Method and system for manufacturing a movable blade with increased chord for an aircraft turbomachine

Abstract

A movable blade (33) of an aircraft turbomachine (2) is modified by obtaining (50) a position (H) in the height of the airfoil (330) of the blade as a function of a deformation of the airfoil in a first natural torsional mode; then modifying (52) the geometry of the airfoil section (602) at said position, the modification comprising stretching (520) the section by elongating a chord (700) connecting the leading edge (BA) of the section to the trailing edge (BF) of the section and reducing (522) the thickness (e) of the stretched section (602') to maintain a constant section surface with the airfoil before modification; then finally connecting the modified section (602'') to the root section (601) and the tip section (600) of the airfoil before modification.

Description

[0001] DESCRIPTION

[0002] TITLE: Method and system for manufacturing a moving blade with augmented chord for an aircraft turbomachine

[0003] technical field

[0004] The present invention relates to the general field of mechanical design of a turbine blade or vane of an aircraft turbomachine.

[0005] Previous techniques

[0006] Climate change is a major concern for many legislative and regulatory bodies worldwide. Indeed, various restrictions on carbon emissions have been, are being, or will be adopted by different countries. In particular, an ambitious standard applies to both new types of aircraft and those already in operation, requiring the implementation of technological solutions to bring them into compliance with current regulations. Civil aviation has been actively working for several years now to contribute to the fight against climate change.

[0007] Technological research efforts have already led to significant improvements in the environmental performance of aircraft. The Applicant takes into account factors impacting all phases of design and development to obtain aeronautical components and products that are less energy-intensive, more environmentally friendly, and whose integration and use in civil aviation have moderate environmental impacts, with the aim of improving aircraft energy efficiency. Consequently, the Applicant is continuously working to reduce its climate impact by employing methods and operating virtuous development and manufacturing processes that minimize greenhouse gas emissions to the minimum possible, thereby reducing the environmental footprint of its activities.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 on-board equipment, the development of the use of electrical technologies to provide propulsion, and finally aviation fuels.

[0008] In this context, aircraft turbomachine blades can be improved.

[0009] Blades are found in various engine components, for example in the fan, low-pressure and high-pressure compressors, and low-pressure and high-pressure turbines. One of the building blocks of these components is the rotor, which is made up of moving blades. Each blade consists of a blade attached at both ends to a root (to the rotor shaft) and to a wingtip or tip.

[0010] During the mechanical design of a blade, it is known to take into account the dynamic dimensioning (or frequency placement) of the blade, and more particularly of the blade blade, especially in order to limit the risks of damage of vibrational origin linked to aerodynamic resonance phenomena (such as wake effects of parts upstream of the blade) or mechanical phenomena (such as imbalances).

[0011] Indeed, the blade's vibrational potential is directly dependent on the upstream excitations (aerodynamic source) experienced by the blade, but also on its dynamic robustness, which is intrinsically linked to the blade's geometry and the materials used. The blade's dynamic robustness depends on its vibrational behavior, which is defined by its natural modes, each natural mode having a natural frequency and a modal deformation.

[0012] During operation, the blades are aerodynamically excited by several flows within the engine, which together form an aerodynamic excitation source. If the excitation frequency associated with these flows is equal to the frequency of one of the natural modes, the blade resonates and deforms, potentially leading to rapid component failure. Therefore, the dynamic dimensioning of a blade is typically performed by constructing its Campbell diagram. This involves plotting the curves representing the evolution of the frequency of a natural mode of the blade (associated with the same mode shape) as a function of the rotor's rotational speed. The excitation frequency curve(s) of this rotor are then superimposed on the natural mode frequency curves to form the Campbell diagram.

[0013] Aircraft engine blades exhibit several types of natural modes, such as torsional and bending modes. More precisely, the natural modes of a blade, in order of increasing frequency, are the first bending mode (called mode 1F), the first torsional mode (called mode 1T), and then subsequent bending and torsional modes. The first modes, 1F and 1T, are generally the most vulnerable because they are the most easily excitable.

[0014] The first step in the dynamic sizing of the blade is to correctly position the mode 1F (this choice largely determines the blade geometry, for example, the radii of the leading edge (BA) and trailing edge (BF)). Once the mode 1F is positioned, the mode 1T is then determined. The mode 1T is a relatively flat mode, meaning its frequency depends very little on the rotor speed. The mode 1T typically exhibits crossovers (or dynamic coincidences) with the excitation curves in the Campbell diagram.

[0015] Figure 1 schematically represents a Campbell diagram on which the engine speed RPM is found on the abscissa and the frequency F on the ordinate. It shows the frequency situation of a blade by superimposing the frequency of an excitation harmonic EXC and the frequency of a single natural mode MP, such as mode 1 T. This superposition shows at what speed RPMO a dynamic coincidence can appear.

[0016] A high-performance blade can therefore be designed, in its geometry and the material used, to limit the risks of dynamic coincidence for usual operating regimes, i.e. with a high rate of occurrence and a long holding time (for example in cruise, takeoff or landing).

[0017] However, the search for new generations of aircraft engines can lead to the development of new architectures that influence the aerodynamic excitation flows within the engine, resulting in a modification of the excitation curves. If a dynamic overlap is observed between the 1T mode and the wake of the new turbomachine architecture for typical operating conditions, the level of vibrational excitation of the existing blades may become unacceptable. Consequently, the existing blades are no longer suitable.

[0018] Description of the invention

[0019] Therefore, there is a need to remove this dynamic coincidence from the engine's operating range, while maintaining the aerodynamic performance of the blade. To achieve this, the frequency of mode 1T can be modified by adjusting the blade geometry.

[0020] Indeed, the geometry of the blade and the material used are elements that can strongly impact the frequency f of a local natural mode, as shown by the following (simplified) formula: where k represents the steepness in the (local) deformation zone and m the mass moving in the zone. Thus, the more one modifies the stiffness or the mass in the deformation zone of the mode, the more one modifies its mode frequency 1 T.

[0021] In this context, it is proposed to modify the geometry of the blade in the main deformation zone, without degrading aerodynamic performance and without modifying the mass of the blade in order not to modify the static stresses.

