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Description  |
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TECHNICAL FIELD
This invention relates to a control apparatus for a magnetic floating type
rotor supported by an electromagnetic bearing and more particularly to an
electromagnetic bearing control apparatus suitable for suppressing to a
minimum the vibration amplitude of whirling motion of the rotor.
BACKGROUND ART
A rotor of rotary machine supported by an electromagnetic bearing using
attraction type electromagnets as a bearing is typically controlled as
will be described below. Electromagnetic coils are arranged along one axis
on the right and left sides of the rotor and when the rotor is displaced
to the right, a control current flows into one electromagnetic coil on the
left side to exert attractive force so that the rotor is forcibly
deflected to the left. Conversely, when the rotor is displaced to the
left, a control current flows into the other electromagnetic coil on the
right side to exert attractive force. In this way, the rotor is
servo-controlled such that responsive to displacement of the rotor to the
right or left, the control current is passed to the electromagnetic coil
on the side opposite to the displacement and attractive force generated by
that electromagnetic coil brings the rotor into the center position.
U.S. Pat. No. 4,128,795 discloses a prior art electromagnetic bearing
control apparatus of this type, which is schematically illustrated in FIG.
14 of this application.
In this known apparatus, detected x and y-component signals of displacement
(hereinafter simply referred to as displacement signals x and y) are
differentiated to produce x and y-component signals of velocity
(hereinafter simply referred to as velocity signals x and y) and the
velocity signals x and y are added to the displacement signals x and y at
blocks 11 and 12, providing ax+bx and ay+by. The displacement signals
added with the velocity signals are passed through a rotation synchronous
tracking filter 7 (triggered by a pulse signal) to extract only rotation
synchronous components of the displacement signals and velocity signals,
x.sub.o =ax.sub.N +bx.sub.N and y.sub.o =ay.sub.N +by.sub.N, which are
respectively added with the displacement signals x and y processed by
being passed through control circuits 6 and 8, respectively. The sum
signals are supplied to electromagnetic coils 2 and 3 through associated
amplifiers 9 and 10 in order to control only a rotation synchronous
unbalanced vibration. Thus, the bearing stiffness can be adjusted by
changing the magnitude of the displacement signals and the bearing damping
can be adjusted by changing the magnitude of the velocity signals.
Disadvantageously, the prior art control apparatus requires that the
velocity signals be produced from the displacement signals by means of the
differentiation circuits, thus complicating the circuit design of the
apparatus. Further the addition of the rotational synchronous components
of displacement and velocity extracted from the displacement signals x and
y and velocity signals x and y by means of the rotation synchronous
tracking filter to the displacement signals x and y prevents the rotation
synchronous unbalanced vibration from being sufficiently suppressed, due
to not to make enough differential signal increase.
DISCLOSURE OF INVENTION
An object of this invention is to provide an electromagnetic bearing
control apparatus capable of reducing the resonance amplitude of rotation
synchronous unbalanced vibration.
According to this invention, to accomplish the above object, a selective
extraction unit, for example, a rotation speed or number tracking filter
for extracting rotor rotation synchronous component signals is provided in
servo-circuits which control currents in X and Y directions being supplied
to electromagnetic coils in accordance with x and y-component signals of
radial displacement of the rotor (displacement signals x and y) such that
the rotor is held in a predetermined radial position, and rotation
synchronous x and y-component signals delivered out of the selective
extraction unit and crossed and added to the servo-circuits so as to add
the processed x-component signal to the y-component signal on the
y-servo-circuit and vice versa.
The expression "crossed and inputted to the servo-circuits so as to be
added in opposite polarities" means that the rotation synchronous
x-component signal is inputted to one servo-circuit for the displacement
signal y so as to be added to the processed displacement signal y, and the
rotation synchronous y-component signal is inputted to the other
servo-circuit for the displacement signal x so as to be subtracted from
the processed displacement signal x or alternatively that the rotation
synchronous x-component signal is inputted to the other servo-circuit for
the displacement signal y so as to be subtracted from the processed
displacement signal y and the rotation synchronous y-component signals is
inputted to one servo-circuit for the displacement signal x so as to be
added to the processed displacement signal x.
