WO2011070391A1

WO2011070391A1 - Method for estimating the angular position, measuring device and sensor bearing

Info

Publication number: WO2011070391A1
Application number: PCT/IB2009/008058
Authority: WO
Inventors: Alexis Gatesoupe
Original assignee: Aktiebolaget Skf
Priority date: 2009-12-10
Filing date: 2009-12-10
Publication date: 2011-06-16
Also published as: EP2510313A1

Abstract

In a method for estimating the angular position (β) of a rotating device (13, 16) with respect to a stationary device (14, 17), first and second signals which represent the angular position (θ) of the rotating device (13, 16) with respect to the stationary device (14, 17) are generated. The first and second signals are phase shifted by approximately 90°. A scaled first signal is generated by multiplying the first signal by a first scaling factor, and a third signal is generated by adding the scaled first signal to the second signal. The first scaling factor is chosen such that the phase shift between the first and the third signals is 90° with better accuracy than the phase shift between the first and second signals. The angular position (θ) of the rotating device (13, 16) with respect to the stationary device (14, 17) is estimated by utilizing the first and third signals.

Description

S p e c i f ic a t i o n

Method for estimating the angular position, measuring device and sensor bearing

Field of the invention

The invention relates to a method for estimating the angular position of a rotating device with respect to a stationary device, to a measuring device, and to a sensor bearing.

Description of the Prior Art

Published U.S. -American application for patent No. 2009/0219016 Al discloses a system for detecting the angular position of a rotating element with respect to a non-rotating element. The system comprises an annular encoder comprised of a plurality of magnetic poles fixed to one of the rotating or the non-rotating elements and at least three magnetic field sensors configured to receive a signal originating from the encoder. The sensors are mounted to the other of the non-rotating or rotating elements in an angularly distributed manner. The system further comprises a computation unit which calculates, utilizing the output signals form the sensors, signals, particularly voltages, equalling the sine and the cosine of the angular position, i.e. orthogonal signals based on the angular position. Utilizing these signals, the angular position can be calculated.

Summary of the invention

It is an object of the present invention to provide a method and a measuring device for allowing improved estimation of the angular position of a rotating device with respect to a stationary device.

The object of the invention is achieved by means of a method for estimating the angular position of a rotating device with respect to a stationary device, comprising the steps of: generating first and second signals which represent the angular position of the rotating device with respect to the stationary device, the first and second signals being phase shifted by approximately 90°;

generating a scaled first signal by multiplying the first signal by a first scaling factor; generating a third signal by adding the scaled first signal to the second signal; the first scaling factor being chosen such that the phase shift between the first and the third signals is 90° with better accuracy than the phase shift between the first and second signals; and estimating the angular position of the rotating device with respect to the stationary device by utilizing the first and third signals.

According to the inventive method, two signals namely the first and second signals are first generated. The first and second signals are phase shifted by approximately 90°, are particularly sinusoidal signals, and comprise information about the angular position of the rotating device with respect to the stationary.

The first and second signals may preferably be generated by generating sensor signals by rotating a plurality of poles, particularly magnetic poles, with the rotating device about a plurality N of angularly distributed sensors fixed to the stationary device; and generating the first and second signals by processing the sensor signals. Alternatively, plurality of sensors may be fixed to the rotating device and the plurality of poles may be fixed to the stationary device.

The object of the invention is also achieved by means of a measuring device configured to estimate the angular position of a rotating device with respect to a stationary device, comprising:

a plurality of poles, particularly magnetic poles, configured to be attached to one of the rotating device or to the stationary device;

a plurality N of angularly distributed sensors configured to be attached to the other of the rotating device or to the stationary device and to generate sensor signals while the rotating device rotates around the stationary device; and

an electronic computing device configured to generate first and second signals which represent the angular position of the rotating device with respect to the stationary device, the first and second signals being phase shifted by approximately 90°;

to generate a scaled first signal by multiplying the first signal by a first scaling factor; to generate a third signal by adding the scaled first signal to the second signal; the first scaling factor being chosen such that the phase shift between the first and the third signals is 90° comprising better accuracy than the phase shift between the first and second signals; and

to estimate the angular position of the rotating device with respect to the stationary device by utilizing the first and third signals.

In order to obtain improved accuracy of the angular position estimation, the third signal is generated by adding to the second signal the scaled version of the first signal. The relevant first scaling factor is chosen such that the phase shift between the first and the third signals is ideally exactly 90° or at least 90° with an improved accuracy compared to the phase shift between the original first and second signals. Then, utilizing the first and third signals for the angular position estimate results in its improved accuracy.