[0022] Thus, the invention relates to a movable turbine blade for an aircraft turbomachine, intended to be centered on a rotational axis, comprising a blade delimited by a leading edge, a trailing edge, an intrados (lower surface), and an extrados (upper surface), the intrados and extrados being connected by the leading and trailing edges. The leading edge is configured to be located upstream and the trailing edge downstream with respect to the direction of gas flow during operation. The blade extends along an extension direction between a blade root end and a blade tip end opposite the root end with respect to the extension direction. The leading and trailing edges have convex profiles, the respective convex portions of which extend in opposite transverse directions.The blade tip has a blade tip cross-section, and the blade root has a blade root cross-section. The blade tip cross-section is parallel to the blade root cross-section. The blade has a mid-height cross-section located, in the bulges of the leading and trailing edges, between 45 and 55%—for example, equidistant—from the height defined between the blade tip cross-section and the blade root cross-section. Each cross-section has a chord, which is the distance between the leading and trailing edges. A first ratio between the chord taken in the mid-height cross-section and the chord taken in the blade root cross-section is within the interval [0.9; 1.2], preferably within the interval [0.95; 1.2].A second ratio between the chord taken in the mid-blade height cross-section and the chord taken in the blade tip cross-section is within the range [1.2; 1.4]. Optionally, a third ratio, measured in the mid-blade height cross-section, between.

[0023] - a projected segment length, on the axis of rotation, of a segment connecting the leading edge to a center of gravity, and

[0024] - a projected length, on the axis of rotation, of the chord (of the mid-height cross-section), is within the interval [0.45; 0.53], preferably within the interval [0.45; 0.51],

[0025] The invention also relates to a movable turbomachine wheel, comprising a disc and at least one movable blade as defined above mounted on the outer periphery of the movable disc, wherein the disc is movable around the axis of rotation and the direction of extension of the blade is a radial direction with respect to the axis of rotation.

[0026] The invention also relates to a method for manufacturing a movable turbine blade for an aircraft turbomachine intended to be centered on a rotational axis, the blade comprising a blade delimited by a leading edge, a trailing edge, an intrados and an extrados, the intrados and extrados being connected to each other by the leading edge and the trailing edge, the leading edge being configured to be located upstream and the trailing edge being configured to be located downstream with respect to the direction of gas flow in operation, the blade extending along an extension direction between a blade root end and a blade tip end opposite to the blade root end with respect to the extension direction, the leading edge and the trailing edge having bulging profiles whose respective bulging parts extend in opposite transverse directions,The process comprises the following steps: obtaining a mid-height position of the moving blade, as a function of a deformation of the blade in a first natural mode of torsion, the mid-height position being located, in the bulging parts of the leading and trailing edges, between 45 and 55% of the height defined between a blade tip cross-section at the level of the blade tip and a blade root cross-section at the level of the blade tip, the blade tip cross-section being parallel to the blade root cross-section; modifying the geometry of a mid-height blade cross-section at said mid-height position, each cross-section having a chord which is a distance taken between the leading edge and the trailing edge, the modification comprising the following operations:

[0027] - stretch the mid-height cross-section of the blade by lengthening the chord taken from the mid-height cross-section of the blade, and

[0028] - reduce the thickness of the stretched section to maintain a constant surface area of ​​the mid-height blade cross-section with the blade before modification, and connect the modified section to the blade root cross-section and the blade tip cross-section before modification, so as to obtain a modified blade blade, in which a first ratio between the chord taken in the mid-height blade cross-section and the chord taken in the blade root cross-section is within the range [0.9; 1.2] and a second ratio between the chord taken in the mid-height blade cross-section and the chord taken in the blade tip cross-section is within the range [1.2; 1.4].

[0029] By stretching the section, we preserve the profile of the blade, and therefore its aerodynamic performance.

[0030] By further reducing the thickness of the section, the center of gravity of the blade is moved upstream (towards the leading edge), thus reducing the thickness of the blade forward and therefore the specific mass of the area of ​​significant deformation.

[0031] In this way, the frequency situation of the blade is modified by significantly lowering the frequency of mode 1 T. This results in an exit from a situation at risk of resonance.

[0032] Finally, by maintaining a constant cross-sectional area, the mass of the blade remains unchanged. The effect of the modification on the static / mechanical stresses of the blade is therefore minimal, or even nonexistent.

[0033] New blades can thus be manufactured / produced from existing blades to adapt to new aircraft turbomachinery architectures.

[0034] Preferably, obtaining the mid-blade height position involves determining a position where the blade deformation is significant relative to a threshold, or even maximal, in a first natural torsion mode.

[0035] In particular, the position along the blade height can be located equidistant from the blade tip cross-section and the blade root cross-section. Indeed, it has been observed that the area of ​​the blade with the greatest resonant displacement (mode 1T) is often the trailing edge at approximately 50% of the height. In one embodiment, the chord taken in the mid-blade height cross-section is lengthened by 5 to 20%, preferably by 10 to 15%, for example, by about 10%. These embodiments represent a compromise between a substantial reduction in the mode 1T frequency (15% for a 10% chord lengthening) and integration constraints (avoiding contact between parts) and manufacturing constraints (too angular a connection with the blade root or tip).

[0036] Preferably, the stretching of the mid-height blade cross-section is carried out using an affinity having as its direction an axis of the chord taken in the mid-height blade cross-section or an axis of a section between two control points of a skeleton of the mid-height blade cross-section, that is to say a geometric transformation in the plane (of the section) which provides a homothety about an axis (formed by the chord or locally by a skeleton of the section), without transformation (i.e., identity function) about an axis orthogonal to the axis of the homothety.

[0037] In one embodiment, reducing the thickness includes: identifying a master frame in the stretched section (i.e., the greatest thickness, normal to the skeleton of the section), and reducing the thickness of the section at the master frame by applying a thickness law between the master frame and each of the leading and trailing edges, until a surface area of ​​the stretched section is obtained equal to a surface area of ​​the mid-height blade cross section before modification.

[0038] In one embodiment, reducing the thickness involves modifying the upper surface profile of the blade in the stretched section, while maintaining an unchanged lower surface profile. This arrangement preserves the aerodynamic performance of the blade.

[0039] Preferably, the radii of curvature of the leading and trailing edges are kept constant when modifying the geometry of the mid-height cross-section of the blade. This arrangement allows the aerodynamic performance of the blade to be maintained.

[0040] In one embodiment, connecting the modified section to the blade root and blade tip cross sections includes: determining a center of gravity of the modified section, aligning the center of gravity with a blade gravity axis, and applying a profile matching law between the section aligned with the gravity axis and the blade root and blade tip cross sections.

[0041] The mechanical stresses on the blade are therefore not modified.

