7/30/2019 10.1.1.116.2858

1/46

Rep. Prog. Phys. 53 (1990) 1049-1094. Printed in the U K

Manufacturing techniques for complex shapeswith submicron accuracy

J FransePhilips Research Laboratories, PO Box 80 000, 5600 JA Eindhoven, The Nether lands

AbstractIn the introduction, applications of parts with submicron accuracy are shown. Thedem and s with regard to the accuracy of these parts a re discussed. The main characteris-tics of various precision-machining processes are outlined. Specific advantages andproblems associated with these processes are indicated.In section 2 different aspects of part accuracy and surface quality are treated inmo re detail. M any parts with submicron accuracy have an optical function, a nd specialattention is paid to the requirements with regard to form accuracy and roughness ofoptical elements. In this section a distinction is made between machine- and process-related problems. T he machining ope ration is introd uced as an overall system contain-ing the machine and process as interacting subsystems.Section 3 discusses techniques used to minimise machine-related part errors in thedesign of precision machine tools. The sensitivity of various processes to particulartypes of ma chin e- an d environment-induced disturbances is outlined.Recent developments in the investigations of material removal mechanisms aredescribed in section 4. These include the mechanical modes of material removal onwhich diamond turning, grinding and polishing (to some extent) are based as well asthe basic chemical phenomena in processes involving etching.After these descriptions of the machine and process aspects, the influence of theinte rac tion between these subsystems o n the surface qua lity is outlined in section 5 .The emphasis here is on the coupled dynam ic behaviour in diamond turning a ndgrinding.The article concludes with an executive summary outlining the areas in whichsignificant progress has been ma de in recent years an d the main unresolved problems.This review was received in its present form in March 1990.

0034-4885/90/081049+46$14.00 @ 1990 IOP Publishing Ltd 1049

7/30/2019 10.1.1.116.2858

2/46

1050 J Frame

Contents1. Introduction

1.1.1.2. Precision-machining processes1.3.1.4.

Applications of complex parts with submicron precisionSystems approach to precision machiningMeasurements; process control for fabrication w ith submicronprecisionDimensions, form and roughness of a partAccuracy specifications for axisymmetric optical elementsIntroduction; the machine as subsystemMachine-induced part errors; error reduction techniquesPrinciples for design of precision instrumentsErrors due to imperfect geometries of machine componentsStatic aspects of machine tool mechanicsThe thermal loop of a machine toolDynamics of machine tools (open-loop)Measurement and control; dynamics of controlled machines

2. Part accuracy2.1.2.2. Surface integrity2.3.3.1.3.2.3.3.3.4.3.5. Tools for precision machining3.6.3.7.3.8.3.9.3.10. The error budg et concept4.1.4.2.4.3.4.4.4.5.4.6.4.7.5.1. Introduction5.2.6. ConclusionReferences

3. Machines and tools for precision machining

4. Tool-part interactionIntroduction; mechanisms of material removalModes of mechanical material removalPlasticity as a mechanism of material removalChip formation and cutting forces in metal cuttingMaterial aspects in mechanical tool-part interactionFracture versus plasticity; ductile regime grindingElectrochemical aspects of material removal5. Dy nam ic behaviour of the closed loop (machine+process)Surface quality in diamond turning and grinding

Page105110511053105710581058105810601061106210621063106410671067106810701071107310771077107710781078108010811083108510871087108810901091

7/30/2019 10.1.1.116.2858

3/46

Manufac turing techniques for complex shapes 1051

1. Introduction1.1. Applications of complex parts with submicron precisionThis article discusses the state of the art and current research topics in precisionmachining. A definition of precision machining is not easily formulated. A workingrule (at this moment) seems to be the fabrication of complex-shaped surfaces with aform accuracy of one micrometre ( p m ) or less and roughness un der 10 nanometres( nm ) ( 1 p m =1 x m =0.039 p in ). T he term complex surfaceexcludes op erat ion s which result in highly accurate surfaces with simple sha pes . Thesecan be fabricated with procedures that naturally tend to yield the desired accuracy.Examples are the polishing of spherical lenses or flat surfaces such as silicon wafersfor the semiconductor industry. In these processes the averaging over time and thelarger material removal rate at high spots (deviations from the desired shape) meantha t the desired shape w ill eventually be created. Th e fabricated sha pe is consideredcomplex if nature does not h elp us and special precautions have to be taken to achieveit. Go od examples are the pro ductio n of aspher ic lenses and polygon mirrors.In 1978 Saito presented an overview of the achievable accuracy and the limitingfactors in diamond turning. At that time, parts could be made with form accuraciesof arou nd 1.5 p m , The m ain limitations were imposed by the machine tool accuracy.Taniguchi (1983) presented a simplified overview of the progress made in precisionmachining with various processes during the last decade (figure 1). The evolution of

m, 1 nm =1x

AchievableMachiningaccuracy Machine tools(process ing equipment) Measuringmstruments(inspection equipment)~-,

x '(Electric or pneumaticmicrometers)Optical comparators

0 I p m , 10 ' - - - - - - -

O.Olpm. 10 >--.

0.001pm. ,I--lnm.(Atomiclattice

O.hm, -, I X.ray micro analyzers,Auger analyzers. ESCAR

i t I (Substance synthesizing)idistance)1900 1920 1940 1960 1980 2000 !ear

Figure 1. Th e progress m ade d uring the last decade in mach ining technology using variousprocesses (aft er Taniguc hi 1983) .

7/30/2019 10.1.1.116.2858

4/46

1052 J Frameprecision engineering as a multidisciplinary field has been sum marised by Evans (1987),and the relation between progress in precision engineering and other fields has beendescribed by Atkinson et a1 (1988).At this moment, form accuracy of precision-ground and diamond-turned partsbetween 0.1 and 1 p m is state of the art. Research in precision engineering an dmachining to day is aiming for the next decimal: 10 nm form accuracy an d roughnesseven less.The majority of complex parts with accuracy to a micron or better are used inoptical systems (Sanger 19 83). Typical optical applications include com ponents forlaser interferometer systems, lenses for compact disc players, telescopes, mirrors toreflect x-rays, scanners in copiers an d laser printers. There are also non-optical productsfo r which subm icron precision is required. Exa mples of non-op tical applications are(McKeown 1987): bearing surfaces for a variety of applications, parts of videorecorders, hard discs for computers, connectors for fibre optics and moulds for veryprecise injection -mou lded com ponen ts.These parts are manufactured in plastics, soft and hard metals, glasses, ceramicsan d layered systems of dissimilar materials. Very accurate parts of a particular materialcan be absolutely necessary to make a design work or desirable for economic reasons.Accuracy of a part is quantified in a way that depends on the function of the part.A m ore thorough discussion of this subject can be found in section 2. Here i t will beillustrated by looking at the accuracies required for some optical applications.Polygonal mirrors are used in laser scanners and printers with high resolution. Saraf(1987) described the specifications for these components (table 1).

Table 1. Specifications of polygonal mirrors (Saraf 1987).

a. Dyn amic facet-to-facet radius errorb. Pyramid angle errorc. Facet-to-facet angle errord. Facet reflectancee. Reflectance variation (facet-to-facet)f:g . Scratch and digh. Flatness variation (facet-to-facet)i. Flatness variation (within a facet)j . Total in tegrated scattering

Reflectance variation (within one facet)

10.001 in (25.4 p m run-out)iz5.0 arcsec (non-cumulative)3~15.0 rcsec (non-cumulat ive)>92% (630-830 nm wavelength)

7/30/2019 10.1.1.116.2858

5/46

7/30/2019 10.1.1.116.2858

6/46

7/30/2019 10.1.1.116.2858

7/46

Man ufacturing techniques fo r complex shapes 1055of polishing is the su btle tool-p art inte ract ion . Th e relative resilience of the polisherensures that high local peak loads do not occur. This is important if crack formationo r alteration of physical pro perties of the part to p layer (deg radation of surface integrity)has to be avoided. Wear rates are hard to p redict an d may vary owing to subtle chemicaleffects. Different regimes of dom ina nt material removal mechanisms ofte n exist (Br ow n1987), which m akes polishing less predicta ble than dia mo nd turning (se ction 4). Polish-ing is mainly used as a finishing tec hniqu e to redu ce the roughness of a part w ith g oodform accuracy or to remove surface layers dam aged in preceding opera tions. Ca re hasto be taken not to degrade the form accuracy as a result of the pressure distributionand uneven dwell time of the lap over various areas of the part. Polishing is thetradit ional p roduction technique used to m anufacture spherical com ponents an d flats,and procedures are well established for these applications (Horne 1972, Fynn andPowell 1988).Precision grinding (figure 4) ranks in between diamond turning and polishing inmany respects. A set of machine tool motions are controlled. Compared to diamondturning , the po sition of the cutting edge of the tool is less certain. At any time, an ythingfrom one to many grains are in contact with the part . Grinding wheels tend to becompliant and wear (Shaw 1972), effects which make it more difficult to achieve th edesired form accuracy tha n with dia m ond turnin g. Besides these disadvanta ges, thereare some notable advantages of precision grinding over dia mo nd turning. With smallwheels an d dep ths of cut it can be used to work brittle materials s uch as ceramics an dglass in a d uctile fashion (ch ip removal by ductile shearin g of material, as in m etalcutting (Bifano 1988, Bifano et al 198 8)). In som e cases the surface finish ob tainedwith precision grinding is so good that polishing is unnecessary. The grin ding processhas the advantage over polishing of higher removal rates and the ability to removevastly different amounts of material from small areas. Thus the grinding operation isparticularly suited to pro duc e especially small complex shapes in materials tha t cannotbe diamond-turned.

