Controlling the dynamic behavior of an aeronautical propulsion system

Abstract

An aeronautical propulsion system (1) comprises bearings (lla-llc) supporting a drive shaft of the fan rotor (9) in the propulsion system (1) whose position satisfies the following formula (I): , where: d2 is the distance between the centers of gravity (Gnb and Gnc) of the rear bearings (11b, 11c) of the drive shaft (11); Rm is a mean radius of the turbine drive unit (8); XN is the limit speed of the drive shaft (11); d1 is the distance between the center of gravity (Glla) of the front bearing (11a) and the center of gravity (Gnb) of the rear bearing (11b) closest to the front bearing (11a); R11b is a mean radius of the rear bearing (11b) closest to the front bearing (11a); and c = 170 (min*tr / min)-1, E1 = 0.18.

Description

[0001] DESCRIPTION

[0002] TITLE: Mastering the dynamic behavior of an aeronautical propulsion system

[0003] TECHNICAL FIELD

[0004] The present application generally concerns the field of propulsion systems, and more particularly aeronautical propulsion systems comprising a ducted or non-ducted fan and having a high, or even very high, bypass ratio.

[0005] STATE OF THE ART

[0006] A propulsion system generally comprises, from upstream to downstream in the direction of gas flow, a fan section, a compressor section which may include a low-pressure compressor and a high-pressure compressor, a combustion chamber and a turbine section which may include in particular a high-pressure turbine and a low-pressure turbine. The high-pressure compressor is rotated by the high-pressure turbine via a high-pressure shaft. The fan and, where appropriate, the low-pressure compressor are rotated by the low-pressure turbine via a low-pressure shaft.

[0007] Technological research efforts have already led to very significant improvements in the environmental performance of aircraft. The Applicant takes into consideration the impact factors in 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.

[0008] Thus, in order to improve the propulsive efficiency of the propulsion system and to reduce its specific consumption as well as the noise emitted by the fan section, propulsion systems have been proposed having a high bypass ratio (BPR, corresponding to the ratio between the flow rate of the secondary air flow and the flow rate of the primary air flow). To achieve such bypass ratios, the fan section can be decoupled from the low-pressure turbine, thus making it possible to independently optimize their respective rotation speeds. Generally, the decoupling is achieved using a reduction mechanism placed between the upstream end of the low-pressure shaft and a rotor of the fan section. The rotor of the fan section is then driven by the low-pressure shaft via the reduction mechanism at a rotation speed lower than that of the low-pressure shaft.

[0009] However, increasing the rotational speed of the low-pressure turbine has an impact on the dynamics of the low-pressure body and in particular on the deformation modes of the low-pressure shaft. This impact is all the more important when seeking to increase the efficiency of the low-pressure turbine.

[0010] PRESENTATION One aim of this application is to optimize the performance of the aeronautical propulsion system in terms of specific consumption, while controlling the dynamic behavior of the low pressure body.

[0011] For this purpose, according to a first aspect, an aeronautical propulsion system is proposed comprising:

[0012] - a fan rotor configured to be driven by a fan shaft;

[0013] - a drive turbine configured to drive the fan rotor via a drive shaft around an axis of rotation;

[0014] - a reduction mechanism coupling the drive shaft and the fan shaft to drive the fan shaft at a rotational speed lower than the rotational speed of the drive shaft;

[0015] - bearings configured to center the drive shaft relative to the axis of rotation, the bearings comprising a front bearing extending upstream of a combustion chamber of the propulsion system and two rear bearings extending downstream of the combustion chamber, wherein a position of the bearings in the propulsion system complies with the following formula: where: d2 is the distance between the centers of gravity of the rear bearings of the drive shaft, in millimeters (mm);

[0016] R m is an average radius of the drive turbine, in millimeters (mm);

[0017] XN is the limiting speed of the drive shaft, in revolutions per minute (rpm); di is the distance between the center of gravity of the front bearing and the center of gravity of the rear bearing closest to the front bearing, in millimeters (mm);

[0018] Rnb is an average radius of the rear bearing closest to the front bearing, in millimeters (mm); and C = 170 (mm*rpm)- 1 , Ei = 0.18.

[0019] Some preferred but non-limiting features of the propulsion system according to the first aspect are the following, taken individually or in combination:

[0020] - the bearings are also positioned in the propulsion system so as to respect the following formula: where E2 = 0.378;

[0021] - the limit speed of the drive shaft complies with the following formula: 10 5 where A = 5500 mm*rpm;

[0022] - the limit speed of the drive shaft complies with the following formula: 10 5 where B = 8,500 mm*rpm; - all or part of the drive shaft bearings are associated with a bearing mode damper;

[0023] - bearing mode dampers include pressurized fluid film damping;

[0024] - each bearing mode damper comprises a deformable cage mounted between an associated bearing ring and a stator part of the propulsion system;

[0025] - the drive shaft bearings comprise at least one front bearing and exactly two rear bearings;

[0026] - the propulsion system further comprises an additional turbine configured to drive an additional compressor via an additional shaft, the additional shaft being configured to rotate at a higher speed than the drive shaft around the axis of rotation, the additional turbine being two-stage;

[0027] - an average radius of an additional turbine bore respects the following formula:

[0028] R m a < E * L HP 2 * XN * 10“ 9 + F, where: R m _a is the mean radius of the additional turbine bore in millimeters (mm); LHP is a distance between an additional compressor inlet and an additional turbine outlet in millimeters (mm); and E = 3.15 (mm.rpm) -1 and Fi = 23 millimeters (mm);

[0029] - an average radius of an additional turbine bore respects the following formula:

[0030] R m _a > EU Hf S XN * 10 9 + F2 where: R m _a is the mean radius of the additional turbine bore in millimeters; LHP is a distance between an additional compressor inlet and an additional turbine outlet in millimeters (mm); and E = 3.15 (mm.rpm) -1 and F2 = 13 millimeters (mm);

[0031] - an average radius of an additional turbine bore respects the following formula: . 2

[0032] R m a < K * I * 10 3 * n + M ] * XN * 10“ 9 + N, where: D is the fan rotor diameter in millimeters, measured in a plane normal to the axis of rotation at an intersection between a tip and a leading edge of the fan rotor blades; BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level; Te is the temperature at the inlet of the drive turbine when the propulsion system is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in degrees Celsius (°C); Tref = 273 K; n is the number of stages in the additional turbine and the additional compressor; GAMMA is the adiabatic coefficient of air; and K = 6.76, L = 153.6 m- 1 .(°C)- 1 / 2 .(rpm)- 1 , M = 421 mm.(°C) 1 / 2 and Ni = -11 millimeters (mm);

[0033] - an average radius of an additional turbine bore respects the following formula: . 2

[0034] R m a > K * * 10 3 * n + M ] * XN * 10“ 9 + N, where: D9 is the fan rotor diameter in millimeters, measured in a plane normal to the axis of rotation at an intersection between a tip and a leading edge of the fan rotor blades; BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level; T e is the temperature at the inlet of the drive turbine when the propulsion system is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in degrees Celsius (°C); Tret = 273K; n is the number of stages in the additional turbine and the additional compressor; GAMMA is the adiabatic coefficient of air; and K = 6.76, L = 153.6 rrr 1 .(°C)- 1 / 2 .(rpm)- 1 , M = 421 mm.(°C) 1 / 2 and N2 = - 21 millimeters (mm);

[0035] - an average radius of the bore of the additional turbine is at least equal to:

[0036] R m a > G * FN * BPR * 10“ 4 + H where: R m _a is the mean radius of the supplementary turbine bore in millimeters; FN is the fan rotor thrust measured when the propulsion system is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in Newton (N); BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in take-off mode in a standard atmosphere and at sea level; and G = 0.16 millimeters per Newton (mm / N) and H = 18 millimeters (mm);

[0037] - an average radius of the bore of the high pressure turbine is at most equal to:

[0038] R m a < I * FN * BPR * 10“ 4 + J where: R m_a is the mean radius of the supplementary turbine bore in millimeters (mm); FN is the fan rotor thrust measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level and is expressed in Newtons (N); BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level; and I = 0.16 millimeters per Newton (mm / N) and J = 28 millimeters;

[0039] - the additional compressor comprises at least eight stages and at most eleven stages;

[0040] - the drive turbine comprises at least three stages and at most five stages; and / or

[0041] - a reduction rate of the reduction mechanism is greater than or equal to 2.5 and less than or equal to 11.

