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Real time control of spindle runout

T. G. BifanoT. A. DowNorth Carolina State UniversityDepartment of Mechanical

and Aerospace EngineeringPrecision Engineering LaboratoryRaleigh, North Carolina 27695 -7910

CONTENTS1. Introduction2. Spindle and control system design

2.1. Control algorithm2.2. Results and discussion

3. Acknowledgment5. References

Abstract. An example of a physical system whose mechanical accuracycan be improved by feedback control is a motor -driven spindle. Such asystem is being used as a test -bed to study measurement and actuationsystems as well as control algorithms. The specific apparatus reportedutilizes an eddy- current probe for runout error measurement, a piezo-electric crystal to move the spindle to reduce the error, and a minicom-puter using a FORTRAN program for the feedback controller. The spindlerunout before correction is in the 2.5 µm (100 Ain.) range; with the errorcorrection system in place, this error is reduced to less than 0.25 µm (10gin.)-an order of magnitude improvement. While the corrected runoutfigures for this spindle are still above those of a precision air -bearingspindle, the technique presents new possibilities for precision spindleperformance including correction for wear, thermal deformations, andunbalanced loads.

Subject terms: optical fabrication; spindle; real -time error correction; precisionfeedback control.Optical Engineering 24(5), 888 -892 (September /October 1985).

1. INTRODUCTIONThe machining of optical components requires precise control ofthe position of the cutting tool with respect to the workpiece. Onemethod of producing such precision parts is single -point diamondturning, in which a stationary diamond tool is used to machine aworkpiece mounted on a rotating spindle. Clearly, the precision ofsuch a diamond turning machine is limited by the performance ofits spindle. Unless compensated for, any errors in the perfection ofthe spindle will be reflected in the cut made by the tool on theworkpiece. Spindle rotation errors can originate from thermaldeformation of the spindle components, imperfections in thespindle support bearings, wear, and imperfections in the squarenessand flatness of the spindle face." In a given sensitive direction,these errors combine to make up the runout of the spindle. Spindlerunout is defined as the total indicator reading between a fixed

Paper 2048 received July 30, 1984; revised manuscript received Jan. 7, 1985; acceptedfor publication Feb. 13, 1985; received by Managing Editor Feb. 22, 1985. This paperis a revision of Paper 508 -17 which was presented at the SPIE conference on Produc-tion Aspects of Single Point Machined Optics, Aug. 23 -24, 1984, San Diego, Calif.The paper presented there appears (unrefereed) in SPIE Proceedings Vol. 508.©1985 Society of Photo -Optical Instrumentation Engineers.

888 / OPTICAL ENGINEERING / September /October 1985 / Vol. 24 No. 5

displacement sensor and a surface of the rotating spindle. It con-sists of the previously mentioned spindle errors combined with anydeformations in the structural loop linking the sensor to thespindle.3

To provide a reference in measuring the radial runout of aspindle axis, a master ball is centered above the axis. Radial runoutis measured with a probe aligned perpendicularly to the spindle axis(Fig. 1), and it arises from five classes of errors: (1) errors in center-ing the master ball above the spindle axis, (2) errors in the sphericityof the master ball, (3) thermal and mechanical deformations of thestructural loop, (4) tilt error motion of the spindle, and (5) radialerror motion of the spindle.

In the past, the tactic most widely used in obtaining anultraprecision spindle has been to carefully construct the spindlefrom precisely machined parts and to use hydrostatic fluid bearingsto support the spindle axis.

The purpose of this paper is to present an alternative method ofobtaining an ultraprecision spindle, by means of closed -loop con-trol of the spindle's radial runout. The aim is to demonstrate thatthe runout of a ball bearing spindle can be controlled by the use ofreal -time feedback to piezoelectric transducers that will move thespindle axis as it rotates, resulting in a substantial decrease in theradial runout.

