Method for determining the expansion of a rotor and associated device

Abstract

Method for determining the expansion of a rotor and associated device A device for determining the expansion of a rotor (3) of an electrical machine supported by at least one magnetic bearing (4, 5) is proposed. The device comprises: - an inductive position sensor (7, 8) measuring a position of the rotor (3), - first determination means (11) configured to determine an air gap (J) separating the rotor from said inductive position sensor, - second determination means configured to determine the value of a current representative of the power supply of the inductive position sensor, and - third determination means (12) configured to determine the value of the expansion of the rotor (3). Figure 1

Description

Title of the invention: Method for determining the expansion of a rotor and associated device Technical field of the invention

[0001] The present invention relates to electrical machines comprising a rotor supported by magnetic bearings and particularly to the determination of the expansion of the rotor.

[0002] The present invention relates more particularly to a method for determining the expansion of a rotor and a device for determining the expansion of a rotor. State of the prior art

[0003] Magnetic bearings are used in various rotating machines such as electric motors, compressors, turbines, or the like in order to maintain the axial and / or radial positions of a rotor by means of magnetic fields acting on the rotor of the machine.

[0004] Inductive position sensors are used in magnetic bearing controllers (MBCs) to measure rotor position.

[0005] The measurements delivered by the position sensors are used to control the magnetic bearings.

[0006] The rotating machines may further have an inductive position sensor arranged at each end of the rotor and a processing unit determining a variation in the rotor length or axial expansion of the rotor from the measurements delivered by the inductive position sensors arranged at the ends of the rotor.

[0007] Axial expansion is caused for example by centrifugal force during rotor rotation and temperature.

[0008] It is advantageous to determine the axial expansion of the rotor to ensure the proper functioning of the machine.

[0009] The installation of the inductive position sensors and the processing unit dedicated to determining the axial expansion of the rotor requires providing an installation space in the machine.

[0010] It is also advantageous to determine a variation in the rotor diameter or radial expansion of the rotor to ensure the proper functioning of the machine. Summary of the invention

[0011] Therefore, the present invention aims to determine the axial or radial expansion of the rotor without adding sensors and a dedicated processing unit.

[0012] According to one aspect, a method for determining the expansion of a rotor of an electrical machine supported by at least one magnetic bearing from an inductive position sensor measuring the position of the rotor.

[0013] The method comprises:

[0014] • during a calibration phase following the installation of the rotor in the bearing magnetic:

[0015] - a determination of an air gap separating the rotor from said inductive position sensor, said air gap being equal to a reference value of the air gap, and

[0016] - determining the value of a current representative of the power supply of the inductive position sensor when the air gap separating the rotor from said inductive position sensor is equal to the reference value of the air gap, the value of said current being a reference value of said current,

[0017] • during a control phase following at least one phase of use of the electric machine:

[0018] - determining the current value of said current,

[0019] • the method further comprising determining the value of the expansion of the rotor from the reference value of said current, the current value of said current and the reference value of the air gap.

[0020] The method makes it possible to determine the value of the axial or radial expansion of the rotor without the addition of position sensors and means for processing the signals delivered by said sensors dedicated to the determination of said expansion.

[0021] The method implements an inductive position sensor which is conventionally already present in the electrical machine for controlling the magnetic bearings to determine the expansion of the rotor.

[0022] By "use of the electric machine" is meant a phase of use of the electric machine so that it performs the task for which it is designed, for example to compress a gas when the electric machine is a motor-compressor or a cryogenic compressor, to deliver a fluid when the electric machine is a pump, to generate a mechanical torque when the electric machine is a turbine of a power plant, to generate electrical energy when the machine is a generator of a power plant, to store energy when the electric machine is a flywheel, to machine material when the electric machine is a machine tool.

[0023] The electric machine may be a high-speed motor. It may be implemented in space equipment.

[0024] Preferably, the expansion value of the rotor is equal to the radial expansion value of the rotor, the inductive position sensor measuring the radial position of the rotor.

[0025] Advantageously, the expansion value of the rotor is equal to the axial expansion value of the rotor, the inductive position sensor measuring the axial position of the rotor.

[0026] Preferably, the current representative of the power supply of the inductive position sensor comprises a reactive power compensation current delivered by a compensation device, the reactive power compensation current supplying the inductive position sensor to compensate for the reactive power consumed by the position sensor, the determination of the rotor expansion value comprises a determination of the reactive power compensation current, the rotor expansion value Vd being determined from the following equation:

[0028] where J(tO) is the reference value of the air gap, Ic(t0) is the reference value of the compensation current and Ic(tl) is the current value of the compensation current.