[0042] In one embodiment, a third ratio, measured in the mid-height blade cross-section after modification, between

[0043] - a projected segment length, on the axis of rotation, of a segment connecting the leading edge to a center of gravity, and

[0044] - a projected length, on the axis of rotation, of the string, is within the interval [0.45; 0.53],

[0045] The invention also relates to a movable turbine blade of an aircraft turbomachine, the geometry of which is modified in accordance with the above method.

[0046] Furthermore, the invention also relates to a manufacturing system for a movable blade for an aircraft turbomachine intended to be centered on a rotational axis, the blade comprising a blade delimited by a leading edge, a trailing edge, an intrados and an extrados, the intrados and extrados being connected to each other by the leading edge and the trailing edge, the leading edge being configured to be located upstream and the trailing edge being configured to be located downstream with respect to the direction of gas flow in operation, the blade extending along an extension direction between a blade root end and a blade tip end opposite to the blade root end with respect to the extension direction, the leading edge and the trailing edge having bulging profiles whose respective bulging parts extend in opposite transverse directions.The system includes: a memory for storing a digital model of a moving blade, a microprocessor configured to, from the digital model: obtain a mid-height position of the moving blade, as a function of a deformation of the blade in a first natural mode of torsion, the mid-height position being located, in the bulging parts of the leading and trailing edges, between 45 and 55% of the height defined between a cross-section of the blade tip at the level of the blade tip end and a cross-section of the blade root at the level of the blade tip end, the cross-section of the blade tip being parallel to the cross-section of the blade root, modify the geometry of a mid-height cross-section of the blade at said mid-height position, each cross-section having a chord which is a distance taken between the leading edge and the trailing edge, the modification comprising the following operations:.

[0047] - stretch the mid-height cross-section of the blade by lengthening the chord taken from the mid-height cross-section of the blade, and

[0048] - reduce the thickness of the stretched section to maintain a constant surface area of ​​the mid-height blade cross-section with the blade before modification, and connect the modified section to the blade root cross-section and the blade tip cross-section before modification, so as to obtain a modified numerical model of the blade blade, and use the modified numerical model to drive a mobile blade production equipment, in which a first ratio between the chord taken in the mid-height blade cross-section and the chord taken in the blade root cross-section is within the range [0.9; 1.2] and a second ratio between the chord taken in the mid-height blade cross-section and the chord taken in the blade tip cross-section is within the range [1.2; 1.4].

[0049] Brief description of the drawings

[0050] Other objects, features and advantages of the invention will become apparent from the following description, given solely by way of non-limiting example, and made with reference to the accompanying drawings in which:

[0051] Figure 1 represents a simplified Campbell diagram identifying a natural mode of a part in relation to an excitation harmonic; Figure 2 illustrates an example of the realization of a turbomachine structure, here a twin-body, dual-flow turbomachine;

[0052] Figure 3 is a partial longitudinal cross-sectional view of a low-pressure turbine from an aircraft turbomachine;

[0053] Figure 4 is a view of a blade of a low-pressure turbine;

[0054] Figure 5 is a flowchart of a method for modifying the geometry of a movable turbine blade of an aircraft turbomachine, according to an example of an embodiment of the invention;

[0055] Figure 6 illustrates the modification of the blade according to an example of an embodiment of the invention;

[0056] Figure 7 illustrates details of modification of a relevant section of the blade according to an example embodiment of the invention;

[0057] Figure 8 illustrates, by superimposition, an initial blade section and a modified blade section 602” according to an example of an embodiment of the invention;

[0058] Figure 9 superimposes the thickness curves of the initial and modified blade sections according to an example of an embodiment of the invention;

[0059] Figure 10 illustrates a system for manufacturing movable blades or blades for movable blades;

[0060] Figure 11 illustrates a cambered or "barrel-shaped" movable blade; and

[0061] Figure 12 illustrates examples of blade frequency gains as a function of three ratios RI, R2, R3 calculated for them.

[0062] For clarity, the same elements are designated by the same references in the different figures. Furthermore, the various figures are not drawn to scale, as is customary in schematic representations.

[0063] Detailed description of at least one embodiment

[0064] In the following description, when referring to absolute positional qualifiers, such as "front," "back," "top," "bottom," "left," "right," etc., or relative positional qualifiers, such as "above," "below," "superior," "inferior," etc., or to orientational qualifiers, such as "horizontal," "vertical," etc., unless otherwise specified, this refers to the orientation of the figures or to a component / device in its normal operating position. Unless otherwise specified, the expressions "about," "approximately," "roughly," and "in the order of" mean within 10%, preferably within 5%.

[0065] Figure 2 schematically illustrates the structure of a twin-spool, twin-flow turbomachine. The turbomachine 2 is centered on an axis of rotation X.

[0066] The double-flow turbomachine 2 comprises successively, in the direction of air circulation, i.e. from upstream (left in the figure) to downstream (right in the figure), an air inlet 20 and a blower 21, which delivers air on the one hand into a primary channel 22 and on the other hand into a secondary channel 23. By "channel", we mean the volume through which an airflow circulates.

[0067] The airflow circulating in the primary stream 22 passes successively through a low-pressure compressor 24a, a high-pressure compressor 24b, a combustion chamber 25, a high-pressure turbine 26a, and a low-pressure turbine 26b, before being ejected through a primary flow nozzle 220, providing the thrust generated by the turbomachine. Alternatively, the turbomachine 2 may comprise two counter-rotating low-pressure turbines, i.e., turbines that rotate in opposite directions around the longitudinal axis X of the turbomachine.

[0068] Furthermore, the secondary airflow circulating in the secondary vein 23 is ejected separately through a secondary flow nozzle 230, after passing through a series of guide vanes 231.

[0069] Whether in the fan 21, the compressors 24a, 24b, or the turbines 26a, 26b, these components include moving blades or rotors. Those of the turbines are driven by the flow of gases in the primary flow nozzle 220. Those of the fan and compressors are driven primarily by the energy recovered by the turbines. Figure 3 partially shows a longitudinal section of a low-pressure turbine 1 of an aircraft turbomachine, representative of turbine architectures comprising moving wheels or rotors, and fixed wheels or distributors, these wheels being equipped with blades.

[0070] It is understood that the present invention applies to any other aircraft turbomachine assembly equipped with movable wheels.

[0071] Figure 3 more precisely represents five stages of a low-pressure turbine 31. Regarding the orientation with respect to the general direction of gas flow through the turbine, the first stage of the turbine is located upstream and the last stage of the turbine is located downstream.

