PH I LI PS TECH N ICAL" 'REVI EWVOLUME 30, 1969, No. 5

A precision lathe with hydrostatic bearings and driveH. J. J. Kraakman and J. G. C. de Gast

Philips Research Laboratories first took up work on precision lathes many years ago be-cause of a needfor turned surfaces of optical quality. Atfirst all the work that was requiredcould be handled by a single lathe with special modifications, but eventually the demandbecame so heavy that more machines had to be built. This provided a suitable opportunityfor introducing an entirely new design, and theftrst precision lathe built to the new designis now in use in the Laboratorie .... A unique feature of the machine is the exclusive use ofhydrostatic bearings and drive; some of the bearings are made to have infinite stiffnessby a special control system. The movements of workpiece and tool are hydraulically con-trolled to an accuracy previously unattainable.

About thirty years ago the need arose for a powerful,wide-angle lens system that was free from sphericalaberration, for projection-television receivers. Theserequirements were met by the Schmidt optical system,which consists of a spherical mirror with a correctionplate. It was found possible to make this correctionplate from gelatine, using a circularly symmetricmould which was copied from a jig on a lathe [1]. Therequired surface quality was obtained by using a dia-mond-tipped tool. A further improvement in finish wasachieved in later years by changing the headstockbearing of the lathe for a precision journal bearingwith clearances less than 1 (J.m[21.

Because of the high dimensional accuracy and goodfinish that could be obtained with this lathe when agood cutting tool was used, it was found to be invalu-able for making objects such as resonant cavities, lensesand mirrors for lasers, parabolic reflectors, pole-piecesfor electron microscopes and electrodes for the minia-ture "Plumbicon" camera tube. Eventually there wasmore work than one machine could handle and it wasdecided to design a completely new precision lathe,which would also be more suitable for workshop con-ditions. This lathe is described in this article.The main spindle and carriages in this lathe are

Ir. H. J. J. Kraakman is with Philips Research Laboratories, Eindho-ven; Ir. J. G. C. de Gast, previously with Philips Research Labora-tories, is now with the Philips Electranies Components and Mat-erials Division (Elcoma), Eindhoven.

supported by hydrostatic bearings, that is to say bear-ings in which the oil film is maintained by the supplyof oil under pressure. In this type of bearing the thick-ness of the oil film between the bearing surfaces, andhence the position of the moving part, is independentof their relative speed. Moreover, under certain condi-tions, the clearances can be quite large (20 to 40 (J.m),which means that large fluctuations in the temperatureof the hydrostatic bearings cannot cause them to seizeup. Since there is never any metallic contact betweenthe moving parts of a hydrostatic bearing, there isno "stick-slip" or wear.

Hydrostatic forces are also used for driving the carri-ages. A linear hydraulic motor, with piston and cylinder,was found to be a good choice of drive since it has noperiodic element. Periodic systems - such as the con-ventionallead-screw and nut - have the disadvantagethat periodic irregularities (known as "ghosts") areproduced in the machined surface [31. The headstockspindle is driven by a rotary hydraulic motor. The speed

[1) H. Rinia and P. M. van Alphen, The manufacture of correc-tion plates for Schmidt optical systems, Philips tech. Rev. 9,349-356, 1947/48.

[2] The diamond-tipped tool and the high-precision bearing weremade by L. M. Leblans; see L. M. Leblans, A high-precisionlathe headstock, Philips tech. Rev. 19, 68-69, 1957/58.

[3] W. R. -Horsfield, Ruling engine with hydraulic drive, Appl.Optics 4, 189-193, 1965. The "ghosts" occur even when thelead-screw is hydrostatically supported in the nut: J. H.Rumbarger and G. Wertwijn, Hydrostatic lead screws,'Machine Design 40, No. 9, 218-224, 1968.

118 PHILlPS TECHNICAL REVIEW VOLUME 30

of this kind of motor can be regulated easily, it issmall enough to be built into the headstock, and it canbe made fairly insensitive to overload.The use of these hydrostatic components means that

oil continuously circulates through and around all theparts of the lathe, so that the lathe quickly assumes thesame temperature as the oil. This makes effective tem-perature control possible. Because of this temperaturecontrol and the absence of wear in the mating surfacesof the hydrostatic bearings, and also because the head-stock motor is not sensitive to overload, all kinds ofturning can be done on the lathe without any gradualdeterioration in the highest standard of finish that canbe attained; in addition, "the time needed to reach thisdegree of finish is negligibly short.In this hydrostatic bearing and drive system' the

control of pressures and rates of flow plays an importantpart. To obtain work with a high standard of finish it isof course essential to keep the speeds of movement oftool and work accurately constant. We have developedthe elements needed for these three functions - bear-ing, drive and control - to the required degree ofaccuracy and it can be expected that the new elementswill be of considerable interest in many other applica-tions besides the lathe described here. Outstandingamong these, elements are the double-film hydrostaticbearings for the car.riages, which can be made to haveinfinite stiffness by means of a special method of pres-sure control, the linear, motor, the rotary hydraulicmotor and the control valves. A method has been foundwhich largely compensates for the unwanted forcesthat arise because of the oil flow through these valves.In the following these four components will be dealtwith at greater length, but first of all we shall give a gen-eral description of the design of the lathe as a wholeand of the hydraulic system.

Design objectives

The lathe was required for machining work up to200mm in length and diameter with a surface finish ofoptical quality. A dimensional tolerance of 1 (.Lm wasgiven as a target figurefor the design, with a maximurnout-of-roundness of 0.1 (.Lm in the finished work.These tolerances, which were laid down purely as atarget, have been achieved in practice; with a readilymachinable material and a good (diamond-tipped)tool it is likely that even closer tolerances could bemet. However, to meet dimensional tolerances ofthis order it, is essential that the temperature of thework remains constant: for example, a piece of brass100 mm long expands by 1.9 (.Lm for a temperatureincrease of 1°C. Where dimensional accuracy is im-portant, it will therefore be necessary to use the lathein a controlled-temperature environment. This, how-

ever, is not necessary to achieve a high surfacé finish,since the control of the temperature of the circulatingoil makes the lathe sufficiently independent of theambient temperature. Achieving a high surface finishwas incidentally the most difficult of the objectives,because the closer one gets to a surface of opticalquality the more every flaw shows up. A scratch only0.1 (.Lm deep is clearly visible.To avoid all causes of surface flaws, the two carriages

that move the tool longitudinally and radially arenot mounted one above the other as they are in a stan-dard lathe. Instead, the tooihoider is mounted on atraversing carriage and the headstock spindle on anidentical carriage which moves longitudinally, i.e. par-allel to the axis of rotation. The tailstock is mountedon a third carriage in line with the headstock, and thecentring cone is fixed (i.e. it does not rotate). The threecarriages are mounted on a lathe bed, with which theyform a compact and rigid assembly. A plan view of thelathe is shown infig. 1.The linear hydraulic motors that apply the longitu-

dinal and traversing motion to the carriages for theheadstock spindle and for the tooiholder are mountedin line with the carriages to ensure well-defined move-ment and a rigid construction. The motor housing, thecylinder Cyl (fig. 2), is fixed to the slideway S and thepiston rod is attached directly to the carriage C.