Grinding spindle ~

Figure 4. In precision contou r grinding, mac hine tool motions a re controlled as in diam ondturning. Th e position of the cut t ing edge depe nds on the compliance of the tool a nd spindleand the wear of the grinding wheel.

Beam processes dep end on the physical in teraction of the ion beam with the surface.Both deposition and removal of material can often be achieved. Metals, glasses andceramics can be worked. Ion beam milling relies on erosion of the par t due to theimpact of the impinging ions (Miyamoto 1987). A typical apparatus ( ion shower) isshown in f igure 5. Ions are produced in a plasma and subsequently move towards thepart . Removal rates are low and depend upon the energy of the incident ions, theinclination angle of the impinging beam and the anisotropy of the worked surface.

7/30/2019 10.1.1.116.2858

8/46

1056 J FranseArgas inlet

Filament/ Magnetic fluxI

Diamond tool holder

1 / I ~ Rotation 1 - 1Figure 5. Ion shower configuration used in ion beam machining (after Miyamoto 1987).

Numerous variations of physical vapour deposition techniques can be used to applylayers of materials on substrates. Low deposition rates, shadow effects, the difficultyin focusing the beam to a very small spot and deformation and sometimes crackingdue to incompatibility of the applied layer material with the substrate hamper theirapplication to produce (especially small) parts with complex-shaped surfaces.In elas?ic emission machining (EEM, figure 6 ) a slurry of very fine particles (sub micronsize) is flushed throu gh a bearing gap ( m icron s in height) formed by a spinning resilientsphere that is moved over the surface. This has been suggested to alter the electrondensity distribution of the surface atoms, increasing the etching rate locally (Mori eta1 1988). Erosion of the surface by the impinging particles has also been suggested toaid the material removal (Loewenthal et al 1988). E E M is one representative of a classof processes (M aeh ata et a1 1987) that are based on locally increasing the etching rateby addition of mechanical, electrical or thermal energy.

Work \S lurry (water +powder particles)State of fluid lubrication(no contact)

Figure 6. I n elastic emission machining, a slurry of very fine particles is forced into arelatively large bearing gap formed by the rotating weight-loaded sphere which is movedover the part (af ter Mori et al 1988).

7/30/2019 10.1.1.116.2858

9/46

Manufacturing techniques fo r com plex shapes 1057

-achine behavior process --c

Concluding, we can say that the processes discussed above have their specificstrengths and weaknesses. However, they have many problem areas in common whenit comes to achieving submicron accuracy. A machine structure, moving components,a tool an d a n interaction b etween the tool a nd the p art ( proc ess) are always involved.To un ders tand how these a nd their interaction determine the results requires a systemsapproach.

surface quality

1.3. Systems approach to precision machiningThe m anufacturing operation can be seen as a closed-loop system in which the machinetool and the process (tool-part interaction) are major subsystems (figure 7) .Machines have mechanical and thermal characteristics. Quantities such as move-ment or force are measured an d controlled using sensors with certain sensitivities an daccuracies. These characteristics of a machine are fixed in the design an d installationstage of a mac hine to ol. Process variables that affect the tool-part interaction ar echosen by the operator, and during the operation external disturbances act on thesystem. The machine behaviour and the tool-part interaction phenomena influenceone another mutually and together they determine the surface quality of a part.This can be illustrated using a dia mo nd-tu rnin g ope ration . Th e inputs of the overallsystem (mach ine +process) a re the values of the controlled variables (desired tool a ndspindle movements); the overall output is the part . The outpu t of the m ach ine subsystemis the actual tool path. Within the machine subsystem various signal paths can beidentified (Donaldson 1980) that determine the susceptibility of a machine to disturb-ances such as cutting forces and temperature effects (figure 8). In sect ion3 theseconcepts are discussed in more detail.Another subsystem in the machining operation is the interaction between tool andpart (remov al process) . The input in the case of d iamon d turning is the desired

@ Tool@ Mirror@ Interferometer Spindle mounts

_ _ _ _ _ Structural and thermal loopMetrology loop

Figure 8. In the m achine structure, s tructu ral , thermal and metrology loops can be identified.Sometimes they coincide , in general they d o not .

7/30/2019 10.1.1.116.2858

10/46

1058 J Franseinstantaneous depth of cut and slide velocities. The output is the cutting force actingon the machine structure and the amount of material removed (actual instantaneouscutting de pt h) . Th e cutting process involves elastic-plastic deformation and sometimescrack form ation . The phe nom ena in the material removal processes are treated insection 4.1.4. Measu rements; process control f o r fabrication with submicron precisionWhen submicron form accuracy is required, tool settings and movements have to becontrolled to within nanometres. This requires high-quality distance measurements,actua tors and guidew ays. Deflections d ue to forces must be kept to a minimum, w hichrequires stiff structures a nd bearings. Com pliances a nd d ynamic properties of machinetools have to be known to be able to choose adequate process parameters. Often adivision of the o pera tion into multiple cutting passes is necessary. Thermal deformationof machine com ponen ts should be kept to a minimum, which calls for correct design,precise tempe rature measurement an d control. The products m ade are often so accuratethat equally sophisticated machinery has to be built to measure them. Materials to becut have to be selected carefully to avoid problems with anisotropy, inclusions andporosity. Heat treatments an d m icroscopic investigation of the microstructure are oftennecessary.Process control for precision machining requires systematic attention to the effectsof even the most minute detail. Disciplines involved are: solid and fluid mechanics,physics, optics, materials science, electronics, co m pu ter science, metrology and controlengineering. Precision ma chin e tool operators sho uld have much experience an d feelingfor how little a nanometre is.

2. Part accuracy2.1. Dimensions, fo r m and roughness of a partThe specified dimensions of a part usually ensure that it can be positioned and movedrelative to oth er comp one nts. A detailed discussion of how to m easu re/inte rpretdimensions of various shapes is given by Foster (1980).An intuitive definition of partsize is: the largest distances between points on the part that ensure that it nowhereextends beyond the bou nda ries of a part with a perfect shap e (figure 9). It is determ inedby com paris on with gau ge blocks, by coordinate-measuring machines (M oo re 1970)or by laser interferometry. Com mercially available machines fea ture accuracies aroun d1 p m over measurement volumes of the order of 0.5 m3.The fo rm speciJicat ion o f a par t usually assures tha t the part will perform its primaryfunction. It places acceptable bou nds o n all the parameters used to describe the sh apeof the part su rface (s) an d the relations between th e various boun darie s of the part.Examples are given in figure 9. If the description of a surface profile is complicated,a wo rst-case acceptable erro r ba nd is often specified. Th e part profile h as to fall withinthis band (H aism a and Gijsbers 1983). Th e measuring process used to evaluate acontour always requires a choice of the spatial interval between measurement data.This also determines the shortest wavelength of a form distortion that can be measured(Nyquist criterion).Form accuracy is measured with mechanical stylus techniques, capacitive probes,interferometric methods (Downs er a1 1985, Wyant et a1 1985), Schlieren optical

7/30/2019 10.1.1.116.2858

11/46

Manufacturing techniques f o r complex shapes 1059Section A - A

Roughness

7/30/2019 10.1.1.116.2858

12/46

1060 J Franse

vi 1 -$ -9 100-e," pm 1 0 -s 1 -

I "vicIw._Eu -

smooth surfaces essentially images the spectrum of the part roughness (Vorburger era1 1986, Brod man n 1986). This can also be used to de termin e the surface roughnessspectrum and the R M S roughness value. Lately, scanning tunnelling microscopy (S T M )has been used to explore surface roughness features of precision-turned surfaces.

Stedman (1987) presen ted a n overview of the amplitu des and wavelengths th at canbe mea sure d with various instruments (figure 10) . In these diagrams horizontal linesindicate the resolution and range limits of the instruments. Sloped boundaries stemfrom limitations with respect to the slop es or curvatures of surface features that ca nbe measured and limits imposed by the accuracy of the guideways of an instrument.The amplitude range and resolution of measurement instruments are usually coupled(larger range , lower resolutio n). Some instrumen ts based on interferometry canno tmeasure surfaces on which relatively steep slopes are present. The spatial resolutionof stylus instruments is limited by the stylus tip radius (and the sampling rate). Foroptical instruments this limit stems from factors such as the pixel distance on thedetector or the numerical aperture and quality of the lenses of the optical system.The frequency content of signals measured with optical and mechanical instrumentsis different. Therefore different values of roughness parameters are determined withthese instrume nts if the sam e surface is evaluated (Ch urc h et a1 1984, Vorburger 1987).

100-10

nm 1 -0.1

-

-0.01 I I I --?- I 1 ,

0.1 1 10 100 I 1 10 100 I 1 10 100 1000nm Pm mm

Wavelength of roughness --+Figure 10. Resolution and range of various roughness measurement instruments. FormTalysurf (FTS), Talystep (rs) n d N a n o su rf ( N S ) are mechanical s tylus instruments; He -Nesss is a laser-scattering measurement device; STM stands for scan ning tunnelling micro-scope .