[0042] According to a second aspect, there is provided an aircraft comprising at least one propulsion system according to the first aspect, attached to the aircraft via a mast.

[0043] According to a third aspect, there is provided a method of dimensioning or manufacturing a propulsion system comprising a reduction mechanism coupling a drive shaft and a fan rotor to drive the fan rotor at a speed lower than a speed of the drive shaft, and bearings configured to center the drive shaft relative to the axis of rotation, the bearings comprising a front bearing extending upstream of a combustion chamber of the propulsion system and two rear bearings extending downstream of the combustion chamber, the propulsion system being dimensioned such that a position of the bearings in the propulsion system complies with the following formula: where: d2 is the distance between the centers of gravity of the rear bearings of the drive shaft, in millimeters (mm);

[0044] Rm is an average radius of the drive turbine, in millimeters (mm);

[0045] XN is the limiting speed of the drive shaft, in revolutions per minute (rpm); di is the distance between the center of gravity (Giia) of the front bearing and the center of gravity of the rear bearing closest to the front bearing, in millimeters (mm);

[0046] Rnb is an average radius of the rear landing closest to the front landing, in millimeters; and

[0047] C = 170 (mm*rpm) -1 , Ei = - 0.18.

[0048] Certain preferred but non-limiting features of the method of sizing or manufacturing a propulsion system according to the third aspect, wherein the propulsion system is sized such that the bearings are also positioned in the propulsion system such that the following formula is observed: where E2 = 0.378;

[0049] - the propulsion system is further dimensioned so that the limiting speed of the drive shaft complies with the following formula: 10 5 where A = 5500 mm*rpm;

[0050] - the propulsion system is also dimensioned so that the limiting speed of the drive shaft also complies with the following formula: 10 5 where B = 8500 mm*rpm;

[0051] - the propulsion system further comprises an additional turbine configured to drive a compressor via an additional shaft, the additional shaft being configured to rotate at a higher speed than the drive shaft around the axis of rotation, an average radius of a bore of the additional turbine complies with the following formula:

[0052] R m a < E * L HP 2 * XN * 10“ 9 + F, where: R m _a is the mean radius of the additional turbine bore in millimeters (mm); LHP is a distance between an additional compressor inlet and an additional turbine outlet in millimeters (mm); and E = 3.15 (mm.rpm) -1 and F1 = 23 millimeters (mm);

[0053] - the propulsion system further comprises an additional turbine configured to drive a compressor via an additional shaft, the additional shaft being configured to rotate at a higher speed than the drive shaft around the axis of rotation, an average radius of a bore of the additional turbine complies with the following formula:

[0054] R m _a > EU Hf S XN * 10“ + F2 where: R m _a is the mean radius of the additional turbine bore in millimeters (mm); LHP is a distance between an additional compressor inlet and an additional turbine outlet in millimeters (mm); and E = 3.15 (mm. rpm) -1and F2 = 13 millimeters (mm); - the propulsion system further comprises an additional turbine configured to drive a compressor via an additional shaft, the additional shaft being configured to rotate at a higher speed than the drive shaft around the axis of rotation, an average radius of a bore of the additional turbine complies with the following formula: where: Dg is the fan rotor diameter in millimeters, measured in a plane normal to the axis of rotation at an intersection between a tip and a leading edge of the fan rotor blades; BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level; T eis the temperature at the inlet of the drive turbine when the propulsion system is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in degrees Celsius (°C); T re f = 273K; n is the number of stages in the additional turbine and the additional compressor; GAMMA is the adiabatic coefficient of air; and K = 6.76, L = 153.6 rrr 1 .(°C)- 1 / 2 .(rpm)- 1 , M = 421 mm.(°C) 1 / 2 and Ni = -11 millimeters (mm);

[0055] - the propulsion system further comprises an additional turbine configured to drive a compressor via an additional shaft, the additional shaft being configured to rotate at a higher speed than the drive shaft around the axis of rotation, an average radius of a bore of the additional turbine complies with the following formula: where: Dg is the fan rotor diameter in millimeters, measured in a plane normal to the axis of rotation at an intersection between a tip and a leading edge of the fan rotor blades; BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level; T e is the temperature at the inlet of the drive turbine when the propulsion system is stationary in take-off mode in a standard atmosphere and at sea level and is expressed in degrees Celsius (°C); T re f = 273K; n is the number of stages in the additional turbine and the additional compressor; GAMMA is the adiabatic coefficient of air; and K = 6.76, L = 153.6 rrr 1 .(°C)- 1 / 2 .(rpm)- 1 , M = 421 mm.(°C) 1 / 2 and N2 = - 21 millimeters (mm);

[0056] - the propulsion system further comprises an additional turbine configured to drive a compressor via an additional shaft, the additional shaft being configured to rotate at a higher speed than the drive shaft around the axis of rotation, an average radius of the bore of the additional turbine being at least equal to:

[0057] R m a > G * FN * BPR * 10“ 4 + H where: R m_a is the mean radius of the additional turbine bore in millimeters (mm); FN is the fan rotor thrust measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level and is expressed in Newtons (N); BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in takeoff mode in a standard atmosphere and at sea level; and G = 0.16 millimeters per Newton (mm / N) and H = 18 millimeters (mm); and / or

[0058] - the propulsion system further comprises an additional turbine configured to drive a compressor via an additional shaft, the additional shaft being configured to rotate at a higher speed than the drive shaft around the axis of rotation, an average radius of the bore of the high pressure turbine being at most equal to:

[0059] R m a< I * FN * BPR * 10“ 4 + J where: R m _a is the mean radius of the supplementary turbine bore in millimeters (mm); FN is the fan rotor thrust measured when the propulsion system is stationary in takeoff regime in a standard atmosphere and at sea level and is expressed in Newton (N); BPR is the bypass ratio of the propulsion system and is measured when the propulsion system is stationary in takeoff regime in a standard atmosphere and at sea level; and I = 0.16 millimeters per Newton (mm / N) and J = 28 millimeters.

[0060] According to a fourth aspect, there is provided a method of manufacturing an aeronautical propulsion system comprising the following steps: dimensioning the aeronautical propulsion system in accordance with the dimensioning method according to the third aspect; and manufacturing the aeronautical propulsion system.

[0061] DESCRIPTION OF FIGURES

[0062] Other characteristics, aims and advantages will emerge from the following description, which is purely illustrative and not limiting, and which must be read in conjunction with the attached drawings in which:

[0063] Figure 1 is a schematic, partial and sectional view of an example of a propulsion system according to a first embodiment, in which the fan section is ducted;

[0064] Figure 2 is a schematic, partial, sectional view of an example of a propulsion system according to a first embodiment, in which the fan section is unducted;

[0065] Figure 3 is a schematic sectional view of an example of a reduction mechanism according to a first variant;

[0066] Figure 4 is a schematic sectional view of an example of a reduction mechanism according to a second variant;

[0067] Figure 5 is an example of an aircraft that may include at least one propulsion system according to the first or second embodiment;

[0068] Figure 6 is a flowchart illustrating examples of steps in a sizing or manufacturing process.

[0069] Throughout the figures, similar elements have identical references.