670

1000

Fig. 1: Plan view of the precision lathe: H headstock. TH tool- .holder. TS tailstock. S slideways of the carriages which carrythese three main units. The dimensions of the lathe bed are givenin millimetres. .

-C 5

Fig. 2. The drive of a carriage C by the oil pressure in cylinderCyl, working on piston P. S is the slideway.

1969, No. 5 PRECISION LATHE 119

The rotary hydraulic motor that drives the mamspindle is incorporated in the headstock which, in astandard lathe, would be a fixed unit. J n our lathe theheadstock unit is mounted on the carriage that moveslongitudinally.

The photograph infig. 3 clearly shows the three mainunits: headstock, tooIholder and tailstock. The frontplate of the lathe contains the operating controls for

Hydraulic system

A diagram of the hydraulic system of the precisionlathe is given infig. 4, with the conventional symbols.The diagram presents the three most important assem-blies 0 f the lathe, the headstock unit H, the tooIholderunit TH and the tailstock unit TS; P is the pump unit.Each unit has its own linear motor (I, 2 and 3). Thelinear motor J of the headstock unit is connected to the

Fig. 3. The precision lathe. Control valves for adjusting the speed of the longitudinal and crossmovements are mounted on the front plate. Instruments that indicate the displacement in thelongitudinal and radial directions to an accuracy of 0.5 fLm can be seen at the rear.

setting positions and spee::ls. Behind the lathe there aretwo decimal counters, which show the displacementsof the longitudinal and cross carriages to within anaccuracy of 0.5 l.Lm.These displacements are measuredby means of an optical system [4].

[-ij An article on this wi·~l1-sC-h-o--crtC-ly---;-b-e-a-p-p-e-ar--=-in-g---C-in---:-;tICCli-s--=-jo-l-Ir-n--'-al.

variable flow-control valve 9 through the directionalvalve 7: the valve 9 regulates the rate of flow at whichthe cylinder of 1 fills up or empties and thus controlsthe speed of movement of the piston. The same arrange-ment is found in the tooIholder unit TH. The systemused for the tailstock unit is different, since here the

J20 PHILlPS TECHNICAL REVIEW VOLUME 30

15 TS

-Fig. 4. Diagram of the hydraulic system of the precision lathe. H headstock unit. TH tooIhoider unit. TS tailstock unit. P pump unit.The colours indicate the various oil pressures: red = supply pressure Ps, yellow = -1Ps, green < tps but higher than atmosphericpressure, blue = atmospheric pressure./,2,3 linear hydraulic motors. 4,5,6 carriages with hydrostatic bearings. 7,8 directional valves. 9,10,// adjustable flow-control valves.12 adjustable pressure-control valve for the tailstock carriage. 13, /4 fine adjustment for the position of the linear motors. 15 backstop.16 rotary hydraulic motor. 17 hydrostatic bearings of the rotary hydraulic motor. 18 preset flow-control valve. /9 backing reservoir.20 main reservoir. 21 auxiliary pump. 22 main pump. 23,24 oil filters. 25 temperature-control system. 26 supply-pressure control valve.

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linear motor serves to maintain a constant pressureagai nst the workpiece.

The headstock unit H also includes the rotary hydrau-lie motor 16. This has a parallel branch with a variableflow control 11. The sum of the flows through bothbranches is kept constant bya fixed flow-control valve18. The motor speed is controlled by varying the flowthrough 11; since the sum of the flows through 16 and11 remains constant, the flow through 16 then varies inthe opposite direction, changing the motor speed ac-cordingly. An advantage of a total flow independentof the motor speed is that any pressure drop in theconnections always remains the same, so that the pres-sure level at all points is independent of the speed of themotor.

The pump unit P supplies the whole hydraulicsystem with clean oil at the required temperature andat a pressure of 40 bars [51. This pressure is ratherlower than is usual in hydraulic systems. The advan-tage of this is that the inevitable pressure fluctuations

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due to the pump are then smaller and easier to smoothout. The am plitude of these pressure fluctuationsdepends not only on the pressure level but also on thepresence of air in the oil. This air has an easy oppor-tunity to escape in the main reservoir 20; the oil re-turned to the backing reservoir 19 is pumped by meansof an auxiliary pump 21 via a filter 23 and a temper-ature-control system with heat exchanger 25 to themain reservoir 20, where it emerges just below thesurface of the oil through a diffuser opening out in theform of a funnel, in which turbulent oil comes to rest.The main pump 22 supplies oil at the rate of 20 litresper minute to the three main units; a pressure-controlvalve 26 at the branching point of the three supplylines keeps the supply pressure constant.

The hydrostatic bearings

In a hydrostatic bearing the parts I and IJ (see fig. 5)are separated by a fluid film whose pressure pr enablesit to support the load F. Since the bearing is not sealed,

1969; No. 5 PRECISION LATHE 121

fluid can escape, the outflow resistance R2 being de-pendent upon the thickness of the film (the gap height)h, the length 1and the width b. The fluid (usually oil)is supplied from an external source through a seriesresistance RI, and at the centre of the bearing the clear-ance is usually deepened to form a recess [61.

The fluid film can be built up by the bearing itself through thepumping action due to the relative movement of the bearingsurfaces. Bearings of this type, which include the Leblans preci-sion bearing mentioned earlier [2) and the spiral-groove bearingdescribed earlier in this journal (7), are called hydrodynamicbearings. In a hydrodynamic bearing the fluid film, and hence theposition of the mating surfaces, depends on the relative speed.For precision machines this is undesirable, particularly if thespeed is sometimes zero, which is often the case for machine-toolcarriages.

It is seen that a hydrostatic bearing always consistsof two resistances RI and R2 in series, which are sup-plied from an external source with a fluid (oil) underpressure. In the steady state the fluid flow through theresistances RI and R2 has the same value cp and thepressure Pr between the resistances depends on R2 inaccordance with the relation:

where ps is the pressure of the source.

F

I

--,IIIII

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Fig. 5. Diagram of a hydrostatic bearing. I and 11 the two partsof the bearing. F load. P oil pump. V pressure-control valve. R;flow restrietor. R2 total outflow resistance, formed by two outletgaps in parallel with width b, length I and height h,Ps supply pres-sure. Pr pressure in the bearing recess; the pressure decreaseacross the bearing gaps is shown in the figure ..

The flow through the gap is laminar; R2 consists ofthe parallel arrangement of two identical bearing gapseach with a resistance 2R2, which follows from theequation for fluid flow through a laminar resistance:

lep _ pr _ bh32 - 2R2 - 121]1 Pr. (2)

In this equation, which we shall encounter severaltimes in this article, 1] is the viscosity coefficient of thefluid. The laminar flow resistance R2 is inversely pro-portional to the third power of the gap height h, Theway in which the recess pressure Pr varies with the gapheight h can most simply be seen if we write:

where R20 and ho are the values of R2 and h for zeroload, and then substitute this in (1). We then obtain:

Ipr = I+ (R!/R20Hh/ho)3 p«. (3)

(1)

We see from this expression that when the gap height his reduced because of an increasing load F, the recesspressure pr in the bearing increases; the higher pressure,acting on the effective bearing surface A, delivers aforce which balances the increased load.

