Real
Real time
time control
control of spindle runout
T.
T. G.
G. Bifano
T.
T. A.
A. Dow
North Carolina
North
Carolina State University
Department
Department of Mechanical
and Aerospace
Aerospace Engineering
and
Engineering Laboratory
Precision Engineering
Precision
27695-7910
Carolina27695
North Carolina
Raleigh, North
-7910
example of a physical system whose mechanical accuracy
Abstract. An example
Such aa
spindle. Such
motor-driven
control isisaamotor
improved by feedback control
can
can be improved
-driven spindle.
test-bed
used as a test
being used
system is being
-bed to
to study
study measurement
measurement and
and actuation
reported
apparatus reported
specific apparatus
The specific
algorithms. The
systems
systems as
as well
well as control algorithms.
piezomeasurement, aa piezoerror measurement,
runout error
utilizes an
current probe
probe for runout
eddy-current
an eddyminicomand aa minicomerror, and
the error,
reduce the
to reduce
spindle to
the spindle
move the
to move
electric crystal to
The spindle
program for
for the feedback controller.
controller. The
FORTRAN program
puter using a FORTRAN
error
the error
range; with the
/iin.) range;
(100 Ain.)
/*m(100
2.5µm
the2.5
correction isis ininthe
runout before correction
(10
/*m (10
0.25µm
than0.25
lessthan
reducedtotoless
errorisisreduced
thiserror
place, this
in place,
system in
correction system
runout
corrected runout
gin.)-an
the corrected
While the
improvement. While
magnitude improvement.
ofmagnitude
order of
an order
^in.)
air-bearing
precisionair
thoseofofaaprecision
above those
stillabove
are still
spindle are
this spindle
figures
figures for this
-bearing
spindle
precision spindle
for precision
new possibilities for
presents new
technique presents
spindle,
the technique
spindle, the
and
deformations, and
thermal deformations,
wear, thermal
for wear,
performance including
performance
including correction for
loads.
unbalanced loads.
real-time
spindle; real
fabrication; spindle;
terms: optical fabrication;
Subject terms:
Subject
-time error correction; precision
precision
feedback control.
1985).
(September/October
888-892
24(5), 888
Engineering 24(5),
Optical Engineering
Optical
-892 (September
/October 1985).
CONTENTS
1.
1. Introduction
design
system design
control system
and control
Spindle and
2. Spindle
algorithm
Control algorithm
2.1.
2.1. Control
discussion
Results and discussion
2.2.
2.2. Results
Acknowledgment
3. Acknowledgment
References
5.
5. References
1.
1. INTRODUCTION
The
The machining
machining of
of optical
optical components
components requires
requires precise
precise control
control of
workpiece. One
the
the position
position of the cutting tool with respect to the workpiece.
diamond
single-point
partsisissingle
precision parts
such precision
producing such
method of
-point diamond
of producing
machine a
used to machine
which aa stationary
turning, in which
turning,
stationary diamond
diamond tool is used
Clearly, the precision
workpiece mounted
workpiece
mounted on
on aa rotating spindle. Clearly,
precision of
such
such aa diamond
diamond turning
turning machine
machine is
is limited
limited by
by the
the performance
performance of
of
its spindle.
spindle. Unless
Unless compensated
compensated for,
for, any errors in the perfection of
the
the spindle
spindle will
willbe
be reflected
reflectedininthe
the cut
cut made
made by
by the
the tool on the
the
thermal
originate from thermal
workpiece.
workpiece.Spindle
Spindlerotation
rotation errors
errors can
can originate
imperfections in
components, imperfections
spindle components,
deformation
deformation of
of the spindle
in the
squareness
the squareness
in the
imperfections in
and imperfections
spindle support
support bearings, wear, and
spindle
direction,
sensitive direction,
givensensitive
1 "4InIna agiven
flatness of
and flatness
of the
the spindle
spindle face.
face."
Spindle
these errors
these
errors combine
combine to
to make
make up
up the
the runout
runout of the spindle. Spindle
fixed
between aa fixed
reading between
indicator reading
total indicator
defined as the total
runout
runout is defined
1985; accepted
1984; revised
Paper 2048
received July
July 30,
30, 1984;
revisedmanuscript
manuscript received
received Jan.
Jan. 7,
7, 1985;
accepted
2048 received
paper
This paper
1985. This
22, 1985.