[0070] DETAILED DESCRIPTION OF THE INVENTION

[0071] A propulsion system 1 has a main direction extending along a longitudinal axis X and comprises, from upstream to downstream in the direction of flow of the gases in the propulsion system 1 when it is in operation, a fan section 2 and a primary body 3, often called a “gas generator”, comprising a compressor section 4, 5, a combustion chamber 6 and a turbine section 7, 8. The propulsion system 1 is here an aeronautical propulsion system 1 configured to be fixed to an aircraft 100 via a pylon (or mast).

[0072] The compressor section 4, 5 comprises a succession of stages each comprising a moving blade wheel (rotor) 4a, 5a rotating in front of a fixed blade wheel (stator) 4b, 5b. The turbine section 7, 8 also comprises a succession of stages each comprising a fixed blade wheel (stator) 7b, 8b behind which a moving blade wheel (rotor) 7a, 8a rotates.

[0073] In the present application, the axial direction corresponds to the direction of the longitudinal axis X, in correspondence with the rotation of the shafts of the gas generator, and a radial direction is a direction perpendicular to this axis X and passing through it. Furthermore, the circumferential (or lateral, or even tangential) direction corresponds to a direction perpendicular to the longitudinal axis X and not passing through it. Unless otherwise specified, internal (respectively, interior) and external (respectively, exterior), respectively, are used in reference to a radial direction so that the internal part or face of an element is closer to the axis X than the external part or face of the same element.

[0074] In operation, an air flow F entering the propulsion system 1 is divided between a primary air flow F1 and a secondary air flow F2, which circulate from upstream to downstream in the propulsion system 1.

[0075] The secondary airflow F2 (also called the "bypass airflow") flows around the primary body 3. The secondary airflow F2 cools the periphery of the primary body 3 and is used to generate most of the thrust provided by the propulsion system 1.

[0076] The primary air flow F1 flows in a primary vein inside the primary body 3, passing successively through the compressor section 4, 5, the combustion chamber 6 where it is mixed with fuel to serve as an oxidant, and the turbine section 7, 8. The passage of the primary air flow F1 through the turbine section 7, 8 receiving energy from the combustion chamber 6 causes rotation of the rotor of the turbine section 7, 8, which in turn drives rotation of the rotor of the compressor section 4, 5 as well as a rotor part 9 of the fan section 2.

[0077] In a twin-spool propulsion system 1, the compressor section 4, 5 may comprise a low-pressure compressor 4 and a high-pressure compressor 5. The turbine section 7, 8 may comprise a high-pressure turbine 7 and a low-pressure turbine 8. The rotor of the high-pressure compressor 5 is rotated by the rotor of the high-pressure turbine 7 via a high-pressure shaft 10. The rotor of the low-pressure compressor 4 and the rotor portion 9 of the fan section 2 are rotated by the rotor of the low-pressure turbine 8 via a low-pressure shaft 11. Thus, the primary body 3 comprises a high-pressure body comprising the high-pressure compressor 5, the high-pressure turbine 7 and the high-pressure shaft 10, and a low-pressure body comprising the fan section 2, the low-pressure compressor 4, the low-pressure turbine 8 and the low-pressure shaft 11.The rotational speed of the high-pressure spool is greater than the rotational speed of the low-pressure spool. In a triple-spool propulsion system 1, the turbine section 7, 8 further comprises an intermediate turbine, positioned between the high-pressure turbine 7 and the low-pressure turbine 8 and configured to drive the rotor of the low-pressure compressor 4 via an intermediate shaft. The fan rotor 9 and the rotor of the high-pressure compressor 5 remain driven by the low-pressure shaft 11 and the high-pressure shaft 10, respectively.

[0078] The low pressure shaft 11 is generally housed, over a section of its length, in the high pressure shaft 10 and is coaxial with the high pressure shaft 10. The low pressure shaft 11 and the high pressure shaft 10 may be co-rotating, i.e. driven in the same direction around the longitudinal axis X. Alternatively, the low pressure shaft 11 and the high pressure shaft are counter-rotating, i.e. driven in opposite directions around the longitudinal axis X. Where appropriate, the intermediate shaft is housed between the high pressure shaft 10 and the low pressure shaft 11. The intermediate shaft and the low pressure shaft 11 may be co-rotating or counter-rotating.

[0079] The fan section 2 comprises at least the fan rotor 9 adapted to be driven in rotation relative to a stator part of the propulsion system 1 by the turbine section 7, 8. Each fan rotor 9 comprises a hub 13 and blades 14 extending radially from the hub 13. The blades 14 of each rotor 9 may be fixed relative to the hub 13 or have a variable pitch. In this case, the root of the blades 14 of each rotor 9 is pivotally mounted along a pitch axis and is connected to a pitch change mechanism 15 mounted in the propulsion system 1, the pitch being adjusted according to the flight phases by the pitch change mechanism 15. The pitch change mechanism 15 is illustrated in broken lines in Figure 1 to show that this feature is optional.

[0080] The fan section 2 may further comprise a fan stator 16, or rectifier, which comprises blades 17 mounted on a hub of the fan stator 16 and have the function of straightening the secondary air flow F2 which flows out of the fan rotor 9. The blades 17 of the fan stator 18 may be fixed relative to the hub or have a variable pitch. In a similar manner to the rotor blades 14, the root of the stator blades 17 is pivotally mounted along a pitch axis X and is connected to a pitch change mechanism 15a, which is generally separate from that of the fan rotor 9, the pitch being adjusted according to the flight phases by the pitch change mechanism.

[0081] The diameter Dg of the fan rotor 9 can then be between 2.032 meters (m) (80 inches) and 4.699 meters (m) (185 inches) inclusive, which makes it possible to obtain thrusts in the ranges described above. When the fan rotor 9 is shrouded, the diameter Dg is for example between 2.159 meters (m) (85 inches) and 3.048 meters (m) (120 inches) inclusive, for example equal to 2.286 meters (m) (90 inches), which makes it possible to integrate the propulsion system 1 in a conventional manner, in particular under the wing of an aircraft. When the fan rotor 9 is unducted, the diameter Dg is for example greater than or equal to 2.54 meters (m) (100 inches), for example between 3.048 meters (m) 120 inches and 3.962 meters (m) (156 inches). The diameter Dg of the fan rotor 9 is measured here in a plane normal to the axis X of rotation at an intersection between a tip 21 and a leading edge 22 of the blades 14 of the fan rotor 9, and is expressed in meters.Note that since Figures 1 and 2 are partial views, the diameter Dg is only partially visible. The fan rotor 9 also comprises at least twelve blades 14 and at most twenty-four blades 14, for example at least sixteen blades 14 and at most twenty-two blades 14. The number of blades 16 in the fan stator 17 depends on the acoustic criteria defined for the propulsion system 1 and is at least equal to the number of blades 14.

[0082] In order to improve the propulsive efficiency of the propulsion system 1 and to reduce its specific consumption as well as the noise emitted by the fan section 2, the propulsion system 1 has a high bypass ratio. By high bypass ratio, we mean here a bypass ratio greater than or equal to 10, for example between 10 and 80 inclusive. To calculate the bypass ratio, the mass flow rate of the secondary air flow F2 and the mass flow rate of the primary air flow F1 are measured when the propulsion system 1 is stationary, uninstalled, in takeoff mode in a standard atmosphere (as defined by the International Civil Aviation Organization (ICAO) manual, Doc 7488 / 3, 3 eedition) and at sea level (conditions known as SLS, for Seal Level Standard). It will be noted that, in the present application, the parameters (pressure, flow rate, thrust, speed, etc.) are systematically determined under these conditions. By "not installed", it will be understood here that the measurements are carried out when the propulsion system 1 is in a test bench (and not installed on an aircraft 100), the measurements then being simpler to carry out. The distances (length, radius, diameter, etc.) are, on the other hand, measured at ambient temperature (approximately 20°C) when the propulsion system 1 is cold, that is to say when the propulsion system 1 has been stopped for a sufficient period for the parts of the propulsion system to be at ambient temperature, it being understood that these dimensions vary little compared to the conditions in which the propulsion system 1 is in take-off mode.