In the design of a hydrostatic bearing the dimensionsare determined by the requiredload-carrying capacityand the required stiffness of. the bearings. The load-carrying capacity of the hydrostatic bearing refers tothe maximum permissible 18ad Fmax (i.e. the load un-der which the bearing surfaces are only just clear of-oneanother). Under this load the bearing gap height his approximately zero, so that the outlet resistance R2tends to infinity and the recess pressure pr becomesequal to the supply pressure ps, giving Fmax = APa.

The bearing stiffness K is equal to the load changeLlF divided by the resultant displacement -tJh of themoving part I towards IJ:

dFK=--.

dh

With F = Apr we can calculate K from (3). Using anapproximation that is permissible if the deviation Llhis small we find:

(4)

[5) 1 bar = 105 N/m2 =).020 at. All pressure levels specified .here refer to the excess pressure above atmospheric pressure.

[6) H. C. Rippel, Design of hydrostatic bearings, Machine De"sign 35, 1963 (10 parts). See also H. Opitz, Aufbau und kon-struktive Auslegung hydrostatisch er Lager, Bericht über die

. VDW-Arbeitstagung am 4. unci 5. Februar 1965, Techn.Hochschule Aachen.

[7)' E. A. Muijderman, New forms of bearing: the gas and thespiral groove bearing, Philips tech. Rev. 25, 253-274,1963/64;E. A. Muijderrnan, Spiral groove bearings, thesis, Delft 1961.

(

122 PHILlPS TECHNICAL REVIEW VOLUME.30

Here; is a dimensionless constant mainly determinedby the inlet resistance orrestrictor RI. The relation (4)indicates the requirement to be met if a stiff bearing isto be obtained with a fixed restrictor: the bearing sur-face and the supply pressure should be large, the gapheight should be small.The same expression, but with a proportionality

constant twice as large, also holds for a hydrostaticbearing of the double-film type (fig. 6). In the double-film hydrostatic bearing the principle illustrated infig. 5 is applied to both sides of the moving part I. Thesymmetrical construction thus obtained considerablyimproves the running and the temperature dependenceof the bearing.

Fig. 6. Diagram of a double-film hydrostatic bearing. I movingpart. 1ft and 112 stationary parts. F load. R flow restrictors. hbearing gap height. ho value of h when F = O.Ps supply pressure.prl and P1'2 pressures in the bearing recesses.

The way in which the type of restrictor employedaffects the bearing stiffness can clearly be seen from thegraph infig. 7. The dashed line in this graph representsthe condition which the rate of flow cp through thebearing should meet for infinite stiffness, i.e. in a bear-ing where the gap height h is independent of the load.If in such a case a force is applied to the part I, theflow rate to the recess with the higher pressure mustincrease and the rate to the other recess must decreasein order to obtain the necessary pressure difference. Thesolid curves indicate the variation of the flow rate cpwith the recess pressure P» for four types of flow re-strictor. Three of these are commonly used in hydro-static bearings [6]: the laminar-flow resistance (L), theturbulent-flow resistance (T) and a constant-flow device(C). Using these restrictors it is not possible, as can be

-PrFig. 7. The oil flow if> through a hydrostatic bearing as a functionof the pressure P» in the bearing recess for different types of flowrestrictor: L laminar-flow resistance, T turbulent-flow resistance,C constant-flow device, MDR membrane double restrictor. Thedashed line indicates how the oil flow should vary with recesspressure in order to give the bearing infinite stiffness. Only theM.D.R. meets this requirement within a specific range.

seen from fig. 7, to make an infinitely stiff bearing. Thefourth curve relates to the variable flow restrictor,known as the "membrane double restrictor" CM.D.R.),developed at Philips Research Laboratories [8]. Withthis device it is possible to meet the requirements forinfinite stiffness within a given range.Unlike the other types of restrictor mentioned, the

membrane double restrictor is affected by load varia-tions, with the result that a feedback control system isobtained. Fig. 8 shows a diagram ofthe device together

-

I

-Fig. 8. Diagram of a double-film hydrostatic bearing with amembrane double restrictor (MDR) which controls the oil flowthrough the bearing. I moving part. 1ft and 112fixed parts of thebearing. Ps supply pressure. With increasing load F the pressurepn: rises and the pressure pr2 drops. This causes the membraneof the M.D.R. to flex upwards, admitting more oil into the lowerbearing recess.

1969, No. 5 PRECISION LATHE 123

with a bearing. When a force F is applied to the movingpart J, a pressure difference Pr2 - pr1 must be created inthe two bearing recesses in order to balance this force.The pressure difference pr2 - pr1 also acts on the mem-brane, causing it to flex towards the side where thepressure is lower. Then the gap height X2 between themembrane and the housing, at the side where the recesspressure ill higher, increases. As the flow through thegap is laminar, the effect of the increased gap heightis greater than that of the reduced pressure differenceps-pr2 (equation 1) and there is therefore an increasein the flow to the recess with the higher pressure.An important feature of the membrane double re-

strictor is that one of the parameters is the supplypressure Ps; this enables the stiffness in an assembledbearing to bemodified - from a positive value, throughinfinity, to a negative value (fig. 9). This facility enableselastic deformations in other parts of the bearing to becompensated.

f

ta8r-------r-~-=~4~OOO~r~~~~~--~---4

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Fig. 9. The load of a double-film hydrostatic bearing withM.D.R. control as a function of the corresponding displacementof the moving part supported in the bearing, for different supplypressures p«: The curves relate to normalized quantities; the ver-tical axis shows the load divided by the load-carrying capacity ofthe bearing ([ = FlAps) and the horizontal axis shows the varia-tion of the bearing gap height divided by the gap height under noload (s = LJhlho). The stiffness ofthe bearing is equal to the slopeof the curve. The M.D.R. is dimensioned in such a way that atPs = 32 bars the bearing stiffness is infinite for moderate loads.At supply pressures greater than 32 bars the bearing stiffness isactually negative over part of its range. For comparison thedashed curve L represents the case in which the flow restrietionis a laminar-flow resistance.

Since the bearing and membrane double restrictorform a feedback system, there is the possibility of insta-bility. In such a system this would take the form ofspontaneous oscillation at a particular freq~ency. Evenwhen the system is stable, it may be so close to insta-

bility that a transient oscillation occurs after everydisturbance. Both the oscillation effects and the exis-tence of dominant resonant frequencies can be avoidedby choosing the bearing dimensions in such a way thatthere is sufficient damping in the system. This can beseen fromfig. 10 where the amplitude and phase angleof the deflection of the bearing under a sinusoidally

900

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Fig. 10. Polar diagram of the amplitude and phase of the deflec-tion of a double-film hydrostatic bearing with M.D.R. controlwhen subjected to a sinusoidally varying load. Each curve con-nects the measured values for different frequencies at a givensupply pressure Ps in the bearing. At ps = 32 bars the bearing hasinfinite static stiffness. The shape of the curve shows that thereare no marked resonances at particular frequencies, so that thesystem is dynamically stable. At the highest frequencies the supplypressure hardly affects the curve, the damping in the bearing thenbeing dominant.The chain-dotted line L represents the dynamic behaviour of

the double-film hydrostatic bearing when a laminar-flow resis-tance is used as the flow restrietion instead of the M.D.R.

varying load are shown for different frequencies anddifferent supply-pressures. No marked resonance thenoccurs at any frequency [91.

