Method for controlling a hybrid drive system attenuating vibrations according to stator phase currents, drive system for implementing this method and aircraft equipped with same

EP4754877A1Pending Publication Date: 2026-06-10SAFRAN AIRCRAFT ENGINES SAS

Patent Information

Authority / Receiving Office
EP · EP
Patent Type
Applications
Current Assignee / Owner
SAFRAN AIRCRAFT ENGINES SAS
Filing Date
2024-07-24
Publication Date
2026-06-10

AI Technical Summary

Technical Problem

Hybrid engine systems in aircraft experience excessive vibrational fatigue due to electromagnetic torque oscillations, which can lead to catastrophic failures, particularly in the kinematic chain, as existing electrical systems fail to effectively manage vibrational phenomena.

Method used

A control process that identifies excitation frequency ranges of torsion modes using stator phase currents and applies a self-adaptive filtering to the reference torque to exclude these frequencies, ensuring the reference torque does not excite torsion modes, thereby reducing vibrational levels and preventing fatigue.

Benefits of technology

The solution effectively reduces vibrational levels and prevents fatigue in the kinematic chain by adapting the filtering frequency based on stator currents, ensuring reliable operation of the hybrid engine system regardless of operating conditions.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention relates to a method for controlling a drive system (M) comprising a turbine engine (TM) coupled to an electric machine (MET), and an electronic control unit (20) for controlling the drive system connected to a power converter (12) for driving the electric machine selectively in engine mode and in generator mode from a reference torque filtered in an auto-adaptive manner so as to exclude a range of excitation frequencies of at least one torsional mode of the drive system according to stator phase currents of the electric machine. The invention also relates to a corresponding drive system and an aircraft including such a drive system.
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Description

[0001] METHOD FOR CONTROLLING A HYBRID MOTORIZATION MITIGATING VIBRATIONS BASED ON PHASE STATOR CURRENTS, MOTORIZATION FOR IMPLEMENTING THIS METHOD AND AIRCRAFT EQUIPPED WITH IT

[0002] The present invention relates to the field of electrical machines and in particular those used in hybrid motorization systems combining an electric machine and a thermal machine.

[0003] BACKGROUND OF THE INVENTION

[0004] Climate change is a major concern for many legislative and regulatory bodies around the world. Indeed, various restrictions on carbon emissions have been, are being, or will be adopted by various states. In particular, an ambitious standard applies to both new aircraft types and those already in operation, requiring the implementation of technological solutions to comply with current regulations. Civil aviation has been mobilizing for several years now to contribute to the fight against climate change.

[0005] Technological research efforts have already made it possible to significantly improve the environmental performance of aircraft. The Applicant takes into consideration the factors impacting all phases of design and development to obtain less energy-intensive, more environmentally friendly aeronautical components and products whose integration and use in civil aviation have moderate environmental consequences with the aim of improving the energy efficiency of aircraft.

[0006] Consequently, the Applicant is constantly working to reduce its negative climate impact by using methods and operating virtuous development and manufacturing processes that minimize greenhouse gas emissions and, more generally, reduce the environmental footprint of its activity. This sustained research and development work focuses on new generations of aircraft engines, the weight reduction of aircraft, particularly through the materials used and lighter onboard equipment, and the development of the use of electric technologies to provide propulsion.

[0007] As part of this work on aircraft motorization, a hybrid thermal / electric motorization was proposed.

[0008] This hybrid engine includes:

[0009] - a turbomachine having a line of shafts running through a high pressure stage and a low pressure stage,

[0010] - an electric machine having a shaft connected to the shaft line of the turbomachine to operate either as a motor by providing mechanical torque to the shaft line of the turbomachine, or as a generator by being driven by the shaft line of the turbomachine,

[0011] - an inverter for controlling the electric machine in the two aforementioned operating modes, the inverter being controlled by an electronic motor control unit,

[0012] - a continuous power supply circuit, for example with batteries, connected to the inverter and arranged to be reversible so as to selectively supply the electric machine when the electric machine operates as a motor or receive the electrical energy supplied by the electric machine when the electric machine operates as a generator.

[0013] The electrical system comprising the electrical machine, the inverter and the power supply circuit must be sized to provide the electrical power necessary to inject power into the turbomachine, in particular to assist the starting of the turbomachine and limit its fuel consumption during certain flight phases, and to guarantee sufficient power to supply the electrical equipment of the aircraft when the electrical machine is operating as a generator.