[0029] Advantageously, the sensor is powered by an alternating supply current delivered by an alternating voltage source, the current representative of the power supply of the inductive position sensor comprising the quadrature component of the alternating supply current, the determination of the value of the expansion of the rotor comprises a determination of the quadrature component of the alternating supply current, the value of the expansion of the rotor Vd being determined from the following equation:

[0030] —-7-7-

[0031] where J(tO) is the reference value of the air gap, Is _q(t0) is the reference value of the quadrature component of the AC supply current and Is q(tl) is the current value of the quadrature component of the AC supply current.

[0032] According to another aspect, the invention also relates to a device for determining the expansion of a rotor of an electrical machine supported by at least one magnetic bearing.

[0033] the device comprising:

[0034] - an inductive position sensor measuring a position of the rotor,

[0035] - first determination means configured to determine an air gap separating the rotor from said inductive position sensor, said air gap being equal to a reference value of the air gap during a calibration phase following the installation of the rotor in the magnetic bearing,

[0036] - second determining means configured to determine the value of a current representative of the power supply of the inductive position sensor when the air gap separating the rotor from said inductive position sensor is equal to the reference value of the air gap, the value of said current being a reference value of said current during the calibration phase following installation of the rotor in the magnetic bearing, and to determine the value of the current representative of the power supply to the inductive position sensor during a control phase following at least one phase of use of the electrical machine, and

[0037] - third determining means configured to determine the value of the expansion of the rotor from the reference value of said current, the current value of said current and the value of the air gap.

[0038] Advantageously, the inductive position sensor is a radial inductive position sensor configured to measure the radial position of the rotor, the expansion value of the rotor is equal to the radial expansion value of the rotor.

[0039] Preferably, the inductive position sensor is an axial inductive position sensor configured to measure the axial position of the rotor, the expansion value of the rotor is equal to the axial expansion value of the rotor.

[0040] Advantageously, the current representative of the power supply of the inductive position sensor comprises a reactive power compensation current delivered by a compensation device, the reactive power compensation current supplying the inductive position sensor to compensate for the reactive power consumed by the position sensor, the second determination means being configured to determine the reference value of the compensation current during the calibration phase, and to determine the value of the compensation current during the control phase, and the third determination means being configured to determine the value of the expansion of the rotor Vd from the following equation: 100411

[0042] where J(tO) is the reference value of the air gap, Ic(t0) is the reference value of the compensation current and Ic(tl) is the current value of the compensation current.

[0043] Preferably, the sensor is powered by an alternating supply current delivered by an alternating voltage source, the current representative of the power supply of the inductive position sensor comprising the quadrature component of the alternating supply current, the second determination means being configured to determine the reference value of the quadrature component of the alternating supply current during the calibration phase, and to determine the quadrature component of the alternating supply current during the control phase, and the third determination means being configured to determine the value of the rotor expansion Vd from the following equation: 100441 vj-

[0045] where J(tO) is the reference value of the air gap, Is _q(t0) is the reference value of the quadrature component of the AC supply current and Is _q(tl) is the current value of the quadrature component of the AC supply current. Brief description of the figures

[0046] Other advantages and characteristics of the invention will become apparent upon examination of the detailed descriptions of the embodiments, this being in no way restrictive. The attached drawings are described below:

[0047] [Fig.l] schematically illustrates a machine according to the invention;

[0048] [Fig.2] schematically illustrates an example of an example of an inductive position sensor power supply circuit according to the invention; and

[0049] [Fig.3] schematically illustrates an example of a method for determining the coefficient of expansion of a rotor according to the invention. Detailed description

[0050] Reference is made to [Fig.l] which schematically represents a partial longitudinal cross-section of a machine 1.

[0051] The machine 1 comprises a housing 2, a rotor 3 supported in the housing 2 by two radial active magnetic bearings 4 and an axial active bearing 5.

[0052] The radial active magnetic bearings 4 radially surround the rotor 3.

[0053] The rotor 3 further comprises a disc 6 surrounded axially by the axial active bearing 5.

[0054] The machine 1 further comprises two inductive position sensors 7 for measuring the radial position of the rotor 3, and two inductive position sensors 8 arranged on either side of the disc 5 for measuring the axial position of the rotor 3.