[0083] The fan rotor 9 is decoupled from the low-pressure shaft 11 by means of a reduction mechanism 19, placed between an upstream end of the low-pressure shaft 11 and the fan rotor 9, in order to independently optimize their respective rotational speed. In this case, the propulsion system 1 further comprises an additional shaft, called the fan shaft 20. The low-pressure shaft 11 connects the low-pressure turbine 8 to an inlet of the reduction mechanism 19 while the fan shaft 20 connects the outlet of the reduction mechanism 19 to the fan rotor 9. The fan rotor 9 is therefore driven by the low-pressure shaft 11 via the reduction mechanism 19 and the fan shaft 20 at a rotational speed lower than the rotational speed of the low-pressure turbine 8.

[0084] This decoupling makes it possible to reduce the rotational speed and the pressure ratio of the fan rotor 9 and to increase the power extracted by the low-pressure turbine 8. Indeed, the overall efficiency of the propulsion systems is conditioned to the first order by the propulsive efficiency, which is favorably influenced by a minimization of the variation in kinetic energy of the air when passing through the propulsion system 1. In a propulsion system 1 with a high bypass ratio, the majority of the flow generating the propulsive force is constituted by the secondary air flow F2 of the propulsion system 1, the kinetic energy of the secondary air flow F2 being mainly affected by the compression that the secondary air flow F2 undergoes when passing through the fan section 2. The propulsive efficiency and the pressure ratio of the fan section 2 are therefore linked: the lower the pressure ratio of the fan section 2, the better the propulsive efficiency will be.In order to optimize the propulsive efficiency of the propulsion system 1, the pressure ratio of the fan, which corresponds to the ratio between the average pressure at the outlet of the fan stator 17 (or, in the absence of a stator, of the fan rotor 9) and the average pressure at the inlet of the fan rotor 9, is less than or equal to 1.70, for example less than or equal to 1.50, for example between 1.05 and 1.45. The average pressures are measured here over the height of the blade 14 (from the surface which radially delimits the flow path at the inlet of the fan rotor 9 to the tip 21 of the fan blade 14).

[0085] The propulsion system 1 is configured to provide thrust between 18,000 Ibf (80,068 N) and 51,000 Ibf (22,2411 N), for example between 20,000 Ibf (88,964 N) and 35,000 Ibf (15,5688 N).

[0086] The fan section 2 may be ducted or unducted. In the case of a ducted fan section 2, the fan section 2 comprises a fan casing 12 and the fan rotor 9 is housed in the fan casing 12.

[0087] A ducted fan section 2 comprises a fan rotor 9 extending upstream of a fan stator. The vanes of the fan stator are then generally called outlet vanes (“Outlet Guide Vane” or “OGV” in English) and have a fixed pitch relative to the hub of the fan stator. Furthermore, the bypass ratio of the propulsion system 1 is for example greater than or equal to 10, for example between 10 and 35 inclusive, for example between 10 and 18 inclusive. The peripheral speed at the tip 21 of the vanes of the fan rotor 9 may also be between 260 m / s and 400 m / s. The vanes 14 of the fan rotor 9 may be fixed or have a variable pitch. The fan pressure ratio may then be between 1.20 and 1.45.

[0088] In an unducted fan section 2, the fan section 2 (which may also be referred to as the propeller) is not surrounded by a fan casing. Since the fan section 2 is unducted, the blades 14 of the fan rotor 9 have a variable pitch. Propulsion systems comprising at least one unducted fan rotor 9 are known by the terms “open rotor” or “unducted fan”. The propulsion system 1 may comprise two unducted and counter-rotating fan rotors 9. Such a propulsion system 1 is known by the acronym CROR for “Contra-Rotating Open Rotor” or UDF for “Unducted Double Fan”. The fan rotor(s) 9 may be placed at the rear of the primary body 3 so as to be of the pusher type or at the front of the primary body 3 so as to be of the tractor type.Alternatively, the propulsion system 1 may comprise a single unducted fan rotor 9 and an unducted fan stator 16 (straightener). Such a propulsion system 1 is known by the English acronym USF for “Unducted Single Fan”. In the case of a propulsion system 1 of the USF type, the blades 17 of the straightener 16 are fixed in rotation relative to the axis X of rotation of the upstream fan rotor 9 and consequently do not undergo centrifugal force. The blades 17 of the straightener 16 are also variable-pitch.

[0089] The removal of the fairing around the fan section 2 makes it possible to increase the bypass ratio very significantly without the propulsion system 1 being penalized by the mass of the casings or nacelles intended to surround the fan section 2. The bypass ratio of the propulsion system 1 comprising an unfaired fan section 2 is thus greater than or equal to 40, for example between 40 and 80 inclusive. The peripheral speed at the tip 21 of the blades 14 of the fan rotor(s) 9 may also be between 210 m / s and 260 m / s. The fan pressure ratio may then be between 1.05 and 1.20, for example.

[0090] The reduction mechanism 19 may comprise, for example, a reduction mechanism 19 with an epicyclic gear train, for example of the “epicyclic” type or of the “planetary” type, single-stage or two-stage.According to a first variant, the reduction mechanism 19 may be of the planetary type (“star” in English) (Figure 3) and comprise a sun gear 19a (input of the reduction mechanism 19), centered on an axis X of rotation of the reduction mechanism 19 (generally confused with the longitudinal axis X) and configured to be driven in rotation by the low pressure shaft 11, a ring gear 19b (output of the reduction mechanism 19) coaxial with the sun gear 19a and configured to drive the fan shaft 20 in rotation around the axis X of rotation, and a series of satellites 19c distributed circumferentially around the axis X of rotation between the sun gear 19a and the ring gear 19b, each satellite 19c being meshed internally with the sun gear 19a and externally with the ring gear 19b.The series of satellites 19c is mounted on a planet carrier 19d which is fixed relative to a stator part 19e of the propulsion system 1, for example relative to a casing of the compressor section 4, 5. According to a second variant, the reduction mechanism 19 may be of the epicyclic type (“planetary” in English) (Figure 4), in which case the crown 19b is fixedly mounted on the stator part 19e of the propulsion system 1 and the fan shaft 20 is driven in rotation by the planet carrier 19d (which is therefore movable in rotation relative to a stator part 19e of the propulsion system 1, for example relative to a casing of the compressor section 4, 5).

[0091] Whatever the configuration of the reduction mechanism 19, the diameter of the crown 19b and the planet carrier 19d are greater than the diameter of the sun gear 19a, so that the rotation speed of the fan rotor 9 is lower than the rotation speed of the low pressure shaft 11.

[0092] The reduction ratio of the reduction mechanism 19 is greater than or equal to 2.5 and less than or equal to 11. In the case of a propulsion system 1 comprising a shrouded fan rotor 9, the reduction ratio may be greater than or equal to 2.7 and less than or equal to 6.0, typically around 3.0. In the case of a propulsion system 1 comprising an unshrouded fan rotor, the reduction ratio may be between 9.0 and 11.0.