2.2. Surface integrityMany applications demand that some physical property of the material under themachined surface is not degraded by the machining operation. An example is the

7/30/2019 10.1.1.116.2858

13/46

Ma nufac turing techniques fo r complex shapes 1061mag netic properties of ferrites used in recording he ad s. Glass lenses used in applicationsinvolving powerful pulsed lasers zapping the surface have to be free of cracks andother defects under the surface to avoid damage resulting from the stress cyclingassociated with the thermal gradients in the material during a laser pulse (Marion1986). Processes that involve more chemical than mechanical action to remove m aterialgenerally induce less structural damage under the surface.Often the surface integrity of a part can be influenced by the choice of the processparameters. In grinding of amorphous metals the infeed of the grinding wheel perrevolution is kept low to avoid high temperatures in the contact zone that might causean undesirable phase transformation in the material. An overview of calculation andexperimental techniques to determine the temperature in the contact zone duringgrinding and cutting was given by Snoeys et a1 in 1978. In glass grinding, material isusually removed in a brittle mode and cracks extend under the surface. At very lowdep ths of cut (0.1 F m typically) a nd sm all forces p er grinding grain the m aterial canbe remo ved by a she ar process involving plasticity rathe r than crack forma tion (ductileregime grinding, see section 4). Experimental techniques used to evaluate surfaceintegrity depend upon the features considered critical. The electromagnetic integrityof recording heads is tested with read-write tests involving signals of appropriatemagnitude and frequency. Transmission electron microscopy, taper polishing (Brown1987) an d microhardness tests (Polvani an d Evans 1988) have been prop osed to m easurestructural dam age introduced by machining.2.3. Accuracy spec ijcations fo r a xisymmetric optical elementsLenses in general give rise to imperfect images because of two broad classes of errors:geometrical aberrations and diffraction effects.Geo metr ical distortions (abe rration s) of the image are caused by form errors of theoptics ( an d by m aterial inhomo geneities in transmissive optic s). An example is theerror in focal poin t (p ow er of the lens) that arises from the inaccurate radius ofcurvature of a spherical optic. Another common error is called coma. It arises, forexample, if two optical elements are not properly aligned so that their optical axes(altho ugh para llel) do not coincide. These errors can be minimised in the fabricationstage and often the optic al system allows one to correct for these errors by alignmentof the optical elements.There are, however, geom etrical errors that can not be corrected this way. Sphericalaber ration s are among these. They can be avoided (W asserman a nd W olf 1949) by theuse of more elements that correct each others errors or by using lenses with surfacesthat deviate from an exactly spherical form (aspheres) (Braat 1983).To limit the geometrical errors in the imaging system, the optical designer specifiesa desired form of the lens surfaces. This is often don e using a description of the surfaceas a series of polynomials. The coefficients of these polynomials determine the form;the allowable deviations of these coefficients determine the allowable form errors inthe part. The geometrical quality of a lens is often quantified in terms of the amountof phase distortion it causes when imaging a particular type of wavefront of mono-chro m e light. If the w avefront distortion caused by a lens (system) owing to geometricalerrors is below one-quarter of the light wavelength, the lens is said to be diffraction-limited since diffraction effects now limit the image quality. The required form toler-ances of a diffraction-limited lens are inversely prop ort ion al to the sm allest wavelengthof light the lens has to image. The tolerances of optical systems in general become

7/30/2019 10.1.1.116.2858

14/46

1062 J Fransemore stringent for optical systems with a larger numeric aperture (NA). The numericaperture of a lens is defined as

N A = n sin uwhere U is the angle indicated in figure 11 and n is the refractive index of the mediumbetween lens and object.

Airy pattern around focal point1

R : 4mmh : 785nm

0.8

0.6

0.4

0.2

n"-8 -6 -4 -2 0 2 4 6 8Distance from focal point (microns)

Figure 11 . The light intensity distribution around a focal spot, known as the Airy pattern.This diffraction pattern is caused by the finite aperture of the lens.

Difract ion due to the finite aperture of even a geometrically perfect lens causes alight intensity distribution around the focal spot (Malacara 1988) known as the Airypa tter n (figure 11). It consists of alternating light an d da rk circles aroun d the focalpoint. The smaller the distance between the central spot and the first dark ring, thehigher is the resolution or information density that can be reached with the opticalsystem. The resolution therefore depends on the wavelength of the light and on thcnum eric apertu re of the lens. The formula in figure 11 is valid for a circular lens withdiameter D.The roughness of the lens surfaces scatters light in all directions, leading to lossof contrast between the light and dark rings. To keep the diffraction effects withinacceptable bounds, the designer will specify a maximum allowable RMS value for theroughness of the lens.

3. Machines and tools for precision machining3.1 . Introduction; the machine as subsystemSection 1 introd uce d the concept of the machining ope ration as a complex system withthe machine and process as interacting subsystems. Within the machine subsystem,various signal paths (lo op s) can be identified (figure 8) . These loops determine theresponse of the machine to inputs (desired motions) and disturbances such as cuttingforces and thermal effects.

7/30/2019 10.1.1.116.2858

15/46

Manufacturing techniques for complex shapes 1063For exa mple, cutting forces are transmitted through com ponen ts of the machinetool and the part. Mechanical properties determine the (dynamic) deflection of themachine structure in this signal path, which is called the structural loop. A thermalloo p can also be identified (M cC lure 1969). It consists of all com pon ents that c ontrib ute

to part errors if they deform due to temperature variations. A third signal path is themetrology loop , which determines how the distance between tool an d part is measured.It determines what can be measured an d corrected by the servo system with regard tothe path the tool describes. Dep ending o n the lay-out of the machine, some loops may(partly ) coincide.To understand and reduce the l imitations which machine behaviour imposes onthe maximum achievable form accuracy and smoothness of parts, a careful erroranalysis is required. In the next subsection the nature of various errors will first beclassified. The n some guidelines comm only used in the design of precision instrumentsto avoid an d minimise errors w ill be discussed. Next some topics in machine behaviourwill be treated in greater detail (sections 3.4-3.8). The section ends with a discussionof the error budget technique, which can be used to analyse the overall accuracy of amachine after the different aspects of its behaviour have been investigated.3.2. Machine-induced part errors; error reduction techniquesThe classification of errors in different categories is important to be able to determinehow to handle them and to indicate their importance and the way they may interact.Machine-induced errors can be classified in four different ways.

( i ) The timescale of errors can be compared to the t ime that tool and part are incon tact. Errors that vary at a similar rate to or slower than th e contact time are calledquasi-static. On the other hand, errors characterised by fluctuations that are rapidcom pared to th e contact t ime are called dynam ic errors (Hoc ken 1980, Weck et a1 1988).Examples of quasi-static errors are the error motions of slides introduced by theimperfect geometry of mach ine com pon ents, deformations du e to the shifting of weightsas components move, and thermally induced deformations. Examples of dynamicerrors are spindle error motions and self-induced or forced vibrations between tooland part with frequencies of the order of a few hundred hertz and above.(i i ) Fixed or variable errors can be distinguished. The magnitude of some errors isfixed in the design stage of the m achine. Others are influenced by th e choice of theprocess parameters. Examples of fixed errors are the straightness of a reference mirroran d the resolution of a position measurement system, chosen in the con ceptu al stageof the machine . So are the compliances of the machine components, but the actualdeflections due to the cutting forces depend on the depth of cut and therefore thiserror is considered variable.( i i i ) Reproducible and random errors can be identified. Reproducible errors arereliably repe ated time an d again. Slide and spind le error motions are generally almostfully repea table provided therm al and gravity effects d o not cause disturbances. V ibra-

tions between tool and part due to ground motions not rejected by the vibrationisolation system are random errors. The distinction between random and repeatableis also very important for the last method to classify errors.(iv) Classification with respect to possible error reduction method(s) (Blaedel 1980).Some errors can be eliminated. Others can be calibrated and compensated for usingthe controller (re pea table slide error mo tions) . Real-time determination an d com pen sa-tion of errors can also be d on e (in process feedforward correction for measured a ngu lar

7/30/2019 10.1.1.116.2858

16/46

1064 J Fransemotion of a spindle, for example). Error contributions may be reduced by decreasingthe source strength (better temperature control, for example). The effect of a givenerror source can often be minimised by improvement of the coupling mechanismthro ugh w hich it results in a par t error (use of low-exp ansion material) (Tsutsumi eta1 1988). Feed back senso rs and control can also be used to p rovide distu rbanc e rejectionof the system with respect to a particular source (Kanai et a1 1988). Some errors arecorrected in an iterative way. They are determined after a first cut and corrected in asecond (tool radius, initial positioning errors with respect to the axis of rotation ofthe part , for example).

Clearly the strategy to limit the various e rror co ntrib utio ns starts with identificationand classification of errors. Next their effects have to be quantified to see which aredominant and if individually or combined they are acceptable. This is called makingan error budget. If some errors are foun d to be unacceptable, a reduction strategy hasto be chose n. In general, elimin ation is best, minimising sou rce or effect and feedforwardor feedback control compete for second place, and iterative correction is the leastviable alternative.In the next subsections, general principles used in the design of precision machinetools and other instruments will first be presented. Using these guidelines, the errorsintroduced by the machine behaviour can be kept to a minimum.3.3. Principles f o r design of precision instrumentsThe principles outlined in this subsection have been applied in the design of machin etools, m easurin g devices a nd other precision instruments. It is not always clear whenand where these guidelines were invented; some of them were applied long beforethey were explicitly stated as design guidance. In the last decade they have emergedexplicitly in courses on precision engineering given at CUPE (Cranfield Unit forPrecision Eng ineering ) an d by the A SPE (Am erican Society for Precision Engineering-short course by Teag ue an d Evans (198 8)). The principles (sometimes called patterns)are not strict laws in the sense that they provide rules which if followed will lead toa goo d design. They c an be used as a checklist to help m ake key decisions with regardto common problems encountered in many precision instruments. Elaborate descrip-tions of the principles are given in the courses mentioned and this article containsmany illustrations of their application. Here only a brief overview is presented. Someof the guidelines provide directions w hich seem at od ds with each o ther. In those casesa compromise is necessary.