[0055] The measurements delivered by the inductive position sensors 6 measuring the radial position of the rotor 3 and the measurements delivered by the inductive position sensors 8 measuring the axial position of the rotor 3.

[0056] The machine 1 further comprises a plurality of supply circuits 9 for the sensors 7, 8.

[0057] Each power supply circuit 9 is connected to a sensor 7, 8 to supply energy to said sensor 7, 8.

[0058] The power supply circuit 9 can be located outside the machine 1 as shown.

[0059] In a variant, the power supply circuit 9 is located inside the machine 1.

[0060] It is assumed that the rotor 3 is separated from the inductive position sensors 7 measuring the radial displacement of the rotor 3 by an air gap Ji and that the disc 6 of the rotor 3 is separated from the inductive position sensors 8 measuring the axial displacement of the rotor 3 by an air gap J2.

[0061] The machine 1 further comprises first determination means 11, second determination means 12 and third determination means 13.

[0062] The inductive position sensor 7, 8, the first determination means 11, the second determination means 12 and the third determination means 13 form a device for determining the expansion of the rotor 3.

[0063] The machine 1 may further comprise fourth determination means 10.

[0064] When the device for determining the expansion of the rotor 3 comprises the sensor 7 measuring the radial position of the rotor 3, the determination device determines the radial expansion Vdr of the rotor 3.

[0065] When the device for determining the expansion of the rotor 3 comprises the sensor 8 measuring the axial position of the rotor 3, the determination device determines the axial expansion Vda of the rotor 3.

[0066] [Fig.2] schematically illustrates an example of the power supply circuit 9.

[0067] The power supply circuit 9 comprises an alternating voltage (AC) source 14 connected to power supply terminals of the inductive position sensor 7, 8.

[0068] The alternating voltage source 14 delivers an alternating supply current Is and a voltage Vs having, for example, a sinusoidal waveform.

[0069] The inductive position sensor 7, 8 consumes a large amount of reactive power which must be compensated.

[0070] The power supply circuit 9 comprises a reactive power compensation device 15 making it possible to compensate for the reactive power consumed by the inductive position sensor 7, 8.

[0071] The compensation device 15 is connected to the supply terminals of the inductive position sensor 7, 8.

[0072] The compensation device 15 generates a compensation current Ic so that the supply current Is is in phase with the supply voltage Vs.

[0073] When the supply current Is is in phase with the supply voltage Vs, the alternating voltage source 14 does not deliver reactive power. The reactive power consumed by the inductive position sensor 7, 8 is compensated by the device 15 generating the compensation current Ic.

[0074] The device 15 extracts or delivers the compensation current Ic to the supply terminals of the sensor 7, 8.

[0075] The extracted compensation current Ic is stored in an energy storage device of the compensation device 15.

[0076] The delivered compensation current Ic is delivered from the energy storage device of the compensation device 15.

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[0089] The sensor 7, 8 is supplied by a global supply current IA equal to the sum of the alternating supply current Is and the compensation current Ic, and a global supply voltage VA. The value of the inductance of the sensor 7, 8 is inversely proportional to the value of the clearance separating the sensor 7, 8 from the rotor 3. As the rotor 3 expands, the clearance between the sensor 7, 8 and the rotor 3 varies so that the value of the inductance of the sensor 7, 8 varies. The variation of the inductance of the sensor 7, 8 modifies the value of the overall supply current IA and the overall supply voltage VA. Since the value of the compensation current Ic depends on the value of the inductance of the sensor 7, 8, the variations in the value of the inductance of the sensor 7, 8 can be determined by observing the value of the compensation current Ic. Alternatively, the power supply circuit 9 does not include the compensation device 15. When the power supply circuit 9 does not include the compensation device 15, the variations in the value of the inductance of the sensor 7, 8 can be determined by observing the value of the quadrature component Is _q of the alternating supply current Is delivered by the alternating voltage source 14. In this case the overall supply current IA is equal to the supply current Is delivered by the alternating voltage source 14. The quadrature component Is q of the supply current Is is determined by known methods from the observation of the supply voltage V and of the supply current Is. Consequently, the value of the clearance separating the sensor 7, 8 from the rotor 3 can be determined from the value of the compensation current Ic when the supply circuit 9 includes the compensation device 15 or from the quadrature component Is q of the supply current Is when the supply circuit 9 does not include the compensation device 15. Let Vd be the value of the rotor expansion of rotor 3. The value of the rotor expansion Vd of rotor 3 can be the value of the radial expansion Vdr or the value of the axial expansion Vda. The value of the expansion Vd is such that: = (1) ru where J(tO) is the value of a reference air gap, L(tO) is a reference value of the compensation current Ic and Ic(tl) is a current value of the compensation current Ic.

