Radial displacement detector device for a magnetic bearing

A device for detecting and correcting a radial oscillations of a rotor, particularly a rotor in a magnetic suspension, for the purposes of creating a restoring force to hold the rotor centrally of the stator, wherein several pairs of radial displacement detectors are coupled together and are relatively spaced such that the signals emanating from diametrically opposite detectors of each pair are cancelled out and the signals emanating from adjacent detectors of each pair are averaged to eliminate the effects of variations in the radius of the rotor.

The present invention relates to an improved detection device for a 
magnetic bearing, which is intended to detect movements, and more 
particularly radial movements, of a rotor mounted on magnetic bearings. 
In order to detect such movements, it has been known for a long time to use 
detectors which can be divided into three main categories, namely optical 
detectors, magnetoinductive detectors and capacitive detectors. 
An optical detector usually consists of a lamp illuminating a 
photo-electric cell, with the lamp beam cut off from view to a greater or 
lesser extent by an opaque circular screen firmly fixed to the rotor and 
oscillating radially with the said rotor. 
A magnetic detector consists of a magnetic component firmly fixed to the 
stator, for example a small "U" made of ferrite, which co-operates with a 
magnetic ring, also for example made of ferrite, so as to complete the 
magnetic flux circuit between the two arms of the said "U" whilst 
remaining apart from the "U" shaped component by a space forming an air 
gap. Variations in the width of the gap, resulting from radial movements 
of the rotor, alter the magnetic characteristics of the flux circuit and 
consequently vary the self-inductance of a coil wound around the U-shaped 
magnetic component. 
Finally, a capacitive detector consists of a condenser, one of the plates 
of which is firmly fixed to the stator and the other to the rotor, the 
dielectric consisting of the space which separates them, and the 
variations in the width of the gap, due to radial movements of the rotor, 
causing changes in the capacity of the said condenser. 
These various type of detectors are thus each suitable for detecting a 
radial movement of a rotor turning in a magnetic bearing and of converting 
it into an electrical signal which is transmitted to a control device of 
known type for bringing the said rotor back to its normal position. 
Several of these known detectors may be combined, for example by placing 
two of them diametrically opposite so as to add their signals 
arithmetically, in fact by algebraic subtraction carried out either 
electrically or electronically, in order thus to double the sensitivity of 
the said detector. However, truly valid geometrical arrangements for a 
plurality of detectors around a circumference centered on the theoretical 
axis of rotation have on the other hand never been proposed. The known 
devices described above would provide a satisfactory solution only if the 
geometry of the rotor were perfectly cylindrical. This condition cannot be 
achieved in practice because it is impossible to machine components of 
rigorous geometry. 
Taking into account the lack of rigorous circularity of the bearings and 
rotors, it is no longer possible to define the position of the axis of the 
rotor with the necessary accuracy. However, these known detection devices 
are incapable of distinguishing between variations in their reference 
distance generated by a radial shift of the axis of the rotor, and a 
movement which in reality corresponds only to a simple dimensional 
variation in the radius of the rotor and thus they can, in a case where 
the axis of the rotor is perfectly aligned, themselves generate a 
vibration of the axis about its original position by a spurious control 
signal due to their detection of the non-circularity of the rotor. 
These spurious detections are the cause of a substantial increase in the 
power consumption of the control device, and this is particularly 
detrimental in the case of use with a limited source of energy, such as in 
a satellite. 
Thus, the aim of the present invention is to propose an improved detection 
device which is suitable for detecting only variations in the so-called 
reference distances resulting from a true radial movement of the axis of 
the rotor and not those due to variations in the radius of the rotor. 