In one embodiment of the inventive method, the first signal is generated according to the following equation:

N N

Si (0 =∑ U_t (0 · cosfa, ) =∑ (O, + A,^■ sin(<yt + φ, )) · cosfa, )

and the second signal is generated according to the following equation:

N N

$2 (0 =∑ (U, (0^■ sin(ft ) (0, + A,^■ sinOt + φ, )) · sinfa, )

wherein N is the number of sensors, Ui(t) is the output signal of the i-th sensor, O, is the dc-Offset of the output voltage of the i-th sensor, A_t is the amplitude of the output voltage of the i-th sensor, and ψ ,· is the phase shift of the output voltage of the i-th sensor with respect to a reference angle. It is also possible to generate the first signal according to the following equation:

S, (t) =∑ U, t) · sinfa, ) =∑ (O, + A,^■ sin(<yt + φ₍ )) · sinfo )

i=l /=1 and to generate the second signal according to the following equation:

S₂ (0 =∑ U, (t)^■ cos(^. ) =∑ (O, + A, · sin(fl* + φ, )) · cosfa. ) .

i=l i=l

If the sensors are regularly angularly distributed over 360°, then the phase shift of the output voltages of the i-th sensor with respect to the reference angle can be estimated as:

N

If the first and second signals are based on the aforementioned equations, then the first and second signals can be rearranged according to the following equations:

S, (0 =∑ (°i + ^Ai^■ sin(a* + φ, ))^■ cos(^ ) =∑0, · cosfa, ) +∑ 4 · cosfa,. ) · sin(fi* + <p_l )

1=1 i=l /V

$i (0 =∑ (O, , + A_t · sin(fi* + φ, ))^■ sinfa, ) =∑ O,^■ sin(^. ) +∑ 4 · sinfa. )^■ sin(<yt + φ. ) i^'=l 1=1 1=1

The signals∑ O₍. · cos( ?,. ) and∑ O₍. · sin( , ) represent each a non-rotating vector, i.e.

1=1 1=1

N

sums of the scaled offsets, and the signals∑4 " ^cos(^i ) ' sin(6¾ + <p₍) and

1=1

∑ · sin(^₍. ) · sin(iyt + φ_ί ) represent each a rotating vector. If the sensors were ideal

. 1=1

sensors, then the rotating vectors would be exactly phase-shifted by 90° and would have the same amplitude. Since the sensors are likely to comprise non-ideal behaviour, the rotating vectors are not exactly phase shifted by 90° and may differ in amplitude. This is illustrated in Fig. 1, wherein the vectors S_{1 }} S₂ represent the first and the second signals based on real-sensor signals and S₃ represents the third signal which is phase shifted by 90° with respect to the first signal with better accuracy.

Real, i.e. non-ideal sensor response may be caused, for instance, by production process variations. In addition, the angular positions are likely to be non-ideal because of positioning tolerances.

The third signal may be estimated according to the following equation: S₃ (i) = S₂ (t) + D_l - S_l (t) wherein D_\ is the first scaling factor. The first scaling factor may particularly be estimated according to the following equation:

¹ Α_λ 180° wherein _/ is the amplitude of the first signal Sj(t), A2 is the amplitude of the second signal and ΔΦ is the deviation from 90° of the the phase shift between the first and second signals.

According to the invention, the third signal is generated utilizing the second signal and a scaled version of the first signal. Interpreting the first, second and third signals as vectors, then the third signal can be estimated by adding a scaled version of the vector representing the first signal to the vector representing the second signal, wherein the scaling factor is chosen such that the relevant vectors are phase-shifted by 90° having better accuracy. In the Fresnel representation shown in Fig. 1 , this vector is also a rotating vector turning at the angular velocity, ω. The first and second signals Sj, <¾ may have amplitudes 15_/1, I ¾l and phases _/ , Φ₂. The phase shift between these two signals is Φ, different from 90°. The difference between 90° and Φ is denoted as ΔΦ. Thus the correction signal, "D" is: π π

•sm ωί + φ- 180^c

Rearranging this equation leads to the following representation:

π

-Αφ-S, ^•COS {'cot + φ)

180°

Since cos(<ztf + φ) = cos(iyt) cos(^) - sin(iyt). sin(^)

π

cos(iyt + φ) « - sin(<st)

S₂ = \S₂ -sin(iyt) follows

As a result, with zl Φ in degree, the scaled first signal, Si ', can be estimated as

or with ΔΦι^'η radian:

In one version of the inventive method, a scaled second signal may be generated by multiplying the second signal by a second scaling factor; a fourth signal may be generated by adding the scaled second signal to the first signal; the first and second scaling factors being chosen such that the phase shift between the third and the fourth signals is 90° having better accuracy than the phase shift between the first and second signals; and the angular position of the rotating device with respect to the stationary device is utilized by utilizing the third and the fourth signals.