Feb. 22,
received by Managing Editor Feb.
1985; received
13, 1985;
Feb. 13,
for publication Feb.
Produc508-17
revision of Paper 508
is a revision
is
-17which
whichwas
waspresented
presentedatat the
the SPIE conference on ProducCalif.
Diego, Calif.
1984, San Diego,
23-24,
Aug. 23
Optics, Aug.
Machined Optics,
Single Point Machined
Aspects of Single
tion Aspects
-24, 1984,
508.
Vol. 508.
Proceedings Vol.
(unrefereed) in
The paper presented
there appears (unrefereed)
in SPIE Proceedings
presented there
The
©1985
©1985 Society
Societyof
of Photo-Optical
Photo -Optical Instrumentation
Instrumentation Engineers.
Engineers.
spindle. It condisplacement
displacement sensor
sensorand
and aa surface
surface of the rotating spindle.
any
with any
combined with
errors combined
spindle errors
sists of the previously mentioned spindle
sists
the
sensor to the
the sensor
linking the
loop linking
structural loop
deformations inin the
deformations
the structural
spindle. 3
spindle.3
To
the radial
radial runout
runout of
of a
measuring the
in measuring
reference in
provide a reference
To provide
runout
Radial runout
spindle axis,
axis, a master ball is centered above the axis. Radial
axis
spindle axis
thespindle
tothe
perpendicularly to
is measured with a probe aligned perpendicularly
classes of errors: (1) errors in center1), and it arises from five classes
(Fig. 1),
(Fig.
sphericity
the sphericity
in the
errors in
(2) errors
axis, (2)
spindle axis,
the spindle
ing the master ball above the
of the master ball, (3) thermal and mechanical deformations of the
radial
(5) radial
and (5)
spindle, and
the spindle,
of the
motion of
structural loop, (4) tilt error motion
structural
spindle.
the spindle.
of the
error motion of
an
obtaining an
in obtaining
used in
widely used
most widely
tactic most
the tactic
past, the
the past,
In
In the
spindle
the spindle
construct the
carefully construct
ultraprecision
spindle has
has been
been to carefully
ultraprecision spindle
bearings
fluid bearings
hydrostatic fluid
use hydrostatic
to use
from precisely machined parts and to
axis.
spindle axis.
the spindle
support the
to support
alternative method of
an alternative
present an
The purpose of this paper is to present
closed-loop
meansofofclosed
bymeans
spindle, by
ultraprecision spindle,
obtaining an ultraprecision
-loop condemonstrate that
is to demonstrate
aim is
The aim
spindle's radial runout. The
trol of the spindle's
be controlled by the use
can be
spindle can
bearing spindle
ball bearing
of aa ball
the runout of
use of
will move the
real-time
real
-timefeedback
feedback to
to piezoelectric
piezoelectric transducers
transducers that will
the
in the
decrease in
substantial decrease
in aa substantial
resulting in
spindle axis
spindle
axis as
as it rotates, resulting
radial runout.
standard
of standard
blend of
spindle is
corrected spindle
The
The concept
concept of a corrected
is that a blend
machining
machining practices
practicesand
and digital
digital feedback
feedback control
control can
can be
be used
used to
to
available
presently available
that isis presently
performance that
spindle performance
level of spindle
achieve a level
achieve
hydrostatic
with hydrostatic
coupled with
machining coupled
ultraprecision machining
through ultraprecision
only through
exceeds
spindleexceeds
feedback-controlled
potential ofofa afeedback
bearings. The potential
bearings.
-controlled spindle
feedthe feedspindle in that the
uncontrolled spindle
ultraprecise uncontrolled
an ultraprecise
even that of an
even
No. 55
24No.
Vol. 24
September/October
ENGINEERING // September
/ OPTICALENGINEERING
888 / OPTICAL
/October 1985 //Vol.
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REAL
REAL TIME
TIME CONTROL OF
OF SPINDLE
SPINDLE RUNOUT
RUNOUT
RADIAL
RUNOUT
CURRENT PROBE
EDDY
EDDY CURRENT
BAIL
MASTER
MASTER BALL
UPPER BEARING SET
LOWER BEARING SET
reference.
bail reference.
master ball
measured with aa master
Fig.