With the above construction, frequency component signals to be controlled
are extracted from the detected displacement signals x and y and crossed
for coupling with the processed displacement signals y and x to ensure
that differentiation signals, i.e., vibration suppressive signals can be
obtained without using differentiation circuits. The vibration attendant
on the rotation of the rotor is of orbital motion which depends on the
rotation number of the motor to take the form of an unstable vibration in
a direction of orbital motion which coincides with the direction of the
rotation of the rotor about its own axis, that is in a direction of
"forward" orbital motion and to take the form of an unstable vibration in
a direction of orbital motion which does not coincide with the direction
of the rotation of the rotor about its own axis, that is, in a direction
of "backward" orbital motion. Addition or subtraction for the crossed
signals is selected by means of a switching unit to prevent either of the
forward and backward unstable vibrations.
BRIEF DESCRIPTION OF DRAWINGS
FIG. 1 is a block diagram illustrating a servo-control system according to
an embodiment of the invention.
FIG. 2 schematically shows a servo-circuit based on the FIG. 1 system for a
rotor supported by an electromagnetic bearing.
FIG. 3 is a diagram of a dynamic model useful in explaining rotor
displacement and unbalancing.
FIG. 4 is a diagram illustrating an orbit of the center of a vibratory
rotational rotor, supported by asymmetric bearing and subject to an
unbalance vibration.
FIG. 5 is a diagram illustrating a vibratory rotational motion trace of the
motion axis of a homogeneous rotor subject to an unbalanced vibration.
FIG. 6 is a block diagram for explaining the principle of a rotation
synchronous filter.
FIG. 7 is a block diagram illustrating a servo-control system according to
a second embodiment of the invention.
FIG. 8 is a graph illustrating unbalanced vibration responses.
FIG. 9 schematically shows a rotary machine model implementing teachings of
the invention.
FIG. 10 is a graph showing the relation between rotation number and natural
vibration frequency in the FIG. 9 rotary machine.
FIG. 11 illustrates a vibratory rotational motion trace of the motion axis
of a rotor undergoing a self-excited vibration.
FIG. 12 is a block diagram illustrating a servo-control system according to
a third embodiment of the invention.
FIG. 13 shows a fourth embodiment of the invention.
FIG. 14 is a block diagram illustrating a prior art servo-control system.
BEST MODE FOR CARRYING OUT THE INVENTION
A first embodiment of the invention will now be described with reference to
FIGS. 1 and 2. An x-component signal of displacement (displacement signal
x) detected by a displacement sensor 4 is supplied to a control circuit 6
which responds to the displacement signal x to determine a control current
in accordance with the right or left displacement of a rotor 1 from the
center position. The control current is amplified at right-side and
left-side power amplifiers 9 to produce control currents i.sub.x which
flow into coils 2. The direction of the input control currents to the
right-side and left-side power amplifiers 9 is set so that attractive
force generated by each electromagnet exerts a centripetal effect upon the
rotor 1. Similarly, a displacement signal y detected by a displacement
sensor 5 is supplied to a control circuit 8 and control currents i.sub.y
delivered out of power amplifier 10 are passed through coils 3. The
displacement signals x and y are also supplied to a rotation synchronous
component tracking filter 7 which extracts from the displacement signals x
and y only rotation synchronous component signals x.sub.N and y.sub.N. The
rotation synchronous components signals x.sub.N and y.sub.N are crossed
and added in opposite polarities to respective the main servo-channels.
The vibratory rotational motion will be described specifically. FIG. 3 is
conveniently used to explain an unbalanced vibration. It is assumed that
the motion axis O.sub.r of the rotor 1 is displaced to take coordinates x
and y as viewed from a spatially fixed coordinate system O-XY, that the
rotor 1 has the center of gravity G located at coordinates .omega..sub.x
and .omega..sub.y as viewed from a rotating coordinate system O.sub.r
-X.sub.r Y.sub.r which is fixed on the rotor 1, and that the rotor 1 has a
rotation speed .OMEGA.. Then, the axis OX and the axis O.sub.r X.sub.r
subtend an angle of .OMEGA.t in terms of the rotary angle at orbitrary
time t.