( i ) Repeatability. As long as errors are repeatable, their cause can be determined,o r at least their effect can b e corrected for.( i i ) Isolation. The system boundaries shou ld be set up so as to prevent dis turban cesfrom the environment from influencing the system (temperature, pressure, humidity,acous tic or electrical noise, m echa nical vibrations).( i i i ) Kine ma tic moun ting versus elastic averaging. With respect to rigid bod y motion,an object has six degrees of freedom (figure 12). Each constra int on the object preventsmo tion in one degree of freedom . A kinematic m ount constrains a body by the minimumam ou nt of c onstrain ts necessary (Pollard 1929, Whitehead 1954, Slocum 1988). If moreconstra ints are applied, th e body will be stressed a nd d eform ed as a result. In general,its exact location and orientation also becomes uncertain. If two bodies are coupledkinematically, movement o r deformatio n in one of them results in rigid body m ovement

7/30/2019 10.1.1.116.2858

17/46

Manufacturing techniques f o r complex shapes 1065no constraints 1 constraint 2 constraints 3 constraints6 degrees of freedom 5 degrees of freedom 4 degree s of freedom 3 de gre es of free dom

4 constraints 5 constraints 6 constraints Practical implication2 degrees of freedom 1 degrees of freedom no degree of freedom using balls bnvgroov es to preciselylocate two partsFigure 12. Each constraint placed on an object prevents motion in one of the six degreesof f reedom ( three t ransla t ions and three ro ta t ions) .

of the other, without inducing deformation of the second. Direct ly opposed to thisprinciple is ano ther on e that is sometimes preferred to connect p arts: elastic averaging.This can be used if high loads have to be carried or the averaging action of havingmany contact areas evens out local effects in part of the contact area, giving betterrepeatability, a lso after som e (w ear) time.(iv) Alignment (Abbe') rinciple. The l ine of measurement an d controlled movem entshould coincide to avoid offset errors caused by angular motion of the moving body(Bryan 1979). If this is impossible, they should at least be parallel and multiplemeasurements shou ld be considered to acco unt for offset errors. The error introduc edif the design goes against this principle is illustrated in figure 13. A tool is mounted a

Metrology hame. kinematically mounted to machine base

- -- --

Figure 13. Error m otions of the slides and d istortion of the m achine base are par t ly correc tedby the m easureme nt system A owing to the A b b t offset. System B measures at centreheightusing a metrology frame and completely corrects these errors.

7/30/2019 10.1.1.116.2858

18/46

1066 J Fransefini te distan ce above the l ine of me asurem ent system A, which in turn is located abovethe centre of gravity of the slide. This offset error results in amplification of slide errormo tions an d larger displacem ents between the tool a nd the p art . The sl ide error motionsare only partially corrected by the position measurement system A. If measurementsystem B is used, the slide error motions are completely corrected since the twomeasurements BI and B2 are performed at centreheight .

(v ) Metrology fram e or metrology loop. Ideally, measurements sho uld be don e usinga reference fram e that is unaffected by time, environmental disturban ces and ma chinemo tions (figure 13, mea surem ent system B). Typically, such a me trology frame is usedon large machines (D ona ldso n an d P atterson 1983). All posit ion measurements are inthat case mad e between references mo unted (kinem atical ly) to this frame an d pointson the tool an d part .An adv anta ge of the m etrology fram e is that its only pur pos e is to sit still in space.It does not have to move accurately, be stiff or fulfil an othe r fun ction . In general, thisprinciple of separat ion of functions between com pone nts is favou rable from a designpoint of view, although it is usually not economically desirable. O n small machines arelat ive measurement between moving components is often used to control motions(figure 13, m eas ure me nt system A ) . In that case the metrology loo p should be as sho rtas possible, yet the max imum am ount of cri tical d isturbanc es shou ld be observed bythe m easurement system to be ab le to reject them.(vi) Ma terials selection optimiJed forf unc tion. Com ponents of a mach ine tool shouldideally each have to fulfil one function only. In that case the materials selection canbe opt imal for that one funct ion. Methods to assign figures of merit for the variousproperties of materials with respect to functions such as stiffness, thermal expansion,etc for compo nents in which mult iple fu nctions are com bined are given, for example,by Chetwynd (1987).

(vii) Short structural loop containing fe w elements and join ts. The structural lo op ina ma chine tool consists of all those c om pone nts on the path through the ma chine overwhich cutting forces are transm itted. Th e relative tool-part com plian ce of machinesis kept to a minim um using a nu mb er of techniques. The structural loo p has to be keptshort (small num ber of e lemen ts). Joints are associated with unce rtain contact areasan d sh ould be avoide d. Bearings a nd geometries and materials of structural elementsin the loop sh ould be optimised for st iffness (a nd dam ping).(viii) Kinem atic drive mechanisms. To avoid the introdu ction of undesired motionsand deformations, only that degree of freedom in which motion is desired should becoupled between the drive mechanism and the driven component .( ix) Tool (o r probe) knowledge. In both machining and inspection the ultimateaccuracy is always limited by the accuracy of the tool (o r probe) and i ts interact ionwith the fa bricated (or inspected) part . The tool and m achine accuracy have to match.(x ) Heat balance, stationary energy flow. The heat balance of the instrument inrelat ion to i ts environment has to be designed so as to create a stationary situationwith respect to the temperature distribution over the machine in the operat ional

si tuat ion.(xi ) Error budget technique. Quantify all conceivable errors, combine themappropriately and predict the overall accuracy of a given design. This technique helpsto judge a design a nd visualises which errors contribu te most to the total erro r. Thistechnique will be discussed in greater detail in section 3.10.(xii) Symmetry. As a result of gravity an d thermal effects, symmetric constructionsin general do not give rise to complicated distort ions that cannot be compensated

7/30/2019 10.1.1.116.2858

19/46

Manufacturing techniques fo r complex shapes 1067without much extra effort. The analysis of symmetric structures also requires lesscom putation al effort, and the predictability of behavio ur will in general be better.3.4. Errors due to imperfect geometries of machine componentsIntend ed movements o n a precision ma chine tool are invariably co mb inations of perfectlinear translations and rotations. The actual position of a point on a slide will differfrom the in ten ded position becau se of translation errors (th e actual axis of translatio ndoes not coincide with the intended) and rotation errors (roll, pitch and yaw due tonon-straightness of the guideways).Translation errors in the direction of motion depe nd m ainly upon the drive mechan-ism used in the machine. Many slides are driven by means of a motor, a set of gearsand a leadscrew. The rolling elements differ somew hat in size, and erro r motion witha period associated with the leadscrew pitch is often observed.A different class of drive systems are friction (capstan) drives. In these the angularmotion of a motor is converted to linear movement by the friction in a contact areabetween the outgoing axis of the motor and a bar connected to the sl ide. These capstandrives can provide more constant speeds and better positioning accuracy of the slide.Techniques to measure translation and rotation errors of sl ides have improvedsignificantly in the last de ca de (H oc ke n 1980, Tlusty 1980, Estler 1985a, b) . Th e majorityof slides used on precision-cutting machines have a travel of up to 0.5 m. It is no t atrivial task to manufa cture a nd m oun t such slides so as to keep the maxim um straight-ness deviatio n within 0.1 p m over the leng th of travel. Som e precision machines a restill equipped with bearings based on rolling contact elements. Lately, rotational andlinear motion has been increasingly realised using full-film oil and air bearings (seesection 3.5).If more ac curate translation is required tha n the slide can provide, repeata ble errorscan be compensated using look-up tables for the measured errors in the numericalcontroller software. An alternative is the use of references for the position m eas ure m entsystem mounted in a metrology frame.As illustrated before, the error motions of a slide may be amplified if the tool ismounted a finite distance above the centre of gravity of the carriage (figure 13).The accuracy of spindle motions has also greatly improved by the use of oil andair bearings. A state-of-the -art air bearing spind le typically has axial and radial run -outsof the order of 25 rim. Optical and capacitive techniques have been used to measurespindle error motions (Holster et a1 1984, Ch apm an 1985).3.5. Tools fo r precision machiningTh e sha pe of the tool is directly m apped into the part su rface in any con tacting materialremoval process.Diam ond-turning tools are m ade of gem-quali ty natural (a nd sometimes synthetic)diamonds. The diamonds are a l igned so that the most favourable crystallographicorientation 'faces ' the part . This is done to ensure minimal wear and homogeneousproperties of the tool over that part of it that comes into contact during cutting.A contouring diam ond tool can be made to have a maxim um deviation of a prescribedradius less than 0.05 p m over an ang ular segment typically 90". This angle and th evalue of the radius are important if strongly curved surfaces have to be made. In tha tcase the contact point between tool an d part shif ts along the tool t ip and this has to

7/30/2019 10.1.1.116.2858

20/46

1068 J Fransebe corrected for to ensure that the desired shape is cut. A new tool has virtually nomeasurable roughness alon g the cutting edge. If the tool wears in an abrasive manner,the cutting edge becomes jagged and this roughness is directly engraved in the workedsurface.