The membrane double restrictor not only gives avery high bearing stiffness; it also has the importantadvantage that it gives sufficient stiffness with alarge gap height, low supply pressure and small bearingdimensions. These arejust the veryconditions that equa-tion (4) shows to be undesirable; however, they are of-ten desirable for other reasons [lOl.

[8] J. G. C. de Gast, A new type of controlled restrictor (M.D.R.)for double-film hydrostatic bearings and its application tohigh-precision machine tools, Advances in machine tool de-sign and research 1966, Pergamon Press, Oxford 1967: .

[0] J.G. C. de Gast, Dynamic behaviour of a double-film hydro-static bearing with variable flow restrictor, to be published inTrans. ASME, J. Lubr. Technol.

[10]Because of this, hydrostatic bearings can also be used forfast rotating shafts (6000 rev/min) with low oil consumptionand friction losses. Stiffness, load-carrying capacity and damp-ing are better in this case than with an air bearing; see H. L.Wunsch, Air bearing applications to machine tools and meas- .uring instruments, Trans. AS ME, J. Lubr. Tèchnol. 90F,680-686, 1968 (No. 4).

124 PHILlPS TECHNICAL REVIEW VOLUME 30

Fig. J I shows how the mem brane dou bie restrictor isincorporated in a slot cut into one of the bearing blocks.Each pair of bearing recesses has its own membranedouble restrictor.

Carriage with slideway

When double-film hydrostatic bearings are used,there are always large preloading forces present (thesemay reach 104 N in the carriage bearings, for example),which can cause severe structural deformation if theforces give rise to bending moments. In the design ofthe slide system, shown in cross-section in fig. 12, thehydrostatic forces are applied in such a way that boththe carriage and the slideway are subjected only tocompressive, tensile and shearing forces that together

Fig. 12. Cross-section of slideway S and carriage C. The slidewayis madein one piece and constructed in such a way that the var-ious forces acting on it result in a tensile force and thus do notdeflect it from a straight line.

Fig . .I J. A bearing block of thecarriage with three pairs of hy-drostatic-bearing recesses. Eachpair has an M. D.R., which islocated in a groove ofthe bearingblock.

form a closed force diagram in the plane of the draw-ing [Ill.

The carriage has three identical bearing blocks (asillustrated in fig. 11), which are mounted on the car-riage frame. Since the blocks are supported in bearingsat both sides, each block is hydraulically balanced sothat the carriage frame is relieved of hydrostatic pre-loading forces. The slideway shown in fig. 12 wasmachined from one piece and all the guide faces wereprecision-ground.

The slideway can also be built up from rectangular bars(fig. /3). This construction is less rigid than that of fig. 12. Thedeformations caused by the hydrostatic forces acting on a slide-way built up in this way have been measured and are shown infig. 14. An important advantage, however, is that the bars can be

Fig. 13. Cross-section of a slideway not made from one piecebut built up from three rectangular bars. With this constructionsmall deviations can be corrected by flexing the bars before theyare clamped in position.

1969, No. 5 PRECISION LATHE 125

Fig. 14. Measured deformationof a slideway of the type shownin fig. 13, a) when only a hori-zontal force is operative, b) whenonlya vertical force is operative,c) when both are operative to-gether. In case (c) there is onlya small residual deformation.

r----------- _.,2000N : :

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assembled in such a way that deviations over a length greater thanhalf the bearing-block length can be corrected by flexing andclamping. Slideways of this type were used for the guides in thestep-and-repeat camera recently described in this journal [12);

for a 5-cm displacement of the carriage the deflection from thestraight is less than 0.03 fLmand the angular rotation of the car-riage is less than 0.1 seconds.

The linear motor

The linear motor used is a combination of pistonand cylinder (jig. 15) with a piston to piston-rod surfaceratio of 2:1. When the piston is stationary and thesupply pressure Ps is applied to the annular space be-tween the cylinder and the piston rod, the pressure inthe oil-filled space to the left of the piston is PI. Tak-ing the equilibrium of forces at the piston, then forthe given surface ratio and zero external forces, PI isgiven by:

If the space to the left of the piston is now connectedvia a resistance to a supply of oil at a pressure ps, the

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Fig. IS. Simplified cross-section of a linear motor. The spaceto the left of the piston communicates through a laminar-f1owresistance R with the supply pressure Ps (piston moves to theright) or with atmospheric pressure (piston moves to the left).The piston surface t:n:(D2 - d2), on which Ps acts, is half thesize of the surface t:n:D2, on which PI acts, so that when thehydraulic forces are balanced, PI = -lPs. The hydrostatic-bearingaction of the piston in the cylinder is obtained by means offour recesses Re with restrictors RI incorporated in the pistonand the flow resistance R2 between piston and cylinder wall.

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,.piston is given a velocity v to the right; if the space tothe left of the piston is connected via R to oil at at-mospheric pressure, then the piston is given an equalvelocity v to the left. In both cases the oil flow rate(jj = (n/4)D2v (D being the inside diameter of thecylinder) is given by:

(jj = Ps - Ps/2.R

The velocity is thus given by:

. 2ps ,_. (6)v= nD2R' i;,i ... , ..

(5)

For a good surface finish it is necessary that v shouldremain constant to within 0.1 %. It can immediately beseen from (6) that the essential condition for this isthat the supply pressure ps should be constant to within0.1 %. The load on the motor should also be constant;this has been neglected in the derivation of (6)', butcan be taken into account by a term to be subtractedfrom Ps- Since it is extremely difficult to keep the supplypressure and particularly the load as constant as this, itwas decided to ensure the uniformity of v directly bykeeping the flow rate (jj at an accurately constant value.This was done by replacing R by a flow-control valve(whose operation is described in the section on controlvalves).The uniformityof the velocity is also adversely af-

fected by the pressure in the cylinder which can causethe inside diameter D of the cylinder to have a slightlydifferent value' at different places. In order to make thedeformation ofthe cylinderwall as uniform as possible,it is not rigidly attached to the cylinder 'head butmounted freely; this can be seen in the detailed cross-section ofthe linear motor shown in fig. I6~ .Another difficulty that can give rise to non-unifor-

[11) J. G. C. de Gast, Berekening en constructie van hydrostati-sche lagers, Polytechn, T. Werktuigbouw 23, 141-150, 187-196, 1968 (Nos. 4, 5):,

[12) F. T. Klostermann, A step-and-repeat camera for makingphotomasks for integrated circuits, Philips tech. Rev. 30,57-70, 1969 (No. 3).

126 PHJLlPS TECHNICAL REVIEW VOLUME 30

mity in the piston velocity is the presence of leakagebetween the piston and the cylinder wall. However, byincluding a control valve (7 in fig. 16) in the piston theoil pressure in the annular grooves and bearing re-cesses in the piston surface can be adjusted in such away that hydrostatic bearing action and a perfect sealare obtained at the same time.

tapering deformation depends upon the cylinder diameter D andthe wall th ickness t and is given by:

LR! 4.5 l/D/.The pressure difference across the piston is now concentrated ina narrow zone of the very thin oil film between the piston andthe cylinder wall. We shall see that this zone is located near thehigh-pressure end (in fig. 16 the right-hand end) of the piston. Theoperation of the linear motor, on the other hand, is based on the

Fig. 16. Complete cross-sectional drawing of the linear motor in the lathe. The colours corre-spond to various oil pressures: red = supply pressure Ps; yellow = -j-ps; green < -j-ps; blue =

atmospheric pressure.1 cylinder. 2 piston. 3 piston rod. 4 cylinder head. 5 thin-walled extension in which the piston rodcan be clamped to hold it accurately stationary. 6 O-ring seal on the head surface of the cylinderjacket. 7 control valve. 8 bearing recesses. 9 annular groove under average bearing-recess pressure.10 outlet slot. The control valve 7 incorporated in the piston 2 keeps the pressure in the bearingrecesses 8 of the piston equal to that on the left of the piston, i.e. equal to -j-ps.