[0014] The electrical system must also be reliable, robust and designed so as not to disrupt the operation of the turbomachine.

[0015] The Applicant has noted that the electrical machine, and in particular the electromagnetic torque generated by the electrical machine, may include a dynamic component (oscillation around the continuous torque) capable of generating an excitation of certain torsion modes of the drive train of the motorization. This excitation results in a torque oscillation which, depending on its frequency, may excite the torsional vibration modes of the drive shafts. The excitation of these torsion modes causes a high increase in vibration levels on the drive shafts (this increase is commonly called overvoltage), phase shifts, as well as damping phenomena at both low and high frequencies. This may result in vibration fatigue of the drive train which may lead, in the worst case, to a break in the drive train. Such a break may be catastrophic if it concerns the turbomachine.

[0016] OBJECT OF THE INVENTION The invention aims in particular to improve these electrical systems, particularly with regard to the control of the vibratory phenomena that they can generate.

[0017] SUMMARY OF THE INVENTION

[0018] To this end, the invention provides a method for controlling a motorization comprising a turbomachine, an electric machine coupled to a first shaft of the turbomachine, an electronic control unit for the motorization, a power converter for controlling the electric machine selectively in motor mode and in generator mode from a reference torque provided by the electronic control unit, and a reversible power supply circuit connected to the power converter to selectively power the electric machine in motor mode or be powered by the electric machine in generator mode. The method comprises the steps of:

[0019] - identify excitation frequency ranges of at least one torsion mode of the turbomachine by the electric machine as a function of phase stator currents of the electric machine;

[0020] - and, during operation of the motorization, determining the phase stator currents of the electric machine, and filtering the reference torque at the level of the electronic control unit, by applying a filter whose cut-off frequency range is adjusted to exclude at least one excitation frequency range corresponding to the determined phase stator currents.

[0021] Thus, filtering the reference torque (as a torque instruction or command) makes it possible to avoid the excitation frequencies of all or part of the mechanical torsion modes. As it is clear that the excitation frequency range of the torsion modes is not constant and depends in particular on the load caused on the motor by the equipment to which it is connected (see Figure 4), the cut-off frequency of the filter used in the invention is adapted according to the phase stator currents of the electrical machine. This ensures that the reference torque does not cause excitation of the torsion modes regardless of the operating conditions of the motor.

[0022] An additional advantage of analyzing stator phase currents for filter cutoff frequency adaptation is that it allows identification of the mechanical torsion mode or modes regardless of whether the electrical machine is operating in motor or generator mode.

[0023] Preferably, the determination of the phase stator currents comprises a spectral analysis of measured stator currents.

[0024] The invention also relates to a motorization comprising a thermal machine, an electric machine coupled to the thermal machine, an electronic control unit for the motorization connected to a power converter driving the electric machine selectively in motor mode and in generator mode from a reference torque, and a reversible power supply circuit connected to the power converter to selectively power the electric machine in motor mode or be powered by the electric machine in generator mode.The electronic control unit comprises a member for determining the phase stator currents of the electrical machine and a self-adaptive filtering member for the reference torque, the self-adaptive filtering member having a determined cut-off frequency range, as a function of the determined phase stator currents, to correspond to a range of excitation frequencies of at least one torsion mode of the first shaft.

[0025] According to optional features, used individually or in whole or in part in combination:

[0026] - the electronic control unit comprises a table relating cut-off frequency ranges of the self-adaptive filtering member and phase stator currents, each cut-off frequency range of the self-adaptive filtering member being substantially equal to the excitation frequency range of at least one torsion mode of the turbomachine for the corresponding phase stator currents.

[0027] - the electronic control unit is connected to a device for acquiring the speed of the first shaft of the turbomachine and to a device for measuring the phase stator currents of the electric machine.

[0028] - the electronic control unit is arranged to implement a hybridization strategy by which it determines at each instant: o whether the electrical machine must operate as a generator or as a motor; o a first mechanical power that the electrical machine must take from the turbomachine when it operates as a generator, and a second mechanical power that the electrical machine must supply to the turbomachine when it operates as a motor; o the reference torque which corresponds to the mechanical power thus determined and which is transmitted to the filtering member.