Th e wear m echanisms of d iam ond are notably different (abras ion, graphitisation)when cutting different materials.A grinding wheel for precision grinding has to be brought into such a conditionthat it has minimal run-o ut (tr uein g). Du ring grinding, the grains protrud ing from thewheel wear, the tool becomes clogged with m aterial transferred from the part, an d thetool has to be re sharp ened periodically (dres sing ). Th e scratches mad e in the part bythe cutting grains determine the part roughness (Franse and de Jong 1987). Relativelyhard wheels are first used to grind a n accurate form; the roughness is then diminishedusing softer wheels. It is difficult not to distort the achieved form accuracy with thesecompliant softer grinding tools.3.6. Static aspects of machine tool mechanicsMachine tool components in the structural loop deform when loaded by forces. Thereare many origins of forces acting on the machine components, the tool and the part.

( i) Gravity provides a load on all components of the machine. As componentsmove, weights shift and on the subm icron level the machine d eforms. Gravity-induceddeformations lead to form errors of parts.( i i) Cuttingforces ar e generated in processes involving mech anical con tact betweentool and part. Typical (static) cutting forces in diamond turning are of the order of250 m N . Obviously, in this area no n-co ntac t machining techniques offer an advantage.

(iii) Changing speeds, in other words accelerations, always involve forces. Anexample can be seen in grinding. If the rotational speed of the grinding spindle ischan ged , the centrifugal forces on the rotor and grinding wheel change in magnitudean d they deform. Th e position of the cutting edge may change significantly due to thiseffect.( iv) UnbaZance of spindles leads to forces and moments that may result in errormotions. In grinding with high-speed spindles the run-out of the grinding wheel can

be affected by the unbalance introduced by the coolant sprayed over the grindingwheel. Unb alan ce of a part s pind le may lead to form errors; grinding wheel unbalan ceusually leads to waviness or roughness on the part.(v ) Par t jx tures exert forces (pre ssure ) on the part. Thin sec tions are easily distortedby vacuum chucks or vices. After machining, the part springs back and shows afingerprint of the clamping device. Techniques to avoid these problems include theuse of fixtures that only deform non-critical areas of the part. Gluing or potting partsto holders is also ap plied . Care has to be taken not to com promise the stiffness of thestructural loop using these techniques. Vacuum chucks, sometimes using porousmaterials to distribute th e vacuum load evenly over the part, are also common practice.Sometimes the springback effect is used deliberately to produce parts (Hedges andParker 1988).The magnitude of the errors caused by forces is proportional to the relativecompliance between the tool and the part (Tlusty 1972), which is the sum of allcompliances in the structural loo p. In the design stage, estimates can b e ma de for thesecompliances using analytical models and numerical techniques such as finite elements.

7/30/2019 10.1.1.116.2858

21/46

Manufacturing techniques fo r complex shapes 1069Th e stiffness of structural m emb ers ca n usually be foun d quite accurately. Th e stiffness(and damping) of joints is not easily estimated owing to uncertainty about the exactlocation and the pressure distribution and friction over the contact area.Bearing technology, especially the field of hydrostatic and aerostatic bearings, isan are a in which much progress has been m ade over the last two d ecad es (Fuller 1969,M uijderman 1979, M uijderma n et a1 1980,1988, Gross et a1 1980, Rowe 1983, She phe rd1985). In these bearings, separation of the bearing surfaces. is the result of pressuregen erated in the film fluidum. This pressure can be generated by wedge effects in thebearing gap and motion-induced viscous effects in the film (self-acting bearing).Alternatively it can be su pplie d from an external source (externally pressurised bearing).Th e pressure distribution in a bearing ga p is governed by Reynolds (1886) differentialequation. It was derived by considering equilibrium of forces and mass conservationas the fluidum flows throu gh th e narrow g ap . The principle of op eratio n of an externallypressurised bearing is illustrated in figure 14. The fluidum is supplied at pressure p sto the bearing gap through a supply restrictor, enters the bearing gap at pressure pran d leaves the bearing g ap at amb ient pressure pa.The bearing ga p an d supply restrictorare resistances from a fluid mechanics point of view tha t determine the fluidum flow.Their size and shape also determine the pressure drop over the supply restrictor andthe pressure distribution over the bearing ga p width. If the bearing g ap height is m adesmaller, the flow decreases. This means th at the pressure dr op over the supply restrictoralso decreases. Therefore the pressure over the bearing g ap increases. T hus a decreasein the bearing gap height results in a force opposing the motion. The magnitude ofthis force depen ds on the s upp ly restrictor an d bearing gap geometry. T he stiffness ofth e bearing is th e derivative of the function describing the load-bea ring ga p relation.In principle, the use of bearing gaps or supply restrictors that change their flowresistance under load even makes it possible to design infinitely stiff bearings (de Gast1966), but this technique has apparently not yet been widely applied in precisionmachine tools.

Supply pressure F s s u r ePs

Gap height p////Aiv///Ambient pressuremPressure over gap lengthat gap height hg2 c h,,M

I Pressure over bearing gapPa I at g ap h eight h,lFigure 14. Principle of opera t ion of an externally pressurised full-film bearing. Th e pressureprofile over the bearing gap is typical fo r a gas bearing.

Th e sta tic stiffness of hydrostatic bearings can be calculated with reasonableaccuracy, altho ugh complex geometries a nd the rma l effects cause non-trivial com puta -tional problems.Th e static stiffness of oil an d ai r bearings is optimised by the use of sm all clearances(typically 5- 15 p m gaps for externally pressurised aerostatic bearings). The stiffness

7/30/2019 10.1.1.116.2858

22/46

1070 J Franseof oil-bearing slides is sometimes increased by the use of an overconstrained design.Components of such designs have to be made with tight tolerances and are difficultto assemble.Dy nam ic properties of hydrostatic bearings can also be influenced by the gapgeometry a nd orifice design (Ro we 1983, Roblee a nd Mote 1986), but the calculationof dynamic properties is still under development (Vermeulen and de Schepper 1989).The compliances of a machine are often determined experimentally. Loads areapplied and deflections are measured at various locations. Relative compliancesbetween tool and part for ultra-precision machines range from 0.05 to 1 p m N - -'( U daet a1 1985, Falter and Dow 1987, Weck and M ode ma nn 1987, Franse an d Roblee1989). These n um bers have steadily decreased over the last decade. A low complianceis not only desirable from a static point of view. The dynamic behaviour of a stiffermachine is generally also better (section 3.8).3.7. The thermal loop of a machine toolIf the temp eratu re distribution of the machine o r its environment changes, the machinecomponents deform. If this happens during cutting and the error motions remainuncorrected by the measurem ent system, it generally results in form errors. Th e changein linear dimension of a p art ( d L ) dep end s on the thermal expansion coefficient a,the nom inal dimension in question, L o , and the temperature change dT:

d L = a L o d TTypical dimensions of concern are of the order of 1 x lo-'- 1 m; a for metals is ofthe order of 1 x "C-.'. Te m per atu re deviations of 1 "C thus give rise to deviationsof 0.1-10 pm. The temperature problems are proportional to part and machine size.Just like the structural loo p, the thermal loop has bo th static and dyn am ic characteristics(M cC lure 1969). The ther ma l response of a com pon ent (n o internal heat sources) isgoverned by the differential equation

)t=,,(d,-+B+di *d T A d'T d2T d 2 TThis indicates that not only the size and conductivity ( A ) but also the heat capacity( p c , ) of the object are important. The step response (change in temperature of thecom ponen t after a sud den step in tem perature of the environment) is found by solvingthe differential equ ation . A new equilibrium situation is generally ap proa che d expo nen -tially. A dimensionless nu m ber typically a ppe ars as the exponent in the solution. It iscalled the Fourier num ber F o :

A tFO=-P C P 2

( D s a characteristic dimension of the element considered). The time constant of acomponent can be found as the t ime t at which the Fourier number becomes three.Typical values for machine components range from seconds for small metal parts tomany h ours fo r a granite m achin e base. Thermal disturbances w ith periods com parableto an d longer than th e shortest time constant of components in the structural loop, ortheir effects, must be reduced to acceptable levels. A variety of methods have beenused to d o this. The temper ature distribution over the machine tool can be kept constantusing liquid (B ryan 1978) o r air (Loewen 1978, H anse n 1983) showers or a com bination

7/30/2019 10.1.1.116.2858

23/46

Manufacturing techniques for complex shapes 1071(Ro blee 1985). Sometimes, local heat removal is used to reduce the strength of a heatsource (initially water-cooled grinding spindles, for example (McKeown 1987)).M easu rem ent and correction for expansion is ano ther strategy used. Lately, a numberof investigators have reported the use of low-expansion ceramics as structural com-pon ents in spindles and slides (Brehm et a1 1985, Furukaw a et a1 1986). Therm al errorsare in general random in nature. This makes it difficult to use mapping techniques tocom pensate for them , al though in some cases this has been applied (D onm ez et a1 1986).