[0072] The first stage comprises a moving wheel formed of a rotor disk 32 on the outer periphery of which are radially mounted a plurality of movable blades 33. The other stages each comprise a distributor formed of a plurality of fixed blades 34 and a moving wheel placed behind the distributor and formed of a rotor disk 32' on which are radially mounted a plurality of movable blades 33'.

[0073] The discs 32, 32' are fixed to each other by means of bolted links 35, making all the discs fixed in rotation around the longitudinal axis XX of the turbomachine.

[0074] Each disk 32, 32' has at least one annular flange 6 which extends towards the disks 32, 32' of the adjacent floors.

[0075] Figure 4 shows a movable blade 33, which comprises a blade 330 extending radially along an extension direction Z between a blade tip end connected to a blade tip 331 and a blade root end connected to a blade root 332, opposite the blade tip end along the extension direction Z. The blade 330 extends longitudinally between a leading edge BA and a trailing edge BF and tangentially between an upper surface 334 and an lower surface 333, which are connected by the leading edge BA and the trailing edge BF, only the lower surface being visible in the figure. The leading edge BA is located upstream of the blade 330 and the trailing edge downstream of the blade 330, with respect to the direction of gas flow during the operation of the turbomachine 2.The Z extension direction is a radial direction of the blade 330 which is equivalent to a direction perpendicular to the X axis of rotation of the rotor when the blade 33 is mounted there.

[0076] A moving blade 33, and more specifically its blade 330, is designed taking into account aerodynamic performance, but also its natural modes and the excitation frequencies related to the upstream gas flow in the engine. In particular, a blade geometry is sought that exhibits a first torsional mode frequency (mode 1T) far removed from the engine's excitation harmonics, i.e., with sufficient dynamic margins with respect to the excitation harmonics.

[0077] The design of this blade geometry can be done by computer, resulting in the creation of a digital model of the moving blade 33 and more particularly of its blade 330.

[0078] As an illustration, a finite element blade modeling, for example using a 3D triangular or tetrahedral mesh, can be used.

[0079] For environmental reasons related to technological research efforts, it is preferable to reuse existing turbine blade geometries in new generations of aircraft engines. However, the evolution of turbomachine architecture leads to a modification of the excitation frequencies related to the gas flow upstream of the blades.

[0080] The method according to the invention for manufacturing and producing moving blades proposes a modification of the geometry of the already existing moving blade to significantly lower its frequency of the mode 1 T and thus get out of a situation at risk of resonance.

[0081] We will now describe, with reference to Figure 5, such a method 5 for modifying the geometry of a moving blade of an aircraft turbomachine, according to an example of implementation.

[0082] This process can be implemented using a computer in a computer-aided design (CAD) approach, starting from an existing digital model of the blade. The resulting design—a modified digital model of the blade—is used to control equipment or machinery for the production of turbine blades and, more generally, moving blades, for example, to control the manufacturing of a foundry mold or to control a 3D printer.

[0083] In step 50, a position is obtained within the blade height of the movable blade 33 to be modified, based on a deformation of the blade in the first natural torsional mode. The objective of this step is to identify a section of the blade 330 where geometric modifications to the cross-sectional profile have a significant effect on the frequency of mode 1T. This is why the blade deformation zones in this mode 1T are taken into account. The blade section is typically a cross-section in the extension direction Z.

[0084] In practice, it has been observed that the blade area with the greatest resonant displacement (generally on the order of hundredths to tenths of a millimeter for conventional aircraft turbomachine blades) is the trailing edge BF at approximately 45 to 55% of the blade height, with 0% corresponding to the blade root and 100% to the blade tip. Therefore, a height H can be chosen within this range, for example, at approximately 50% of the total height.

[0085] Furthermore, measurements on a real blade or computer simulations allow us to obtain a blade deformation profile. In this case, we can therefore choose a height H where the blade deformation is significant, that is, greater than a predefined threshold. A special case is when we choose the height corresponding to the maximum blade deformation 330.

[0086] Typically, a computer-aided design tool can define the 330 blade through several blade sections, including a blade tip section at the upper end of the blade, a blade root section at the lower end of the blade, and one or more intermediate blade sections at different height levels.

[0087] Figure 6, section (a), illustrates, for example, a blade 60 defined by three blade sections, including a blade tip section 600, a blade root section 601, and a single intermediate section 602 at mid-height (50%). Of course, other embodiments with a greater number of intermediate sections (for example, every 25%, 20%, 10%, or 5% of the height) can be considered. The three sections are typically transverse to the Z-extension direction and therefore parallel to each other.

[0088] The profile of the 610 blade between successive sections can follow a profile transition law. For example, the profile transition law can be a linear law. Alternatively, more complex laws can be used to smooth the profile while avoiding significant geometric changes.

[0089] The position obtained in the blade height can, for example, correspond to the position of the intermediate section closest to the maximum deformation of the blade (in its BF zone), i.e. at mid-height (H=50%) in the example of Figure 6.

[0090] Once position H is obtained, and consequently the blade cross-section 602 at this position H is known, step 52 consists of modifying the geometry of the blade cross-section, while maintaining the same surface area. The objective of this step is to move the center of gravity of the cross-section upstream (i.e., towards the leading edge BA), without altering its mass or its general shape, which defines its aerodynamic performance. In this way, the frequency of mode 1T can be significantly lowered without modifying the static / mechanical stresses of the blade, thus avoiding a situation at risk of resonance.

[0091] E' modification step 52 comprises two successive sub-steps 520 and 522, illustrated by Figure 7.

[0092] Sub-step 520 consists of stretching the 602 section by lengthening the 700 chord of the section profile, i.e., increasing the length of the segment connecting the leading edge BA of the section to the trailing edge BF of the section. A stretched 602' section is obtained.

[0093] Several stretching functions can be used.

[0094] For example, we can establish an affinity along the chord axis (director axis) with an affinity ratio X greater than 1, meaning that section 602 undergoes increasing homothety only along the axis XI formed by chord 700, the component along the axis Y1 perpendicular to the chord remaining unchanged (identity function). Taking the reference frame (O,X1,Y1) of Figure 7 section (a), the geometric transformation of each point P(x,y) forming the profile of section 602 in this reference frame leads to a point P'(Xx,y) shown in Figure 7 section (b).