[0090] The value of the expansion Vd is such that:

[0091] (2)

[0092] where Is _q(t0) is a reference value of the quadrature component Is _q of the supply current Is, and Is q(tl) is a current value of the quadrature component Is q of the supply current Is.

[0093] The reference value J(tO) of the air gap, the reference value Ic(tO) of the compensation current Ic, the reference value Is _q(t0) of the quadrature component Is _q of the alternating supply current Is are determined during a calibration phase following the installation of the rotor 3 in the active magnetic bearings 4.

[0094] The current value J(tl) of the air gap, the current value Ic(tl) of the compensation current Ic, the current value Is _q(tl) of the quadrature component Is q of the alternating supply current Is are determined during a control phase following at least one phase of use of the electrical machine 1 as detailed below.

[0095] [Fig.3] illustrates an example of a method for determining the expansion Vd of the rotor 3.

[0096] It is assumed that the exemplary method determines the radial expansion Vdr of the rotor 3 from the measurements delivered by the inductive position sensor 7 measuring the radial position of the rotor 3.

[0097] The method implements the device for determining a coefficient of expansion of the rotor 3.

[0098] The calibration phase following the installation of the rotor 3 in the magnetic bearings 4 comprises a step 20.

[0099] During step 20, the first determination means 11 determine an air gap J1 separating the rotor 3 from the inductive position sensor 7 measuring the radial position of the rotor 3. The measured air gap is equal to the reference value of the air gap J(tO).

[0100] Furthermore, the second determination means 12 determine the value of a current representative of the power supply of the inductive position sensor 7 when the air gap separating the rotor 3 from said inductive position sensor 7 is equal to the reference value of the air gap J(tO).

[0101] The value of said current is a reference value of said current.

[0102] The current representative of the power supply of the inductive position sensor 7 comprises the compensation current Ic when the power supply circuit 9 comprises the compensation device 15 or the power supply current Is when the power supply circuit 9 does not comprise the compensation device 15.

[0103] When the current representative of the power supply of the inductive position sensor 7 comprises the compensation current Ic, the value of the compensation current Ic is determined from the current delivered by the device 15, for example by measuring the current delivered by the device 9. The value of the compensation current Ic determined during this step is equal to the reference value Ic (t0) of the compensation current L- The reference value of the current representative of the power supply of the inductive position sensor 7 is equal to said reference value Ic(t0).

[0104] When the current representative of the power supply of the inductive position sensor 7 comprises the supply current Is, the value of the quadrature component Is q of the alternating supply current Is delivered by the source 14 is determined.

[0105] The value of the quadrature component Is q of the alternating supply current Is determined during this step is equal to the reference value Is _q(t0) of the alternating supply current Is. The reference value of the current representative of the power supply of the inductive position sensor 7 is equal to said reference value Is q(t0).

[0106] The calibration phase is followed by a phase of use 21 of the electrical machine 1 during which the machine 1 performs the task for which it is designed, for example to compress a fluid when the machine 1 is a motor-compressor.

[0107] The use phase 21 is followed by a control phase comprising two steps 22 and 23.

[0108] During step 22, the second determination means 12 determine the value of the current representative of the power supply of the inductive position sensor 7.

[0109] The value of the current representative of the power supply of the inductive position sensor 7 determined during this step is equal to a current value of said current.

[0110] When the current representative of the power supply of the inductive position sensor 7 comprises the compensation current Ic, the value of the compensation current Ic is determined from the current delivered by the device 15, for example by measuring the current delivered by the device 9. The value of the compensation current Ic determined during this step is equal to the current value Ic (tl) of the compensation current Ic. The current value of the current representative of the power supply of the inductive position sensor 7 is equal to said value Ic (tl).

[0111] When the current representative of the power supply of the inductive position sensor 7 comprises the supply current Is, the value of the quadrature component Is q of the alternating supply current Is is determined.

[0112] The value of the quadrature component Is q of the alternating supply current Is determined during this step is equal to the current value Is _q(tl) of the alternating supply current Is. The current value of the current representative of the power supply of the inductive position sensor 7 is equal to said value Is _q (tl).