3.8. Dynamics of machine tools (open-loop)The d yna mic behaviour of a machine tool determines which vibrations result fromexcitations (forces or ground motion, for example). Both the excitations and theresponses (resulting motion) are characterised by magnitude, frequency and phase.For most cases i t suffices to consider the machine as a linear system. Responseinvestigations are done in the time domain or in the Laplace domain. The Laplacetransf orm ation provides the mathematical connection between the two d omains if timeis considered as contin uou s. A signal f t ) in the t ime dom ain is transferred to a signalL ( s ) n the Laplace domain (s is a complex n um ber). This is appropriate for systemsin which control is exerted continuously (ana logu e, for instance ). If a digital controlscheme is used or sampling occurs at such intervals that it notably influences thedynamics of the system, the so-called 2 transform (van de Vegte 1986) sho uld be used.Usually, the open-loop (no control loop closed) response of the mechanical system isfirst consid ered . Next th e closed-loop behaviour is investigated. The measurement an dcontrol loop generally also contains dynamic elements to optimise the dynamicbehaviour of the machine tool. In this section a similar scheme is followed. Thissubsection continues with a consideration of the open-loop dynamics of the machine.The next subsection gives an overview of feedback control topics in precisionmachining.The machine tool is excited in different ways. These excitations act on variouscomponents and their magnitude and frequency contents are notably different.A number of vibration types are associated with these excitations.

( i ) Externally forced vibrations. To this category belong the low-frequency vibra-tions caused by gro und motion of the environment. Precision m achine tools are usuallydecoupled from the ground by a vibration isolation system. Various types are used,but they usually involve mounting the machine components on a heavy mass, and thismass in turn is set on a soft spring-damper system. Figure 15 (a ) shows the transmissionratio (ratio of table and ground motion) for the simplest possible system at differentdam ping ratios. Th e idea is to let the isolation system have as low a natu ral frequencyas possible. Above th e natu ral frequency of such a system the transmission rate decaysrapidly. Increasing the damping is seen to decrease the maximum transmission ratioat resonance. However, th e high-frequency atte nua tion is also less. A more sophisticatedsystem (Ru zick a an d Derby 1971) is seen in figure 1 5( b) . With the elastically co uple ddamper, increased damping also decreases the peak value of the transmission ratio atresonance, w hile the high-frequency atten uatio n stays virtually th e same. O ther sourcesof externally forced vibrations are air-conditioning systems, pressure variations dueto oil and water pumps (N aka no et a1 1986), imp act of coolants an d excitations thro ughcables and hoses connected to machine components. All these excitations have to beminimised and if possible isolated from the machine.

7/30/2019 10.1.1.116.2858

24/46

1072 J FranseTransfer function X(s)/U(s)

. . . . . . . . .10' -- 0.81J-\................-.- .....

q. .1 t--??Y t;....,:

lo-' ' I Ylo-' I O 0 IO'Frequency ratio w / w

Figure 15. Transmission ratio for ( a ) directly and ( b ) lastically coupled spring-dampercombinations used in typical vibration isolation systems. Increased damping affects themax imum at re sonanc e and the high-frequency roll-off ( k =1 N firl-', =1 kg).

(ii) Internally forced vibrations. Forces due to unbalance of rotating spindles andthe fluctuating forces from run- out of a grinding wheel are excitations th at induce thistype of vibration. The same holds for the forces and motions introduced by the servosystem.(iii) Selfgenerared vibrations (chatter). This type of vibration stems from the inter-action of the cutting process with the machine structure. It is essentially a closed-loopdynamical problem and will be discussed in greater detail in section 5 .Th ese types of vibrations having been identified, it remains to determine what kind ofmotion they induce between the part and the tool. This is determined by the transferfunction (com plian ce) between the excitation an d the relative tool-part motion. Thereis a tendency to build stiffer machine tools an d improve their dam ping properties. Th ebenefits of this approach can be explained using the two-degrees-of-freedom modelshown in figure 16.

7/30/2019 10.1.1.116.2858

25/46

Manufacturing techniques for complex shapesTransfer function X P ( s ) / F ( s )

1073

I x2-I I

10' 1o2 1o3 1o4Frequency ratio (radisec)

Figure 16. Two-degrees-of-freedom model to i l lustrate the prob lems associated with thedynamics of precision machine tools (m I=40 kg , m2=4 kg; case A-k, =1 N pm-', , =5 N p m - ' , =6 =0.02 [&=c , / 2 J (k , m ) ] ;case B-k, =4 N y m - ' , k , =5 N p m - ' ,0.02, ( 2 =0.2).

A slide with mass m , is mounted on the drive system with a stiffness k , and adamping c , .A tool with stiffness k , , damping c, and mass m , is mou nted on the slide.An excitation F ( s ) results in a response X,(s)tool motion) of the linear system. Infigure 16 th e transfer functions between excitation force F ( s ) an d resultant tool motionX , ( s ) (compliance) can be seen for two cases. The differences between the two arethe values of the static stiffness k , and the damping coefficient c 2 . Below the firstresonance frequency the compliance is mainly governed by the static stiffness of thesystem. The relative compliance has a local maximum at resonance frequencies. Theassociated vibration modes determine if the surface quality is degraded. Resonancepeaks are broader and peak compliances are less for better-damped resonances.Resonances occur at higher frequencies if the static stiffnesses are higher and/or themoving masses are lower.A far more difficult question that has not yet been answered completely is: howstiff is eno ug h? A sensible answe r can only be fou nd if the influence of the measurem entan d control system is take n into a ccou nt. This discussion will be continued in section 5.In recent years an increasing amount of effort has been made to characterise thedynamical behaviour of m achin e tools both analytically a nd experimentally (W eckan d M odem ann 1987, Franse and Roblee 1990, Lo-A-Foe 1989) using lum ped para-meter models, finite element calculations and modal analysis techniques.

3.9. Measurement and control; dynamics of controlled machinesPart accuracy is directly related to our ability to prescribe, measure and control therelative position of tool and part. These aspects are discussed successively in thissubsection.3.9.1. Setpoint generation. The fabrication of complex contours requires coordinatedcontinuous movement of a number of axes of motion of the machine. To realise this,the com pute r numerical controller (CNC) has to perform a num ber ofta sks (an overview

7/30/2019 10.1.1.116.2858

26/46

1074 J Franseon this subject was given by Koren in 1986). The basic components of a continuouspath controller are indicated in figure 17. The so-called part program divides the desiredpath into segments and calculates the endpoint coordinates of these chords. Theinterpolator then determines which velocities of the axes of motion are required tomake the desired contour and generates appropriate commands for the servo loops.The difference between the command signal and the actual position is called theposition error signal. This signal is used to manipulate, for instance, the current througha DC motor and influence its rotational speed. The various functions indicated in figure17 can be implemented in many different ways (Erdelyi et a1 1980, Masory 1986).3.9.2. Measurements fo r control of precision machine tools. As in any measurementsystem, resolution, noise level, dynamic range, frequency response and accuracy areof interest. To measure speed, tachometers are employed, in which resolution andelectrical noise are important issues. Position information is usually provided by linearscales (Ernst 1988) or laser interferometer systems (Koch 1975). Today, interferometersystems can provide resolutions in the 5 nm range; scales seldom go further than0.1 pm. A laser interferometer distance measurement system is shown schematicallyin figure 18. A reference beam travels a fixed distance and then interferes with a beamthat travels between the interferometer and a mirror mounted on the moving object.The interference results in a fringe pattern. If the object is moved, the fringe patternmoves as well and the detector counts fringes. The fringe spacing depends on theparticular arrangement of the optical components (single- or double-path arrangementas depicted in figure 18). In reality the light intensity on the detector changes graduallyand interpolation techniques are used to achieve amplitude resolutions of nanometres.Typically, 633 nm He-Ne lasers are used. However, the wavelength of the laser lightdepends upon the optical path length, which in turn is a function of the temperatureand the partial pressures of gas components in the beam path. Motion of air andparticles in the beam paths also causes diffraction, which can give noisy measurementsignals and loss of fringe contrast (Estler 1985a, b) . Compensation for some effectscan be applied if temperature and pressure or the index of refraction are monitoredin the beam path. Another strategy is to surround the beam path with a vacuum

planning,generationof velocityReference pulses

AxisnositinnAmplilier

1Tachometer I I IIPosilionmeasurement I

Figure 17 . The control loop of a continuous path C N C machine consists of a part program-mer, an in terpolator an d the servo loops driving the axes of the machine .

7/30/2019 10.1.1.116.2858

27/46

Ma nufac turing techniques fo r complex shapes 1075Single path interferometer Double pathCube cornerattached to moving object

interferometern

Reference beam

2, 4 Reference beame,LL-

Direction ofreturningdetectorMeasurement beam beam and

Figure 18. Com mo n laser interferometer arrang emen ts used in precision machine tools.The fr inge spacing is the movement that causes a path difference h / 2 between the referencebeam and the m easurement beam.