[0095] The affinity (or homothety) ratio X defines the elongation of the chord 700, and therefore of the segment BA-BF. This ratio is between 5 and 20%. Preferably, it is chosen between 10 and 15%, for example 10% as illustrated in the Figure.

[0096] The basis of the affinity is a straight line A that intersects the chord 700 perpendicularly (i.e., the segment BA-BF), at a point denoted C. A represents the points invariant under the implemented geometric affinity. For example, C is the leading edge BA, or the trailing edge BF, or the foot of the height passing through the mid-section 701 (at its midpoint, as in the Figure) corresponding to the maximum thickness of the section along a normal to the skeleton (or mean or median line) 702 of the section 602, or the foot of the height passing through the center of gravity CG I of the section 602, or any other location on the chord.

[0097] Each point P is therefore transformed by homothety with ratio X and center the point of intersection between A and the parallel to the chord 700 passing through P.

[0098] As an alternative to a general affinity, a local affinity can be used where the direction of the affinity is the axis defined by two successive control points of the 702 skeleton of the blade section. Thus, each "subsection" of the blade section 602 is modified by its own affinity, the direction of which varies. The affinity ratio X remains the same.

[0099] Figure 7 section (a') illustrates, for example, the blade section 602 with its skeleton 702 on which PCx control points have been positioned. The PCx control points can be defined at regular intervals, for example every 5% or 10% of the skeleton 702 between the leading edge and the trailing edge.

[0100] The blade section is constructed, for example, by defining two profile points P1 and P2 (one intrados point and one extrados point) for each of the control points PC, typically on a normal to the skeleton and at a defined distance (which varies for each PC point). A local affinity to the subsection between control point PC1 and control point PCj consists of using the (PC1 PCj) axis as the direction of scaling, simply increasing the distance PC1 PCj. As illustrated in section (b') of Figure 7, the distance d of the segment (PC1 PCj) is stretched to equal Xd in the stretched section 602'. The two points P1 and P2 are maintained at a (defined) distance from their control point PCx.

[0101] For illustrative purposes, for conventional turbomachine blades, the elongation will be on the order of a few millimeters at most, typically between 0.5 mm and 2 mm.

[0102] The minimum value of 5% guarantees a substantial reduction in the frequency of mode 1T as desired for the invention. The maximum value of 20% guarantees compliance with integration constraints such as the presence of other parts in the vicinity of the blade 33 and manufacturing constraints such as the absence of angular joints at the blade root or tip.

[0103] Once the stretched section 602' is obtained (Figure 7 section (b) or (b')), the thickness of the stretched section 602' is reduced in substep 522 to maintain a constant cross-sectional area with the blade before modification. In other words, if the area of ​​the section 602 before modification is S and that of the section 602' after stretching is S' > S, the reduction 522 consists of reducing the area of ​​the stretched section 602' to S.

[0104] For aerodynamic performance reasons related to the blade 33, some embodiments prefer a modification of the upper surface profile 334, while keeping the lower surface profile 333 unchanged. Other aerodynamic performance improvements can be achieved by modifying only the lower surface profile 333 while keeping the upper surface profile 334 unchanged.

[0105] Similarly, for similar aerodynamic performance considerations, a thickness reduction is preferred that does not alter the radii of curvature of the leading edge BA and trailing edge BF. Typically, the mid-section 701 of the stretched section 602 can be identified, then the thickness e of the section can be reduced at the mid-section 701 by applying a thickness law between the mid-section and each of the leading edge BA and trailing edge BF (while not modifying the upper surface profile in some embodiments), until a surface area S' of the stretched section 602 equals a surface area S of the section 602 before modification.

[0106] Preferably, the thickness law is that used in the original design of blade 33 before modification. Of course, other laws can be used.

[0107] A modified 602” section is obtained, as illustrated in Figure 7, section (c) or (c'), in which only the 333 intrados profile has been modified. Figure 8 also illustrates, by superimposition, the original 602 section and the modified 602” section resulting from step 52. This figure illustrates the 10% stretching of the section.

[0108] By modifying the geometry of section 602, the center of gravity CG1 of section 602 has shifted upstream (towards the leading edge BA, CG2 in Figure 7, section (c)), reducing the local mass and stiffness on the trailing edge side BF where the resonant deformation is greatest. The frequency of mode 1T is thus reduced, without altering the static / mechanical stresses of the blade 33, since the mass (surface area) remains unchanged.

[0109] Figure 9 shows a diagram superimposing the thickness (in mm) of the original 602 and modified 602 sections as a function of their position (in mm) along the X-axis of the motor (the origin being the leading edge BA). This diagram shows a reduction of approximately 5% in the greatest thickness (between the main frames 701) as well as a displacement of the main frame upstream (BA), from an initial position at approximately 37% of the total length along the motor axis to a final position at approximately 23% of the total length along the motor axis. This results in a displacement of approximately 14 points. Consequently, the center of gravity is also displaced upstream by approximately 10 to 20%. Returning to Figure 5, once the modified 602 section is obtained, step 54 consists of connecting the modified section to the foot section 601 (at 0% height) and the Head section 602 (at 100% height) of blade 330 before modification.That is to say, the foot and tip sections remain identical to those they were in the original 330 blade.

[0110] Connecting involves linking the section profiles using a profile matching law, typically the same profile matching law that was used to establish the 610 profile of the original blade. Of course, other laws can be used.

[0111] To perform the connection, the different sections are superimposed (at their respective heights) with their centers of gravity aligned. Figure 6, section (a), shows the alignment of the centers of gravity (represented by crosses, including CG I of section 602) of the sections forming the original blade 60, on the axis of gravity 699.

[0112] Also, in some embodiments, during step 54, the center of gravity CG2 of the modified section 602” (Figure 6, section (b)) is determined and aligned with the axis of gravity 699 (Figure 6, section (c)). This alignment moves the modified section 602” back downstream, since the center of gravity CG2 is moved upstream. Only then is the airfoil matching law applied between the sections to obtain the modified blade.

[0113] Aligning the centers of gravity prevents altering the mechanical stresses on the blade.

[0114] As shown schematically in Figure 6 section (c), the geometric profile of the blade (in solid lines 610) is modified compared to the geometric profile of the initial blade (in dotted lines), due to the modification made to section 602.

[0115] This gives us a modified digital model of the blade or moving blade corresponding to the modified blade 60'.

[0116] This digital model is then used in step 56 as part of blade production, for example for manufacturing foundry molds or for controlling a 3D printer. The digital model is therefore used to control moving blade production equipment.