1. Radial
Radial runout of a spindle measured
Fig. 1.
changes in
provides the unique ability to compensate for changes
in
back loop provides
spindle loading,
spindle
loading, vibration,
vibration, and thermal deformations.
discussed
spindle discussed
feedback-controlled
Although the feedback
-controlled ball bearing spindle
spindle, the
air-bearing
an airof an
designed to
is designed
is
to rival
rival the performance of
bearing spindle,
combining
Ultimately, combining
exclusive. Ultimately,
mutually exclusive.
not mutually
two approaches are not
appropriate
spindle and appropriate
ultraprecision spindle
feedback control
feedback
control with
with an ultraprecision
in
increase in
substantial increase
transducerdetector systems
systems could
could result in a substantial
transducer-detector
performance.
spindle performance.
of spindle
art of
the state of the art
DESIGN
SYSTEM DESIGN
CONTROL SYSTEM
AND CONTROL
SPINDLE AND
2.
2. SPINDLE
rnni bore
12 mm
9,, 12
ABEC 9,
of ABEC
pair of
At the
the heart
heart of the apparatus is a pair
At
duplex ball
ball bearings
bearings mounted
mounted on a steel shaft (Fig. 2). The bearings
cantilever
eight cantilever
by eight
attached by
that isis attached
steel housing that
are press fit into aa steel
housspindle support housThe spindle
housing. The
spindle support housing.
springs
to the spindle
springs to
The
vibration-isolated
to aavibration
connected to
rigidly connected
ing in turn isis rigidly
-isolated table. The
cantilevers
are designed
designed to
to allow
allow motion
motion in
in one
one horizontal direction
cantilevers are
perpenand in the vertical
extremely stiff in a perpenare extremely
vertical direction z but are
xx and
dicular horizontal
horizontal direction
transducers are
piezoelectric transducers
Three piezoelectric
direction y. Three
dicular
mounted in
in the spindle
spindle support housing. In response
changes in
response to changes
mounted
voltage, these
these PZTs
PZTs expand
expand or
or contract,
contract, providing
providing aa proporproporinput voltage,
tional force to move the bearing housing against the restoring force
horizontally in
springs. Two
Two PZTs
PZTs are mounted horizontally
in
cantilever springs.
of the cantilever
the least
least stiff
stiff direction
direction xx of
of the bearing
at the upper and
housing at
bearing housing
the
beneath
lower bearing centers. The third PZT
vertically beneath
mounted vertically
PZT isis mounted
the center
center of the spindle axis
axis zz and provides
axial
provides the potential for axial
the
this
in this
error motion control of the
presented in
data presented
the data
For the
spindle. For
the spindle.
upper
paper, runout
using only
only the
the upper
accomplished using
correction is accomplished
runout correction
paper,
horizontal PZT. This is the simplest configuration that
demonstrates the
the correction technique.
demonstrates
(1 in.)
in.) thick
thick aluminum plate
100 mm (4 in.) diameter by 25 mm (1
A 100
mounted on
on the
the tapered
tapered end
end of the spindle
shaft and forms the
spindle shaft
isis mounted
spindle face.
face. The
The plate
plate and
and shaft
shaft are
are rotated by means of a dc serspindle
incremental encoder,
pulse/revolution
vomotor and a belt.
/revolution incremental
500 pulse
belt. AA 500
vomotor
once-per-revolution
withaaonce
also belt
belt driven,
driven, is used in conjunction
-per -revolution
conjunctionwith
also
spindle
the spindle
magnetic pickup
pickup to
to trigger
trigger data
data collection.
collection. On
On top of the
magnetic
three-on aa three
rests on
that rests
the 37
37 mm
mm (1.5
(1.5in.)
in.) diameter
diameter master ball that
face isis the
point support.
support. The
The support
support rests
rests on
on the spindle
face and
and can
can be
be
spindle face
point
axis.
spindle axis.
the spindle
over the
tapped lightly
to center
center the master ball over
lightly to
tapped
-current probe
probe isis mounted horizontally in
eddy-current
A noncontacting eddy
The
ball. The
the spindle's
x- directionand
andfaces
facesthe
theequator
equator of
of the
the ball.
spindle's x-direction
the
capable of resolving
microinch changes
changes in
in the position of
resolving microinch
probe is capable
master ball.
ball. It
It isis mounted
mounted in
in a support frame that is bolted to
the master
linking the probe
the spindle
support housing.