(D ona ldso n and Patterson 1983) or to make sure that the composit ion of the environ-ment is constant (saturated with oil vapour or filled with helium, for example).For very-high-resolution measurements over limited ranges, capacitive and induc-tive methods can be used. Piezoelectric elements are useful to measure velocity andacceleration in a d yna mic sense. Piezo elements are also used as very accurate a ctuato rswith limited range (Patterson and Magrab 1985). Piezo actuators can be made light-weight and stiff, which allows them to be controlled to high frequency bandwidth(1 kH z). Their accuracy in such applications is often determined by the stability of thepower supply needed to drive them.3.9.3. Dynamics of a controlled machine tool. Th e dyna mic behaviour of the controlledmachine tool (relative tool-p art compliance, ban dw idth, disturbance rejection) dep end supon the combination of the dynamics of the mechanical elements, feedback sensorsan d controller com pon ents. Th e servo loops of precision machine tools usually employvelocity and position feedback. The controlled variable such as the motor current isregulated proportionally to th e position error, the integral over this erro r and a velocityerror signal generated in the inner ( tach o) loop. Thus a combination of propo rtional,integral and derivative action is used. The gains of the proportional, integral andderivative action ( K p , Ki and Kd) determine how fast a servo system follows thecom man d signal (speed of response ), whether it overshoots the co mm anded posit ionan d if the final position deviates from the co mm and ed position (steady state error Ess;see figure 19). Th e gains and dyn am ic elements in the loops also determine how well

7/30/2019 10.1.1.116.2858

28/46

1076 J Frame

l o

an d up to wh at frequency (b and wid th) the servo system wil l follow com man ded inp utsan d resist disturb ances such as forces (provided they are observed by the servo system).Obviously, a high ban dw idth is desirable. H owever, in a ma chine tool it has to be keptwell below the first resona nce in the m achine structure to ensure stabi li ty. Fo r thesereasons a st i ff structural loop and high damping are also favourable from a controlpoint of view.Knowledge of the dynamic behaviour of a control led machine has been used todesign ele ctron ic filters to co mp ens ate the tra nsfe r fun ction of the m achine. Using thistech niqu e, non -axis ym m etric optical elements were fabricated containing wavelengthsthat could otherwise not have been realised (Schenz et a1 1988). Lately, the use ofdigital signal processors for control of machine tool components has also beenreported (Luttrel l et al 1987). Th e ap plicat ion of adap tive control an d mult ivariablecon trol tech niqu es in precision machining are cu rren t topics of research at variousinstitutes.

Ko.4 K l =3

Transfer function X(s)$U(s)"' 1 K O = K =0

O 2 K g =4 Ki.3

1 0 - ' L .0 10 10Frequency ratio w / w

. Transfer function X!sl U(sl

I 10 10'Frequency ratio w / w

=12a ' - = =

Stepresponse in time domainBi?C8

Time (sec)Stepresponse in time domain

K p=12w 0 6 Kp=2

0 4Ki 0

0 5 10 15 20 25Time ( s e c )

Stepresponse in time domain

0 4

Figure 19. T he effects of proportional, integral a nd derivative gain in a si mple servo system.

7/30/2019 10.1.1.116.2858

29/46

Manufacturing techniques fo r complex shapes 10773.10. The error budget conceptIn the design of systems containing many optical elements it is common practice tospecify the allowable errors and to divide them among the various contributing errorsources. This idea has been adapted for precision machine tools. It will be illustratedhere using figure 20 , borrowed from Donaldson (1980). As a first step, a list is madeof all possible error sources in a (pr op ose d) machine design. Information is neededabout the nature of the error sources, the physical properties and geometries of thedesign. These error sources will somehow (through a coupling mechanism) result ina displacement error between th e tool an d the part. The magnitudes of these errors inthe critical directions in terms of relative tool-part motion are determined by calculationo r from experiments. Th e time an d spa tial scale of the erro r contributions is alsoindic ated (form or roughness error categories are distin guis hed ). Th e contributions ofall the errors combined (using a combinatorial rule) must stay within the desiredtolerances. It is in this part of the concept (com bina tion of errors) that uncertaintiesarise. Often error sources are related and the total error is, for instance, the sum ofthe maximum values of the individual errors. Sometimes, however, they counteracteach other or they are uncorrelated. The expectation of the RMS value of randomuncorrelated errors can be fou nd as the RMS average of the RMS values of these errors.In practice, a limited number of errors dominate the budget; many smaller ones canusually be neglected. If a design d oes not meet the budget requirements, the contributingerrors have to be reduced using the strategies mentioned in section 3.2.

Errorsource Errordirectionsor ~

WorkpiecegeometryCombinationalrule Resultantdlsplacement

$ ,-errorE A r e r r o r

Figure 20. Principle of t h e error budget concep t (Donald son 1980)

4. Tool-part interaction4.1. Introduction; m echanisms of material removalThis section gives an overview of the material removal mechanisms in precision-machining processes. In diamond turning and grinding, the tool-part interaction is

7/30/2019 10.1.1.116.2858

30/46

1078 J Fransemechanical in nature and chemical effects are of second order. In polishing, bothmechanical and chemical effects play an important role. In techniques based on etching,chemical reactions at the surface are clearly dominant. In that case mechanical actioncan be considered as one of many ways to enhance the etching rate. In the followingsubsections the mechanical tool-part interaction will first be considered; then materialremoval by chemical etching is discussed.4.2. Modes of mechanical material removalMechanical interaction can result in different types of material deformation andassociated modes of material removal. The tool-part contact generates stresses andstrains in the material. If these are elastic on a macroscopic scale, there are no lastingdeformations unless fracture occurs. Fracture is one material removal mode often usedin conventional grinding of brittle materials. Under repeated elastic load cycles, materialmay be removed by fatigue, a process involving repeated plastic flow in microscopicallysmall regions in the material (Suh 1977). Fatigue is a common material removal modein wear processes but unusual in precision machining. If the stresses exceed the yieldstrength of the material, plastic deformation results.In diamond turning and plastic flow grinding (ductile regime grinding), the contactbetween the tool and the part generally results in chip formation. In that case materialis separated from the part. The separation involves intense plastic shear and ductilerupture of the material at the tool tip (Trent 1977). Plastic flow is the predominantmode of material removal in diamond turning and ductile regime grinding. At veryshallow depths of cut, however, it appears that there is no chip formation, merelyplastic deformation of material (burnishing). The fabrication of diffraction gratings isan example of such a burnishing process. Fundamental questions arise.

(i ) What are the conditions (sharpness, cutting depth and geometry of the tool)under which chip formation or just burnishing occurs?(i i ) Will the material response (crystals, anisotropy of properties, relaxation ofstresses afterwards) prevent us from cutting surfaces with a smoothness only limitedby atomic roughness?The phenomena of plastic flow, fracture and materials aspects in diamond turningand grinding will be discussed in somewhat greater depth.

4.3. Plasticity as a mechanism of material removalThe tool-part contact results in stresses in the material. In the elastic regime the stressfield is related to the deformation field linearly by Hooke's law (metals and ceramics).On the faces of an arbitrary cube in the deformed material, normal and shear stressesact (figure 21). The magnitude of these stresses is such that the cube is in static (force)equilibrium. It can be shown that the (very small) cube can always be rotated so thatonly normal stresses (principal stresses) act on it . At orientations under 45" with anytwo principal stress directions, the shear stresses on the cube faces reach a maximum,at a value of half the difference of the principal stresses under consideration. Plasticflow is governed by shear stresses (differences between principal stresses). To determinewhether a given stress state in the material results in plastic flow requires a yieldcriterion. The von Mises criterion is the most widely used (Dieter 1981). In terms ofthe principal stresses a, , and the flow stress of the material, U,. , , the von

7/30/2019 10.1.1.116.2858

31/46

Ma nufac turing techniques fo r complex shapes 1079

Y

k

COY

bX

Figure 21 . On an arbitrary cubic element of material, normal and shear stresses act. Byrotation of the cub e, an orientat ion can be foun d in which only normal s tresses (principalstresses U,,, z2 n d u ~ ~ )ct on it.

Mises criterion is expressed as( a l l - a 2 * ) ' + ( a l l -%A2+ ( U 2 2 -a d 2=2 U f l .

Any stress state can be separated into a hydrostatic pa rt (th ree principal stresscomponents of equal magnitude) and a deviator part (stresses after discarding thehydrostatic com pon ents) . Th e hydrostatic stress does not alter the von Mises stress. Ifthe von Mises criterion for an isotropic material is depicted in the stress space(coordinate system formed by principal stress directions) it becomes a cylinder (figure2 2 ) . The axis of the cylinder represents pure hydrostatic stress states. For anisotropicmaterial the yield locus becomes acylindrical (H ill 1971). After initial yield th e relationbetween the strain an d stress in the material (constitutive equ ation ) changes. The flowstress of the material may increase (hardening) or decrease (softening) with strain.Most metals harden under plastic flow. The plastic part of the stress-strain relationcan often reasonably b e described m athematically by either a kinematic or an isotropichardening rule. Kinematic hardening means that the yield locus maintains its shapeand size but its centre shifts in the stress space. An isotropic hardening rule assumesthe centre of the yield locus to stay in place; the radius (flow stress) increases. Mixedhard enin g models are also used. Significant te mp eratu re increase may result in softeningof a material. The flow stress is also a function of the strain rate. Generally, the flowstress becomes larger at higher strain rates, provided the temperature in the materialdoes not become so high that thermal softening prevails.

Yield occurs

c73

Figure 22. The yon Mises criter ion becomes a cylinder in the stress space ( a coord ina tesystem in which principal stress directions form the axes) .

7/30/2019 10.1.1.116.2858

32/46

1080 J Franse4.4 . Chip form ation and cutting forces in metal cuttingC hi p form ation results if the material separa tes at o r close to the tool t ip (figure 23).In general , a non-l inear relat ion between the cutt ing force and the depth of cut canbe expected owing to the tool geometry, the material propert ies and the temperaturerise in the contact zone. Various theories and experimental techniques have been usedto study material flow, temperature distribution and cutt ing forces in turning andgrinding of metals (Trent 1984, Carrol et al 1986, Lo-A-Foe 1989). Lee and Schaffer(1951) developed a model based on the id ea tha t the material shears plast ical ly alonga plane to form the chip. Their model assumed the material to be ideal ly plast ic,mea ning the yield stress does no t depe nd o n strain rate and strain ( n o harde ning),an d elast ic stresses an d strains were no t con sidered. Challen an d Oxley (1979) refinedthe a pp ro ac h by using slip line fields ( Ro w e 1979) to describe the velocity field ofmaterial flowing into the chip and along the tool more realistically. They were alsoable to show how frict ion an d ha rdening of the material affect the results.