[0117] A plurality of blades 33 with blade 60' thus modified are manufactured and installed on a rotor in the blower 21, compressors 24a, 24b and / or turbines 26a, 26b.

[0118] Figure 11 illustrates a blade and a movable curved or "barrel-shaped" blade 33 thus obtained.

[0119] In the Figure, the blade 33 comprises a blade 330 extending radially along the extension direction Z (perpendicular to the X axis of rotation of the moving wheel) between a blade tip end (at the top) connected to a first platform forming the lower surface of the blade tip (or "heel") 331, and a blade root end, opposite the blade tip end, connected to a second platform forming the upper surface of the blade root 332. The blade 330 thus extends between the two blade root and blade tip platforms.

[0120] The 331 blade has an overall domed or "barrel-shaped" form: each of the leading (LA) and trailing (BF) edges has a bulbous profile, that is, one that is convex or arched axially relative to the blade in a plane transverse to the Z-axis extension direction. As illustrated, the leading edge BA extends slightly upstream (left) in the figure, following the curvature of a barrel segment, defining an overall protruding hump relative to a straight profile. Similarly, the trailing edge BF extends slightly downstream (right) in the figure, again following the curvature of a barrel segment—but in the opposite direction—defining an overall protruding hump that extends axially in a transverse direction opposite to the domed profile of the leading edge BA. The 331 blade is thus double-bellied.

[0121] As illustrated, the blade head 331 may include one or more sealing strips 339, which extend radially outward from the blade head 331, i.e., from an external surface of the platform to which the blade head end is connected. These strips are fitted to be arranged opposite an internal surface of a stator housing in which the rotating wheel carrying the blade 33 is located.

[0122] A blade section corresponds to a cut of the blade in a plane normal to the radial direction Z. Such a section is called a "cross section".

[0123] The blade tip 331 and / or the blade root 332 may be inclined with respect to a plane normal to the Z direction. Therefore, a blade tip cross-section ST and a blade root cross-section SP are defined, corresponding to the two most extreme solid sections, located respectively at the blade tip and the blade root. "Solid" means that the section consists only of the blade, and not of a portion of the tip or root. SP is the first (along the Z direction) complete blade cross-section not including the blade root 332. It is typically the section tangent to the blade root platform 332. ST is the last complete blade cross-section not including a portion of the wing root 331. It is typically the section tangent to the blade tip platform 331.

[0124] A blade mid-height cross-section (SMH) is any cross-section located between 45% and 55% (alternatively 49% and 51%) of the height defined between the blade tip section (ST) and the blade root section (SP). Typically, the SMH is located at 50%, that is, equidistant from the SP and ST cross-sections. As illustrated in the figure, the blade mid-height cross-section (SMH) is located in the bulging parts of the blade, for example, where one or more of the leading edge (BA) and trailing edge (BF) antinodes are substantially maximal.

[0125] These three cross-sections are parallel and each has a chord extending between the leading edge BA and the trailing edge BF. These chords have respective distances, denoted CT, CMH and CP for sections ST, SMH and SP, respectively.

[0126] The dimensioning of the blades according to the invention leads to particular ratios R1 = CMH / CP and R2 = CMH / CT, i.e. ratios between the lengths of the chords taken in the mid-height cross-section of the blade and respectively the cross-section of the blade root and the cross-section of the blade tip, as described below.

[0127] Furthermore, a displacement of the center of gravity CGMH in the mid-height cross-section of the blade is achieved. For this purpose, the length LMH is defined as corresponding to the projected length, on the axis of rotation X, of the chord CMH, and the length LCGMH as corresponding to the projected length, on the axis of rotation X, of the segment connecting the leading edge BA to the center of gravity CGMH. The dimensioning of the blades according to the invention can also lead to a specific ratio R3 = LCGMH / LMH (reflecting the forward or aft position of the center of gravity of the mid-height section) measured in the mid-height cross-section of the blade SMH.

[0128] Surprisingly, a beneficial gain in frequency (a substantial reduction) is observed in mode 1T when:

[0129] RI belongs to the interval [0.9; 1.2], preferably [0.95; 1.2], and even more preferably [0.97; 1.2].

[0130] R2 belongs to the interval [1,2; 1,4], preferably [1,225; 1,325],

[0131] This gain is, surprisingly, improved when R3 belongs to the interval [0.45; 0.53], preferably [0.45; 0.51].

[0132] The curved shape of the blade (reflecting the RI and R2 ratios) together with an appropriate placement of the center of gravity at mid-height of the blade (reflecting the R3 ratio) leads to a lowering of the mode 1 T frequency of more than 500 Hz, which is particularly beneficial to new (next generation) aircraft engine architectures.

[0133] Figure 12 illustrates examples of blade frequency gains as a function of the three ratios RI, R2, R3 calculated for them. A prior art reference blade (PR) is typically positioned at (R1 = 0.88; R2 = 1.15; R3 = 0.52).

[0134] The subspace delimited by the thick lines is a preferred space where the observed frequency gains are suitable for new aircraft engine architectures. This preferred subspace in the Figure is defined by RI less than 0.97, typically in the interval [0.97; 1.02] and potentially up to 1.2, R2 greater than 1.225, typically in the interval [1.225; 1.325] and potentially up to 1.4, and R3 less than 0.51, typically in the interval [0.49; 0.51] and potentially down to 0.45.

[0135] Four other blades (PI, P2, P3, P4) according to the invention are illustrated, with an indication of the resulting frequency gain (-550, -630, -750 Hz).

[0136] With RI fixed in the interval [0.95; 1.2] (preferably [0.97; 1.2]), increasing the ratio R2 reduces the frequency of the 1T mode. Similarly, increasing the ratio R3 further reduces the frequency of the 1T mode.

[0137] Figure 10 illustrates a system 10 for manufacturing movable blades or blades for movable blades. The system includes a blade design unit 11 and a blade production unit 12.

[0138] The blade design equipment 11 can be a simple computer with a microprocessor 110 and non-volatile memory 111. Typically, a computer has other components (e.g., volatile memory, communication interface, input / output interface, etc.) not shown here for brevity.

[0139] Memory 111 stores an initial digital model 112 of a moving blade whose geometry is modified according to the teachings of the present invention.

[0140] The microprocessor 110 is configured to implement these teachings, and in particular the process of Figure 5, a process in which a modified digital model 113 is produced by modifying the geometry of the blade defined in the initial digital model 112. The modified digital model 113 is stored in memory 111.