According to the present invention there is provided a device for detecting 
radial oscillations of a rotor relative to a stator along a diametral 
reference plane of the stator comprising 2.sup.(x) pairs of detectors 
fixed to the stator and symmetrically arranged with respect to the 
reference plane, each pair consisting of two detectors placed 
diametrically opposite one another relative to the axis of rotation of the 
rotor and responsive to changes in the radial positioning of a periphery 
of the rotor during rotation; the 2.sup.(x) detector pairs being arranged 
as 2.sup.(x-1) class 1 groups each consisting of two pairs of detectors 
with the diameter joining the two detectors of one pair angularly 
displaced from that of the other pair by an angle of 
##EQU1## 
2.sup.(x-2) class 2 groups, each consisting of two class 1 groups with the 
diametral axis of symmetry (as hereinafter defined) of one of said class 1 
groups angularly displaced from that of the other group by an angle of 
##EQU2## 
generally 2.sup.(x-a) class a groups each consisting of two class (a-1) 
groups with the diametral axis of symmetry (as hereinafter defined) of one 
of said class (a-1) groups angularly separated from that of the other 
groups by an angle of 
##EQU3## 
down to the two class (x-1) groups being arranged as one class x group 
consisting of 2 class (x-1) groups with the diametral axis of symmetry (as 
hereinafter defined) of one of said class (x-1) groups angularly separated 
from that of the other class (x-1) group by an angle of 
##EQU4## 
where x is a positive integer such that all the odd "harmonics" as 
hereinafter defined are eliminated up to the (1+2x) harmonic and a is an 
integer and 1.ltoreq.a.ltoreq.x; the two diametral axes of symmetry of the 
class (x-1) group being placed symmetrically with respect to said 
diametral reference plane so that said reference plane contains the 
diametral axis of symmetry (as hereinafter defined) of the class x group; 
the various detectors being connected together so that all those detectors 
which are symmetrically disposed around one diametral end of said 
reference plane are connected together to have their signals algebraically 
added and all the remaining detectors which are symmetrically arranged 
about the other diametral end of said reference plane are also connected 
together to have their signals algebraically added, and the resultant 
signal from the detectors at one end of the reference plane is 
algebraically subtracted from the resultant signal of the said remaining 
detectors at the other end of the reference plane. 
The term "diametral axis of symmetry" of any group, for example a class 
(a-1) group, denotes that one of the two diametral axes of symmetry of the 
group which bisects the smallest sector to embrace one detector from each 
of the detector pairs constituting said group. 
In this way, according to the present invention the essential advantage is 
achieved of eliminating from the signal transmitted by the detection 
device to the control device controlling the magnetic bearings, all the 
disturbances originating from dimensional variations in the radius of the 
rotor. 
In fact, it is known from theory that a curve can generally be broken down 
into a Fourier series, in which the amplitudes are decreasing for the 
majority of the time. 
Thus if it is assumed that the cylinder forming the rotor is unwound (i.e. 
a development is formed) and the variations in its radius in a 
cross-sectional plane perpendicular to its axis, are plotted on a graph as 
the ordinate, as a function of the corresponding polar angle plotted as 
the abscissa, it is possible to consider the usually very small defects 
(of the order of a few microns) in the circularity of the cross-section of 
the rotor as being due to superposition, on a first fundemental circle of 
theoretically perfect cross-section, of a series of sinusoidal curves of 
wavelength equal to the successive whole fractions of the perimeter of the 
said circle. These curves are commonly called "harmonics" because as the 
rotor rotates they will generate signals of frequencies which are 
multiples of those generated by the off-centre position of the axis of the 
rotor. 