[0093] The low pressure shaft 11 is supported by three or four bearings 11a, 11b and / or 11c, in order to control the deformation modes of the low pressure shaft 1. The low pressure shaft 11 can thus comprise one or two front bearings 11a, which extend upstream of the combustion chamber 6, and two rear bearings 11b, 11c, which extend downstream of the combustion chamber 6. The bearings 11a, 11b, 11c comprise an inner ring mounted on the low pressure shaft 11 and an outer ring mounted on a stator part of the propulsion system 1, typically on a casing of the propulsion system 1 through which forces pass in the propulsion system 1. Thus, a first front bearing 11a can be mounted on the one hand on the low pressure shaft 11 and on the other hand on an inlet casing 26 of the propulsion system 1, which extends between the fan rotor 9 and the low pressure compressor 4.If necessary, a second front bearing can be mounted on the one hand on the low pressure shaft 11 and on the other hand on an inter-compressor casing 23 (or intermediate casing) or on the inlet casing 26 of the propulsion system 1, i.e. between the low pressure compressor 4 and the high pressure compressor 5. A first rear bearing 11 b can be mounted on the one hand on the low pressure shaft 11 and on the other hand on the inter-turbine casing 24 (i.e. on the casing extending between the high pressure turbine 7 and the low pressure turbine 8), upstream of the low pressure turbine 8. Alternatively, the first rear bearing 11 b can be mounted on the exhaust casing 27, which extends immediately downstream of the low pressure turbine 8. The first rear bearing 11 b extends downstream of the bearing 12b furthest downstream of the high pressure shaft 10. The second rear bearing 11c can be mounted on the exhaust casing 27 or, if integration allows, on the inter-turbine casing.If necessary, the first and second rear bearings 11b, 11c can be mounted on the same cylindrical shell, which is itself fixed to the exhaust casing 27.

[0094] In one embodiment, the low pressure shaft 11 is supported by a front bearing 11a and two rear bearings 11b, 11c.

[0095] The dual-body propulsion system 1 may in particular comprise a two-stage high-pressure turbine 7, a high-pressure compressor 5 comprising at least eight stages and at most eleven stages, a low-pressure turbine 8 comprising at least three stages and at most five stages and a low-pressure compressor 4 comprising at least two stages and at most four stages.

[0096] The presence of the reduction mechanism 19 between the low pressure shaft 11 and the fan shaft 20 makes it possible to significantly increase the rotational speed of the low pressure spool (which comprises the low pressure turbine 8, the low pressure shaft 11 and, where appropriate, the low pressure compressor 4 in the case of a twin-spool propulsion system), in comparison with a direct drive engine (where the fan shaft 20 is driven directly by the low pressure shaft 11 and rotates at the same rotational speed as the low pressure shaft 11) and to reduce the number of stages in the low pressure turbine 8. This thus makes it possible to reduce the radial and axial size of the low pressure turbine 8 as well as its mass, which improves the specific consumption of the propulsion system 1.At the same time, the reduction in the fan pressure ratio reduces the amount of energy required to drive the fan rotor 9, so that the inlet flow rate of the high-pressure compressor 5 and therefore the inlet section of the high-pressure compressor 5 can be reduced. This, however, has the consequence of limiting the space available for the low-pressure shaft 11 (since the low-pressure shaft 11 is housed within the high-pressure shaft 10) and therefore contributes to reducing the diameter of the low-pressure shaft 11.

[0097] These modifications to the propulsion system 1 have the effect of modifying the deformation modes of the low pressure shaft 11. As a result, the low pressure shaft 11 is likely to exceed a critical speed and enter into resonance in the operating ranges of the low pressure body. At resonance, which occurs when the low pressure shaft 11 passes through the critical speed, the latter undergoes overvoltage phenomena which amplify the deformations and forces caused by the (inevitable) unbalances of the low pressure body. In order to control the dynamic behavior of the low pressure shaft 11 and to move the deformation modes of the low pressure shaft 11 into an operating range of the low pressure body which is not likely to damage the propulsion system 1, the bearings 11a, 11b, 11c of the low pressure shaft 11 are placed radially and axially so as to comply with the following formula: where: d2 is the distance between the centers of gravity Giib and Gnc of the rear bearings 1 1 b, 11c of the low pressure shaft 11 , in millimeters (mm);

[0098] R m is an average radius of the low pressure turbine 8, in millimeters (mm);

[0099] XN is the limiting speed of the low pressure shaft (11), in revolutions per minute (rpm); di is the distance between the center of gravity Gna of the front bearing 11a and the center of gravity Giib of the rear bearing 11b closest to the front bearing 11a, in millimeters (mm);

[0100] Rnb is an average radius of the rear bearing 11b closest to the front bearing 11a, in millimeters (mm); and

[0101] C = 170 (mm*rpm) -1 , Ei = 0.18 (dimensionless). di, d2, Rm, Riib, and Dg being distances, these parameters are determined when the propulsion system 1 (and therefore the fan section 2) is cold, as specified above.

[0102] The average radius Rmof the low pressure turbine 8 corresponds to the arithmetic mean of the mean radii of the rotors 8a (moving blade wheels) of the low pressure turbine 8. In a given stage, the mean radius R1 of a rotor 8a corresponds to the arithmetic mean between the external radius of the rotor 8a and the internal radius of the rotor 8a, where the external radius and the internal radius are measured between the axis of rotation X and the internal radial surface of the rotor 8a (which radially delimits the blade of the rotor 8a on the inside), when the propulsion system 1 is cold. It will be noted that the external radius and the internal radius are both measured in a plane normal to the axis of rotation X of the low pressure turbine 8 at the midpoint between the leading edge 8c at the tip of the moving blades and the trailing edge 8d at the tip of the moving blades (i.e. at 50% of the chord at the tip of the blade), between the axis of rotation X and the external radial surface of the rotor 8a (which radially delimits on the outside the blade of the rotor 8a).

[0103] The mean radius Rnb of the rear bearing 11b (respectively Rua of the front bearing 11a) corresponds to the distance, measured in a plane normal to the longitudinal axis X, between the axis X and the center of gravity Gnb of the rear bearing 11b closest to the front bearing 11a, i.e. the furthest upstream (respectively the center of gravity Gna of the rear bearing 11a). It will be noted here that a bearing comprises an outer ring and an inner ring which are coaxial as well as bearings (balls, rollers, etc.) mounted between the inner ring and the outer ring and configured to allow relative movement of the inner ring with respect to the outer ring. The inner ring is mounted on the low pressure shaft 11 and driven in rotation by the low pressure shaft 11; the outer ring is mounted on a stator part (inlet casing 26, inter-compressor casing 23, inter-turbine casing 24, exhaust casing 27, etc.) of the propulsion system 1.The center of gravity of a bearing then corresponds to the center of gravity of the assembly formed by the inner ring, the outer ring and the bearings. When the inner ring and / or the outer ring is formed integrally and in a single piece with a support (flange, ferrule, enclosure, etc.) of the propulsion system 1 so that the ring cannot be distinguished from the support, the center of gravity is determined without taking into account the ring in question.

[0104] When the low pressure shaft is supported by two front bearings upstream of the combustion chamber, the distance di is measured between the front bearing 11a closest to the combustion chamber 6 (i.e. the most downstream front bearing 11a) and the rear bearing 11b closest to the combustion chamber 6 (i.e. the most upstream rear bearing 11b). In other words, the distance di corresponds to the smallest distance between the centers of gravity of the front bearings 11a and the rear bearings 11b.

[0105] When the low pressure shaft 11 is supported by exactly two rear bearings 11b, 11c (and one or two front bearings 11a), the distance d2 is measured between the centers of gravity Giib and Gnc of these two bearings 11b and 11c. When the low pressure shaft 11 is supported, in addition to the front bearing(s) 11a, by exactly three rear bearings, the distance d2 is measured between the most upstream bearing and the most downstream bearing of the rear bearings.

[0106] The limiting speed XN corresponds to the absolute maximum speed likely to be encountered by the low pressure shaft 11 during the entire flight (according to the European certification regulation EASA CS-E 740 (or according to the American certification regulation 14-CFR Part 33)). The limiting speed corresponds to the maximum rotation speed when the propulsion system is healthy (and potentially at the end of its life). It is therefore likely to be reached by the low pressure shaft 1 1 in flight conditions. This limiting speed is part of the data declared in the engine certification (type certificate data sheet). Indeed, this rotation speed is usually used as a reference speed for the dimensioning of propulsion systems 1 and in certain certification tests (such as blade loss or rotor integrity tests).