[0141] The modified digital model 113 is communicated to the blade production equipment 12 by any means. For example, the microprocessor 110 controls the equipment 12 via a communication network and provides it with the modified digital model 113 to produce new moving blades, for example, to create or configure foundry molds corresponding to said modified digital model, or to control a 3D printer. New blades and moving blades are thus manufactured.

[0142] The invention makes it possible to drastically reduce (by approximately 15%) the frequency of the first torsional mode of the moving blades of an aircraft turbomachine, and therefore the associated coincidence regime. The frequency of mode 1T is thus sufficiently low that coincidence does not occur in the usual operating ranges of the engine with the new holding architecture (for example, during cruise, takeoff, or landing).

[0143] In particular, it was found that a 10% increase in the chord length of the mid-section of the 330 blade, combined with a reduction in thickness at the mid-sectional area while maintaining the original thickness law, leads to a 15% decrease in the frequency of mode 1 T. This decrease is sufficient to get out of dynamic coincidence under normal engine operating conditions.

[0144] An advantage linked to lowering the frequency of mode 1 T is also that the excitation regime is lowered and therefore the excitation pressure at the origin of the aerodynamic forces seen by the blade is reduced: the vibratory potential of the blade is thus improved.

[0145] Of course, the present invention is not limited to the embodiments described above by way of example; it extends to other variants.

[0146] In particular, if the invention is described above in connection with the modification of a single section (at mid-height in some examples), it can be implemented for the modification of a plurality of blade sections (for example at 25%, 50%, 75% of height, or 45%, 50% and 55% of height to be more precise in the area of ​​high deformation) before connecting the sections together.

Claims

DEMANDS 1. Movable turbine blade (33) of an aircraft turbomachine intended to be centered on an axis of rotation (X), comprising a blade (330, 60) delimited by a leading edge (BA), a trailing edge (BF), an intrados and an extrados, the intrados and extrados being connected to each other by the leading edge (BA) and the trailing edge (BF), the leading edge (BA) being configured to be located upstream and the trailing edge (BF) being configured to be located downstream with respect to the direction of gas flow in operation, the blade (330, 60) extending along an extension direction (Z) between a blade root end and a blade tip end opposite to the blade root end with respect to the extension direction (Z), the leading edge (BA) and the trailing edge (BF) having bulging profiles whose respective bulging parts extend in transverse directions opposites,in which the blade tip has a blade tip cross-section (600, ST) and the blade root end has a blade root cross-section (601, SP), the blade tip cross-section (600, ST) being parallel to the blade root cross-section (601, SP) and the blade (330, 60) having a mid-blade height cross-section (602, SMH) which is located, in the bulging parts of the leading (BA) and trailing (BF) edges, between 45 and 55% of the height defined between the blade tip cross-section (600, ST) and the blade root cross-section (601, SP), and in which each cross-section (601, SP, 602, SMH, 600, ST) has a chord (700, CT, CMH, CP) which is a distance taken between the leading edge (BA) and the trailing edge (BF), and in which a first ratio (RI) between the chord (CMH) taken in the mid-height cross-section of the blade (602,SMH) and the chord (CP) taken in the blade root cross-section (601, SP) is within the interval [0.9; 1.2] and a second ratio (R2) between the chord (CMH) taken in the mid-blade height cross-section (602, SMH) and the chord (CT) taken in the blade tip cross-section (600, ST) is within the interval [1.2; 1.4].

2. Movable blade (33) according to claim 1, wherein the first ratio (RI) is within the range [0.95; 1.2].

3. Movable blade (33) according to claim 1 or 2, wherein a third ratio (R3), measured in the mid-blade height cross-section (MSH), between - a segment length (LCGMH) projected, onto the axis of rotation (X), of a segment connecting the leading edge (BA) to a center of gravity (CGMH), and - a length (LMH) projected, onto the axis of rotation (X), of the string is within the interval [0.45; 0.53], 4. Movable blade (33) according to claim 3, wherein the third ratio (R3) is within the range [0.45; 0.51], 5. Movable blade (33) according to any one of claims 1 to 4, wherein the blade tip cross section (600, ST) is the last solid section of the blade in the direction of the blade tip end and the blade root cross section (601, SP) is the last solid section of the blade in the direction of the blade root end.

6. Movable blade (33) according to any one of claims 1 to 5, wherein the mid-height cross section (MHT) is located at an equal distance from the blade tip cross section (600, ST) and the blade root cross section (601, SP).

7. Movable blade (33) according to any one of claims 1 to 6, comprising a blade head (331) having a first platform to which the blade head end is connected and comprising a blade foot (332) having a second platform to which the blade foot end is connected.

8. Movable blade (33) according to claim 7, comprising at least one sealing strip, which projects from the first platform of the blade head (331) 9. A rotating turbine wheel (2), comprising a disc (32) and at least one rotating blade (33) according to any one of claims 1 to 6 mounted on the outer periphery of the rotating disc, wherein the disc (32) is movable about the axis of rotation (X) and the direction The extension (Z) of the blade (330) is a radial direction relative to the axis of rotation (X).

10. Method of manufacturing a movable blade (33) for an aircraft turbomachine (2) intended to be centered on a rotational axis (X), the blade comprising a blade (330, 60) delimited by a leading edge (BA), a trailing edge (BF), an intrados and an extrados, the intrados and extrados being connected to each other by the leading edge (BA) and the trailing edge (BF), the leading edge (BA) being configured to be located upstream and the trailing edge (BF) being configured to be located downstream with respect to the direction of gas flow in operation, the blade (330, 60) extending along an extension direction (Z) between a blade root end and a blade tip end opposite the blade root end with respect to the extension direction (Z), the leading edge (BA) and the trailing edge (BF) having convex profiles whose parts their respective bulges extend in opposite transverse directions,the process comprising the following steps: obtaining (50) a mid-height position (H) of the blade (330, 60) of the movable blade (33), as a function of a deformation of the blade in a first natural mode of torsion, the mid-height position being located, in the bulging parts of the leading (LA) and trailing (LF) edges, between 45 and 55% of the height defined between a blade tip cross-section (600, ST) at the level of the blade tip end and a blade root cross-section (601, SP) at the level of the blade tip end, the blade tip cross-section (600, ST) being parallel to the blade root cross-section (601, SP), modifying (52) the geometry of a mid-height cross-section of the blade (602, SMH) at said mid-height position, each cross-section (601, SP, 602, SMH, 600, ST) presenting a chord (700, CT, CMH, CP) which is a distance taken between the leading edge (BA) and the trailing edge (BF),the modification including the following operations: - stretch (520) the mid-height cross-section of the blade (602, SMH) by lengthening the chord (700, CMH) taken from the cross-section of halfway up the blade, and - reduce (522) the thickness (e) of the stretched section (602') to maintain a constant surface area (S) of the mid-blade height cross-section (602, SMH) with the blade before modification, and connect (54) the modified section (602') to the blade root cross-section (601) and to the blade tip cross-section (600) before modification, so as to obtain a modified blade blade (60'), in which a first ratio (RI) between the chord (700, CMH) taken in the mid-blade height cross-section (602, SMH) and the chord (CP) taken in the blade root cross-section (601, SP) is in the range [0.9; 1.2] and a second ratio (R2) between the chord (700, CMH) taken in the mid-blade height cross-section (602, SMH) and the chord (CT) taken in the cross section of blade head (600, ST) is within the interval [1.2; 1.4]. 1 1. Method according to claim 10, wherein obtaining (50) the position (H) at mid-blade height comprises determining a position where the deformation of the blade is significant relative to a threshold, or even maximum, in a first natural mode of torsion.