The permissible deviations in the cylinder diameter are verysmall. The effect on the velocity of a deviation LID in the diameterof the cylinder may be deduced from (6) and, neglecting terms ofhigher order, may be written as:

Llv 2L1DDo'vo

where vo and Do are the normal values of v and D. If LI v is re-quired to be less than 1O-3vo, then the error due to a deviation ofdiameter should be about an order of magnitude smaller, sincethere are other sources of error. We then have:

2L1D < 10-4 Do.

For a cylinder diameter of 80 mm the deviations LID must there-fore be less than 411-m. Now LID has reached 10 I1-mfor a pressuredifference of 40 bars and a wall thickness of 6 mm. If the cylinderwere constructed as shown in fig. J 5, this deviation would occurat the centre of the cylinder but not at the two ends. This is be-cause one end is reinforced by the cylinder head and the O-ringseals off the other end from the pressure. In the design shown infig. 16 these effects are avoided by mounting the cylinder freelyand not rigidly connected to the cylinder head 4 and by apply-ing the seal 6 to the end face of the cylinder tube.

Deformation of the cylinder is also caused by the pressure dif-ference across the piston. The length L subject to this slightly

displacement of oil by the left-hand end ofthe piston. The cylinderdeformation here due to the pressure difference should beimperceptible, which implies that the piston length should atleast be equal to the deformation length L.

The sealing of the piston, which has the pressure differencePs - Pi across it, calls for special measures, since the running ofthe piston must not be unfavourably affected by the seal. It is ofcourse essential that the piston and piston rod should be accu-rately centred in their guides for proper running of the piston,otherwise, owing to the high surrounding pressure, these mov-ing parts could seize up against the cylinder wal! or cylinder headas soon as they came into contact with them. In hydraulic engi-neering this effect is known as "hydro-lock" [131. The necessarycentring is obtained by supporting both the piston and the pistonrod in hydrostatic bearings. The four bearing recesses (Re in fig.15) provided for this in the piston circumference are connectedvia four identical resistances Rl to the annular high-pressurespace between the piston rod and the cylinder. The oil from thesebearing recesses does not flow into the low-pressure space on theleft of the piston [14], but into an annular groove situated be-tween the recesses and the high-pressure space and open to at-mospheric pressure via the hollow piston rod.

The piston seal thus becomes a seal between the space withthe pressure p: and the bearing-recess pressure p-. We take Pr =±Ps, since a hydrostatic bearing works best with this ratio be-

1969, No. 5 PRECISION LATHE

tween recess pressure pr and supply pressure p»; since also PI =tPs (see equation 5), the pressure difference to be sealed is small.

With a simple rubber seal, such as an Ovr ing, this small pres-sure difference, which is independent of the pressure level, can beadequately sealed without adversely affecting the movement ofthe piston. What will be affected is the positioning of the piston,because of the hysteresis of the material, while the static friction isalso a function of time. An element giving such a complete seal isnot necessary, however, provided PI and PI· do not differ by morethan 0.01 bar, at which level the leakage of oil through the gap isnegligible. This has been achieved by means of a pressure-controlvalve incorporated in the piston (seefig.16) which builds up a suf-ficiently high pressure in the annular outlet groove JO (green) tokeep the average recess pressure (present in the annular groove 9on the left of the recesses in fig. 16) equal to the pressure tPs(yellow).

Keeping the piston stationary for a long period to an accuracyof better than 0.1 [Lm requires special measures. This is a featureof the lathe that is vital, and has been achieved by hydraulicallyclamping the piston rod. The clamping action is provided by athin-walled cylindrical extension on the inside of the cylinder head(5 in fig. 16). The pressure is always high on the outer side of thiscylindrical extension and a decrease in pressure between theextension and the piston rod causes an elastic deformation andhence the clamping action. The low pressure is adjusted by bring-ing the two adjacent annular grooves up to atmospheric pressureby means of a magnetically operated valve. The pressure-control

valve in the piston, which keeps the pressure in the bearing re- Fig. 17. Cross-sectional drawing of headstock spindle S and vanecesses of the piston at tps, ensures that in the clamped state the motor M. A thrust bearing. R journal bearings.pressure PI in the space behind the piston does not rise or fall asa result of slight oil leaks. F

It can also be seen from fig. 16 that the cylinder hasa double wall: this construction has been used to giveproteetion to the inner cylinder wall and to permit oilof controlled temperature to be circulated around theoil space behind the piston. The piston rod is hollowand is provided with two backlash-free universal jointcouplings. This enables the cylinder to be fixed to theslideway and the drive shaft to the carriage; a misalign-ment of ±2° is permissible. The piston also has aninternal high-pressure passage, instead of flexible tu-bing, for supplying oil to the carriage, etc. Sufficient oilcirculates through the linear motor to bring the com-plete unit to the controlled temperature ofthe oil underall operating conditions.

Headstock spindle and motor

The accuracy of rotation of the headstock spindlewhen hydrostatic bearings are used is determined bythe circularity of the spindle itself, and can even bebetter than this, the shape of the bearing bush being ofsecondary importance. For example, an experimental

[13] J. Boyd, The influence of fluid forces on the sticking and thelateral vibration of pistons, Trans. ASME, J. appl. Mech. 31,397-401, 1964.

[14] See A. A. Raimondi and J. Boyd, Fluid eentering of pistons,Trans. ASME, J. appl. Mech. 31, 390-396, 1964.

[15] If the tilt of the main spindle is not minimized but the radialdeviation of the chuck instead, another expression must beused (see reference [11]).

shaft machined on a headstock spindle with an out-of-roundness ofO. 7 [Lmwas found to have an out-of-round-ness of 0.1 [Lm. It was decided to give the headstockspindle a cylindrical shape without protrusions, sincethis shape can be made accurately circular to within0.1 urn by lapping.

The distance d between the two journal bearings(seefig. 17) was chosen so as to minimize the tilt of the

a b

Fig. 18. A force F acting on the projecting part of the headstockspindle presses the spindle sideways. A relatively large deviationmay be caused by tilting of the whole spindle if the distance dbetween the bearings is small (a), and by flexing of the spindle ifthe distance between the bearings is large (b). Between these thereis an optimum distance d which gives the least deviation.

headstock spindle in the front bearing due to a radialforce acting from outside the bearings (seefig. 18). Thistilt is to be avoided because it changes the direction ofthe axis of rotation of the workpiece clamped in thechuck. The optimum distance d depends on the modu-lus of elasticity E, on the linear moment of inertia I ofthe cross-sectional area of the headstock spindle andon the bearing stiffness K; the relation is:

where the constant c is about 16 if all quantities arein sr units [15l.