housing. The structural loop linking
spindle support
to the spindle
consists of
of the
the probe
probe support and the spindle support
spindle consists
housing. Any deformations in this structural
to
contribute to
will contribute
loop will
structural loop
the measured
spindle runout.
measured spindle
feedback control
A schematic
of the
the runout signal path used for feedback
schematic of
runout
radial runout
detects radial
eddy-current
The eddy
is shown
-current probe detects
3. The
Fig. 3.
shown in Fig.
probe
the probe
between the
and outputs aa voltage
gapbetween
thegap
to the
proportional to
voltage proportional
face and the master ball. Since
Since the probe is noncontacting, its outface
always offset
offset at
at some
some dc
dc level
levelproportional
proportional to
to the initial gap
put is always
apparatus.
spindle apparatus.
Fig.
Experimental spindle
2. Experimental
Fig. 2.
EDDY
CURRENT
PROBE
PIEZOELECTRIC
TRANSDUCER
E
I PIT AMPUFlER
SIGNAL CONDITIONER
OA
PREAMPUFlER
CONVERTER
AD
CONVERTER
DIGITAL
CONTROL
AU:KAT HM
Fig. 3.
3. Schematic of feedback
path.
signal path.
feedback signal
Fig.
889
OPTICAL
ENGINEERING
/ September /October1985
1985/ /Vol.
Vol.24
24No.
No.5 5/ / 889
/ September/October
OPTICAL ENGINEERING
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BIFANO,
BIFANO, DOW
width.
This dc level
level is
manually adjusting
adjusting aa signal
signal
width. This
is subtracted by manually
conditioning
level
conditioning operational amplifier circuit until the signal's dc level
is
nearly zero.
amplified and
input to the
the
is nearly
zero. The
The signal
signal isis then
then amplified
and input
minicomputer
the real
real-time
software.
minicomputer that contains the
-time control software.
algorithm is
The output of the control algorithm
is transferred
transferred from
from aa D/A
port on the computer to the PZT amplifier,
amplifier, which
which provides
provides a driving
spindle's
ing voltage
voltage for
for the
the piezoelectric
piezoelectricactuator
actuator adjacent
adjacent to the spindle's
bearing set.
of this
this integrated
integrated system
system is
is to ininupper bearing
set. The net effect of
crementally tilt
runout so
so as
as
crementally
tilt the
the spindle
spindle in
in opposition
opposition to any radial runout
eliminate that
to eliminate
that runout.
2.1.
Control algorithm
algorithm
2.1. Control
The control
feedback conThe
control algorithm
algorithm isis aa discrete
discrete form of integral feedback
In aa continuous
continuous system,
system, integral feedback control is
is governed
governed
trol. In
following formula:
by the following
K
( EdT = G,
KEdT=G,
(1)
(1)
where
where K
K isisthe
thegain,
gain, EE isisthe
the error
error signal,
signal, T is
is the time, and G is the
output signal.
signal. In this particular case, E represents the runout signal
signal
and G represents
represents the
While TT isis
the feedback
feedback signal
signal sent
sent to
to the PZT. While
equal to time,
time, itit can
can be
be converted
converted into
into an
an equivalent
equivalent angular
angular spindle
spindle
displacement
speed is
is known.
known.
displacement ifif the
the spindle
spindle rotational speed
Differentiating Eq.
(1), we obtain
Differentiating
Eq. (1),
dG
KE
ICE =
=
dT
(2)
To bring
bring this
this equation
equation into
into discrete
discrete form,
KEt = AG
AT
Gt --Gt
Gt-AT
Gt
-AT
AT
(3)
Rearranging,
(KAT)Et + Gt_AT
(KOT)Et
Gt_oT = Gt .
(4)
Replacing
yields
Replacing KAT
KOTwith
withan
an equivalent
equivalent gain
gain K' yields
K'E
= Gt
Gt ,,
K' Et + Gt -oT =
(5)
which
which isis exactly
exactlythe
thecomputational
computational algorithm
algorithm used
used by
by the
the feedback
feedback
control software.
This FORTRAN
digital runout
This
FORTRAN program
program beings
beings by
by obtaining
obtaining aa digital
sample EE from a 12
12 bit successive
successive approximation
sample
approximation A/D
A/D converter.
The sample
sample isis multiplied
multiplied by
appropriate scaling
scaling factor that
that
The
by an appropriate
depends
[see Eq. (4)].