[0113] During step 23, the third determination means 13 determine the value of the radial expansion Vdr of the rotor 3 from the reference value of the current representative of the power supply of the inductive position sensor 7 and the reference value of the air gap J(tO) determined in step 20, from the current value of said current determined in step 22 and from one of the equations (1) and (2).

[0114] When the current representative of the power supply of the inductive position sensor 7 comprises the compensation current Ic, the value of the radial expansion Vdr of the rotor 3 is determined from the reference value Ic(t0) of the compensation current L, the reference value L(tl) of said current, the reference value of the air gap J(tO) and equation (1).

[0115] When the current representative of the power supply of the inductive position sensor 7 comprises the supply current Is, the value of the radial expansion Vdr of the rotor 3 is determined from the reference value Is _q(t0), the current value Is q(tl), the reference value of the air gap J(tO) and equation (2).

[0116] When the value of the expansion of the rotor is determined and the machine 1 comprises the fourth determination means 10, during a step 24, the fourth determination means 10 determine the current value of the air gap J(tl) equal to the difference between the reference value of the air gap J(tO) and the value of the expansion of the rotor 3.

[0117] The current value of the air gap J(t 1 ) makes it possible to adjust alert thresholds in real time so that the distance between the radial magnetic bearings 4 and the rotor 3 is reduced while alerting of a probable collision if said distance is less than said thresholds.

[0118] Of course, the use phases can alternate with the control phases, the use phases being of the same operating duration of the machine 1 in use or of different operating durations of the machine 1 in use.

[0119] Alternatively, the exemplary method determines the axial expansion Vda of the rotor 3 from the measurements delivered by the inductive position sensor 8 measuring the axial position of the rotor 3.

[0120] During step 20, the first determination means 11 determine an air gap J2 separating the rotor 3 from the inductive position sensor 8 measuring the axial position of the rotor 3. The measured air gap is equal to the reference value of the air gap J(tO) and the second determination means 12 determine the value of a current representative of the power supply of the inductive position sensor 8 when the air gap separating the rotor 3 from said inductive position sensor 8 is equal to the reference value of the air gap J(tO).

[0121] During step 22, the second determination means 12 determine the value of the current representative of the power supply of the inductive position sensor 8.

[0122] During step 23, the third determination means 13 determine the value of the axial expansion Vda of the rotor 3 from the reference value of the current representative of the power supply of the inductive position sensor 8 and the reference value of the air gap J(tO) determined in step 20, and from the current value of said current determined in step 22.

[0123] When the current representative of the power supply of the inductive position sensor 8 comprises the compensation current Ic, the value of the axial expansion Vda of the rotor 3 is determined from the reference value L(tO) of the compensation current Ic, the reference value Ic(tl) of said current, the reference value of the air gap J(tO) and equation (1).

[0124] When the current representative of the power supply of the inductive position sensor 8 comprises the supply current Is, the value of the axial expansion Vda of the rotor 3 is determined from the reference value Is q(t0), the current value Is q(tl), the reference value of the air gap J(tO) and equation (2).

[0125] According to another variant, the method simultaneously determines the radial and axial expansion values ​​from the measurements delivered by the inductive position sensor 7 measuring the radial position of the rotor 3 and by the inductive position sensor 8 measuring the axial position of the rotor 3.

[0126] The method for determining the expansion makes it possible to determine the value of the axial or radial expansion of the rotor 3 without the addition of position sensors and means for processing the signals delivered by said sensors dedicated to the determination of said value.

[0127] The method for determining the expansion of the rotor 3 uses an inductive position sensor already present in the machine 1 for controlling the magnetic bearings 4 to determine the value of the expansion of the rotor 3.

Claims

Claims

1. Method for determining the expansion of a rotor (3) of an electrical machine (1) supported by at least one magnetic bearing (4, 5) from an inductive position sensor (7, 8) measuring the position of the rotor (3), the method comprising: • during a calibration phase following the installation of the rotor (3) in the magnetic bearing (4, 5): - determining an air gap (Jl, J2) separating the rotor from said inductive position sensor, said air gap being equal to a reference value of the air gap, and - determining the value of a current (Ic, Ia) representative of the power supply of the inductive position sensor when the air gap separating the rotor from said inductive position sensor is equal to the reference value of the air gap, the value of said current being a reference value of said current,• during a control phase following at least one phase of use of the electrical machine: - determining the current value of said current (Ic, Ia), • the method further comprising determining the value of the expansion of the rotor from the reference value of said current, the current value of said current and the reference value of the air gap.,

2. A method according to claim 1, wherein the expansion value of the rotor (3) is equal to the radial expansion value of the rotor, the inductive position sensor (7) measuring the radial position of the rotor.