Because of unbalancing, x and y-components of force F exerting on the rotor
1 are,
##EQU1##
where m is the mass of rotor. The force F can be indicated on the complex
plane as F=F.sub.x +iF.sub.y which is,
##EQU2##
where i is the imaginary unit and .epsilon.=.epsilon..sub.x
+i.epsilon..sub.y. Therefore, the force F is forward force which rotates
in the same direction as that of the rotor rotation.
A vibration of the rotor 1, on the other hand, can be detected in terms of
x and y-components x and y. The vibration frequency coincides with the
rotation speed .OMEGA. and the x and y-components x and y of the vibration
are expressed as,
##EQU3##
where a.sub.x and a.sub.y represent the amplitude of the x and
y-components x and y, and .theta..sub.x and .theta..sub.y represent the
phase delay as viewed from the rotation angle. Thus, vibration can
likewise indicated on the complex plane, demonstrating that the motion
axis traces an elliptical orbit as shown in FIG. 4. Since .theta..sub.y
-.theta..sub.x <180.degree., the direction of the orbit is the same as
that of the rotation speed .OMEGA. and is therefore forward as indicated
by arrow.
If the bearing support stiffness by the electromagnet under the control of
the x-component servo-control circuit equals that by the electromagnet
under the control of the y-component servo-control circuit, that is, when
x and y-components of bearing stiffness are set homogeneously, the x and
y-components x and y of vibration have the same amplitude. The phase
difference between the x and y-components x and y is 90.degree. with the
x-component x 90.degree. leading relative to the y-component y. This is
indicated by,
##EQU4##
In this particular case wherein x and y-components F.sub.x and F.sub.y of
unbalance force exert on the rotor symmetrically as indicated in equation
(2) and the stiffness of the bearing supporting the rotor is symmetrical.
The x and y-components x and y of rotor vibration become:
##EQU5##
where a substitutes for a.sub.x =a.sub.y and .theta. substituted for
.theta..sub.x. Thus, the vibration can likewise indicated on the complex
plane, demonstrating that the center of the rotor motion traces a circular
orbit as shown in FIG. 5. The direction of the orbit is the same as that
of the rotation speed .OMEGA. and is therefore forward.
As described above, the rotor vibration traces a circular orbit when the
bearing stiffness is homogeneous but traces an elliptical orbit for the
inhomogeneous bearing stiffness. The direction of the orbit coincides with
that of the rotor rotation and is therefore forward. Accordingly, when
describing the displacement in complex expression which is,
Z=x+iy (6)
the displacement takes formulas as below depending upon whether the bearing
stiffness is homogeneous or inhomogeneous.
For a homogeneous bearing,
Z=ae.sup.i.OMEGA.t (7)
and for an inhomogeneous bearing,
Z=a.sub.f e.sup.i.OMEGA.t +a.sub.b e.sup.-i.OMEGA.t (8)
where a, a.sub.f and a.sub.b are complex numbers indicative of complex
amplitude, and .vertline.a.sub.f .vertline.>.vertline.a.sub.b .vertline..
Generally, the electromagnetic bearing support tends to be inhomogeneous
for low-speed rotation but approaches to homogeneity as the rotation speed
increases.