The thrust bearing (A in fig. 17) is fitted at the end ofthe headstock spindle S and is supported by a flat platebolted to the headstock. This is a hydrostatic single-film

127

128 PHILIPS TECHNICAL REVIEW VOLUME 30

bearing pre-Ioaded by the supply pressure. The designis such that there is no interaction between the jour-nal and the thrust bearings, and the front journalbearing lies as close as practicable to the chuck. Thisis the best arrangement for accurate running and for thestiffnessof the headstock spindle. One disadvantage isthat the thrust bearing is a long way from the chuck,which means that the axial position of the workclamped in the chuck is dependent on the temperatureofthe headstock spindle. Fluctuations in this tempera-ture are very small, however, on account of the methodof regulating the speed of the headstock motor.We have seen on page 120 that this is done by

varying the flow through a parallel branch and at thesame time keeping the sum of the flows through motorand parallel branch constant. Since the pressure is alsokept constant, this constant total flow supplies to theheadstock a hydraulic power (pressure X volume flow)which is independent of the motor speed. This hydraulicpower is dissipated partly in the hydrostatic bearing of.the motor and the spindle by friction and partly bythrottling in the flow-control valve in the parallelbranch. In addition, energy is used up in machining, butfor a light finishing operation (e.g. a cut of 20X 12 fLm)the power required is negligible. The heat generatedin the hydrostatic bearings increases with the motorspeed; since however the total dissipated power is inde-pendent of speed, the heat developed in the flow-con-trol valve decreases equally. The oil flows from the two'parallel branches are now mixed between the twoheadstock bearings, and the mixed flow,which thus sup-plies a quantity of heat independent of the speed, cir-culates around the headstock spindle, which thereforeremains at the same temperature at different speeds.The headstock motor is of the vane type. Since a

uniform angular velocity can be obtained with thistype of motor, it can be attached directly to the head-stock spindle without the need for a coupling to smoothout deviations from uniformity. Moreover, no speed-selection mechanism is necessary for the transmissionsince the speed of the motor can- be continuously regu-lated within wide limits, between 300 and 1200rev/ruinin our lathe. In addition it is hydraulically balancedradially and axially and is small.A vane-type motor consists of a rotor with a number

of vanes, and a stator (jig. 19). The stator containsseveral "chambers", two in our case, with a stroke h;the chamber walls are cylindrical and concentric withthe inner bore over an are of e radians. The inner boreis also cylindrical over an are of e radians, and thereis a smooth transition from chamber to inner bore. Thevanes are kept in contact with the transition part ofthe wall by a spring. In the chambers the vanes aresubjected on the one side to the supply pressure P» and

on the other to a lower pressure Pm: The pressure dif-ference acting on the projecting part of the vane causesa force to act on the vane. This force gives rise to acouple that drives the rotor. Oil is supplied and removedon the transition curves and there is always at least onevane between feed and outlet.

Given an angular displacement rp the vane displaces a volumeV of oil given by:

V_'dD+Iz-tl =r:»:

Owing to the symmetrical design of the motor, the same volurneis displaced by the vane in the chamber at the opposite side, sothat the volume displaced for each radian that the motorrotates is:

Vr = hd (D+Iz),

which is referred to as the swept volume per radian. Since Iz isconstant over the arc e of the chamber, the volume displaced perradian is independent of the position of the rotor, so that thistype of motor has in theory a uniform angular velocity to, This isdetermined by the oil feed (/> and the oilleakage (/>!:

(/> - (/>!W = ----v.:- .

In spite of slight deviations the oil leakage (/>! may readily bedefined in a wide operating range as a linear function of the pres-sure difference Ps - Pm. The change in cp! can therefore be com-pensated in the precision lathe by using a membrane load com-pensator like the one developed some time ago at these Labora-tories for a linear servomotor [161.As soon as a vane has reached the end ofa chamber (see fig. 19)

the next vane has to take over the sealing action. Consequently

g

Fig. 19. a) Cross-section and b) plan view of a vane motor.Ps pressure at input side and pm pressure at output side of themotor. " height of stroke.

1969, No. 5 PRECISION LATHE 129

the number of vanes must be at least 2n/G. With this numberofvanes, however, there is no overlapping at all at the change-overand there is an irregularity at each change-over.lt is therefore bet-ter to use more vanes so that there is some overlap. Even then,some change-over irregularity remains: since it is impossible toavoid a small amount of play in the grooves for the vanes, eachvane "flips" across as it takes up the pressure difference; moreover,the leakage is halved during each short interval when the twovanes are in series. In addition, successive vanes take up pressuresimultaneously in the two chambers, because the rotor must re-main radially balanced. The resultant irregularities are visibleon a trial workpiece after a plane perpendicular to the axis hasbeen machined. These irregularities can be removed by usingtwice the number of vanes, so that the seal is always effected bytwo vanes in series. Even then there is still some unevenness inthe leakage flow since there is a short overlap period in whichthree vanes are ill series. This difficulty can be overcome bycutting 20 fl-m deep "relief" grooves in the overlap part of thechamber, to permit sufficient additional leakage for the flow dur-ing the overlap period to be equal to the leakage rate when thereare two vanes in series.

The motor used in the lathe has two chambers with18vanes and an overlap of 10°. The diameter of the ro-tor is 60 mm, its width is 7 mm and the stroke is 2 mm. Atthe maximum speed of 1200 rev/ruin a power of 250 Wis available at the chuck. The power is kept as lowas this because the present lathe is used only for finish-ing, and even this small amount of power is seldom re-quired. However, if necessary, a higher power could beused with a headstock of these dimensions.

The control valves

In the foregoing we have several times referred tocontrol valves whose purpose was to keep a pressureor a flow to a prescribed value. Flow control can alwaysbe reduced to the control of a pressure difference acrossa fixed flow resistance, so that in fact all control require-ments amount to controlling a pressure difference. Inthe precision lathe this must be done with an accuracyas good as 0.1 %, whereas the best that conventionalcontrol valves can give is about I to 2%. It was there-fore necessary to design new control valves for theprecision lathe, paying special attention to all theunwanted forces that arise as a result of fluid flowsor friction in the valves. The required accuracy wasachieved by compensating the forces associated withthe fluid flow and by making further use of hydro-static bearing action.

A hydraulic control valve operates by varying theopening of a flow orifice under the action of varyingpressure levels. In the precision lathe described hereeach control valve consists of a moving piston whichcontrols the opening of the outlet ports in a cylinder.

Two cases are to be distinguished for a constantpressure. In the first case a pressure-control valvekeeps the pressure constant at the input to the valve;

the oil flow through the valve is then a bypass flow.This case is illustrated infig. 20; the regulated pressurepc at one end of the piston balances the spring force Facting on the piston. A schematic diagram represent-ing this case is also shown in fig. 20. (/) is the mainflow, (/)2 the bypass flow. The dashed line indicates

-.,II

-~

Fig.20. a) Simplified cross-section of a control valve that keepsthe pressure at the input to the valve to a constant value Pc.The force due to Pc acting on the piston balances the force F,usually derived from a spring. The oil flow f/>2 through the outletport is a bypass flow, required for the control action. The outflowdirection makes an angle fJ with the axis of the valve.b) Diagram of the hydraulic circuit containing the control valve.The dashed line indicates that the pressure at the input to thevalve affects the magnitude of the flow orifice. f/> main flow. R in-ternal resistance of the pressure source.

that the pressure at the input to the valve affects themagnitude of the flow orifice. The second case is tbatof the red uction of a higher pressure to a constant val uepc, independently of the flow. Pressure-control valvesfor this purpose (reducing valves) carry the main flow,the pressure being controlled on the output side of thevalve (see fig. 21).