The concept of a corrected spindle is that a blend of standardmachining practices and digital feedback control can be used toachieve a level of spindle performance that is presently availableonly through ultraprecision machining coupled with hydrostaticbearings. The potential of a feedback -controlled spindle exceedseven that of an ultraprecise uncontrolled spindle in that the feed-

Real time control of spindle runout

T. G. Bifano T. A. DowNorth Carolina State University Department of Mechanical

and Aerospace Engineering Precision Engineering Laboratory Raleigh, North Carolina 27695-7910

Abstract. An example of a physical system whose mechanical accuracy can be improved by feedback control is a motor-driven spindle. Such a system is being used as a test-bed to study measurement and actuation systems as well as control algorithms. The specific apparatus reported utilizes an eddy-current probe for runout error measurement, a piezoelectric crystal to move the spindle to reduce the error, and a minicomputer using a FORTRAN program for the feedback controller. The spindle runout before correction is in the 2.5 /*m (100 /iin.) range; with the error correction system in place, this error is reduced to less than 0.25 /*m (10 ^in.) an order of magnitude improvement. While the corrected runout figures for this spindle are still above those of a precision air-bearing spindle, the technique presents new possibilities for precision spindle performance including correction for wear, thermal deformations, and unbalanced loads.

Subject terms: optical fabrication; spindle; real-time error correction; precision feedback control.Optical Engineering 24(5), 888-892 (September/October 1985).

CONTENTS1. Introduction2. Spindle and control system design

2.1. Control algorithm2.2. Results and discussion

3. Acknowledgment 5. References

1. INTRODUCTIONThe machining of optical components requires precise control of the position of the cutting tool with respect to the workpiece. One method of producing such precision parts is single-point diamond turning, in which a stationary diamond tool is used to machine a workpiece mounted on a rotating spindle. Clearly, the precision of such a diamond turning machine is limited by the performance of its spindle. Unless compensated for, any errors in the perfection of the spindle will be reflected in the cut made by the tool on the workpiece. Spindle rotation errors can originate from thermal deformation of the spindle components, imperfections in the spindle support bearings, wear, and imperfections in the squareness and flatness of the spindle face. 1 "4 In a given sensitive direction, these errors combine to make up the runout of the spindle. Spindle runout is defined as the total indicator reading between a fixed

Paper 2048 received July 30, 1984; revised manuscript received Jan. 7, 1985; accepted for publication Feb. 13, 1985; received by Managing Editor Feb. 22, 1985. This paper is a revision of Paper 508-17 which was presented at the SPIE conference on Produc- tion Aspects of Single Point Machined Optics, Aug. 23-24, 1984, San Diego, Calif. The paper presented there appears (unrefereed) in SPIE Proceedings Vol. 508. ©1985 Society of Photo-Optical Instrumentation Engineers.

displacement sensor and a surface of the rotating spindle. It consists of the previously mentioned spindle errors combined with any deformations in the structural loop linking the sensor to the spindle. 3

To provide a reference in measuring the radial runout of a spindle axis, a master ball is centered above the axis. Radial runout is measured with a probe aligned perpendicularly to the spindle axis (Fig. 1), and it arises from five classes of errors: (1) errors in centering the master ball above the spindle axis, (2) errors in the sphericity of the master ball, (3) thermal and mechanical deformations of the structural loop, (4) tilt error motion of the spindle, and (5) radial error motion of the spindle.

In the past, the tactic most widely used in obtaining an ultraprecision spindle has been to carefully construct the spindle from precisely machined parts and to use hydrostatic fluid bearings to support the spindle axis.

The purpose of this paper is to present an alternative method of obtaining an ultraprecision spindle, by means of closed-loop control of the spindle's radial runout. The aim is to demonstrate that the runout of a ball bearing spindle can be controlled by the use of real-time feedback to piezoelectric transducers that will move the spindle axis as it rotates, resulting in a substantial decrease in the radial runout.

The concept of a corrected spindle is that a blend of standard machining practices and digital feedback control can be used to achieve a level of spindle performance that is presently available only through ultraprecision machining coupled with hydrostatic bearings. The potential of a feedback-controlled spindle exceeds even that of an ultraprecise uncontrolled spindle in that the feed-

888 / OPTICAL ENGINEERING / September/October 1985 / Vol. 24 No. 5

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REAL TIME CONTROL OF SPINDLE RUNOUT

EDDY CURRENT PROBE

RADIALRUNOUT

MASTER BALL

UPPER BEARING SET

LOWER BEARING SET

Fig. 1. Radial runout of a spindle measured with a master ball reference.

back loop provides the unique ability to compensate for changes inspindle loading, vibration, and thermal deformations.