12. Method according to claim 10 or 11, wherein the mid-height position of the blade is located at an equal distance from the cross-section of the blade tip (600, ST) and the cross-section of the blade root (601, SP).

13. A method according to any one of claims 10 to 12, wherein the chord (700) taken in the mid-height cross section of the blade (602, SMH) is lengthened by 5 to 20%, preferably by 10 to 15%, for example by about 10%.

14. Method according to claim 13, wherein the stretching (520) of the mid-height cross-section of the blade (602, SMH) is carried out using an affinity having as its direction an axis (XI) of the chord (700) taken in the mid-height cross-section of the blade or an axis of a section between two control points (PC) of a skeleton (702) of the mid-height cross-section of the blade.

15. A method according to any one of claims 10 to 14, wherein reducing (522) the thickness (e) comprises: identifying a mid-section (701) in the stretched section (602'), and reducing the thickness of the section at mid-blade height at the mid-section by applying a thickness law between the mid-section and each of the leading (LA) and trailing (BF) edges, until a surface area of ​​the stretched section is obtained equal to a surface area of ​​the mid-blade cross-section before modification.

16. A method according to any one of claims 10 to 15, wherein reducing (522) the thickness (e) comprises modifying an extrados profile (334) of the blade (330, 60) in the stretched section (602'), while keeping an intrados profile (333) of the blade unchanged.

17. Method according to any one of claims 10 to 16, wherein radii of curvature of the leading edge (BA) and trailing edge (BF) are kept constant during modification (52) of the geometry of the mid-height cross section of the blade (602, SMH).

18. A method according to any one of claims 10 to 17, wherein connecting (54) the modified section (602”) to the blade root (601, SP) and blade tip (600, ST) cross sections comprises: determining a center of gravity (CG2) of the modified section (602”), aligning the center of gravity with a gravity axis (699) of the blade, and applying a profile matching law between the section aligned with the gravity axis and the blade root and blade tip cross sections.

19. A method according to any one of claims 10 to 18, wherein a third ratio (R3), measured in the mid-blade height (MSH) cross-section after modification, between - a segment length (LCGMH) projected, onto the axis of rotation (X), of a segment connecting the leading edge (BA) to a center of gravity (CGMH), and - a length (LMH) projected, on the axis of rotation (X), of the chord (CMH), is within the interval [0.45 ; 0.53] , 20. Movable blade (33) of aircraft turbomachine, the geometry of which is modified by a method according to any one of claims 10 to 19.

21. System (10) for manufacturing a movable blade (33) for an aircraft turbomachine (2) intended to be centered on a rotational axis (X), the blade comprising a blade (330, 60) delimited by a leading edge (BA), a trailing edge (BF), an intrados and an extrados, the intrados and extrados being connected to each other by the leading edge (BA) and the trailing edge (BF), the leading edge being configured to be located upstream and the trailing edge being configured to be located downstream with respect to the direction of gas flow in operation, the blade (330, 60) extending along an extension direction (Z) between a blade root end and a blade tip end opposite the blade root end with respect to the extension direction (Z), the leading edge (BA) and the trailing edge (BF) having bulged profiles whose respective bulged portions 'extend in opposite transverse directions,The system comprises: a memory (111) for storing a digital model (112) of a moving blade (33), a microprocessor (110) configured to, from the digital model (112): obtain a mid-height position (H) of the moving blade (330), as a function of a blade deformation in a first natural torsion mode, the mid-height position being located, in the bulging parts of the leading (LA) and trailing (BF) edges, between 45 and 55% of the height defined between a blade tip cross-section (600, ST) at the blade tip and a blade root cross-section (601, SP) at the blade tip, the blade tip cross-section (600, ST) being parallel to the blade root cross-section (601, SP), modify the geometry of a mid-height cross-section of blade (602, SMH) at said mid-height position, each cross section (601, SP, 602, SMH, 600,ST) featuring a chord (700, CT, CMH, CP) which is a distance taken between the leading edge (BA) and the trailing edge, (BF), the modification comprising the following operations: - stretch the mid-blade height cross-section (602, SMH) by lengthening the chord (700, CMH) taken from the mid-blade height cross-section, and - reduce the thickness (e) of the stretched section (602') to maintain a constant surface area of ​​the mid-blade height cross-section (602, SMH) with the blade before modification, and connect the modified section (602") to the blade root cross-section (601) and to the blade tip cross-section (600) before modification, so as to obtain a modified numerical model (113) of the blade, and use the modified numerical model to drive a movable blade production device (12), wherein a first ratio (RI) between the chord (700, CMH) taken in the mid-blade height cross-section and the chord (CP) taken in the blade root cross-section is in the range [0.9; 1.2] and a second ratio (R2) between the chord (700, CMH) taken in the mid-blade height cross-section and the chord (CT) taken in the cross-section the blade tip is within the interval [1.2; 1.4].

22. System (10) according to claim 21, wherein a third ratio (R3), measured in the mid-blade height (MSH) cross-section after modification, between - a segment length (LCGMH) projected, onto the axis of rotation (X), of a segment connecting the leading edge (BA) to a center of gravity (CGMH), and - a length (LMH) projected, on the axis of rotation (X), of the chord (CMH), is within the interval [0.45 ; 0.53] ,

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