The invention also provides a device for detecting radial oscilations of a 
rotor relative to a stator, comprising several pairs of detectors firmly 
fixed to the stator each pair consisting of two detectors placed 
diametrically opposite one another relative to the axis of rotation of the 
said rotor, the said pairs being grouped in twos in such a way that, for 
at least one particular reference diametral plane, there is a combination 
of four detectors situated in one and the same plane perpendicular to the 
said axis of rotation, the said detectors being connected in such away 
that in each pair of detectors the signals transmitted by two detectors 
from that pair are subtracted algebraically from one another whilst the 
signals transmitted by two pairs from one and the same group of two pairs 
are added algebraically to one another, the median diametral planes 
joining the detectors of each of the pairs of the said group of two pairs 
each make an angle of 30.degree. with the said reference diametral plane 
relative to which the said median planes are symmetrical and the signals 
of two detectors placed symmetrically relative to the said reference plane 
are added algebraically so that the overall signal transmitted by the said 
group of two pairs is related to the movement of the axis of the rotor in 
the said reference plane. The detection of the radial movements of the 
axis of the rotor is affected only by periodic variations in the radius of 
the said rotor of a frequency at least equal to five times that of the 
rotation of the rotor and it will consequently be possible to eliminate 
them thereafter in a manner which is in itself known, by a suitable 
filtering of the signal. 
The invention further provides a device for detecting radial oscillations 
of a rotor relative to a stator comprising several pairs of detectors 
firmly fixed to the stator each pair consisting of two detectors placed 
diametrically opposite one another relative to the axis of rotation of the 
said rotor, the said pairs being grouped in twos in such a way that in at 
least one particular reference diametral plane there is a combination of 
eight detectors situated in one and the same plane perpendicular to the 
said axis of rotation in such a way that the four median diametral planes 
joining the detectors of each of the pairs are symmetrical two by two 
relative to the said reference diametral plane with which the said median 
planes each make an angle of 12.degree. in the case of the pairs of the 
group of two pairs, or of 48.degree. in the case of the pairs of the 
second group of two pairs, the said detectors being connected in such a 
way that in each pair the signals transmitted by the two detectors are 
subtracted algebraically from one another whilst the signals transmitted 
by two pairs from one and the same group of two pairs are added 
algebraically to one another, the signals of two detectors placed 
symmetrically relative to the said reference plane being added 
algebraically and the signals transmitted by the two groups of two pairs 
being added algebraically to one another in such away that the overall 
signal transmitted by the combination of the eight detectors is related to 
the movement of the axis of the rotor in the said reference plane.

As can be seen in FIG. 1, a radial movement detector 1 according to the 
present invention can be placed at the level of each of the two ends 2a 
and 2b of a rotor 2 mounted by means of magnetic bearings 3 on a stator 4. 
Each of the bearings 3 consists of windings 3a wound around a magnetic 
material 3b consisting of a stack of magnetic metal laminations. 
A motor 5 consisting of windings 5a wound around a magnetic material 5b 
drives the rotor 2 for rotation about the axis 6 due to the forces which 
it exerts on the magnetic material 5c firmly fixed to the rotor 2. 
The axial position of the rotor 2 is controlled by an axial magnetic 
detector 7 consisting of a "U" shaped magnetic component 7a, for example 
made of ferrite, firmly fixed to the upper end 4a of the stator 4, around 
which is wound an induction coil (not shown), which co-operates with a 
circular component 7b, made of ferrite, and placed opposite the said "U"- 
shaped component 7a, so as to complete the magnetic flux circuit of the 
component 7a. The component 7a is mounted firmly fixed to the central part 
of the upper end forming the cap 2c of the rotor 2. 
This axial magnetic detector 7 controls, by means of a control circuit (not 
shown) of a known type, the flux density flowing in the two coils 8a and 
8b of an annular electro-magnet 8 which is integral with the stator 4 and 
which has in its air gap a ring 8c made of magnetic material firmly fixed 
to the rotor 2. 
As shown in FIG. 2 each of the radial movement detectors 1 of the rotor 2 
consists of a disc 1a mounted at centre 1b situated on the theoretical 
axis of rotation of the rotor 2. The disc 1a is placed perpendicularly to 
the said axis of rotation and is firmly fixed to the stator 4. 
Eight detectors 1d, 1e, 1f, 1g, 1h, 1i, 1j and 1k, each consisting of a 
small "U"-shaped magnetic compenent, for example made of ferrite, are 
placed on the circumference 1c of the disc 1a. All these small "U"-shaped 
components are placed in the plane of the disc 1a so that the hollow of 
their "U" faces away from the centre 1b of the disc 1a and so that the 
ends of the two branches of their "U" pointing radially, are situated on 
the circumference 1c of the said disc 1a. 