Although the feedback -controlled ball bearing spindle discussedis designed to rival the performance of an air- bearing spindle, thetwo approaches are not mutually exclusive. Ultimately, combiningfeedback control with an ultraprecision spindle and appropriatetransducer- detector systems could result in a substantial increase inthe state of the art of spindle performance.

2. SPINDLE AND CONTROL SYSTEM DESIGNAt the heart of the apparatus is a pair of ABEC 9, 12 mm boreduplex ball bearings mounted on a steel shaft (Fig. 2). The bearingsare press fit into a steel housing that is attached by eight cantileversprings to the spindle support housing. The spindle support hous-ing in turn is rigidly connected to a vibration -isolated table. Thecantilevers are designed to allow motion in one horizontal directionx and in the vertical direction z but are extremely stiff in a perpen-dicular horizontal direction y. Three piezoelectric transducers aremounted in the spindle support housing. In response to changes ininput voltage, these PZTs expand or contract, providing a propor-tional force to move the bearing housing against the restoring forceof the cantilever springs. Two PZTs are mounted horizontally inthe least stiff direction x of the bearing housing at the upper andlower bearing centers. The third PZT is mounted vertically beneaththe center of the spindle axis z and provides the potential for axialerror motion control of the spindle. For the data presented in thispaper, runout correction is accomplished using only the upperhorizontal PZT. This is the simplest configuration thatdemonstrates the correction technique.

A 100 mm (4 in.) diameter by 25 mm (1 in.) thick aluminum plateis mounted on the tapered end of the spindle shaft and forms thespindle face. The plate and shaft are rotated by means of a dc ser-vomotor and a belt. A 500 pulse /revolution incremental encoder,also belt driven, is used in conjunction with a once -per -revolutionmagnetic pickup to trigger data collection. On top of the spindleface is the 37 mm (1.5 in.) diameter master ball that rests on a three -point support. The support rests on the spindle face and can betapped lightly to center the master ball over the spindle axis.

A noncontacting eddy -current probe is mounted horizontally inthe spindle's x- direction and faces the equator of the ball. Theprobe is capable of resolving microinch changes in the position ofthe master ball. It is mounted in a support frame that is bolted tothe spindle support housing. The structural loop linking the probeto the spindle consists of the probe support and the spindle supporthousing. Any deformations in this structural loop will contribute tothe measured spindle runout.

A schematic of the runout signal path used for feedback controlis shown in Fig. 3. The eddy -current probe detects radial runoutand outputs a voltage proportional to the gap between the probeface and the master ball. Since the probe is noncontacting, its out-put is always offset at some dc level proportional to the initial gap

Fig. 2. Experimental spindle apparatus.

EDDYCURRENT

PROBE

SIGNAL CONDITIONER

PREAMPUFlER

A DCONVERTER

PIEZOELECTRIC

TRANSDUCER

E

DIGITALCONTROL

AU:KAT HM

I PIT AMPUFlER

OACONVERTER

Fig. 3. Schematic of feedback signal path.

OPTICAL ENGINEERING / September /October 1985 / Vol. 24 No. 5 / 889


EDDY CURRENT PROBE MASTER BAIL

Fig. 1. Radial runout of a spindle measured with a master bail reference.

back loop provides the unique ability to compensate for changes inspindle loading, vibration, and thermal deformations.

Although the feedback-controlled ball bearing spindle discussed is designed to rival the performance of an air-bearing spindle, the two approaches are not mutually exclusive. Ultimately, combining feedback control with an ultraprecision spindle and appropriatetransducer-detector systems could result in a substantial increase in the state of the art of spindle performance.

2. SPINDLE AND CONTROL SYSTEM DESIGNAt the heart of the apparatus is a pair of ABEC 9,, 12 rnni bore duplex ball bearings mounted on a steel shaft (Fig. 2). The bearings are press fit into a steel housing that is attached by eight cantilever springs to the spindle support housing. The spindle support housing in turn is rigidly connected to a vibration-isolated table. The cantilevers are designed to allow motion in one horizontal direction x and in the vertical direction z but are extremely stiff in a perpen- dicular horizontal direction y. Three piezoelectric transducers are mounted in the spindle support housing. In response to changes in input voltage, these PZTs expand or contract, providing a proportional force to move the bearing housing against the restoring force of the cantilever springs. Two PZTs are mounted horizontally in the least stiff direction x of the bearing housing at the upper and lower bearing centers. The third PZT is mounted vertically beneath the center of the spindle axis z and provides the potential for axial error motion control of the spindle. For the data presented in this paper, runout correction is accomplished using only the upper horizontal PZT. This is the simplest configuration that demonstrates the correction technique.