[0029] - the filtered reference torque is transmitted to a current loop driving the power converter and, preferably, the current loop comprises a space vector pulse width modulation device.

[0030] - the turbomachine comprises two first shafts, one belonging to a high pressure stage and the other to a low pressure stage, and the motorisation comprises two electrical machines, namely a first one whose second shaft is coupled to the first shaft of the high pressure stage and a second one whose second shaft is coupled to the first shaft of the low pressure stage.

[0031] The invention finally relates to a vehicle and more particularly an aircraft provided with such a motorization.

[0032] Other characteristics and advantages of the invention will emerge from reading the following description of particular and non-limiting embodiments of the invention.

[0033] BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Reference will be made to the attached drawings, including:

[0035] [Fig. 1] Figure 1 is a schematic view of an aircraft according to the invention;

[0036] [Fig. 2] Figure 2 is a schematic view of a motorization of this aircraft, according to a particular embodiment of the invention;

[0037] [Fig. 3 Figure 3 is a more detailed schematic view of this motorization;

[0038] [Fig. 4] Figure 4 is a schematic view of the motorization according to a variant of this particular embodiment;

[0039] [Fig. 5] Figure 5 is a graph showing the evolution of the excitation frequency of the first torsion mode as a function of the power supplied by the electric machine [Fig. 6] Figure 6 is a Bode diagram representing a frequency analysis of the mechanical transmission chain of the thermal machine.

[0040] DETAILED DESCRIPTION OF THE INVENTION

[0041] With reference to figures 1 and 2, the invention is described in application to a hybrid engine M of an aircraft A. The hybrid engine M here comprises a turbomachine TM and an electric machine MEL.

[0042] The TM turbomachine - here more particularly a turbojet, a turboprop or a turboshaft engine - is known in itself and will only be roughly described here. The TM turbomachine comprises a high-pressure stage HP and a low-pressure stage LP. The high-pressure stage HP comprises a shaft coupled via a set of gears (not shown) to a shaft of the low-pressure stage LP, forming a kinematic chain comprising a line of shafts L.

[0043] The electric machine MEL comprises an electric motor 10 having an output shaft 11 coupled via a set of gears G to one and / or the other of the shafts of the turbomachine TM. The electric motor 10 is here a permanent magnet motor.

[0044] The electric motor 10 has electromagnetic windings connected to power electronics comprising a DC / AC power converter such as here an inverter 12 arranged to operate the electric motor 10 either in motor mode or in generator mode. The inverter 12 is itself connected to a power supply circuit 13 which is connected to the electrical circuit E of the aircraft A comprising batteries and is arranged to be reversible so as to selectively power the electric motor 10 from the batteries to rotate the output shaft 11 when the electric motor 10 of the electric machine MEL is in motor mode or to be powered by the electric machine MEL when the electric motor 10 of the electric machine MEL is in generator mode in order in particular to recharge the batteries and / or to directly power electrical equipment connected to the electrical circuit E of the aircraft A.The electric machine MEL, and in particular the electric motor 10, the inverter 12 and the power supply circuit 13 are known per se.

[0045] The motorization M comprises a control unit 20 arranged to control the turbomachine TM and the electric machine MEL. The control unit 20 is an electronic unit (of the integrated circuit, FPGA, ASIC, microcontroller type, etc.) comprising, for example, one or more processors and one or more memories containing one or more computer programs for controlling the motorization M. The control unit 20 here comprises a control module 21 of the turbomachine TM and a control module 22 of the electric machine MEL and implements a hybridization logic symbolized at 23. The control module 21 of the turbomachine TM is of the FADEC or EEC type known per se. The control module 22 of the electric machine MEL comprises a current loop controlling the inverter 12 as a function of:

[0046] - a current setpoint Iq* provided by the hybridization logic 23,

[0047] - current values ​​(ia, ib, ic) of the phases of the electric motor 10 provided by a current acquisition device 24, here Hall effect, connected to the control unit 20,

[0048] - an angular position Sméca and an angular speed Qméca of the output shaft 11 of the electric motor 10 provided by a resolver 25 connected to the control unit 20. The angular data Qméca and Qméca are conventionally derived from the processing of the signals from the resolver 25. The control of the electric machine MEL is carried out in the control module 22 using:

[0049] - the currents ia and ip which are the a and p axis currents resulting from the Clarke transform receiving as input the phase currents ia, ib, ic;

[0050] - the currents id and iq which are the d and q axis currents resulting from the Park transform receiving the currents ia and ip as input;

[0051] - the current instructions Id* and Iq* which are the current instructions of axes d and q.