These eight detectors are intended to co-operate with a circular ring 2d of 
magnetic material, for example ferrite, situated in the same plane as the 
disc 1a and firmly fixed to the rotor 2. 
In the ideal theoretical position of the rotor, the centre 2e of the 
circular ring 2d must be situated on the axis of rotation and must thus 
overlie the centre 1b of the detection device 1 which is intended to 
detect the radial movements of this centre 2e relative to the fixed center 
1b. 
Since the disc 1a is located with reference to the two perpendicular axes 
x'x and y'y passing through the centre 1b of the said disc 1a, as is 
represented in FIG. 2, the four detectors 1d, 1e, 1f and 1g are intended 
to detect the movements of the centre 2e along a direction parallel to 
axis x'x whilst the remaining four detectors 1h, 1i, 1j and 1k are 
intended to detect the movments of the said centre 2e along a direction 
parallel to axis y'y. 
For this purpose, the pair of detectors 1d and 1e are fixed to the disc 1a 
so as to have their plane of symmetry passing through the perpendicular to 
the disc 1a, at the centre 1b of the disc 1a, and so that the lines of 
intersection of the said radial planes of symmetry with the reference 
plane x'x, y'y make angles of 30.degree. with the axis x'x. The straight 
line of each of these intersections coming from the centre 1b and cutting 
the detector 1d, or the detector 1e, forms an algebraic angle of 
-30.degree., or respectively of +30.degree., with the half straight line 
1b-x. 
Similarly the two detectors 1f and 1g are fixed to the disc 1a 
symmetrically relative to both the perpendicular to the disc 1a, at its 
centre 1b, and to the respective detectors 1d and 1e. 
The four detectors 1h, 1i, 1j and 1k are fixed in the same positioning 
relative to the axis y'y as are the four detectors 1d, 1e, 1f and 1g, 
respectively, relative to the axis x'x. In other words, their position can 
be deduced respectively from that of each of the above four detectors by a 
rotation of 90.degree. around the centre 1b of the disc 1a. 
A wire 1l is wound successively around each of the branches of the four 
detectors 1d, 1e, 1f and 1g mounted in series in the order 1e, 1d, 1g 1f. 
The two ends of the wire 1l are connected to a generator of a type which 
is in itself known and which is not represented. The coils of the wire 1l 
around each of the branches of the detectors are wound in such a way that, 
when that detector is connected to the generator, a north pole appears on 
one of the branches and a south pole appears on the other branch of each 
detector, the north and the south poles being placed symmetrically 
relative to the axis x'x and to the axis y'y as is represented in FIG. 2 
by the reference letters N and S. 
Likewise, a wire 1m is wound successively around each of the branches of 
the four detectors 1h, 1i, 1j and 1k mounted in series in the order 1j, 
1k, 1h 1i. The two ends of the wire 1m are connected to a generator of a 
type which is in itself known and which is not represented. The coils of 
the wire 1m around each of the branches of the detectors are wound in such 
a way that, when it is connected to the said generator, a north pole 
appears on one of the branches and a south pole on the other branch of 
each of the detectors, the north and south poles being placed 
symmetrically relative to the axis x'x and to the axis y'y as is 
represented in FIG. 2 by the reference letters N and S. 
A wire 1n intended to transmit the signal corresponding to movements 
parallel to the axis x'x of the centre 2e detected by the group of two 
pairs of detectors formed by the pairs consisting of the detectors 1d-1f 
and 1e-1g is connected at one of its ends to the wire 1l between the 
detectors 1d and 1g at its other end to a control circuit which is in 
itself known and which is not represented. 