A 100 mm (4 in.) diameter by 25 mm (1 in.) thick aluminum plate is mounted on the tapered end of the spindle shaft and forms the spindle face. The plate and shaft are rotated by means of a dc ser- vomotor and a belt. A 500 pulse/revolution incremental encoder, also belt driven, is used in conjunction with a once-per-revolution magnetic pickup to trigger data collection. On top of the spindle face is the 37 mm (1.5 in.) diameter master ball that rests on a three- point support. The support rests on the spindle face and can be tapped lightly to center the master ball over the spindle axis.

A noncontacting eddy-current probe is mounted horizontally in the spindle's x-direction and faces the equator of the ball. The probe is capable of resolving microinch changes in the position of the master ball. It is mounted in a support frame that is bolted to the spindle support housing. The structural loop linking the probe to the spindle consists of the probe support and the spindle support housing. Any deformations in this structural loop will contribute to the measured spindle runout.

A schematic of the runout signal path used for feedback control is shown in Fig. 3. The eddy-current probe detects radial runout and outputs a voltage proportional to the gap between the probe face and the master ball. Since the probe is noncontacting, its output is always offset at some dc level proportional to the initial gap

Fig. 2. Experimental spindle apparatus.

Fig. 3. Schematic of feedback signal path.

OPTICAL ENGINEERING / September/October 1985 / Vol. 24 No. 5 / 889


BIFANO, DOW

width. This dc level is subtracted by manually adjusting a signalconditioning operational amplifier circuit until the signal's dc levelis nearly zero. The signal is then amplified and input to theminicomputer that contains the real -time control software.

The output of the control algorithm is transferred from a D/Aport on the computer to the PZT amplifier, which provides a driv-ing voltage for the piezoelectric actuator adjacent to the spindle'supper bearing set. The net effect of this integrated system is to in-crementally tilt the spindle in opposition to any radial runout so asto eliminate that runout.

2.1. Control algorithmThe control algorithm is a discrete form of integral feedback con-trol. In a continuous system, integral feedback control is governedby the following formula:

KEdT=G, (1)

where K is the gain, E is the error signal, T is the time, and G is theoutput signal. In this particular case, E represents the runout signaland G represents the feedback signal sent to the PZT. While T isequal to time, it can be converted into an equivalent angular spindledisplacement if the spindle rotational speed is known.

Differentiating Eq. (1), we obtain

ICE = dGdT

To bring this equation into discrete form,

AG Gt - Gt -ATKEtAT AT

Rearranging,

(KOT)Et + Gt_oT = Gt .

Replacing KOT with an equivalent gain K' yields

K' Et + Gt-oT = Gt ,

(2)

(3)

(4)

(5)

which is exactly the computational algorithm used by the feedbackcontrol software.

This FORTRAN program beings by obtaining a digital runoutsample E from a 12 bit successive approximation A/D converter.The sample is multiplied by an appropriate scaling factor thatdepends on both the gain K and the sampling rate AT [see Eq. (4)].This scaled error is added to the previous output value Gt_oT, andthe resulting sum Gt is sent out through a digital -to- analog port tothe PZT amplifier.

The integral control algorithm described by Eqs. (1) through (5)is intentionally straightforward and concise. It will serve to demon-strate the dramatic potential for real -time ultraprecision control us-ing no more than a rudimentary algorithm coupled with a conven-tional ball bearing spindle.

2.2. Results and discussionThe master ball to be used as a reference can be centered by tappingits support base lightly while following a trace of the runout on anoscilloscope and manually rotating the spindle. Using this simpletechnique, the runout can be reduced to a level of less than 2.5 µm(100 gin.) peak -to -peak.

With a perfect axis of spindle rotation and a perfectly sphericalmaster ball, the radial runout measured against an off -center ballwould be (in rectilinear coordinates of runout versus rotation


angle) a sinusoidal wave having an amplitude equal to themagnitude of the centering error and a period of one spindlerevolution. In polar coordinates, the runout would appear as acircle with a center displaced from the polar chart center by themagnitude of the centering error. Although it is common to at-tempt to separate radial spindle axis error motion (i.e., tilt errormotion and radial error motion) from centering errors in evaluatinga spindle's performance, the two are generally impossible to de-couple; a once -per -revolution runout component can occur in-distinguishably from either.