[0107] The Applicant has noticed that the position of the bearings 11a-11c of the low pressure shaft 11 has an impact on the embedding of the low pressure shaft 11. In particular, the closer the rear bearings 11a-11c are to each other (low d2), the greater the embedding of the low pressure shaft 11, the lower the stiffness of the low pressure shaft 11 and the lower the deformation modes of the low pressure shaft 11 and the more likely they are to be within the operating range of the low pressure body. Similarly, the larger the diameter of the shaft (which is proportional to the mean radius of the rear bearing, Rm>) and / or the smaller the distance between the front and rear bearings (di), the lower the deformation modes. Thus, when the position of the bearings 11a-11c respects the formula (1), the stiffness of the low pressure shaft 11 increases sufficiently to better embed the low pressure shaft 11.Typically, for a propulsion system comprising a reduction mechanism 19, the first mode of deformation of the low pressure shaft 11 then occurs at a transient speed corresponding for example to a speed lower than the idle speed and is therefore not likely to damage the propulsion system 1. Thus, a transient speed is chosen which only occurs for a very short time in the operation of the propulsion system 1. For example, the propulsion system is dimensioned so that the critical speed corresponds to a speed occurring only at the beginning of the start or at the end of the stop of the propulsion system 1, such as a speed lower than the idle speed or higher than the idle speed but outside a regular operating range or in a very little used and transient operating range during the operation of the propulsion system 1.The low pressure shaft 1 1 can therefore be supercritical while having a controlled dynamic situation.

[0108] It is possible to modify the critical speed XN of the low pressure shaft 11 by acting on the following elements of the propulsion system 1:

[0109] 1. Shaft geometry (outer diameters and inner diameters). The outer diameter of the low pressure shaft impacts the design of the high pressure body, since the low pressure shaft 11 passes through the high pressure shaft 10 and constrains the bore radius of the high pressure turbine 7. In addition, variations in the internal shape allowing an increase in the critical speed of the low pressure shaft 11 are limited by the manufacturing constraints of the low pressure shaft 11.

[0110] 2. The material of the low-pressure shaft 11 (effect of the Young's modulus / density ratio). Conventionally, steels are used with small variations in Young's modulus. Alternatively, the low-pressure shaft 11 can also be made of metal matrix composite materials, which have a significantly higher Young's modulus / density ratio but a lower torque transfer capacity at the interfaces than conventional steels.

[0111] 3. The number and position of the bearings 11a-11d of the low pressure shaft 11. Indeed, an architecture in which the low pressure shaft 11 is supported by four bearings makes it possible to increase the critical speed XN of the low pressure shaft 11. The addition of a bearing in comparison with a three-bearing configuration, however, increases the integration difficulties. If necessary, the rear bearings of the low pressure shaft 11 can be integrated upstream of the low pressure turbine 8, which makes it possible to increase the critical speed XN of the low pressure shaft 11 at the expense of the engine length.

[0112] 4. The stiffness of the journals between the rotors of the low pressure body. Indeed, increasing the stiffness of the journals makes it possible to increase the critical speed XN of the low pressure shaft 11. However, increasing the stiffness of the journals also increases the difficulties of production and integration.

[0113] In the case of propulsion systems with a high bypass ratio (BPR) and high overall compression ratio (OPR), the outside diameter of the low pressure shaft 11 and the distance between the low pressure bearings are strongly constrained by the integration of the high pressure spool, which leads to a supercritical dynamic situation that must be controlled. In order to avoid the length penalty linked to the integration of bearings for the low pressure shaft 11 upstream of the low pressure turbine, an adjustment of the distance d2 between the centers of gravity of the two rear bearings 11b, 11c of the low pressure shaft 11 in accordance with formulas (1) and (2) makes it possible to obtain the desired dynamic situation. Dimensioning the limiting speed XN so as to comply with formulas (3) and (4) (see below) also makes it possible to optimize the integration of the high pressure spool while remaining within accessible ranges for the other parameters mentioned above.

[0114] Preferably, the bearings 11a, 11b, 11c of the low pressure shaft 11 are placed radially and axially so as to comply with the following formula: where: E2 = 0.378 (dimensionless).

[0115] When the position of the bearings 1 1a-11 c complies with formula (2), the bearings remain close enough to allow their integration under the low pressure turbine 8 and / or the exhaust casing 27 of the propulsion system 1 and limits the axial length of the low pressure body and therefore the weight and size of the propulsion system 1.

[0116] Preferably, the propulsion system 11 is dimensioned so that a limiting speed of the drive shaft 11 complies with the following formula: 10 5 (3) where A = 5500 mm*rpm.

[0117] The limiting speed XN of the low pressure shaft 11 may for example be between 8,500 revolutions per minute and 12,000 revolutions per minute, preferably between 9,000 revolutions per minute and 11,000 revolutions per minute.

[0118] When the limiting speed XN complies with formula (3) and the embedding of the bearings 11a-11c (i.e. the radial and axial position of the bearings 11a-11c) complies with formula (1) and where appropriate formula (2), the limiting speed is sufficiently high to ensure that the first deformation mode of the low pressure shaft 11 is within a rotational speed range of the low pressure shaft 11 in which the dynamic situation of the low pressure shaft 11 can be controlled.

[0119] Preferably, the speed limit XN also respects the following formula:

[0120] XN < B * ^ * 10 5 (4) where B = 8500 mm*rpm.

[0121] When the low pressure shaft 11 does not comply with formula (4), its limiting speed becomes too high and implies an unfavorable dynamic situation of the turbine shaft.

[0122] If necessary, in order to further improve the control of the dynamic situation and the vibration levels of the low pressure shaft 11, the bearings 11a-11c of the low pressure shaft 11 comprise a bearing mode damper 25 comprising a pressurized oil film configured to dampen the mode transition (viscous damping). This type of damping is generally known by the English term “squeeze film”. All or part of the bearings 11a-11c may also comprise a flexible cage, mounted between the outer ring and a rigid support fixedly secured to a stator part (inlet casing 26, inter-compressor casing 23, inter-turbine casing 24, exhaust casing 27, etc.) of the propulsion system 1 in order to control the stiffness of the bearings 11a-11c and to refine the position of the first deformation mode.The cage comprises for this purpose a generally cylindrical wall mounted between the rigid support and the outer ring of the bearing and radially deformable columns so as to allow radial displacement of the generally cylindrical wall and therefore of the bearing 11a-11c relative to the rigid support. Examples of bearings with flexible cage and of a pressurized fluid film damper comprising a flexible cage are described in documents WO 2021 / 001610 and WO 2022 / 195198 in the name of the Applicant. Damping the response of the low pressure shaft 11 using these bearing mode dampers 25 thus makes it possible to limit the resonance of the low pressure shaft when its frequency reaches the first deformation mode.

[0123] The bearings 11a-11c of the low pressure shaft 11 preferably comprise exactly three bearings, namely the front bearing 11a and the two rear bearings 11b, 11c.

[0124] It will be noted that formula (1) applies to any type of bearing. For example, the front bearing 11a may comprise a ball bearing, a tapered roller bearing or an angular contact ball bearing, and the rear bearings 11b, 11c may each comprise a roller bearing.

[0125] The low pressure shaft 11 being housed in the high pressure shaft 10, its diameter is constrained by the average radius R m_a of the bore of the high pressure turbine 7. However, the larger the diameter of the low pressure shaft 11, the more its natural modes appear at high rotational speeds (or, in other words, the more the shaft deformation modes are shifted towards high frequencies). In order to obtain a compromise between a small diameter average bore radius of the high pressure turbine 7 - which makes it possible to improve the overall compression ratio of the propulsion system and its BPR bypass ratio - while controlling the dynamic situation of the low pressure shaft 11, the average radius R m _a of a bore of the high pressure turbine 7 respects the following formula, in particular when the fan section 2 is shrouded:

[0126] R m a < E * L HP 2 * XN * 10“ 9 + F, (5) where: R m _a is expressed in millimeters (mm);

[0127] LHP is the length of the high pressure body, in millimeters (mm);

[0128] E = 3.15 (mm.rpm)' 1 and Fi = 23 millimeters (mm).

