a little better. Perhaps high-speed cutting will become availableone day. But recalling the nanometre-scale accuracy reached routinely todayin the workshop and the high degree of geometric flexibility offered by multi-axis machines and ion beam contouring of diamond tools, one rather has theimpression that the development of diamond machining has achieved maturity.

This is not quite true for precision grinding. Although impressive advances havebeen made regarding surface roughness and the sub-surface integrity of precisionground hard and brittle materials, mainly because of the introduction of ELIDgrinding, the wear problem of fine-grained diamond wheels is as yet unsolved,preventing deterministic ultra-precision grinding of surfaces larger than a fewsquare centimetres. It is believed that precision grinding will have a bright futureif the wear problem can be solved, perhaps with a new type of grinding tool,and if ultra-precision grinding machines and spindles can be designed for higherspeeds and high stiffness.

However, the micro-machining processes that are least developed and leastunderstood but that have a huge potential are the polishing processes. As hasbeen learnt from diamond machining and precision grinding, the key to gainingcontrol over the removal process is controlling tool wear. In precision turning





and milling, this problem has been solved by using diamonds. In precisiongrinding, the problem is not solved satisfactorily. In a polishing process, whateverthe tool might be (a polishing pad and slurry, a water jet, or an ion beam),the removal function must be known precisely at any time. Measuring andcontrolling the removal function is still a big challenge, even more so becausetribology and surface chemistry are involved. The need to develop microscopicwear models in order to understand the polishing process at the atomic level issuggesting an answer to the question set out in the Introduction. As Fung & Tong[1, pp. 1–2] write in their classical text: ‘Almost all engineers . . . find that they donot have all the needed information. Most often, they are limited by insufficientscientific knowledge. Thus, they study mathematics, physics, chemistry, biologyand mechanics. Often they have to add to the sciences relevant to their profession.Thus, engineering sciences are born.’ It is in this context that precision engineersnow might add quantum mechanics to their tool box.

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