(4)].
depends on
on both the gain K and the sampling rate AT [see
This
This scaled
scaled error
error isis added
added to
to the previous
previous output value Gt_AT,
Gt_oT, and
resulting sum
through aadigital
digital-to-analog
the resulting
sum Gt is
is sent out through
-to- analog port
port to
amplifier.
the PZT amplifier.
The integral
described by Eqs. (1)
(1) through (5)
integral control algorithm described
is intentionally
and concise.
concise. ItIt will
will serve
serve to demonis
intentionally straightforward
straightforward and
potential for
for real
real-time
strate the dramatic potential
-time ultraprecision control usalgorithm coupled
coupled with
with aa convenconvening no more than a rudimentary algorithm
tional ball bearing spindle.
Results and
and discussion
discussion
2.2. Results
The master ball to be used as a reference can be centered by tapping
its support base lightly
lightly while
while following
followingaatrace
trace of
of the
the runout
runout on an
oscilloscope
spindle. Using
Using this
this simple
simple
oscilloscopeand
and manually
manually rotating the spindle.
technique,
be reduced
reduced to
to aa level
level of
of less
less than 2.5 µm
/*m
technique, the runout can be
(100
peak-to-peak.
(100 /an.)
gin.) peak
-to -peak.
With
axis of spindle rotation and
and aa perfectly
perfectly spherical
spherical
With a perfect axis
master
runout measured
measured against
against an
anoff
off-center
ball
master ball,
ball, the radial runout
-center ball
would
(in rectilinear
rectilinear coordinates
coordinates of runout
runout versus
versus rotation
rotation
would be
be (in
sinusoidal wave
wave having
having an
amplitude equal
the
a sinusoidal
an amplitude
equal to
to the
magnitude of
the centering
centering error
period of
ofone
onespindle
spindle
magnitude
of the
error and aa period
revolution. In
polar coordinates,
coordinates, the
would appear
appear as
as a
revolution.
In polar
the runout would
circle with
center displaced
displaced from
chart center
center by
by the
the
circle
with aa center
from the polar chart
magnitude of
centering error.
Although it is
is common
common to atatmagnitude
of the centering
error. Although
separate radial
radial spindle
spindle axis
axis error motion (i.e.,
(i.e., tilt
tilt error
error
tempt to separate
angle)
radial error
error motion)
motion)from
fromcentering
centeringerrors
errorsin
in evaluating
evaluating
motion and radial
spindle's performance,
performance, the
the two
two are
aregenerally
generally impossible
impossible to
to dedea spindle's
couple; a once
once-per-revolution
occur inincouple;
-per -revolutionrunout
runout component
component can
can occur
distinguishably from either.
distinguishably
Clearly, ball
centering errors
unrelated to
to spindle
spindle perforperforClearly,
ball centering
errors are unrelated
mance; they represent a type of
of systematic
systematic measurement
measurement error. To
mance;
interpret
signal measured
measured against
against a master
master ball,
ball, the
the
interpret the
the runout signal
assumption is usually made that
that the
the spindle
spindle itself
itself has
has no
no once
once-per-perrevolution runout component.
component. Using
Using this
this assumption,
assumption, spindle
spindle error
can be measured from
from aa statistically
statistically or
orgeometrically
geometrically derived
derived center
center
based
based on
on the
the entire
entire record
record of
of runout data.
postprocessing of
data to
to eliminate
eliminate centering
centering erThis postprocessing
of the runout data
problem for
for real
real-time
which the
rors poses a problem
-time feedback
feedback control, in which
spindle's center
must be
be predefined
predefined as aa reference
reference for
spindle's
center of rotation must
correction purposes.
purposes. Thus, the
the control
control algorithm
algorithm does
does not
not permit
permit
correction
the use
use of an
an averaged
averaged center
center of rotation,
rotation, and
and runout
runout measuremeasurethe
ments are not compensated for
for ball
ball centering
centering errors. One
One solution
solution
ments
first roughly
roughly center
center the
the ball,
ball, then
then use
use the
the ververto this problem is to first
axis of the ball as the assumed
assumed center of the
the spindle
spindle rotation.
tical axis
In
way, the ball
ball is
is assumed
assumed to
to be
be perfectly
perfectly centered,
centered, and all
all
In this way,
radial
is contributed to either
either spindle error motion, master
master
radial runout is
ball
In
ball out-of-roundness,
out -of- roundness,orordeformations
deformations inin the
the structural
structural loop.
loop. In
effect, this creates a predefined
predefined spindle
spindle axis
axis free
free from
from ball
ball centering
errors.
evaluate or control
control the
the spindle
spindle runout are
errors. All
All efforts
efforts to evaluate
made against this newly
newly defined spindle
spindle axis.
axis.