[0052] Typically, the current loop of the control module 22 also involves:

[0053] - the voltages Vd** and Vq** which are the d and q axis reference voltages from the PI correctors receiving the Id*-id and Iq*-iq signals as input respectively;

[0054] - the voltages Vd* and Vq* which are the reference voltages of axes d and q resulting from the decoupling of the voltages Vd** and Vq** as a function of the currents iq and id and the angular speed Qmeca;

[0055] - the voltages Va* and vp* which are the reference voltages of axes a and p resulting from the inverse Park transform receiving as input the voltages Vd* and Vq*.

[0056] The Park transforms are also carried out using Qélec which is the electrical angular position of the electric motor 10 and which is equal to the angular position Oméca multiplied by the number of pairs of poles of the electric motor 10 (block noted ©correction in figure 2).

[0057] The voltages Va* and vp* supply a space vector pulse width modulation device SVM providing duty cycle ratios Duty 1, Duty 2, Duty 3 for controlling the inverter 12.

[0058] A reference voltage Vdc supplied by the power supply circuit 13 supplies the PI correctors, the space vector pulse width modulation device SVM and the inverter 12.

[0059] The hybridization logic 23 is arranged to implement a hybridization strategy (block 231) by which it determines at each instant, as a function of the orders of the pilot of the aircraft, the flight phase and the signals coming to it from the sensors of the aircraft:

[0060] - whether the MEL electrical machine must operate as a generator or as a motor;

[0061] - the mechanical power that the MEL electric machine must draw from the PM turbomachine when it operates as a generator and the mechanical power that the MEL electric machine must supply to the PM turbomachine when it operates as a motor;

[0062] - a torque setpoint or reference torque C*_avant corresponding to the mechanical power determined in the previous step.

[0063] The hybridization logic 23 receives as input an angular speed Q of the output shaft 11 from the resolver 25 and phase stator currents from the current acquisition device 24. The hybridization logic 23 is arranged to carry out a frequency analysis of the phase stator currents (block 232) and to determine, as a function of the amplitude and frequencies of the phase stator currents and the rotation speed of the electric motor 10, a range of cut-off frequencies fc corresponding to excitation frequencies of torsion modes of the shaft line L (block 233).

[0064] The determination of the cut-off frequency range as a function of the phase stator currents is for example obtained by using a two-dimensional table (Look-up-Table type) which relates the cut-off frequencies with values ​​of the phase stator currents as a function of the rotation speed of the thermal machine TM (more precisely the rotation speed of the shaft, HP or BP, to which the output shaft 11 of the electric motor 10 is coupled). Such a table is for example obtained by determining the excitation frequencies of the torsional modes of the kinematic chain of the motorization as a function of the phase stator currents either by simulation or by experience from tests of an electric machine MEL coupled to a speed-regulated load machine to simulate the turbomachine TM over the entire range of speeds and torques.These tests aim to search for the frequencies which amplify the torque oscillations on the kinematic chain of the M engine.

[0065] We are particularly interested in the harmonics produced by the MEL electric machine and whose frequencies are close to the torsion modes of the TM turbomachine. Some harmonics, in particular those of low order, have more energy than others and, if they have frequencies close to the torsion modes, can generate overvoltages (in fact, the higher the order of the harmonic, the lower the energy levels of the latter). In addition, low-frequency modes generate high vibrational displacements. Harmonics likely to generate high overvoltages include:

[0066] - harmonic 1 produced by a mechanical unbalance;

[0067] - harmonic 2 produced by a coaxiality defect between the rotor and the stator;

[0068] - the harmonic whose rank corresponds to the product of the number of poles and the number of phases of the electric motor 11 and produced by a torque oscillation;

[0069] - the harmonic whose rank corresponds to the product of the number of teeth and the number of notches and produced by stator toothing forces.