The x and y-components of the above-described displacement due to the
unbalanced vibration are detected by the displacement sensors 4 and 5. The
detected displacement signals x and y are supplied to the rotation
synchronous tracking filter 7 which extracts only the rotation synchronous
component signals x.sub.N and y.sub.N from the displacement vibration
components of the rotor. When the bearing reaction forces is symmetrical,
the rotation synchronous unbalance vibration Z.sub.N =x.sub.N +iy.sub.N is
prescribed by equation (7) and becomes
Z.sub.N =ae.sup.i.OMEGA.t (9)
where
x.sub.N =a.sub.N cos (.OMEGA.t-.theta..sub.N)
y.sub.N =a.sub.N sin (.OMEGA.t-.theta..sub.N) (10)
and a=a.sub.N e.sup.-i.theta.N
Now, it is of significance to appreciate that
##EQU6##
stands. When the unbalance vibration traces a circular orbit proceeding
from x-axis to y-axis in the same direction as that of the rotor rotation
as shown in FIG. 5, a signal which precedes an x-direction vibration by
90.degree. is corresponded by y-direction vibration and a signal which
precedes a y-direction vibration by 90.degree. is predicted by a
x-direction vibration. This prediction means a differentiation operation
which physically agrees with the above equation (11).
When considering only the rotation synchronous vibration components,
equation (11) is valid and the output signal x.sub.N of the tracking
filter 7 may conveniently be taken for the differentiation signal y.sub.N
and the output signal y.sub.N may conveniently be taken for the
differentiation signal -x.sub.N. Therefore, in order to obtain y-component
damping, the signal x.sub.N is multiplied by .alpha. and inputted for
addition to the y-component channel. On the other hand, in order to obtain
x-component damping, the signal y.sub.N is multiplied by -.alpha. and
inputted for addition to the x-component channel. Thus, in FIG. 1, the
signal y.sub.N is multiplied by .alpha. and inputted for subtraction to
the x-component channel.
For rotation synchronous vibration components, the signals x.sub.N and
y.sub.N are crossed and inputted for addition and subtraction to the
o-posite channels in this manner to provide reactive force as indicated
by,
F.sub.x =-.alpha.y.sub.N .ident.k.sub.xy y (12)
F.sub.y =+.alpha.x.sub.N .ident.+k.sub.yx x (13)
For k.sub.xy <0, k.sub.yx >0 is set. Thus, damping against the formed
vibration of the rotor can be purposely improved.
Although better results may be obtained with larger coefficient for the
channel-crossing addition and subtraction inputting, the value of the
coefficient is limited from the standpoint of preventing saturation of
electronic circuits and gain for .alpha. may be adjusted so that suitable
resonance amplitude can be obtained.
Next, the principle of the tracking filter 7 will be described with
reference to FIG. 6. When the rotor rotates near a resonance point in the
bending moment mode, the rotor vibration is caused partly but principally
because of the forward rotation synchronous vibration components and
partly because of a fluctuation of the rotor due to external force
attributable to, for example, shaking of the casing. The fluctuation has a
vibration frequency which approximates a natural vibration frequency in
the rigid body mode and which is therefore lower than the rotation number
of the rotor. Accordingly, the tracking filter 7 is supplied with an input
rotor vibration Z.sub.in the complex expression of which is so governed by
equation (7) as to be indicated as,
Z.sub.in =(fluctuation)+ae.sup.i.OMEGA.t (14)
and it delivers only a rotation synchronous component Z.sub.out (complex
form) which is,
Z.sub.out =ae.sup.i.OMEGA.t (15)
In principle, the tracking filter is then constructed as shown in block
form in FIG. 6.
Referring to FIG. 6, the input signal Z.sub.in is first multiplied by
e.sup.-i.OMEGA.t so as to be converted into a signal Z.sub.1 as viewed
from the rotating coordinate system. This is indicated by,
Z.sub.1 .ident.e.sup.-i.OMEGA.t Z.sub.in
.ident.(fluctuation)xe.sup.i.OMEGA.t +a (16)
Equation (16) shows that the rotation synchronous component
ae.sup.i.OMEGA.t in equation (14) is converted into a DC component a in
the signal Z.sub.1 as viewed from the rotating coordinate system. It is
also noted that the first term of low frequency in the fixed coordinate
system for Z.sub.in changes to the first term of high frequency in the
rotating coordinate system for Z.sub.1.