[0129] Indeed, and as we saw above, the deformation frequency of the low pressure shaft 1 1 is proportional to the ratio between the diameter of the low pressure shaft 1 1 and the distance squared (di 2 ) between the bearings 11a-11b of the low pressure shaft 11. Thus, the further apart the bearings 11a-11b supporting the low pressure shaft 11 are, the lower the deformation frequency (and therefore the deformation modes) of the low pressure shaft 11. However, the position of the bearings 11a-11b of the low pressure shaft 11 depends on the length of the high pressure body. By defining the average radius R m_a of the bore of the high pressure turbine 7 as a function of the length of the high pressure body LHP (which is formed of the high pressure compressor 5 and the high pressure turbine 7), the dynamic behavior of the low pressure shaft 11 can therefore be better controlled.

[0130] Preferably, the average radius R m _a of the bore of each disc of the high pressure turbine 7 respects the formula (5).

[0131] A propulsion system 1 with an average radius R m _a of the bore of the high pressure turbine 7 complies with formula (5) can then achieve an overall compression ratio, which corresponds to the pressure ratio between the pressure at the outlet of the high pressure compressor 5 and the pressure at the inlet of the fan rotor 9 (measured at the level of the foot of the fan rotor 9), to be greater than or equal to 40 and less than or equal to 70, preferably greater than or equal to 44 and less than or equal to 55.

[0132] The rotational speed of the high-pressure turbine 7 can then be between 15,000 revolutions per minute and 27,000 revolutions per minute. When the rotational speed of the high-pressure turbine (and therefore of the high-pressure shaft 10) is within this interval and its average radius R m _a respects the formula (4), the mechanical loading of the rotors 7a is acceptable for the high pressure turbine 7.

[0133] The length of the LHP high pressure body can, for example, be between 950 mm and 1450 mm for a high pressure body comprising between ten and thirteen compressor and turbine stages.

[0134] The average radius R m _a of a bore of the high pressure turbine 7 also respects the following formula, in particular when the fan section 2 is shrouded:

[0135] R m _a > EU HP 2 * XN * 10 9 + F2(6) where: F2 = 13 millimeters (mm).

[0136] Sizing the mean bore radius to comply with formula (6) ensures a minimum radius for the high pressure turbine and therefore guarantees its ability to withstand centrifugal forces.

[0137] In some cases, the average bore radius R m _a of the high pressure turbine 7 is dimensioned before the length of the high pressure body LHP can be determined. In this case, the mean bore radius can be determined from the fundamental dimensioning parameters of the diameter D9 of the fan rotor 9, the bypass ratio BPR of the propulsion system 1 or the limiting speed XN of the low pressure shaft 11, rather than the length of the high pressure body (as defined in formulas (5) and (6): Q5. 2 GAMMA \ ( T e + T ref CAMMA ~ 1 * 10 3 * n + MI * XN * 10“ 9 + N, (7) where: BPR is the dilution ratio of propulsion system 1;

[0138] Te is the inlet temperature of the low pressure turbine 8, in degrees Celsius;

[0139] Tref = 273 K; n is the number of stages in the high-pressure body (i.e. in the high-pressure turbine 7 and in the high-pressure compressor 5);

[0140] GAMMA is the adiabatic coefficient of air;

[0141] K = 6.76, L = 153.6 m- 1 .(°C)- 1 / 2 .(rpm)- 1 , M = 421 mm.(°C) 1 / 2 and Ni = - 11 millimeters (mm).

[0142] As specified for formula (6), when the average bore radius R m _a of the high pressure turbine 7 respects the formula (7), the dynamic behavior of the low pressure shaft 11 can therefore be better controlled.

[0143] Preferably, the average radius R m _a of the bore of each disc of the high pressure turbine 7 respects the formula (7).

[0144] In addition, the average bore radius also follows the following formula: 1 - . 2

[0145] / / Q 5 GAMMA \

[0146] R m a > K * L * * ( + T ref ) ' * 10 3 * n + MI * XN * 10“ 9 + N2(8) where N2 = - 21 millimeters (mm).

[0147] Preferably, the average radius R m _a of the bore of each disc of the high pressure turbine 7 complies with formula (8). Preferably, the propulsion system 1 is also dimensioned so that the average radius R m _a of the bore of the high pressure turbine 7 further complies with the following formula, in particular when the fan section 2 is shrouded:

[0148] R m a < I * FN * BPR * 10“ 4 + J (9) where: FN is the thrust of the fan rotor 9, in Newton (N); and

[0149] I = 0.16 millimeters per Newton (mm / N) and J = 28 millimeters (mm).

[0150] Indeed, the torque transmitted by the low pressure shaft 11 to the fan rotor 9 is linked to the thrust of the fan rotor 9 and to the BPR dilution ratio of the propulsion system 1. Furthermore, increasing the BPR dilution ratio of the propulsion system 1 makes it possible to reduce the diameter of the high pressure body, and therefore the average radius R m _a of the bore of the high pressure turbine 7. Thus, by dimensioning the propulsion system so that the average radius R m _a of the bore of the high pressure turbine 7 also respects the formula (9), we obtain a propulsion system 1 in which the size of the high pressure body and the diameter of the low pressure shaft 11 are dimensioned according to the thrust of the fan rotor 9 (which contributes mainly to the overall thrust of the propulsion system 1) and the BPR bypass ratio.

[0151] Preferably, the average radius R m_a of the bore of each disc of the high pressure turbine 7 respects the formula (9).

[0152] For example, the average radius of the high-pressure turbine bore is at most 300 mm.

[0153] In one embodiment, in order to maintain the possibility of introducing and passing the low pressure shaft 11 into the high pressure shaft 10, while ensuring the ability of the low pressure shaft 11 to transmit the torque necessary for the fan rotor 9 and the low pressure compressor 4, the average radius R m _a of the bore of the second turbine 7 further complies with the following formula, in particular when the fan section 2 is shrouded:

[0154] R m a > G * FN * BPR * 10“ 4 + H (10) where: G = 0.16 millimeters per Newton (mm / N) and H = 18 millimeters (mm).

[0155] Preferably, the average radius R m_a of the bore of each disc of the high pressure turbine 7 respects the formula (10).

[0156] Comparative example:

[0157] Engine 1 is a double-body propulsion system comprising a shrouded fan section 2 corresponding to the current technical standard (at the date of filing of this application) which we seek to improve.

[0158] The engine 2 is a double-body propulsion system 1 comprising a shrouded fan section 2 in accordance with the teaching of the present application, the drive shaft of which (i.e. here the low-pressure shaft) is supported by bearings which comply with the formulas (1) and (2) defined above. The engine 1 and the engine 2 both have a low-pressure shaft supported by exactly one bearing upstream of the combustion chamber and two bearings downstream of the combustion chamber. In addition, the front bearing comprises damping by a film of pressurized fluid.

[0159]

[0160] The ratio between the mean radius of the low pressure turbine and the inter-bearing distance d2 is greater than the maximum value defined by formula (2) as a function of the limiting speed of the low pressure shaft, the inter-bearing distance di and the radius of the upstream rear bearing Rnb of the low pressure shaft. The consequence is that the first deformation mode of the low pressure shaft, which is supercritical, occurs at a transient regime close to the take-off regime. As a result, the vibration loads seen during the mode transition are high despite the presence of the bearing mode damper. This is also evident from the fact that the limiting speed of the low pressure shaft of engine 1 is lower than the minimum limiting speed defined by formula (3) as a function of the radius of the upstream rear bearing Rnb of the low pressure shaft and the inter-bearing distance di.