Clearly, ball centering errors are unrelated to spindle perfor-mance; they represent a type of systematic measurement error. Tointerpret the runout signal measured against a master ball, theassumption is usually made that the spindle itself has no once -per-revolution runout component. Using this assumption, spindle errorcan be measured from a statistically or geometrically derived centerbased on the entire record of runout data.

This postprocessing of the runout data to eliminate centering er-rors poses a problem for real -time feedback control, in which thespindle's center of rotation must be predefined as a reference forcorrection purposes. Thus, the control algorithm does not permitthe use of an averaged center of rotation, and runout measure-ments are not compensated for ball centering errors. One solutionto this problem is to first roughly center the ball, then use the ver-tical axis of the ball as the assumed center of the spindle rotation.In this way, the ball is assumed to be perfectly centered, and allradial runout is contributed to either spindle error motion, masterball out -of- roundness, or deformations in the structural loop. Ineffect, this creates a predefined spindle axis free from ball centeringerrors. All efforts to evaluate or control the spindle runout aremade against this newly defined spindle axis.

Correction is based upon the distance between the stationary eddy -current probe and the rotating master ball; consequently, any out -of-roundness of the ball or thermal expansions in the structural loopbetween the ball and the probe will not be compensated for by thecontrol algorithm. In effect, the control loop forces the spindle tofollow a rotational profile equivalent to the profile of the master ball.The master ball used on this spindle is a Grade 5 tungsten carbideball, conforming to a tolerance of ±0.1 µm ( + 5 gin.) sphericity.

As mentioned previously, deformations in the structural loop arenot diminished by the control algorithm. To reduce these errors, theentire apparatus is mounted on a vibration -isolated table located in atemperature -controlled clean room ( ±0.1 °C). Under these condi-tions, static drift of the displacement sensor with respect to themaster ball is reduced to less than 10 gin. over a period of 12 h.

The remaining radial runout consists primarily of spindle errormotion due to tilt and radial error motions. Polar coordinate plotsare a standardized method of representing this type of spindle errormotion. The important parameters of such a plot of error motionarea (1) polar chart center (PC), the center of the polar chart; (2)minimum radial separation center (MRS), the center that minimizesthe radial difference between two concentric circles that contain theerror motion polar plot; and (3) total error motion value (TEMV),the scaled difference in radii of two concentric circles from the er-ror motion center (either PC or MRS) just sufficient to contain theerror motion plot.

The MRS center is used as a standard for calculations of radialand tilt error motions. It is used instead of the PC center in an ef-fort to minimize master ball centering errors. As described pre-viously, the master ball on this spindle defines the spindle axis. Alltotal error motion values therefore will be computed with respect tothe polar chart center. The plot of the perfect spindle rotation,then, would be a circle centered upon the origin of the polar plot.

Figure 4 shows an oscilloscope trace of runout versus angularspindle position for approximately five revolutions of the spindle(time duration = 20 s). The peak -to -peak runout in this case cor-responds to 2.5 µm (100 gin.) of spindle error motion in the radialdirection. The same data are presented in polar coordinates in Fig.5. Note that the presence of a significant once -per -revolution com-

BIFANO, DOW

width. This dc level is subtracted by manually adjusting a signal conditioning operational amplifier circuit until the signal's dc level is nearly zero. The signal is then amplified and input to the minicomputer that contains the real-time control software.

The output of the control algorithm is transferred from a D/A port on the computer to the PZT amplifier, which provides a driv- ing voltage for the piezoelectric actuator adjacent to the spindle's upper bearing set. The net effect of this integrated system is to in- crementally tilt the spindle in opposition to any radial runout so as to eliminate that runout.

2.1. Control algorithmThe control algorithm is a discrete form of integral feedback control. In a continuous system, integral feedback control is governed by the following formula:

K ( EdT = G, (1)

where K is the gain, E is the error signal, T is the time, and G is the output signal. In this particular case, E represents the runout signal and G represents the feedback signal sent to the PZT. While T is equal to time, it can be converted into an equivalent angular spindle displacement if the spindle rotational speed is known.