Then the third signal may be estimated according to the following equation:

S₃ (t) = S₂ (t) + D S_] (t) and the fourth signal may be estimated according to the following equation:

S₄ (t) = S_l (t) + D₂ - S₂ (t) wherein D_\ is the first scaling factor particularly estimated according to the following equation: n _{= ΔΦ} A. π

12

4 180° and Di is the second scaling factor particularly estimated according to the following equation:

Depending on the embodiment, one of the first or second signals or both, the first and the second signals, are corrected. Consequently, depending on the embodiment and particularly with reference to Fig. 2, the third or fourth signals may be estimated, if only one of the first or second signals is corrected, as following: π

S S₂ + ^•S.

S, 180°

If the first and the second signals are corrected, then the third and the fourth signals may be estimated as following:

Brief description of the drawings

The invention will be described in greater detail hereafter, by way of non-limiting examples, with reference to the embodiments shown in the drawings.

Figs. 1, 2 are phasor diagrams;

Fig. 3 is a measuring device for estimating the angular position of a rotating device with respect to a stationary device;

Fig. 4 is an alternative circuit of the measuring device of fig. 3;

Fig. 5 is an electric motor comprising the measuring device; Fig. 6 is a bearing comprising the measuring device.

Description of embodiments

Figures 1 and 2 and have been described above.

Fig. 3 shows a measuring device for measuring the angular position Θ of a rotating device with respect to a stationary device.

For the exemplary embodiment, the measuring device comprises a plurality of sensors 1, for instance five magnetic field sensors 1 which preferably are regularly distributed circumferentially around a coder annulus 2. Two adjacent sensors 1 are displaced by an angle, φ. The sensors 1 are, for instance, Hall-effect probes.

The coder annulus 2, which can rotate with respect to the sensors 1, comprises a North pole 3 occupying an angular sector of 180° and a South pole 4 occupying an angular sector of 180°.

The coder annulus 2 may be manufactured by magnetizing a magnetic alloy, a plasto- ferrite, or an elasto-ferrite, and generates a magnetic field, B. The sensors 1 detect the magnetic field and generate, in response to detecting the magnetic field, electric signals, particularly electric voltages, U t), as output signals. If the coder annulus 2 rotates with constant angular velocity, ω, with respect to the sensors 1, then the electric signals generated by the sensors 1 are sinusoidal. Since for the example embodiment two adjacent sensors 1 are displaced by the angle, <p, the signals generated by two adjacent sensors 1 are phase shifted by φ.

The measuring device further comprises a computational circuit 5 whose input signals are the signals generated by the sensors 1. The computational circuit 5 may be a digital device first digitizing the signals from the sensors 1 or may be an analog device. The

computational circuit 5 may comprise discrete electric devices and/or integrated devices, for instance, a microcontroller or a microprocessor. The computational device 5 may be powered, for instance, by an appropriate voltage source 6. For the example embodiment shown in Fig. 3, the computational circuit 5 comprises a first computing device 7 and a second computing device 8. The input signals for the computing devices 7 and 8 are the output signals of the sensors 1, i.e. the voltages Ui(t).

In general, if utilizing N sensors 1 being displaced circumferentially around the coder annulus 2 and having displacement angles ψι with respect to a reference angle, then the first computing device 7 is configured to generate an output signal S_c(t):

N N

S_c (0 =∑ U_t (t)^■ cosfa. ) =∑ (0,. + A,^■ sinOt + φ, )) · cosfa. )

(=1 1=1

The output signal S_c(t) of the first computing device 7 is also one of the output signals of the computational device 5.

The second computing device 8 is configured to generate an output signal S_s(t):

N N

S_s (t) =∑ £/,. ( · sinfa, ) =∑ (Ο,. + A, · sin(<yt + <p. )) · sinfa. )

=l i=l wherein N is the number of sensors 1, £/,(¾) is the output signal (output voltage) of the i-th sensor 1 , O, is the dc-Offset of the output voltage of the i-th sensor 1 , A_t is the amplitude of the output voltage of the i-th sensor 1, and φ , is the phase shift of the output voltage of the i-th sensor 1 with respect to the reference angle.