Compensation of flow force

In both types of control valve there is an equilibriumof forces which is given by the equation:

where D is the diameter of the piston. The force F mustbe independent of the position of the piston and of theflow rate through the valve to ensure that the controlledpressure Pc remains constant. The force F that actuallyappears in the valve, however, contains in addition tothe component derived from a spring a component

[16] T. J. Viersma, Investigations into the accuracy of hydraulicservomotors, thesis, Delft 1961. The deviations from thelinear relationship between volume flow and pressure whichapplies for laminar flow arise because the shape ofthe leakagegap and the temperature of the oil, and hence its viscosity,are pressure-dependent.

130 PHILlPS TECHNICAL REVIEW VOLUME 30

Fig. 21. a) Simplified cross-section of a control valve that keepsthe pressure on the output side of the valve at a constant value Pc·The force due to Pc acting on the piston balances the force F,usually derived from a spring. The oil supplied under pressure Psexerts no force on the piston, the main flow (/;J goes through thevalve. b) Diagram of the control valve. The dashed line indicatesthat the pressure at the output of the valve affects the magnitudeof the flow orifice.

that varies with the valve orifice, the flow force F; Thisforce, which may be regarded as a reaction force appliedto the piston by the outflowing fluid, can amount to20 % of the applied spring force Fs, and thus seriouslyinterferes with the operation of the control valve. Wehave now built a control valve in which the flow forceis compensated in the following way.

The flow force is proportional to the fluid massflowing out per unit time, e(/J (e is the density of thefluid), and to the axial component of the outflowvelocity v. The relation is:

F, = e(/Jv cos ~ ,

where ~ is the angle between the outflow direction andthe axis of piston and cylinder (see fig. 20). It is possibleto apply a compensating counter-force, proportionalto (/J (see below), but there is the complication thatF, is also proportional to v. It turns out, however,that the effect of this proportionality is opposite tothat of another undesirable effect that we have not yetmentioned. This is the variation of the spring force F.~with the position of the piston, and by suitably choos-ing the spring stiffness the two effects can be made toapproximately cancel out in the operating region ofthe valve.

The variation of the spring force F« with a displacement x of

the piston is given by:

r, = Fso +Ksx, . . . . • . . (8)

where K« is the spring stiffness and Fso the spring force actingat the point chosen as x = O. If we take x = 0 for the positiona t which the piston just closes the outlet ports, then x can beexpressed in terms ofthe outflow velocity v and the outlet flow (/;J.

Let xb be the area of the outflowopening, b being the width ofthe outlet ports; then the flow rate (/;J is given by:

(/;J = «xbv, (9)

Here IX is a flow coefficient; in a wide range IX is approximately

equal to 0.7 [171.Equations (7), (8) and (9) show that the total force F acting

on the piston is given by:

F = Fso + (/;J (~: + QV cos /3).

We see that the factor between brackets contains one term pro-portional to V and one term inversely proportional to v. An ex-pression of this kind is fairly constant in a particular range of the(independent) variable v. If the spring stiffness K« is given asuitable value, this range can be situated about the operating pointof the control valve. If the outflow velocity is VD at this operatingpoint, then with proper dimensioning the force F is given by:

(V02

)F = ho + (/;J cos /3 -; + v . (10)

The variation of the factor in brackets is shown in fig. 22. It canbe seen from this that the unwanted force proportional to (/;J hasbeen made approximately independent of the outflow velocityin the vicinity of the operating point.

(7)

5

3

2

%~----~----~2------~3----_..L

va

Fig. 22. Variation of the expression (v02jv + v) with v. The min-imum is obtained when v = VD; in a range about this point thevalue of this expression is virtually constant.

To compensate the flow force the oil flow (/J, afterleaving the valve, is passed through a laminar resistanceR (see fig. 23, a more detailed cross-sectional drawingof the pressure-control valve, whose principle is illus-trated in fig. 20). The pressure drop across a laminarresistance is proportional to the quantity of oil flow-ing through it (see equation (2) which relates to lami-nar flow in a hydrostatic bearing) and the pressure p

1969, No. 5 PRECIsrON LATHE 131

Fig. 23. A more detailed cross-sectional drawing of the controlvalve in fig. 20. A fixed laminar resistance R is included in thebypass flow. The resultant pressure p acts on an additional pistonsurface, thus providing compensation for the flow force.

built up by the resistance R is thus proportional to W.This compensating pressure p acts on an extra pistonface with reduced diameter d and exerts a force on thepiston which is opposite to the flow force and cancelsit for every value of W if R is correctly chosen [18J.

The only reservation here relates to the effect of tem per-ature on the viscosity of the oil and hence on the mag-nitude of the resistance R; this may sometimes make itimpossible to achieve perfect compensation.

Design of the valves

The speed at which the oil leaves the outlet ports isfairly high (e.g. 65 mis at a pressure difference of 20bars). To allow the fast-flowing oil to settle down again,an annular groove is cut in the cylinder wall (see fig. 23).If this groove were rectangular in cross-section, theoil flow would create an undesired pattern in it (19),

and the inlet angle fJ would continuously fluctuate. Thewall along which the oil enters the groove is thereforeplaced at an angle of 60° as indicated in fig. 23; the oilflow thus follows the wall [20J, and the inlet angle isstabilized. To guide the oil flow along the piston thereare two (or four) slots. The oil in the annular grooveflows away through a wide opening in the piston.The pistons of the control valves may seize up because

of hydro-lock [21J. To prevent this the pressure differ-ence that always exists across the pistons is used toprovide them with a hydrostatic bearings action. Anadditional effect is that the accuracy of 1 to 2 % usuallyobtainable with control valves has been improved to0.1 %; a pressure-control valve responds reproduciblyto a variation as small as 10-3 bar at a pressure levelof 10 bars.

Fig. 24 gives an idea of the dimensions of the controlvalves, showing cylinder and piston for two versionswith piston diameters of 12 and 6 mm.

Servo-operated pressure-control valve

The pressure-control valve shown in fig. 23 is usedfor keeping the supply pressure of the lathe constant.Owing to the system of speed control employe::!, theoil flow through the lathe is always about the same,and consequently the bypass flow through the valvealso remains relatively constant. As a result thisvalve is able to keep the supply pressure accuratelyconstant.

Marked differences in the flow will occur, however,in the control valve whose function is to keep the tail-stock pressed against the workpiece with the same force

Q

b

Fig. 24. Piston and cylinder of two control valves incorporatedin the precision lathe. a) Large version, diameter of piston 12 mm;b) small version, diameter 6 mm.

at all times however quickly it is moving (valve J 2 infig. 4). In this case the method described for cornpensa-ting the flow forces in the control valve is not suf-ficiently accurate, and to obtain higher accuracy it isnecessary to use a pressure-control valve in which anextra controlling force, derived from a pilot valve, IS

applied in addition to the forces described above.The circuit of a well-known valve of this type is

shown in fig. 25a. The pressure-control valve C has to

[17] L. Gross, Bestimmung der Durchflussbeiwerte verschiedenerDrosselelemente, besanders bei kleinen Druckunterschieden,Ölhydraulik und Pneumatik 12, 3-8, 1968 (No. I).