Differentiating Eq. (1), we obtain

KE = dG dT

(2)

To bring this equation into discrete form,

AGKEt =Gt - Gt-AT

AT AT

Rearranging,

(KAT)Et + Gt_AT = Gt .

Replacing KAT with an equivalent gain K' yieldsK'E = Gt ,

(3)

(4)

(5)

which is exactly the computational algorithm used by the feedback control software.

This FORTRAN program beings by obtaining a digital runout sample E from a 12 bit successive approximation A/D converter. The sample is multiplied by an appropriate scaling factor that depends on both the gain K and the sampling rate AT [see Eq. (4)]. This scaled error is added to the previous output value Gt_AT , and the resulting sum Gt is sent out through a digital-to-analog port to the PZT amplifier.

The integral control algorithm described by Eqs. (1) through (5) is intentionally straightforward and concise. It will serve to demonstrate the dramatic potential for real-time ultraprecision control using no more than a rudimentary algorithm coupled with a conven- tional ball bearing spindle.

2.2. Results and discussionThe master ball to be used as a reference can be centered by tapping its support base lightly while following a trace of the runout on an oscilloscope and manually rotating the spindle. Using this simple technique, the runout can be reduced to a level of less than 2.5 /*m (100 /an.) peak-to-peak.

With a perfect axis of spindle rotation and a perfectly spherical master ball, the radial runout measured against an off-center ball would be (in rectilinear coordinates of runout versus rotation

angle) a sinusoidal wave having an amplitude equal to the magnitude of the centering error and a period of one spindle revolution. In polar coordinates, the runout would appear as a circle with a center displaced from the polar chart center by the magnitude of the centering error. Although it is common to at- tempt to separate radial spindle axis error motion (i.e., tilt error motion and radial error motion) from centering errors in evaluating a spindle's performance, the two are generally impossible to de- couple; a once-per-revolution runout component can occur in- distinguishably from either.

Clearly, ball centering errors are unrelated to spindle performance; they represent a type of systematic measurement error. To interpret the runout signal measured against a master ball, the assumption is usually made that the spindle itself has no once-per- revolution runout component. Using this assumption, spindle error can be measured from a statistically or geometrically derived center based on the entire record of runout data.

This postprocessing of the runout data to eliminate centering errors poses a problem for real-time feedback control, in which the spindle's center of rotation must be predefined as a reference for correction purposes. Thus, the control algorithm does not permit the use of an averaged center of rotation, and runout measure- ments are not compensated for ball centering errors. One solution to this problem is to first roughly center the ball, then use the vertical axis of the ball as the assumed center of the spindle rotation. In this way, the ball is assumed to be perfectly centered, and all radial runout is contributed to either spindle error motion, master ball out-of-roundness, or deformations in the structural loop. In effect, this creates a predefined spindle axis free from ball centering errors. All efforts to evaluate or control the spindle runout are made against this newly defined spindle axis.

Correction is based upon the distance between the stationary eddy- current probe and the rotating master ball; consequently, any out-of- roundness of the ball or thermal expansions in the structural loop between the ball and the probe will not be compensated for by the control algorithm. In effect, the control loop forces the spindle to follow a rotational profile equivalent to the profile of the master ball. The master ball used on this spindle is a Grade 5 tungsten carbide ball, conforming to a tolerance of ±0.1 /im (-1-5 /tin.) sphericity.

As mentioned previously, deformations in the structural loop are not diminished by the control algorithm. To reduce these errors, the entire apparatus is mounted on a vibration-isolated table located in a temperature-controlled clean room (±0.1 °C). Under these condi- tions, static drift of the displacement sensor with respect to the master ball is reduced to less than 10 /iin. over a period of 12 h.

The remaining radial runout consists primarily of spindle error motion due to tilt and radial error motions. Polar coordinate plots are a standardized method of representing this type of spindle error motion. The important parameters of such a plot of error motion are3 (1) polar chart center (PC), the center of the polar chart; (2) minimum radial separation center (MRS), the center that minimizes the radial difference between two concentric circles that contain the error motion polar plot; and (3) total error motion value (TEMV), the scaled difference in radii of two concentric circles from the error motion center (either PC or MRS) just sufficient to contain the error motion plot.