The computational circuit 5 may include filters, particularly high pass or band pass filters, which may be configured to remove or at least attenuate dc components of the signals U_t(t) coming from the sensors 1.

Ideally, i.e. if the sensors 1 were ideal sensors, the output signals S_c(t), S_s(t) are both sinusoidal and have a phase shift of exactly 90°, i.e. S_c(t)=U cos(o)t) and S_s(t)-U sinfoDt Then, the angular position, Θ, of the coder annulus 2 with respect to the rotating sensors 1 with reference to the reference angle can be estimated utilizing the Arctan function which may be implemented in a device 11 whose input signals are the signals S_c(t), S_s(t). Due to, for instance, real device behavior of the sensors 1, the signals S_c(t), S_s(t) may have a phase shift differing from 90°. The deviation of this phase shift from 90° is denoted as ΔΦ.

In order to at least partly correct for the phase shift, at least one of the signals S_c(t), S_s(t) is compensated by adding a signal, C, which is derived from the other of the signals S_c(t), S_s(t). For the exemplary embodiment, the output signal S_s(t) of the second computing device 8 is compensated by a signal C_c(t) which is derived from the output signal S_c(t) of the first computing device 7.

For the exemplary embodiment, the signal C_c(t) is generated by a gain device 9 having an adjustable gain D. The signal C_c(t) is added to the output signal S_s(t) of the second computing device 8 by a summation device 10. Thus, the output signal S_Stmod(t) of the summation device 10, which is another output signal of the computational device 5, is:

S,_mo_d (0 = S, (0 + C_c (t) = S, (t) + D - S_c (t)

In order to obtain the correct value or at least a sufficient accurate value for the gain D, the gain D is calibrated such that the phase shift between the signals S_c(t), S_s>mod(t) is 90° within a sufficient accuracy, for instance, depending on the application. An example of the calibration procedure will be explained below.

For the example of embodiment, the gain D can be obtained according to the following equation:

A. 180° wherein A_s is the amplitude of the signal S_s(t), A_c is the amplitude of the signal S_c(t), and ΔΦ is the deviation from the exact phase shift of 90° between the two signals S_c(t), S_s(t). In order to obtain the angular position Θ of the coder annulus 2 with respect the sensors 1, the output signals S_c(t), S_s,mod(t) of the computational device 5 can be fed to the device 11 which can, for instance, calculate the angular position Θ by subjecting the signals S_c(t), S_s.m_od(t) to an Arctan function.

Fig. 4 shows an alternative computational device 5a which is configured to compute the signals S_c(t), S_s,m0d(t) utilizing the output signals Ui(t) of the sensors 1. Similar to the computational device 5 of fig. 3, the computational device 5a of fig. 4 comprises the first computing device 7 configured to calculate the output signal S_c(t) and the gain device 9. Instead of the summation device 10 and the second computing device 8, the computational device 5 a comprises a third computing device 8a whose input signals are the output signals Ui(t) of the sensors 1 and the output signal C_c(t) of the gain device 9. The third computing device 8a is configured to internally compute the signal S_s,mod(t)-

Figure 5 shows an exemplary application of the measuring device. Figure 5 shows an electric motor 12 comprising a rotating shaft 13. The shaft 13 rotates with respect to stationary parts of the electric motor 12, for instance its stator 14. The code annulus 2 is mounted on the shaft 13 and thus rotates with the shaft 13 with the angular velocity, ω, relative to the stator 14. The sensors 1, which may be placed on a printed circuit board not explicitly shown in the figures, are fixed to the stator 14 or other stationary parts of the electric motor 12. The computational device 5 or 5a and the device 1 1 may also be fixed to the circuit board. As a result, the angular position Θ of the shaft 13 with respect to the stationary parts of the electric motor 12 can be measured utilizing the measuring devices of figures 3 or 4.

Figure 6 shows another exemplary application of the measuring device. Figure 6 shows a sensor bearing 15 which comprises inner and outer braces. The inner brace or rotating ring 16 of the bearing 15 supports the annulus coder 2 and the outer brace or stationary ring 17 supports the sensors 1 including the computational device 5, 5a and the device 1 1. The bearing 15 can be used in various applications, for instance, to support an electric motor shaft. Consequently, the angular position Θ of the rotating ring 16 with respect to the stationary ring 17 can be measured utilizing the measuring devices of figures 3 or 4. In the exemplary embodiments shown, the signal S_s(t) is modified utilizing the signal the signal S_c(t). It is also possible to modify the signal the signal S_c(t) utilizing the signal S_s(t) or to modify both signals S_c(t), S_s(t).