Correction is based upon
upon the
thedistance
distancebetween
betweenthe
thestationary
stationaryeddy
eddy-probe and
and the
the rotating
rotatingmaster
masterball;
ball;consequently,
consequently, any
any out
out-ofcurrent probe
-ofroundness of the ball
ball or
or thermal
thermal expansions
expansions in
in the
the structural
structural loop
loop
roundness
between the
will not be
be compensated
compensated for by the
between
the ball
ball and the probe will
algorithm. In effect,
effect, the
the control
control loop
loop forces
forces the
the spindle
spindle to
to
control algorithm.
follow
to the
the profile
profile of
of the
the master
master ball.
follow aa rotational
rotational profile equivalent to
on this
this spindle
spindle isis aa Grade
Grade55tungsten
tungsten carbide
carbide
The master ball used on
ball, conforming
conforming to a tolerance of ±0.1
±0.1µm
/im( (-1-5
/tin.) sphericity.
sphericity.
+ 5 gin.)
As mentioned
mentioned previously,
previously, deformations
deformations in
in the structural
structural loop
loop are
not diminished
diminished by
reduce these errors,
by the control algorithm. To reduce
errors, the
is mounted
mounted on
onaavibration
vibration-isolated
entire apparatus is
-isolated table located in a
temperature-controlled
°C). Under
Under these
these condiconditemperature
-controlled clean
clean room ((±0.1
±0.1 °C).
tions, static
static drift of
of the
thedisplacement
displacement sensor
sensor with
with respect
respect to the
the
tions,
less than 10
10 gin.
/iin. over
over aa period
period of
of 12
12 h.
h.
master ball
ball is
is reduced
reduced to less
The remaining
remaining radial
consists primarily
primarily of spindle
spindle error
radial runout consists
motion due to tilt and radial error
error motions.
motions. Polar
Polar coordinate
coordinate plots
plots
are a standardized method of
of representing
representing this type of spindle
spindle error
error
motion.
motion. The important parameters of such a plot of error motion
are3
center of the polar chart; (2)
(2)
area (1)
(1) polar
polar chart
chart center
center (PC),
(PC), the center
minimum radial separation center (MRS),
(MRS), the center that
that minimizes
minimizes
the radial difference between two concentric circles
circles that
that contain
contain the
the
error motion polar plot; and
and (3)
(3) total
total error
error motion
motion value
value (TEMV),
(TEMV),
the scaled
scaled difference
concentric circles
circles from the erdifference in
in radii
radii of two concentric
ror motion center (either PC or MRS)
MRS) just sufficient to contain the
error motion plot.
MRS center
for calculations
calculations of radial
The MRS
center is
is used
used as
as a standard for
motions. ItIt isis used
used instead
instead of
of the
the PC
PC center
center in an efand tilt error motions.
to minimize
minimize master
master ball
ball centering
centering errors.
errors. As
As described
described preprefort to
viously,
this spindle
spindle defines
defines the
the spindle
spindle axis.
axis. All
All
viously, the master ball on this
error motion
motion values
values therefore
thereforewill
will be
be computed
computed with
with respect
respect to
total error
the polar chart
chart center.
center. The
The plot
plot of
ofthe
theperfect
perfect spindle
spindle rotation,
rotation,
the
circle centered
origin of the polar plot.
then, would be a circle
centered upon the origin
Figure 44 shows
shows an oscilloscope
oscilloscope trace
runout versus
versus angular
angular
Figure
trace of runout
spindle
approximately five
five revolutions
revolutions of
of the
the spindle
spindle
spindle position
position for approximately
(time duration ==2020s).
s).The
Thepeak
peak-to-peak
runout in
in this
this case
case cor(time
-to -peak runout
/mi (100
(100 /tin.)
motion in
in the
the radial
radial
responds to 2.5 µm
gin.) of spindle error motion
direction. The same data are
are presented
presented in
in polar
polar coordinates
coordinates in Fig.