Chip ,

---\ -- Part materialFigure 23. Chip formation in cutting involves plastic deformation in regions in front ofthe tool and in the chip. Sometimes a s tagnant zone of material adhe res to the tool (buil t-upedge) .

The ir mode l also explains the occurrence of a d ead metal region or stagnant zonebetween the flowing material and the tool (figure 23). In this region the material doesnot move; sh ear occurs along a boun dary in the material i tself. Such a rim of materialadh ere d to the tool has bee n observed experimentally in quick-stop tests in which thetool is retracted very fast from the part. It is generally called a built-up edge. Itsform ation dep end s up on th e incl inat ion of the tool and part material to adhe re to eachother, which is governed by the surface energies and the chemical affinity of thematerials (ch ang e in surface energy if they a re brought into contact) (B owd en an dTabor 1950, Rabinowicz 1965, Smith et a1 1988). The geometry of the tool can alsopromote buil t -up edge formation (Bredel and Prins 1982, Nishigushi et a1 1988). If,for instance, negative rake angles are used, high pressure in the region under the toolpromotes welding of the part material to the tool .In grinding, a co mp arable contact si tua t ion arises between a grinding grain an dthe part. The rake angle of the grain in contact is usually negative. This means chipflow is m ore difficult , impo sing high dem and s upon the cooling and lubrication in thecontact zone. The dressing process used to sh arp en a grinding wheel also has to en surethat adequate space is avai lable between the grains in the wheel to t ransport debrisaway without rubbing them in the contact area.

7/30/2019 10.1.1.116.2858

33/46

Manufacturing techniques for complex shapes 1081Recently, plastic flow in metal deformation processes has been studied usingnumerical m etho ds. These techniques can take geometrical an d material non-linearityinto ac cou nt a s well as the effects of residual stresses and thermal effects (Strenkowskiand Car ro l 1985). For problems involving large plastic deformations, finite element

methods using the updated Langrange technique have been used successfully. Themesh is tied to the material and deforms with it. Application of these techniques tometal cutting has been hampered by uncertainty about a realistic ductile rupturecriterion. A critical value of the effective plastic strain has been assumed as separationcriterion in the chip formation studies mentioned. This seems to work from anengineering point of view in the sense that the results qualitatively agree with experi-ments. From a materials science and physics point of view there is, however, noapparent reason why strain should be the limiting factor (instead of a critical stresslevel or cavity formation criterion, for instance (Leroy et a1 1981)) . An overview ofductile failure theories was given by Dodd and Bai in 1987.Another approach to the study of chip formation with numerical techniques is touse a Eulerian reference frame to simulate the material flow. In this case the mesh isstationary and the velocity field of the elastoviscoplastic material flowing through themesh is calculated. The metal flows like a liqu id; no sepa ration criterion is necessary.The disadv antage of this technique is that the free boundary of the chip surface ( chipshap e) has to be guessed beforeh and. A combination of the two m ethods has also beenused (Strenkowski and Mitchum 1987). The Eulerian approach is used in the shearzone close to the tool, and the Langrangian approach is used further away from thetool tip to predict the chip geometry accurately. Reasonable agreement was obtained

between calculated and measured cutting force data for aluminium.The numerical models described above ca n be expected to contribute to o urunderstand ing of the condit ions under w hich chip form ation or burnishing will takeplace.Th e question w hether there is a minimal chip thickness that can be cut is unlikelyto be answered using continuum mechanical models. At the atomic level the materialcontains vacancies, dislocations and impurities that make it widely different from anisotropic co ntinu um in its mechanical behaviour. Experimentally, Syn (1988) has shownthat chips with a thickness of about 30 A can be cut. The investigators felt they werelimited in their efforts to produce even thinner chips by the thermal and dynamicbehaviour of their machine rather than by the sharpness of their diamond tool or thecontact mechanics of the cutting process. The latest development in the modelling ofmaterial removal is to simulate the movem ent of individual atoms (atom ic modelling(Hoover 1982, 1984)).Th e bonding of adjacent atoms is described by a L ennard-Jon espotential function and the equations of motion are solved in successive time steps inwhich the tool (ato m s) is moved th roug h the part. Ironically, these methods werecalled upo n because con tinuum m echanics app roaches were fel t to become inadequ ateat the atomic level . The atom ic modell ing app roac h, however, needs so many a tomsan d time steps to model th e cutting process that its proper application is at this pointawaiting even larger and faster computers to become available.4.5. Material aspects in mechanical tool-part interactionMany of the materials which are diamond-turned are polycrystalline. This means thetool constantly en co un ters different mec hanical prop erties (figure 24) . Owing to thedeformation, stresses are introduced in the metal. The variations in residual stresses

7/30/2019 10.1.1.116.2858

34/46

1082 J Frame

Figure 24. Th e material properties depen d on the orientation o f crystals in the surface ofthe material. The response of the crystals to the cutting action is different and the crystalboundaries may become visible after cutting.

and relaxation phenomena in individual crystals may result in protrusions (order ofnanometres) of the crystals above the surfaces. These effects depend upon the depthof cut and the sharpness of the diamond tool (Ohmori and Takada 1982).

Another practical limitation of the achievable surface finish is the amount and sizeof hard impurities in the material. Alloys are generally obtained from oxide or sulphideores. Some impurities from the pyrometallurgic treatment and refinement processesapplied are always present. These hard particles can cause chipping of the diamondtool; sometimes they are merely dragged through the surface for a while, which resultsin scratches.

Another effect that has been observed experimentally, which is very difficult toincorporate in continuum models of chip formation, is that plastic deformation insome materials happens intermittently in very localised shear zones (figure 2 5 ) . I tappears as if the deformation has become unstable in very small regions. The chipshows a lamellar structure, the boundaries of the lamellae being the areas i n whichintense shearing has occurred. Obviously, the best results are obtained with either very

Figure 25. Chip formation sometimes involves shear in very local shear zones, resultingin a distinct lamellar chip structure.

7/30/2019 10.1.1.116.2858

35/46

Manufacturing techniques fo r complex shapes 1083clean materials having a very fine crystal structure or, even better, an amorphousmatrix (Taylor et a1 1985).4.6. Fracture versus plasticity; ductile regime grindingA distinct transition between modes of material removal is observed in precisionmachining of brittle materials. Fracture is a common mode of material removal inrough grinding. At small depths of cuts (0.1 p m typically), most glasses, ceramics an dalso silicon and germanium can be removed in a ductile fashion by shearing of thematerial into chips, much as in metal cutting (Broese van Groenou et a1 1978, Bifanoet a1 1987). This transition has been a ttribute d to mechan ical, chemical and ther m aleffects. In conventional glass grinding, conditions can be such that the generation ofheat in the c onta ct zon e leads to thermal softening or even melting of glass (Schinkerand Doll 1984). In precision grinding, thermal effects are less prominent (Bifano 1988)an d the transition is probably more d etermined by mechanical effects (the competitionbetween fracture an d plastic flow ph en om en a). In the fracture mode of materialremoval , cracks extend dee p unde r the surface (10-20 p m typical ly). Such a damag edlayer has to be removed by polishing or etching. It can be more economical to grindor turn und er such condi t ions so as to avoid cracking and prolonged polishing.The phenomena in grinding with regard to plasticity and cracking are often com-pared to those encou ntered in indentat ion of glass and ceramics. In indentat ion testsa distinction is made between blunt an d sh arp indenters. The events und er these typesof indenters are markedly diff eren t (La wn and W ilshaw 1975).Unde r blunt indenters, compressive stresses develop after initial contact ( Ha milto n1966, Swain an d Ha gan 1976, Lawn a nd M arshall 1978, Ostojic an d McP erson 1987).Tensile stresses arise at the perimeter of the contact area. At a load which dependsup on the ind ente r geometry, friction coefficient an d Youngs m odu lus of the materials,cone cracks initiate at the perimeter of the contact area (figure 26). Further loadingof the indenter can provide the driving force to extend them in such a direction as to

Loading UnloadingA

Spherical indenter

Plastic4 3 -one Cone crackLoading

IUnloading

A

Figure 26 . Under spherica l indenters , cone cracks are observed. Using sharp indenters,median. radial and lateral cracks are observed.

7/30/2019 10.1.1.116.2858

36/46

1084 J Franseavoid the compressed region under the indenter. If plastic flow occurs, it will be in ahemispherical region under the surface of the glass. If a blunt indenter is further loadedafter the cone cracks have occurred, a so-called median crack will initiate. This cracktype originates subsurface from the boundary of the plastically deformed zone. Itextends down into the material. During unloading, the cracks tend to close. Smallmismatches prevent this from happening completely.Un der sharp indenters, the stresses at the tip of a sharp indenter always cause plasticflow. Boussinesqs solution (Timoshenko and Goodier 1970, Johnson 1985) for theelastic stress field under a point load on an infinite half-space predicts tensile stressesunder the tip of the indenter and in a region adjacent to it at the surface. Stress fieldsunder indenters of finite sharpness and size are more compressive in nature. At a loadwhich depends upon indenter geometry, friction and material properties, a mediancrack may initiate (figure 26). It extends downward and sideways to form a penny-shaped crack. The sideways extension may make the crack visible from the surface.Cracks visible at the surface running in the radial direction are called radial cracks.Sometimes these cracks are independently formed; oft