3. A method according to claim 1, wherein the expansion value of the rotor (3) is equal to the variation in the length of the rotor, the inductive position sensor (8) measuring the axial position of the rotor.

4. Method according to one of claims 1 to 3, in which the current representative of the power supply of the inductive position sensor comprises a reactive power compensation current (Ic) delivered by a compensation device (15), the reactive power compensation current supplying the inductive position sensor to compensate for the reactive power consumed by the position sensor (7, 8), the determination of the value of the expansion of the rotor comprises a determination of the current of reactive power compensation Ic, the value of the rotor expansion Vd being determined from the following equation: where J(tO) is the reference value of the air gap, Ic(tO) is the reference value of the compensation current and Ic(tl) is the current value of the compensation current.

5. Method according to one of claims 1 to 3, in which the sensor is powered by an alternating supply current (Is) delivered by an alternating voltage source (14), the current (Is) representative of the power supply of the inductive position sensor comprising the quadrature component of the alternating supply current, the determination of the value of the expansion of the rotor comprises a determination of the quadrature component of the alternating supply current, the value of the expansion of the rotor Vd being determined from the following equation: / \ jt ï} Vd-A10)- ,s » where J(tO) is the reference value of the air gap, IA_q(tO) is the reference value of the quadrature component of the alternating supply current and Is _q(tl) is the current value of the quadrature component of the alternating supply current.

6. Device for determining the expansion of a rotor (3) of an electrical machine supported by at least one magnetic bearing (4, 5), the device comprising: - an inductive position sensor (7, 8) measuring a position of the rotor (3), - first determination means (11) configured to determine an air gap (J) separating the rotor from said inductive position sensor, said air gap being equal to a reference value of the air gap (Jl, J2) during a calibration phase following the installation of the rotor (3) in the magnetic bearing (4, 5), - second determination means configured to determine the value of a current (Ic, IA) representative of the power supply of the inductive position sensor when the air gap separating the rotor from said inductive position sensor is equal to the reference value of the air gap,the value of said current being a reference value of said current during the calibration phase following the installation of the rotor (3) in the magnetic bearing (4, 5), and to determine the value of the current (Ic, Ia) representative of the power supply to the inductive position sensor during a control phase following at least one phase of use of the electrical machine, and - third determination means (12) configured to determine the value of the expansion of the rotor (3) from the reference value of said current, the current value of said current and the value of the air gap.

7. Device according to claim 6, wherein the inductive position sensor (7) is a radial inductive position sensor configured to measure the radial position of the rotor, the expansion value of the rotor is equal to the radial expansion value of the rotor.

8. Device according to claim 6, wherein the inductive position sensor (7) is an axial inductive position sensor configured to measure the axial position of the rotor, the expansion value of the rotor is equal to the axial expansion value of the rotor.

9. Device according to one of claims 6 to 8, in which the current representative of the power supply of the inductive position sensor comprises a reactive power compensation current (Ic) delivered by a compensation device (15), the reactive power compensation current supplying the inductive position sensor to compensate for the reactive power consumed by the position sensor (7, 8), the second determination means (12) being configured to determine the reference value of the compensation current during the calibration phase, and to determine the value of the compensation current (Ic) during the control phase, and the third determination means (12) being configured to determine the value of the expansion of the rotor Vd from the following equation 4(rt)Oi) where J(tO) is the reference value of the air gap,Ic(tO) is the reference value of the compensation current and Ic(tl) is the current value of the compensation current.,

10. Device according to one of claims 6 to 8, in which the sensor is powered by an alternating supply current (Is) delivered by an alternating voltage source (14), the current (Is) representative of the power supply of the inductive position sensor comprising the quadrature component of the current alternating current supply, the second determining means (12) being configured to determine the reference value of the quadrature component of the alternating current supply during the calibration phase, and to determine the quadrature component of the alternating current supply during the control phase, and the third determining means (12) being configured to determine the value of the rotor expansion Vd from the following equation: / \ Vd - J\tO) - ..... v / isjto) where J(tO) is the reference value of the air gap, Is _q(t0) is the reference value of the quadrature component of the AC supply current and Is _q(tl) is the current value of the quadrature component of the AC supply current.

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