5.
that the
the presence
presenceofofaasignificant
significantonce
once-per-revolution
5. Note that
-per -revolution com-
890 /
OPTICAL ENGINEERING
24 No.
No. 55
ENGINEERING/ /September/October
September /October1985
1985 // Vol. 24
890
/ OPTICAL
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REAL
REAL TIME
TIME CONTROL
CONTROL OF
OF SPINDLE
SPINDLE RUNOUT
OPM e
VZR e
OPM 8
UZR 8
V
8 UFM
I
MflH STOREDt
194.1* /
Fig.
five
Fig.4.4. Uncorrected
Uncorrectedradial
radialrunout
runoutversus
versusangular
angularspindle
spindle position
position for
for live
revolutions.
1.3 ^m
revolutions.Vertical
Verticalscale
scale == 1.3
µm (55
(55 jtin.)
gin.)/ Idivision;
division; horizontal
horizontal scale
scale =
180°
180° rotation
rotation /I division.
Fig.
runout to controlled
controlled spindle
spindle
Fig. 6.8. Transition
Transition from
from uncontrolled
uncontrolled spindle
spindle runout
runout.
1.3 µm
^m (55
(55 /tin.)
180°
runout. Vertical
Vertical scale
scale = 1.3
µIn.) /I division;
division; horizontal
horizontalscale
scale == 180°
rotation /I division.
V2R
OPW A
190,41)
SS
124
15*.
180.
33*.
24*.
27*.
3**.
Fig. 5.5. Uncorrected
Fig.
Uncorrectedradial
radial runout
runout versus
versus angular
angular spindle
spindle position
position for
for five
revolutions.
2.5 Mm
revolutions. TEMV
TEMV == 2.5
µm (102 /tin.).
µln.).
ponent
ponent in
in the rectilinear
rectilinear plot
plot of
of Fig.
Fig. 44 appears
appears as
as aa center
center offset
offset in
in
the polar plot. Using the PC center, a total error
error motion
motion value
value is
is 2.5
/on (102 fiin.).
/tin.).
It is important
important to note
note that
that this
this TEMV
TEMV is
is based
based on aa spindle
spindle
center
is defined
defined along
along the
the axis
axis of
of the
the master
master ball.
ball.
center of rotation that is
A TEMV
data would
would be
TEMV based
based on
on an
an average
average center
center for
for the runout data
somewhat
indicative of the spindle's
somewhat less
lessthan
than 2.5
2.5 jim
µm and
and is
is more indicative
actual uncontrolled
/an TEMV, however, is
uncontrolled performance. The 2.5 µm
the magnitude of the error that must
must be
be corrected and is therefore a
more
data in
in this
this case.
case.
more relevant
relevant representation
representation of
of the runout data
Figure
Figure 66 shows
shows an
an oscilloscope
oscilloscopetrace
trace of
of the
the radial
radial runout during
the
transition from
from uncontrolled
uncontrolled to controlled
controlled spindle
spindle motion,
motion,
the transition
illustrating
illustratingaa dramatic
dramatic decrease
decreaseinin the
the spindle's
spindle's total
total radial error
motion.
rectilinear trace
controlled spindle
spindle runout over
over
motion. A rectilinear
trace of the controlled
approximately
approximatelyfive
fiverevolutions
revolutionsisisshown
shownininFig.
Fig. 7,7, while
while Fig.
Fig. 88
shows
is easy
easy to see
see from these
shows the
the polar
polar plot
plot of
of the
the same
same data. It is
plots
algorithm is
plots that
that the
the effect
effect of the control algorithm
is to center
center the
the rotation
spindle around
reduce the higher
higher
tion of the spindle
around the
the ball
ball axis
axis and
and to reduce
order
fluctuations of the centered
centered spindle
spindle motion.
motion. The
The resulting
resulting
order fluctuations
total error
error motion
motion value
value isis approximately
approximately 0.25
0.25 µm
jun (10
(10 gin.),
/*in.),
total
representing an
magnitude improvement
improvement in
radial
representing
an order
order of magnitude
in the radial
runout.
e WFM
1;e,3_11
Fig.
Corrected radial runout
runout versus
versus angular
angular spindle
spindle position
positionfor
forfive
fiverevolurevoluFig. 7.
7. Corrected
tions.
(55/Jn.)/division;
horizontal scale = 180°
180° rotarotations. Vertical
Vertical scale
scale = 1.3/tin
1.3µm (55
in.)/ division; horizontal
tion /I division.