In order to obtain a sufficient accurate gain D, the measuring device may be calibrated as following:

The measuring device is mounted on the electric motor 12. After one turn of the shaft 13 at constant angular velocity, co, of, for instance, 100 rpm, and using, for instance, a reference annulus coder, the output signals S_c(t), S_s(t) are obtained, i.e. their amplitudes A_c, A_s and the phase shift with respect to each other. Utilizing these values, the gain D can be calculated.

Although modifications and changes may be suggested by those skilled in the art, it is the intention of the inventor to embody within the patent warranted hereon all changes and modifications as reasonably and properly come within the scope of his contribution to the art. For instance, the coder annulus can comprise a plurality of pairs of poles, the poles being for instance magentic or optical poles.

Claims

C l a i m s

Method for estimating the angular position, measuring device and sensor bearing

A method for estimating the angular position (ff) of a rotating device (13, 16) with respect to a stationary device (14, 17), comprising the steps of:

generating first and second signals which represent the angular position (Θ) of the rotating device (13, 16) with respect to the stationary device (14, 17), the first and second signals being phase shifted by approximately 90°;

generating a scaled first signal by multiplying the first signal by a first scaling factor; generating a third signal by adding the scaled first signal to the second signal; the first scaling factor being chosen such that the phase shift between the first and the third signals is 90° with better accuracy than the phase shift between the first and second signals; and

estimating the angular position (Θ) of the rotating device (13, 16) with respect to the stationary device (14, 17) by utilizing the first and third signals.

The method of claim 1, further comprising

generating sensor signals by rotating a plurality of poles (3, 4), particularly magnetic poles, with the rotating device (1 , 13, 16) about a plurality N of angularly distributed sensors (1) fixed to the stationary device (14, 17); and

generating the first and second signals by processing the sensor signals.

The method of claim 1, further comprising

generating sensor signals by rotating a plurality N of angularly distributed sensors (1) fixed to the stationary device (14, 17) about a plurality of poles (3, 4), particularly magnetic poles, with the rotating device (1, 13, 16); and

generating the first and second signals by processing the sensor signals. The method of claim 2 or 3, comprising generating the first signal according to the following equation:

N N

S (t) =∑ U, (t) · cosfa, ) =∑ (0,. + A, · sin(<yt + φ, )) · cosfa, )

i =1 and generating the second signal according to the following equation:

N N

S₂ (0 =∑ U, (/) · sinfa, ) (0,. + A,^■ sin(i^yt + φ, )) · sinfa )

i =1 wherein Nis the number of sensors (1), Ui(t) is the output signal of the i-th sensor 1, 0, is the dc-Offset of the output voltage of the i-th sensor I, A_t is the amplitude of the output voltage of the i-th sensor 1, and φ , is the phase shift of the output voltage of the i-th sensor (1) with respect to a reference angle,

or

generating the first signal according to the following equation:

N N

S_x (t) =∑ U, (t)^■ sin ,. ) (0,. + A,^■ sin(6tf + φ, )) · sinfa. )

=1 and generating the second signal according to the following equation:

N N

S₂ (0 =∑ U, (t)^■ cosfa. ) =∑ (0,. + A_s ^■ sm(cat + <p. )) · cosfa. ) .

=1 =1

The method of claim 4, comprising generating the third signal according to the following equation:

S, (t) = S₂ (t) + D S_l (t) wherein D] is the first scaling factor and is particularly estimated according to the following equation:

¹ A_l 180° wherein Ai is the amplitude of the first signal Si(t), A2 is the amplitude of the second signal Si(t), and ΔΦ is the deviation from the phase shift between the first and second signals and 90°.

The method of one of the claims 1 to 5, further comprising

generating a scaled second signal by multiplying the second signal by a second scaling factor;

generating a fourth signal by adding the scaled second signal to the first signal; the first and second scaling factors being chosen such that the phase shift between the third and the fourth signals is 90° comprising better accuracy than the phase shift between the first and second signals; and

estimating the angular position (Θ) of the rotating device (13, 16) with respect to the stationary device (14, 17) by utilizing the third and the fourth signals.