To extract the rotation synchronous DC component a, the signal Z.sub.1 is
passed through a low-pass filter 12. The low-pass filter 12 produces an
output signal Z.sub.2 which is,
Z.sub.2 .apprxeq.a (17)
The cut-off frequency of the low-pass filter 12 is smaller than the
rotation number and is typically set to several Hz or less, amounting to
about 0.1 Hz. The gain of this low-pass filter 12 is 1 (one).
Subsequently, the signal Z.sub.2 on the rotating coordinate system is
multiplied by e.sup.i.OMEGA.t so as to be inversely converted into a
signal on the fixed coordinate system. As a result, only the rotation
synchronous component can be extracted from the input signal Z.sub.in to
provide the output signal Z.sub.out of equation (15).
FIG. 7 illustrates a second embodiment of the invention. A circuit
arrangement shown in FIG. 7 is for suppressing the unbalanced vibration of
equation (8) for inhomogeneous bearing stiffness tracing the elliptical
orbit of FIG. 4.
In this embodiment, the forward vibration term a.sub.f e.sup.i.OMEGA.t in
equation (8) can be suppressed in the same manner as in the previous
embodiment of FIG. 1. For the sake of suppressing the backward vibration
term a.sub.b e.sup.-i.OMEGA.t, the processing for the forward vibration
may be reversed. More particularly, a rotation synchronous tracking filter
11 for the backward rotation is additionally provided and rotation
synchronous components x.sub.NB and y.sub.NB (forward rotation synchronous
components are designated by x.sub.NF and y.sub.NF in FIG. 7) are
subjected to channel-crossing addition and subtraction inputting by using
coefficient .beta. which is opposite in polarity to .alpha.. By using this
type of the tracking filter, it's possible to surpress the unbalance
vibration of the rotor supported by asymmetrical bearing.
By using the rotation synchronous tracking filter and the channel-crossing
in accordance with the invention, experimental data as graphically
illustrated in FIG. 8 can be obtained, where abscissa represents the
rotation number and ordinate the vibration amplitude. The curve is on
excursion designated by "ON" when the FIG. 1 system of this invention is
operated and on excursion designated by "OFF" when the channel-crossing is
disconnected with .alpha. rendered zero. It will be seen that the
vibration amplitude is abruptly decreased at "ON" and it recovers a large
level at "OFF".
As will be seen from the foregoing description, the unbalanced vibration
can be suppressed actively through fundamental steps as below. In the
first place, x and y-components of a rotor vibration (displacement signals
x and y) are detected and supplied to the tracking filter which extracts
rotation synchronous component signals x.sub.N and y.sub.N from the
displacement signals x and y and in the second place, the extracted
signals x.sub.N and y.sub.N are crossed and respectively inputted to the
y-component channel so as to be added to the processed displacement signal
y and to the x-component channel so as to be added to the processed
displacement signal x. Polarities of addition of the signals x.sub.N and
y.sub.N are opposite to each other, one representing addition and the
other representing subtraction.
To sum up, this invention features that frequency component signals to be
controlled are extracted from the detected displacement signals x and y
and crossed for coupling in opposite polarities with the main
servo-circuit in x and y direction to ensure that differentiation signals,
i.e., vibration suppressive signals can be obtained.
Incidentally, a rotor enclosing liquid undergoes a self-excited vibration
with the frequency which is independently of the rotation speed. Such a
self-excited vibration can be suppressed as will be described below.
FIG. 9 shows an instance wherein a rotor undergoes a self-excited vibration
due to flow of fluid inside the rotor. Referring to FIG. 9, a rotor
comprises a drum 15 connected to a single rotary shaft 14 which is
supported by upper and lower ball bearings 16 and 12 of conventional
passive type. This rotor constitutes a centrifugal separator in which
fluid is charged through an upper portion of the rotary shaft 14 into the
drum 15 and discharged through a lower portion of the rotary shaft 14. The
axial flow of liquid in the rotor causes a self-excited rotor vibration
with frequency shown in a certain frequency domain A as illustrated in
FIG. 10. This vibration happens within a certain rotation speed region B.