[0070] For example, a Campbell diagram of the TM turbomachine is used to determine the natural frequencies of the components of the TM turbomachine as a function of the rotation speed. On such a diagram, oblique lines are drawn which are the natural frequencies of the different components of the engine, horizontal lines corresponding to the frequencies of the torsion modes and vertical lines corresponding to the minimum speed of the TM turbomachine and the maximum speed of the TM turbomachine. The risk zones correspond to the intersection of the natural frequency lines with the frequency lines of the torsion modes obtained by a frequency analysis using a Bode diagram to identify the frequency(ies) most at risk. In Figure 6, a maximum value of the torsion mode is observed at a frequency of approximately 29 Hz with an amplification of approximately 50 dB.This therefore clearly constitutes the risk zone where the harmonics carrying the most energy (such as torque oscillation) must be controlled in order to minimize their impact on the overvoltage generated. We therefore seek to control the most energetic harmonics that may cross the frequency(ies) at risk.

[0071] Three excitation components are preferably taken into account here:

[0072] - a natural component of torque oscillation which is due to the salience of the poles of the electric motor

[0073] 10 and which appears independently of the operation of the power electronics;

[0074] - a component linked to the control of the electric motor

[0075] 11 which generates a torque oscillation via harmonic 6;

[0076] - a component linked to the inverter's dead times which also generates a torque oscillation via harmonic 6.

[0077] The hybridization logic 23 also comprises a self-adaptive filter 234, of the band-stop type, receiving as input the torque setpoint C*_before and providing as output a filtered torque setpoint C*_after. The self-adaptive filter 234 has a cut-off frequency, or rather a range of cut-off frequencies fc, which is adjusted as a function of the phase stator currents to filter the torque setpoint C*_before so as to exclude the excitation frequency ranges fc of the torsion modes.

[0078] The filtered torque setpoint C*_after is then transformed into a current setpoint (block 235) to form the current setpoint Iq* used at the input of the current loop of the control module 22.

[0079] The torque and speed measurements are preferably carried out on the output shaft 11 upstream of the gear set coupling the output shaft 11 and the shaft line of the turbomachine TM. For the speed measurement, it is possible to use the derivative of the mechanical position angle Oméca given by the resolver 25. Alternatively, it is possible to use the measurement at the output of the gear set because it is difficult to carry out a measurement at the coupling point: the measurement at the output of the gear set makes it possible to go back to the torque and speed of the output shaft 11 by knowing the gear set gear ratio (calculated from the number of teeth or the diameter of each pinion). In the context of the invention, these measurements are used to calculate, in real time and during operation of the motorization M, phase stator currents.The frequency and amplitude of the phase stator currents serve as inputs to the table of block 233 and the output of block 233 is the cutoff frequency of filter 234 which is therefore also provided in real time.

[0080] Filter 234 has more precisely the following AND form: . with the following parameters:

[0081] •f0 is the cut-off frequency, i.e. the rejected central frequency;

[0082] •K is the width of the rejected band;

[0083] •s is the Laplace variable.

[0084] The filter thus defines a frequency range which must be attenuated between two limits (two cut-off frequencies given by the width of the K band around the central cut-off frequency).

[0085] It is understood that the parameters of filter 234 (cutoff frequency and bandwidth) are updated in real time according to the phase stator currents determined at each instant according to a given periodicity.

[0086] The method of the invention thus comprises a preliminary step of identifying the excitation frequency ranges of at least one torsion mode of the shaft line of the motorization M and steps carried out by the control unit 20 during operation of the motorization M, namely: determining phase stator currents and filtering the torque setpoint to exclude the excitation frequency range corresponding to the determined phase stator currents.

[0087] Of course, the invention is not limited to the embodiment described but encompasses any variant falling within the scope of the invention as defined by the claims.

[0088] In particular, the motorization may have a different structure than that described.

[0089] The motorization can include:

[0090] - a single MEL BP electric machine, coupled to the BP shaft of the low pressure BP stage of the turbomachine, or

[0091] - a single MEL HP electric machine, coupled to the HP shaft of the HP high pressure stage of the turbomachine, or

[0092] - a MEL BP electric machine coupled to the BP shaft of the low pressure BP stage of the turbomachine and a MEL HP electric machine coupled to the HP shaft of the high pressure HP stage of the turbomachine as in the second embodiment of figure 3. In this case, the filtering can be carried out for only one of the electric machines or both electric machines.