Likewise, a wire 1o intended to transmit the signal corresponding to 
movements parallel to y'y of the centre 2e detected by the group of two 
pairs of detectors formed by the pairs consisting of the detectors 1h-1j 
and 1i-1k is connected at one of its ends to the wire 1m between the 
detectors 1k and 1h and at its other end to a control circuit which is in 
itself known and which is not represented. 
It follows from what is stated above that the apparatus functions in the 
following way: 
If the rotor perfectly circular a reference system in which the polar angle 
subtended between any radius whatsoever and a particular reference radius 
is plotted as abscissa, and the length of the said radius is plotted as 
ordinate, as in FIG. 3, the curve 10 obtained will be a line parallel to 
Ox of ordinate equal to the radius of the said rotor. 
Now if instead the rotor has a slightly oval, for example elliptical, shape 
teaches that the variations .DELTA.y of the radius of the rotor as a 
function of the polar angle subtended by the said radius are then 
represented by a sinusoidal curve 11 (see FIG. 4) with a period equal to 
180.degree., that is to say half of the length of the curve 10. 
In the limiting case, any variation whatsoever of the said radius as a 
function of the corresponding polar angle can be considered as being the 
superposition of a very large number of sinusoidal curves with periods 
equal to successive whole fractions of 360.degree., for example, the 
curves 12 and 13 in FIG. 6 having respective periods (360.degree./3) = 
120.degree., and (360.degree./4) = 90.degree.. 
It can thus be understood that these periodic variations of the radius will 
give rise to corresponding periodic variations of the width of the air gap 
of the magnetic detectors during the rotation of the rotor, and the 
frequency of these variations will thus be a multiple of that of the rotor 
and are thus referred to as harmonics. 
It is thus seen that the facts of placing detectors diametrically opposite 
one another and of connecting them in opposition, as are the two detectors 
forming each pair, so that the signals which they emit are subtracted 
algebraically, eliminates at the very start all the even "harmonics" of 
the resultant signal; in fact, it can be seen in the Figures that since, 
in the case of all the even harmonics, these two detectors are separated 
by a whole number of wavelengths of the sinusoides of the said 
"harmonics", they will detect the same thing and will thus transmit two 
identical signals, the subtraction of which will thus be zero. 
However, in addition, and it is on this point that the invention hinges; it 
can also be seen that two detectors which are spaced 60.degree. apart, and 
are connected in series so that the signals which they emit are added 
algebraically as is each of the detectors of one group of two pairs 
relative to one of the detectors of the other pair of the same group of 
two pairs, are separated by half a wavelength with respect to the third 
harmonic, and that they thus detect opposite quantities and thus transmit 
opposite signals, the sum of which will consequently be zero. 
Of course, this phenomenon will occur again for any higher uneven 
"harmonic" generally the (1+2x) harmonic where x is an integer so that 
(1+2x) is an odd number greater than 3. Thus, in order to eliminate all 
the odd "harmonics" up to and including the (1+2x) "harmonic" it will 
suffice to replace each of the detectors necessary to eliminate the 
previous uneven harmonic (i.e. the [1+2(x-1)] harmonic) by two detectors 
which will have their signals added and which will be placed symmetrically 
relative to the position of the single detector which they replace, being 
spaced apart from one another by half a wavelength for the said harmonic, 
in other words by 
##EQU5## 
Thus for the 5th harmonic the spacing between the two detectors of a pair 
will be 
##EQU6## 
i.e. 36.degree.. Since for the third harmonic each detector is placed at 
.+-.30.degree. relative to a radial plane of symmetry, each of these 
detectors will be replaced by a pair of detectors 36.degree. apart but 
symmetrically disposed around the siting of the corresponding third 
harmonic detector i.e. at .+-.(30.degree. + 18.degree.) and 
.+-.(30.degree. - 18.degree.), more specifically .+-.48.degree. and 
.+-.12.degree.. The one or more pairs of detectors for eliminating the 
desired harmonics comprise a detecting unit. 