The frequency of the self-excited vibration is plotted as indicated by
".DELTA." symbol in FIG. 10. To suppress this self-excited vibration, an
electromagnetic bearing 13 is provided as shown in FIG. 9. A sensor 17
detects an amount of displacement of the rotary shaft 14 and produces a
displacement signal. A control signal based on the displacement signal is
passed through the electromagnetic bearing 13 to suppress the self-excited
vibration.
To detail the prevention of the self-excited vibration, the frequency
designated at ".DELTA." of the self-excited vibration is different from
the rotation speed and well predictable, in the phase of design as a
natural vibration frequency which depends upon the rotor configuration and
the support stiffness of ball bearings. Curves W.sub.f and W.sub.b are
respectively representative of predictive values of a forward natural
vibration frequency and a backward natural vibration frequency. The
direction of the self-excited vibration due to fluid flow is forward as
illustrated in FIG. 11. Thus, the measured frequency .DELTA. of the
self-excited vibration can be predicted by the calculation as forward
natural vibration frequency W.sub.f as will be seen from FIG. 10. The
self-excited vibration can be prevented by means of a control circuit as
shown in FIG. 12 which forms another embodiment of the invention.
Referring to FIG. 12, x and y-component control circuits 6 and 8 are
identical to those of the previous embodiments. In the FIG. 12 embodiment,
to trigger a tracking filter 7, a signal W.sub.n is used in place of the
pulse, the signal W.sub.n being generated from an oscillator 18 of the
same frequency as a natural vibration frequency of the self-excited
vibration. The tracking filter 7 extracts x and y-component signals
x.sub.f and y.sub.f of the self-excited vibration from the displacement
signals x and y. Particularly, due to the fact that the self-excited
vibration is forward, the component signals x.sub.f and y.sub.f are
crossed so that the component signal y.sub.f is negatively added to the
x-component channel and the component signal x.sub.f is positively added
to the y-component channel. Consequently, the electromagnetic bearing 13
can generate vibration preventive damping as in the case of the unbalanced
vibration.
As shown in FIG. 10, the frequency of the self-excited vibration slightly
changes with the rotation speed. However, the self-excited vibration
frequency is inherent to the rotor and predictable within a certain
extent. Accordingly, band-pass filters 19 and 20 are used in a tracking
filter 7' as illustrated in FIG. 13 for extracting desired frequency
component signals x.sub.n and y.sub.n from the displacement signals x and
y. Again considering that the self-excited vibration is forward, the
output signals x.sub.n and y.sub.n from the tracking filter 7' are crossed
and inputted to the y and x-component channels so as to be added to the
processed displacement signals y and x in opposite polarities.
The self-excited vibration tends to be backward as the rotation speed
increases. For instance, the backward self-excited vibration converging to
low natural vibration frequencies as indicated by symbol ".quadrature." in
FIG. 10. To prevent the backward self-excited vibration, the tracking
filter 7' of FIG. 13 is constituted with low-pass filters 19' and 20' and
extracts low-frequency component signals x.sub.n and y.sub.n from the
displacement signals x and y. The output signals x.sub.n and y.sub.n from
the tracking filter 7' are crossed and inputted to the y and x-component
channels so as to be added to the processed displacement signals y and x
in opposite polarities. The totalling point is set to be positive at the
x-component channel and negative at the y-component channel, thereby
making it possible to suppress the backward self-excited vibration.
In this manner, the output signals from the filter for extracting vibration
frequency signals within a desired frequency region are crossed and
inputted to the x and y-component channels so as to be added to the main
servo in x and y channel in opposite polarities. The polarity of the
totalling point at the x and y-component channels depends on whether the
vibration to be controlled is forward or backward.
Since the direction of the vibration changes with the rotation speed of the
rotor, a switch provided to precede the filter circuit may be operated in
accordance with the rotation number to selectively suppress the forward or
backward vibration. It can be seen from FIG. 10 that th | | |