[0093] The table can be defined to have input values ​​of constant intervals (e.g. 5, 10, 15, 20) or not (e.g. 3, 5, 7, 10, 15, 20, 25...if the excitation frequency varies significantly between 3 and 10). The table can be replaced by a law matching stator phase currents and frequencies to be avoided.

[0094] The cut-off frequency range of the filtering device as a function of the phase stator currents can be determined to avoid excitation of one or more torsion modes of the shaft line as a function of the impact of these torsion modes on the reliability of the motorization M.

[0095] The electric motor 11 can be of any type, including a wound rotor motor, a permanent magnet motor or an asynchronous motor.

[0096] The invention can be used with any turbomachine and is not limited to use of this engine on aircraft.

Claims

CLAIMS 1. Method for controlling a motorization (M) comprising a turbomachine (TM), an electric machine (MEL) coupled to a first shaft of the turbomachine, an electronic control unit (20) of the motorization, a power converter (12) for controlling the electric machine selectively in motor mode and in generator mode from a reference torque provided by the electronic control unit, and a reversible power supply circuit (13) connected to the power converter to selectively power the electric machine in motor mode or be powered by the electric machine in generator mode, characterized in that the method comprises the steps of: identifying excitation frequency ranges of at least one torsion mode of the turbomachine by the electric machine as a function of phase stator currents of the electric machine;and, in operation of the motorization, determining phase stator currents of the electric machine, and filtering the reference torque at the level of the electronic control unit, by applying a filter whose cut-off frequency range is adjusted to exclude at least one excitation frequency range corresponding to the determined phase stator currents.; 2. Method according to claim 1, wherein the determination of the phase stator currents comprises a spectral analysis of measured stator currents.

3. Motorization (M) comprising a turbomachine (TM), an electric machine (MEL) coupled to a first shaft of the turbomachine, an electronic control unit (20) of the motorization, a power converter (12) for controlling the electric machine selectively in motor mode and in generator mode from a reference torque supplied by the electronic control unit, and a reversible power supply circuit (13) connected to the power converter to selectively supply the electric machine in motor mode or be supplied by the electric machine in generator mode, characterized in that the electronic control unit (20) comprises a member for determining phase stator currents of the electric machine and a self-adaptive filtering member (234) of the reference torque, the self-adaptive filtering member having a determined cut-off frequency range, as a function of the determined phase stator currents, to correspond to a range of excitation frequencies of at least one torsion mode of the turbomachine.

4. Motorization (M) according to claim 3, in which the electronic control unit (20) comprises a table relating cut-off frequency ranges of the self-adaptive filtering member (234) and phase stator currents, each cut-off frequency range of the self-adaptive filtering member (234) being substantially equal to the excitation frequency range of at least one torsion mode of the turbomachine for the corresponding phase stator currents.

5. Motorization (M) according to claim 3 or 4, in which the electronic control unit (20) is connected to a device for acquiring a speed of the first shaft of the turbomachine and to a device for measuring the stator phase currents of the electric machine (MEL).

6. Motorization (M) according to any one of claims 3 to 5, in which the electronic control unit (20) is arranged to implement a hybridization strategy (231) by which it determines at each instant: - whether the electrical machine (MEL) must operate as a generator or as a motor; - a first mechanical power that the electric machine must draw from the turbomachine (TM) when it operates as a generator, and a second mechanical power that the electric machine must supply to the turbomachine when it operates as a motor; - the reference torque (C*_avant) which corresponds to the mechanical power thus determined and which is transmitted to the filtering member (234).

7. Motorization (M) according to any one of claims 3 to 6, in which the filtered reference torque is transmitted to a current loop controlling the power converter (12).

8. Motorization (M) according to claim 7, in which the current loop comprises a space vector pulse width modulation device.

9. Motorization (M) according to any one of claims 3 to 8, in which the turbomachine (TM) comprises two first shafts, one belonging to a high pressure stage (HP) and the other to a low pressure stage (LP) and the motorization comprises two electrical machines (MEL), namely a first (MEL HP) whose second shaft is coupled to the first shaft of the high pressure stage (HP) and a second (MEL BP) whose second shaft is coupled to the first shaft of the low pressure (LP) stage.

10. Aircraft comprising a motorization (M) according to any one of claims 3 to 9.