The MRS center is used as a standard for calculations of radial and tilt error motions. It is used instead of the PC center in an ef- fort to minimize master ball centering errors. As described previously, the master ball on this spindle defines the spindle axis. All total error motion values therefore will be computed with respect to the polar chart center. The plot of the perfect spindle rotation, then, would be a circle centered upon the origin of the polar plot.

Figure 4 shows an oscilloscope trace of runout versus angular spindle position for approximately five revolutions of the spindle (time duration = 20 s). The peak-to-peak runout in this case cor- responds to 2.5 /mi (100 /tin.) of spindle error motion in the radial direction. The same data are presented in polar coordinates in Fig. 5. Note that the presence of a significant once-per-revolution com-




Fig. 4. Uncorrected radial runout versus angular spindle position for liverevolutions. Vertical scale = 1.3 µm (55 gin.) I division; horizontal scale =180° rotation I division.

Fig. 5. Uncorrected radial runout versus angular spindle position for fiverevolutions. TEMV = 2.5 µm (102 µln.).

ponent in the rectilinear plot of Fig. 4 appears as a center offset inthe polar plot. Using the PC center, a total error motion value is 2.5

(102 /tin.).It is important to note that this TEMV is based on a spindle

center of rotation that is defined along the axis of the master ball.A TEMV based on an average center for the runout data would besomewhat less than 2.5 µm and is more indicative of the spindle'sactual uncontrolled performance. The 2.5 µm TEMV, however, isthe magnitude of the error that must be corrected and is therefore amore relevant representation of the runout data in this case.

Figure 6 shows an oscilloscope trace of the radial runout duringthe transition from uncontrolled to controlled spindle motion,illustrating a dramatic decrease in the spindle's total radial errormotion. A rectilinear trace of the controlled spindle runout overapproximately five revolutions is shown in Fig. 7, while Fig. 8shows the polar plot of the same data. It is easy to see from theseplots that the effect of the control algorithm is to center the rota-tion of the spindle around the ball axis and to reduce the higherorder fluctuations of the centered spindle motion. The resultingtotal error motion value is approximately 0.25 µm (10 gin.),representing an order of magnitude improvement in the radialrunout.

I t

Fig. 8. Transition from uncontrolled spindle runout to controlled spindlerunout. Vertical scale = 1.3 µm (55 µIn.) I division; horizontal scale = 180°rotation I division.

OPW A V2R 190,41) SS

e WFM 1;e,3_11Fig. 7. Corrected radial runout versus angular spindle position for five revolu-tions. Vertical scale = 1.3µm (55 in.)/ division; horizontal scale = 180° rota-tion I division.

Fig. 8. Corrected radial runout versus angular spindle position. TEMV = 0.25µm (10 gin.).

OPTICAL ENGINEERING / September /October 1985 / Vol. 24 No. 5 / 891


OPM e VZR e OPM 8 UZR 8

V

8 UFM 194.1* /Fig. 4. Uncorrected radial runout versus angular spindle position for five revolutions. Vertical scale = 1.3 ^m (55 jtin.) / division; horizontal scale = 180° rotation / division.

MflH STOREDFig. 6. Transition from uncontrolled spindle runout to controlled spindle runout. Vertical scale = 1.3 ^m (55 /tin.) / division; horizontal scale = 180° rotation / division.

124

15*.

180.

33*.

24*. 27*. 3**.

Fig. 5. Uncorrected radial runout versus angular spindle position for five revolutions. TEMV = 2.5 Mm (102 /tin.).

ponent in the rectilinear plot of Fig. 4 appears as a center offset in the polar plot. Using the PC center, a total error motion value is 2.5 /on (102 fiin.).

It is important to note that this TEMV is based on a spindle center of rotation that is defined along the axis of the master ball. A TEMV based on an average center for the runout data would be somewhat less than 2.5 jim and is more indicative of the spindle's actual uncontrolled performance. The 2.5 /an TEMV, however, is the magnitude of the error that must be corrected and is therefore a more relevant representation of the runout data in this case.