The method of claim 4 and 6, comprising generating the third signal according to the following equation:

S₃ (t) = S₂ (t) + D S_l (t) and generating the fourth signal according to the following equation:

S₄ (t) = S_l (t) + D₂ - S₂ (t) wherein D_\ is the first scaling factor particularly estimated according to the following equation: π

12

180° and D is the second scaling factor particularly estimated according to the following equation:

A measuring device configured to estimate the angular position (Θ) of a rotating device (13, 16) with respect to a stationary device (14, 17), comprising:

a plurality of poles (3, 4), particularly magnetic poles, configured to be attached to one of the rotating device (13, 16) or to the stationary device (14, 17);

a plurality N of angularly distributed sensors (1) configured to be attached to the other of the rotating device (13, 16) or to the stationary device (14, 17) and to generate sensor signals while the rotating device (13, 16) rotates around the stationary device (14, 17); and

an electronic computing device (5, 5a) configured

to generating first and second signals which represent the angular position (Θ) of the rotating device (2, 13, 16) with respect to the stationary device (1 , 14, 17), the first and second signals being phase shifted by approximately 90°;

to generate a scaled first signal by multiplying the first signal by a first scaling factor; to generate a third signal by adding the scaled first signal to the second signal; the first scaling factor being chosen such that the phase shift between the first and the third signals is 90° with better accuracy than the phase shift between the first and second signals; and

to estimate the angular position (Θ) of the rotating device (2, 13, 16) with respect to the stationary device (1, 14, 17) by utilizing the first and third signals.

The device of claim 8, the electronic device (5, 5a) being configured to generate the first signal according to the following equation: S| (0 =∑ U, (0 · cos(p, ) =∑ (0,. + A,^■ sin(<^yt + φ. )) · cos( , )

=1 =1 and to generate the second signal according to the following equation:

S₂ (0 =∑ U, (0 · sin(p, ) =∑ (0,. + 4 · sin(i^yt + _Ψ )) · sinfa, )

=1 =1 or the electronic device being configured to generate the first signal according to the following equation:

N N

S, (0 =∑ £/. (0 · sinfa,. ) (O, + · sin(<yt + . )) · sinfa )

=1 =1 and generating the second signal according to the following equation:

$2 (0 =∑ Ui (t) · cosfa. ) =∑ (0,· + A,^■ sinOt + p. )) · cosfa. )

=1 =1 wherein N is the number of sensors (1), Ui(t) is the output signal of the i-th sensor 1, Oi is the dc-Offset of the output voltage of the i-th sensor 1, Ai is the amplitude of the output voltage of the i-th sensor 1, and φ ,^■ is the phase shift of the output voltage of the i-th sensor (1) with respect to a reference angle,

10. The device of claim 9, the electronic device (5, 5a) being configured to generate the third signal according to the following equation:

S, (t) = S₂ (t) + D S_i (t) wherein Dj is the first scaling factor and is particularly estimated according to the following equation: π

A, 180° wherein A_/ is the amplitude of the first signal Sj(t), A2 is the amplitude of the second signal and ΔΦ is the deviation from the phase shift between the first and second signals and 90°.

1 1. The device of one of the claims 8 to 10, the electronic device (5, -5 a) being configured to generate a scaled second signal by multiplying the second signal by a second scaling factor;

to generate a fourth signal by adding the scaled second signal to the first signal; the first and second scaling factors being chosen such that the phase shift between the third and the fourth signals is 90° with better accuracy than the phase shift between the first and second signals; and

to estimate the angular position (Θ) of the rotating device (2, 13, 16) with respect to the stationary device (1, 14, 17) by utilizing the third and the fourth signals.

12. The device of claim 9 and 11, the electronic device (5, 5a) being configured to

generate the third signal according to the following equation:

S_i( = S₂ (t) + D S_l (t) and to generate the fourth signal according to the following equation:

wherein D_\ is the first scaling factor particularly estimated according to the following equation:

and JJ>₂ is the second scaling factor particularly estimated according to the following equation: π

12.

A₂ 180°

13. A sensor bearing device, comprising

- A stationary ring (17);

- A rotating ring (16) configured to rotate about the stationary ring (17); and

- A measuring device of one of the claims 8 to 12, the plurality of poles (3, 4) being attached to the rotating ring (16) and the plurality N of angularly distributed sensors (1) being attached to the stationary ring (16).

14. The bearing device of claim 13, wherein the electronic device (5, 5a) of the measuring device is attached to the stationary ring (17).