[0161] In comparison, the ratio between the mean radius of the low-pressure turbine and the inter-bearing distance d2 of engine 2 complies with formulas (1) and (2). The stiffness of the low-pressure shaft is therefore increased, so that the first deformation mode of the low-pressure shaft, which is supercritical, occurs in a transient operating range closer to idle. The bearing mode damper also dampens the mode transition, knowing that the vibration loads are moderate in engine 2 in this operating range in comparison with the vibration loads experienced by engine 1. In addition, since the low-pressure shaft is more recessed, its diameter can be limited, despite the fact that it only drives seven stages in total (three compressor stages 4 and four turbine stages 8). The bearings that support the low-pressure shaft, however, remain sufficiently close to allow their integration under the low-pressure turbine.Finally, the average radius of the low pressure turbine 8 of engine 2 is smaller than that of engine 1, despite a greater number of stages, so that the low pressure turbine 8 of engine 2 is more radially compact than the low pressure turbine of engine 1.

[0162] Furthermore, the limiting speed of the low pressure shaft of engine 2 is higher than the minimum limiting speed defined by formula (3), so that the second deformation mode of the low pressure shaft is outside the operating range of engine 2. The limiting speed of the low pressure shaft of engine 2, however, remains lower than the maximum limiting speed defined in formula (4) to limit the vibration loads seen during the mode transition. The mechanical stresses in the low pressure shaft and in the low pressure turbine therefore remain acceptable, as is evident in particular from the mechanical loading parameter of the low pressure turbine XN 2Ss.

[0163] To move from engine 1 (reference) to engine 2 (compliant with the disclosure), the fan diameter Dg and the bypass ratio BPR were increased, which made it possible to improve the propulsive efficiency and to maintain a comparable fan thrust taking into account the reduction in the pressure ratio of the fan section 2. Furthermore, the overall compression ratio was increased, as well as the inlet temperature of the high pressure turbine 7, which made it possible to increase the thermal efficiency of the propulsion system 1.

[0164] Furthermore, the outside diameter of the low pressure turbine shaft 11 has been reduced to facilitate the integration of the high pressure body, in particular while respecting the mechanical dimensioning of the high pressure turbine discs.

[0165] The adjustment to obtain a critical speed of the first deformation mode of the low pressure shaft 11 in the speed range defined by formulas (1) to (4) was made by adapting the distance d2 between the centers of gravity of the rear bearings of the low pressure shaft 11 and by optimizing the internal geometry of the low pressure shaft 11 while respecting the manufacturing constraints of the shaft 11.

[0166] The number of bearings supporting the low pressure shaft was kept equal to 3 (and was not increased to 4) for reasons of integration of the bearing upstream of the low pressure shaft, taking into account the position of the low pressure compressor vein.

[0167] The solution of moving one of the two bearings or both bearings downstream of the low-pressure turbine upstream of it has also been ruled out to avoid lengthening engine 2 and a problem of misalignment between the two bearings.

Claims

CLAIMS 1. Aeronautical propulsion system (1) comprising: - a fan rotor (9) configured to be driven by a fan shaft (20); - a drive turbine (8) configured to drive the fan rotor (9) via a drive shaft (11) around an axis of rotation (X); - a reduction mechanism (19) coupling the drive shaft (11) and the fan shaft (20) in order to drive the fan shaft (20) at a rotational speed lower than the rotational speed of the drive shaft (11); - bearings (11a-11c) configured to center the drive shaft (11) relative to the axis of rotation (X), the bearings (11a-11c) comprising a front bearing (11a) extending upstream of a combustion chamber of the propulsion system (1) and two rear bearings (11b, 11c) extending downstream of the combustion chamber, wherein a position of the bearings (11a-11c) in the propulsion system (1) complies with the following formula: where: d2 is the distance between the centers of gravity (Gnb and Gnc) of the rear bearings (11 b, 11 c) of the drive shaft (11 ), in millimeters (mm); R m is an average radius of the drive turbine (8), in millimeters (mm); XN is the limiting speed of the drive shaft (1 1 ), in revolutions per minute (rpm); di is the distance between the center of gravity (Giia) of the front bearing (11a) and the center of gravity (Gnb) of the rear bearing (11 b) closest to the front bearing (11a), in millimeters (mm); Rnb is an average radius of the rear bearing (11b) closest to the front bearing (11a), in millimeters (mm); and C = 170 (mm*rpm)- 1 , Ei = 0.18 and E2 = 0.

378.

2. Propulsion system (1) according to claim 1, in which the limiting speed of the drive shaft (11) complies with the following formula: r 10 5 where A = 5500 mm*rpm.

3. Propulsion system (1) according to one of claims 1 and 2, in which the limiting speed of the drive shaft (11) complies with the following formula: r 10 5 where B = 8500 mm*rpm.

4. Propulsion system (1) according to one of claims 1 to 3, in which all or part of the bearings (11a-11c) of the drive shaft (11) are associated with a bearing mode damper (25).

5. A propulsion system according to claim 4, wherein the bearing mode dampers (25) comprise pressurized fluid film damping.

6. Propulsion system according to one of claims 4 and 5, in which each bearing mode damper (25) comprises a deformable cage mounted between an associated bearing ring and a stator part (23, 24, 26, 27) of the propulsion system (1).

7. Propulsion system according to one of claims 1 to 6, in which the bearings of the drive shaft (11) comprise at least one front bearing (11a) and exactly two rear bearings.

8. Propulsion system according to one of claims 1 to 7, further comprising an additional turbine (7) configured to drive an additional compressor (5) via an additional shaft (10), the additional shaft (10) being configured to rotate at a higher speed than the drive shaft (11) around the axis of rotation (X), the additional turbine being two-stage.

9. Propulsion system (1) according to claim 8, wherein the additional compressor (5) comprises at least eight stages and at most eleven stages.

10. Propulsion system (1) according to one of claims 1 to 9, in which the drive turbine (8) comprises at least three stages and at most five stages.

11. Propulsion system (1) according to one of claims 1 to 10, in which a reduction ratio of the reduction mechanism is greater than or equal to 2.5 and less than or equal to 1 1.

12. Aircraft comprising at least one propulsion system (1) according to one of claims 1 to 11 fixed to the aircraft by means of a mast.

13. A method for dimensioning a propulsion system (1) comprising a reduction mechanism (19) coupling a drive shaft (11) and a fan rotor (9) to drive the fan rotor (9) at a speed lower than a speed of the drive shaft (11), and bearings (11a-11c) configured to center the drive shaft (11) relative to the axis of rotation (X), the bearings (11a-11c) comprising a front bearing extending upstream of a combustion chamber of the propulsion system (1) and two rear bearings extending downstream of the combustion chamber, the propulsion system being dimensioned such that a position of the bearings (11a-11c) in the propulsion system (1) complies with the following formula: where: d2 is the distance between the centers of gravity (Giib and Gnc) of the rear bearings (11b, 11c) of the drive shaft (11), in millimeters (mm); R m is an average radius of the drive turbine (8), in millimeters (mm); XN is the limiting speed of the drive shaft (1 1 ), in revolutions per minute (rpm); di is the distance between the center of gravity (Giia) of the front bearing (11a) and the center of gravity (Gnb) of the rear bearing (11 b) closest to the front bearing (11a), in millimeters (mm); Rnb is an average radius of the rear bearing (11b) closest to the front bearing (11a), in millimeters (mm); and C = 170 (mm*rpm)- 1 , Ei = - 0.18 and E2 = 0.

378.

14. Method for dimensioning a propulsion system (1) according to claim 13, wherein the propulsion system (1) is further dimensioned so that the limiting speed of the drive shaft (11) complies with the following formula: r 105 where A = 5500 mm*rpm.

15. A sizing method according to one of claims 13 and 14, wherein the propulsion system is also sized so that the limiting speed of the drive shaft (11) further complies with the following formula: r 10 5 where B = 8500 mm*rpm.

16. Method of manufacturing an aeronautical propulsion system comprising the following steps: - dimensioning the aeronautical propulsion system in accordance with the method according to one of claims 13 to 15; and - manufacture the aeronautical propulsion system.

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