Depending upon the value of x, there is no reason why the angles obtained 
should be an integral number of degrees of angle. 
FIG. 6 shows on one and the same graph the four curves 14, 11, 12 and 13 
corresponding respectively to the signals relating to an off-centering of 
the axis of the rotor relative to that of the detectors and which forms 
the fundamental or first "harmonic" (curve 14), and to those relating to a 
non-circularity of the said rotor about its axis of elliptical type 
("second harmonic", curve 11), of "pear-shaped" or triangular type ("third 
harmonic", curve 12) or of square type ("fourth harmonic", curve 13). 
The detectors 1d, 1e, 1f and 1g forming the group of two pairs ensuring the 
detection of movements of the rotor along x'x have been represented 
diagrammatically in this Figure in the positions corresponding to those 
which they occupy on the stator 4. The arrows and the operational signs 
indicated show the transmissions and the operations which are carried out 
from the signals transmitted by the detectors by means of the connections 
described above. 
In another embodiment of the present invention, the eight detectors 1d, 1e, 
1f, 1g, 1h, 1i, 1j and 1k, and the disc 1a on which they are fixed, can be 
replaced for economical reasons by a single stack of metal sheets cut out 
to have the same shape as that indicated in FIG. 2 and thus possessing a 
succession of radial lugs replacing the branches of the detectors and 
around which the wires 1l and 1m are wound as indicated above. 
Likewise, and for the same reasons, the ring 2d firmly fixed to the rotor 
can consist of a single conducting ring which may or may not be magnetic. 
From the above it will be seen that in order to eliminate all the even 
"harmonics" and all the odd harmonics up to and including a particular 
one, generally the (1+2x) "harmonic" where x is a positive integer, each 
reference plane must be associated with 2.sup.(x) detector pairs and the 
positioning of the detectors can be analysed as a series having the first 
two terms as: 
(i) 2.sup.(x-1) class 1 groups each consisting of two pairs of detectors 
with the diameter joining the two detectors of one pair angularly 
displaced from that of the other pair by an angle of 
##EQU7## 
(ii) 2.sup.(x-2) class 2 groups, each consisting of two class 1 groups with 
the diametral axis of symmetry (as hereinbefore defined) of one of said 
class 1 groups angularly displaced from that of the other group by an 
angle of 
##EQU8## 
there class 2 groups being arranged as . . . 
The last term of the series is: . . . one class x group consisting of 2 
class (x-1) groups with the diametral axis of symmetry (as hereinbefore 
defined) of one of said class (x-1) groups angularly separated from that 
of the other class (x-1) group by an angle of 
##EQU9## 
where the two diametral axes of symmetry of the class (x-1) group are 
placed symmetrically with respect to said diametral reference plane so 
that said reference plane contains the diametral axis of symmetry (as 
hereinbefore defined) of the class x group. 
The general term of this series is: 
a set of 2.sup.(x-a) class a groups each consisting of two class (a-1) 
groups with the diametral axis of symmetry (as hereinbefore defined) of 
one of said class (a-1) groups angularly separated from that of the other 
group by an angle of 
##EQU10## 
where a is a positive integer and 1.ltoreq.a.ltoreq.x. 
It must be understood that each of the terms of this series constitutes a 
different way of defining the position of the same 2.sup.(x) pairs of 
detectors, but all terms of the series must be applicable to the detector 
to satisfy the overall requirements of the present invention. 
The various detectors must be connected together so that all those 
detectors which are symmetrically disposed around one diametral end of 
each reference plane are connected together to have their signals 
algebraically added and all the remaining detectors which are 
symmetrically arranged about the other diametral end of the same reference 
plane are also connected together to have their signals algebraically 
added, with the resultant signal from the detectors at one diametral end 
of the reference plane being algebraically subtracted from the resultant 
signal of the said remaining detectors at the other diametral end of the 
reference plane. 
In FIG. 2, x is 1 and the third harmonic and all the even harmonics are 
eliminated.