[18] Subsequent adjustment is possible in this method, unlikethe one described by J. F. Blackburn, G. Reethof and J. L.Shearer, Fluid power control, M.l.T. Technology Press, NewYork 1960: in this method the part of the cylinder thatreceives the outflowing oil and also thepistonsurfaceoppositeare specially shaped.

[19] See page 362 of the book mentioned in [18].

[20] This effect is known in fluid logic as the Coanda effect; seeP. E. Russ Henke, Fluidics control: yesterday, today and to-morrow, Electromechanical Design, May 1968, page 12.

[21] This effect has been mentioned earlier in the description ofthe linear motor on p. 125.

132 PHILlPS TECHNICAL REVIEW VOLUME 30

keep the pressure pc to a preset value for widely differ-ent flows through C. Since the position of the pistonis different for different flows, a spring is unable todeliver a constant reference force. Instead of th is a forcederived from a constant pressure PI is used as the refer-ence force. This control pressure PI is kept constant bythe pilot valve P. Since the orifice plate A gives a virtu-ally constant flow through P, PI is held accuratelyconstant. This is referred to as a pilot-operated con-trol valve.

c

Q IIIIII P, P~v

A/\ I IL ...J

r-----, ,....----.,I I' I P

vI A /\ ,L ~

Fig. 25. a) Orthodox version of pilot-operated pressure-controlvalve. Since the flow rate through the control valve C may varyand therefore with it the position of the piston in the valve, aspring cannot supply a constant reference force. This is nowsupplied by the control pressure Pi kept at a constant value inthe control valve P. Because of the action of the orifice plate Athe flow through P changes very little and can thus be used foraccurate pressure regulation. Flow forces in C are not corrected.b) Serve-operated pressure-control valve as used in the precisionlathe. The small pilot valve P here reacts to the pressure Pc tu becontrolled and delivers a control pressure Pi that exerts a correct-ing force on the control valve C. Unlike the situation in (a), thishas the result that the flow forces in C are also corrected.

Since the reference force in this system must remainaccurately constant, the varying flow forces in C occur-ring with varying flow will show up as variations in pc,as already described. This difficulty is countered hereby using the control system shown in fig. 25b. Herethe pilot valve P responds directly to the pressure pcto be regulated, thus generating a control pressure PIwhich acts upon the control valve C in such a way thatall deviations are corrected, including those arisingfrom varying flow force and spring force. The resultantfeedback system is referred to as a serve-operated con-trol valve.

The pilot valve P in fig. 25b is shown in cross-sectionin jig. 26. The control pressure PI is regulated in thevalve but does not itself exert any force on the piston.The same control valves are also fitted in the pistonsof the linear motors for the headstock and tooihoider

Fig. 26. The pilot valve of the servo-operated pressure-controlvalve. Deviations in the regulated pressure pc cause fiuctuations inthe control pressure Pi, which exert a corrective action on thepressure-control valve. The control pressure Pi does not itsel fexert any force on the piston of the pilot valve.

slide systems (see fig. 16). There, however, the referenceforce is not delivered by a spring but by the supplypressure p« (red) which acts upon a piston surface c fhalf the size and balances the half supply pressure 1{Js

(yellow) acting upon the whole piston surface. Thevalve keeps the pressure in the bearing recesses 8 athalf the supply pressure and thus provides a seal forthe piston (see page 126).

A force can also be exerted on the control valvethrough the pressure indicated in blue in fig. 16. Thisscheme can be used for applying a correction to theregulated pressure if required in connection with man-ufacturing tolerances, and it can also be used to-set upa small intentional pressure difference across the seal-ing gap. This pressure difference will give a very smalllaminar flow through this gap, thus giving the pistona constant low velocity. This principle has been appliedin a more elaborate form in a laminar flow-controlvalve which is used at Philips Research Laboratories incombination with a linear motor for pulling crystalsfrom a melt by the Czochralski method. This systemreadily permits piston velocities of 1 [J.mjs or less [22J.

Flow-control valve

This laminar flow-control valve is only suitable forvery small flows. From about 0.25 cm3js a turbulent-flow valve is used, consisting of a pressure-reducingvalve with a resistance or orifice plate in series with it,through which the flow is turbulent. Although it would

(22] This method is therefore an alternative to the one describedby H. von Weingraber, Vorschubeinrichtung für extremlangsarne Geschwindigkeiten, Annals C.T.R.P. 11, 90-95.

1969, No. 5 PRECISION LATHE 133

be possible to build a laminar-flow control valve forthese higher flows, the use of a turbulent flow has theadvantage of reduced température dependence. Thismay be seen from the Bernoulli expression for tur-bulent flow through an orifice of area A, where the vol-ume flow is given by:

qy = CiA -V~(Pl; P2) .

Here the coefficient c. is a constant related to the con-striction of the flow; it usually has a value of about0.7 [17]. The factor PI - P2 represents the pressure dif-ference across the orifice and (! is the density of thefluid; the density varies very little with temperature,unlike the viscosity coefficient 'YJ, which plays a rolein Iaminar flow (see equation 2).

All the flow-control valves in the precision lathe -used for controlling the speed of the headstock motor

Fig. 27. Flow-control valve. The volume flow (/J produces apressure difference Pi - P2 across the orifice plate of aperture A.This difference acts on the piston, which tries to keep it equal toa preset value determined by the spring force F.

and the speeds of the linear motors - are therefore ofthe turbulent-flow type. The orifice-plate aperture ofarea A is incorporated near the valve (fig. 27). Thepressure difference PI - jJ2 across the orifice plate ex-erts a pressure on the piston which balances a springforce. Since the flow rate qy through the valve remainsconstant, it is not necessary here to cornpensate for theflow force; however, the spring stiffness must be correct-ly chosen since the flow force is again proportionalto the velocity.

G. H. Veld huizen of the rnechanical design group inthis Laboratory had an important share in thedevelopment of the precision lathe described here.'The external design of the lathe is entirely his work.

Summary. A precision lathe has been designed and built atPhilips Research Laboratories for use there. All moving partsof this lathe run in hydrostatic bearings. The lathe has threecarriages, each driven by a linear motor, consisting of a pistonand cylinder. The double-film hydrostatic bearings ofthe carriagespossess infinite stiffness through feedback of the bearing pres-sure to a variable flow restrictor, referred to as a membrane dou-ble restrictor. The main spindle is driven by a hydrostatic vanemotor. The lathe can machine work up to 200 mm in length anddiameter with a dimensional tolerance of I [Lm; the out-of-roundness of turned work is less than 0.1 [Lm and the finish ofthe machined surfaces is of optical quality. The finish does notdepend on the ambient temperature, but to achieve a dimensionaltolerance of I [Lm it is necessary to keep the ambient tempera-ture constant, purely because of the thermal expansion of theworkpiece. The displacements ofworkpiece and tool are measuredwith an optical system to within an accuracy of 0.5 [Lm, and themeasurement is displayed on a digital indicator. The articledescribes in detail the design and operation of the main parts,in partjeular the slide systems with their hydrostatic bearings,the linear motors, the vane motor and the contol valves usedin many parts of the lathe. The accuracy of the valves has beenraised to 0.1 %.