Figure 6 shows an oscilloscope trace of the radial runout during the transition from uncontrolled to controlled spindle motion, illustrating a dramatic decrease in the spindle's total radial error motion. A rectilinear trace of the controlled spindle runout over approximately five revolutions is shown in Fig. 7, while Fig. 8 shows the polar plot of the same data. It is easy to see from these plots that the effect of the control algorithm is to center the rotation of the spindle around the ball axis and to reduce the higher order fluctuations of the centered spindle motion. The resulting total error motion value is approximately 0.25 jun (10 /*in.), representing an order of magnitude improvement in the radial runout.

Fig. 7. Corrected radial runout versus angular spindle position for five revolutions. Vertical scale = 1.3/tin (55/Jn.)/division; horizontal scale = 180° rotation / division.

12*.

15*.

18*.

33*.

3**.

Fig. 8. Corrected radial runout versus angular spindle position. TEMV = 0.25 urn (10 n\n.).

OPTICAL ENGINEERING / September/October 1985 / Vol. 24 No. 5 / 891


BIFANO, DOW

Although the corrected spindle's total error motion valuerepresents a substantial increase in the spindle performance, by nomeans has a minimum runout limit been reached for this system.Planned improvements promise to extend capabilities of thisspindle in a variety of respects. To permit the spindle to operate athigher rotational speeds, an assembly language control loop will beimplemented, increasing the A/D sampling rate and decreasing thedeleterious effects of phase lag between error input and feedbackoutput. In addition, the horizontal piezoelectric transducer locatedat the spindle's lower bearing set will be incorporated into the con-trol scheme, allowing more complete control over radial and tilt er-ror motions. To include this transducer, a more complex controlalgorithm will be utilized, including compensation for instan-taneous error velocity.

After the radial runout for this spindle has been optimized, thenext step involves simultaneously controlling both radial and axialrunout.

Clearly, the potential for reducing spindle error motion throughfeedback control is substantial. An order of magnitude decrease in

radial runout can be accomplished with a single detector -forcetransducer pair, controlled by a simple integral control algorithm.Refinements of this technique, including two- and even three -axiscontrol, are possible, promising new possibilities for the state of theart of ultraprecision spindle performance.

3. ACKNOWLEDGMENTThe research program that resulted in the development of the feed-back system described is part of a Selected Research Opportunity inPrecision Engineering funded by the Office of Naval Research,Contract No. N00014 -83 -K -0064.

4. REFERENCES1. J. Bryan, R. Clouser, and E. Holland, American Machinist Special

Report No. 612, 149 (Dec. 4, 1967).2. Robert Donaldson, American Machinist, 57 (Jan. 8, 1973).3. American National Standards Institute, Ann. CIRP 25(2), 545 (1976).4. John M. Casstevens, Oak Ridge Y -12 Plant Document Y /DA -7751

(1978).


BIFANO, DOW

Although the corrected spindle's total error motion value represents a substantial increase in the spindle performance, by no means has a minimum runout limit been reached for this system. Planned improvements promise to extend capabilities of this spindle in a variety of respects. To permit the spindle to operate at higher rotational speeds, an assembly language control loop will be implemented, increasing the A/D sampling rate and decreasing the deleterious effects of phase lag between error input and feedback output. In addition, the horizontal piezoelectric transducer located at the spindle's lower bearing set will be incorporated into the control scheme, allowing more complete control over radial and tilt error motions. To include this transducer, a more complex control algorithm will be utilized, including compensation for instan- taneous error velocity.

After the radial runout for this spindle has been optimized, the next step involves simultaneously controlling both radial and axial runout.

Clearly, the potential for reducing spindle error motion through feedback control is substantial. An order of magnitude decrease in

radial runout can be accomplished with a single detector-force transducer pair, controlled by a simple integral control algorithm. Refinements of this technique, including two- and even three-axis control, are possible, promising new possibilities for the state of the art of ultraprecision spindle performance.

3. ACKNOWLEDGMENTThe research program that resulted in the development of the feedback system described is part of a Selected Research Opportunity in Precision Engineering funded by the Office of Naval Research, Contract No. N00014-83-K-0064.

4. REFERENCES1. J. Bryan, R. Clouser, and E. Holland, American Machinist Special

Report No. 612, 149 (Dec. 4, 1967).2. Robert Donaldson, American Machinist, 57 (Jan. 8, 1973).3. American National Standards Institute, Ann. CIRP 25(2), 545 (1976).4. John M. Casstevens, Oak Ridge Y-12 Plant Document Y/DA-7751

(1978). s



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