12*.
15*.
18*.
33*.
3**.
Corrected radial runout
runout versus angular spindle position. TEMV
TEMV = 0.25
0.25
Fig. 8.
8. Corrected
urn
(10 n\n.).
µm (10
gin.).
OPTICAL
/ September/October
1985
/ /Vol.
891
OPTICALENGINEERING
ENGINEERING
/ September /October
1985
Vol.24
24No.
No.5 5/ / 891
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BIFANO,
BIFANO, DOW
Although
corrected spindle's
error motion
motion value
value
Although the
the corrected
spindle's total
total error
represents aa substantial
represents
substantial increase
increase in
in the
the spindle
spindle performance,
performance, by
by no
no
means
this system.
system.
means has
has aa minimum
minimum runout
runout limit been reached for this
Planned
extend capabilities
capabilities of
this
Planned improvements
improvementspromise
promisetoto extend
of this
spindle
spindle in
in aa variety
varietyof
ofrespects.
respects.To
To permit
permit the
the spindle
spindle to
to operate
operate at
at
higher
will be
higher rotational
rotational speeds, an assembly language control loop will
implemented, increasing
sampling rate
rate and
and decreasing
decreasing the
the
implemented,
increasing the
the A/D
A/D sampling
deleterious effects
deleterious
effects of
of phase
phase lag
lag between
between error
error input
input and feedback
In addition,
addition, the
thehorizontal
horizontalpiezoelectric
piezoelectric transducer
transducer located
located
output. In
the conconat the spindle's lower bearing set will be incorporated into the
scheme, allowing
and tilt
tilt erertrol scheme,
allowing more
more complete control over radial and
ror motions.
motions. To include
include this
this transducer,
transducer, aa more
more complex
complex control
control
algorithm will
utilized, including
including compensation
compensation for instaninstanalgorithm
will be
be utilized,
velocity.
taneous error velocity.
After
this spindle
spindle has been optimized,
optimized, the
After the
the radial
radial runout for this
the
and axial
axial
next step involves
involves simultaneously
simultaneously controlling
controlling both
both radial and
runout.
Clearly,
Clearly, the
the potential
potential for
for reducing
reducing spindle
spindle error
error motion
motion through
through
feedback control
of magnitude
magnitude decrease
decrease in
feedback
control isis substantial.
substantial. An order of
radial runout
runout can
can be
beaccomplished
accomplished with
witha asingle
singledetector
detector-force
radial
-force
controlled by
by aa simple
simple integral
integral control algorithm.
algorithm.
transducer pair, controlled
this technique,
technique,including
includingtwotwo-and
andeven
eventhree
three-axis
Refinements of this
-axis
are possible,
possible, promising
promising new
new possibilities for the state of the
control, are
of ultraprecision
ultraprecision spindle
spindle performance.
performance.
art of
ACKNOWLEDGMENT
3. ACKNOWLEDGMENT
The research program that resulted
resulted in
in the
the development
development of
of the feedfeedback system described is
is part
part of a Selected Research Opportunity
Opportunity in
Precision
Office of
ofNaval
Naval Research,
Research,
Precision Engineering
Engineering funded
funded by
by the Office
Contract
No.N00014
N00014-83-K-0064.
Contract No.
-83 -K -0064.
4. REFERENCES
REFERENCES
1. J. Bryan,
Bryan, R.
R. Clouser,
Clouser, and
andE.E.Holland,
Holland,American
AmericanMachinist
MachinistSpecial
Special
Report No. 612,
612, 149
149 (Dec.
(Dec. 4,
4, 1967).
1967).
2.
RobertDonaldson,
Donaldson, American
American Machinist,
Machinist, 57
57 (Jan.
(Jan. 8,8,1973).
1973).
2. Robert
3.
American National
National Standards
StandardsInstitute,
Institute,Ann.
Ann.CIRP
CIRP25(2),
25(2),545
545(1976).
(1976).
3. American
4.
JohnM.
M.Casstevens,
Casstevens,Oak
OakRidge
RidgeY Y-12
PlantDocument
DocumentY Y/DA-7751
4. John
-12 Plant
/DA -7751
s
(1978).
/ OPTICALENGINEERING
ENGINEERING // September/October
Vol. 24
24No.
No. 55
892 / OPTICAL
September /October 1985 //Vol.
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