FR3146949A1 - BLADED WHEEL FOR AIRCRAFT TURBOMACHINE, COMPRISING AN IMPROVED DYNAMIC DAMPING DEVICE, EQUIPPED WITH ANGULAR WHEEL SECTORS WITH FIXED BEADS AND WITH MOBILE BEADS - Google Patents

Abstract

The invention relates to a bladed wheel (20) for an aircraft turbomachine, the wheel being formed by first and second angular wheel sectors (26a, 26b), each first angular sector having a fixed heel (32a) secured to the blade head and each second angular sector (26b) having a movable heel (32b) mounted radially movable on the blade head (46). In addition, the fixed heel (32a) comprises at least one first friction surface (42a, 44a), and the movable heel (32b) comprises at least one second friction surface (42b, 44b) intended to cooperate by friction with the first friction surface(s), so as to form a dynamic damping device (40). Figure for abstract: Figure 3

Description

BLADED WHEEL FOR AIRCRAFT TURBOMACHINE, COMPRISING AN IMPROVED DYNAMIC DAMPING DEVICE, EQUIPPED WITH ANGULAR WHEEL SECTORS WITH FIXED BEADS AND WITH MOBILE BEADS

The present invention relates to the field of aircraft turbomachines, and more precisely to the design of the bladed wheels forming the turbines and compressors of these turbomachines.

It concerns more specifically the dynamic damping by friction of the angular wheel sectors which follow one another in the circumferential direction. As is known, each angular wheel sector forms a single blade of the wheel, or several directly consecutive blades connected to the same heel.

The invention applies to all turbomachine designs, for example turbojets with a fan driven directly by a low-pressure body, or driven indirectly by a reducer.

STATE OF PRIOR ART

The compressors and turbines of aircraft turbomachines are made by an axial succession of fixed and mobile bladed wheels, also called stator bladed wheels and rotor bladed wheels. In the case where such a bladed wheel is angularly sectorized, namely according to the circumferential direction of the wheel, it is usually appropriate to limit the vibration constraints on the angular sectors of the wheel.

To do this, means are implemented to ensure dynamic damping of these sectors, by dissipating the resonance energy by friction between the heels. Such a damping solution is for example known from document FR 3 085 712 A1.

Another more classic solution consists of implementing a contact friction technology, between the heels of adjacent blades with particular shapes. This technology, also called "pretorsion", is characterized by a specific cut of the two opposite circumferential faces of the heel, with a protrusion on the extrados side, and a complementary shaped imprint on the intrados side. The two-by-two cooperation of these circumferential faces allows the two adjacent heels to be held in relation to each other, in the axial direction. This pretorsion technology is also called "interlock" in English.

When assembling the blades, a support of the circumferential contact faces is generated by means of an angular deformation of the blade, constituting the desired pre-torsion.

In operation, blade vibrations induce relative slippage at the circumferential faces of the heels, which, coupled with contact pressures, create friction damping.

With this technology, the contact force between the heels can vary during the operation of the turbomachine. This variation can come from the natural rotation of the blade around its twist axis (clockwise or counterclockwise), or from the relative movement of adjacent heels in the circumferential direction (approaching or spreading). When assembling the blades, it is necessary to take into account these possible variations in operation, and to ensure that at high speed, i.e. at the speed where dynamic damping is mainly sought, the target contact force is achieved. This can lead to applying a very high contact force when assembling the blades, which results in significant static over-stresses, likely to weaken the blades and/or reduce their service life. This drawback proves to be more or less restrictive, depending on the material used and its capacity to withstand such stresses. For example, for blades made of ceramic matrix composite material, also known as CMC material, the permissible mechanical stresses often remain low, which makes the blades not very tolerant of this pre-torsion principle. Thus, when a blade is made of CMC material, it may prove incompatible with the need to apply a high pre-torsion during assembly, required for the purposes of satisfactory damping at the desired speed.

This problem is observed when the bladed wheel is sectorized into a plurality of adjacent blades distinct from each other, as mentioned above, but also when the wheel has angular wheel sectors each comprising several blades, as well as the same heel secured to these blades. In other words, in the latter case, each angular wheel sector can be assimilated to a plurality of adjacent blades, secured to each other.

Other dynamic damping solutions are known, such as the addition of friction elements to the interface between the heels, at the level of their circumferential faces which cooperate two by two. These solutions generally have the disadvantage of generating aerodynamic disturbances at the level of the vein.

To address the drawbacks mentioned above, the invention firstly relates to a bladed wheel for an aircraft turbomachine, the wheel being formed by several angular wheel sectors succeeding one another in a circumferential direction of the wheel, each angular wheel sector comprising one or more blades as well as a heel arranged at the head of said one or more blades.

According to the invention, the wheel comprises a first angular wheel sector and a second angular wheel sector adjacent to the first, the first angular wheel sector having a fixed heel secured to the head of said one or more blades of this first sector, while the second angular wheel sector has a movable heel mounted radially movable on the head of said one or more blades of this second wheel sector. In addition, the fixed heel comprises at least one first friction surface, and the movable heel comprises at least one second friction surface intended to cooperate by friction with said at least one first friction surface, so as to form a dynamic damping device.

The invention thus provides a simple, reliable, high-performance and low-mass solution to the problem set out above, the principle of which makes it possible to overcome the constraints associated with the principle of pre-torsion of the blades encountered in the prior art. In particular, it is no longer necessary to introduce high static pre-torsion constraints in the angular sectors during their assembly, and the machining of complementary complex shapes on the opposite circumferential faces of the heels is no longer required. Advantageously, the invention allows the use of various materials for the production of the angular wheel sectors, including CMC materials.

Thanks to the movable nature of the movable heel of the second angular wheel sector, in the radial direction, this movable heel can then come into contact with the fixed heel of the first adjacent angular wheel sector, and generate with it a vibration damping friction.

The invention also has the advantage of not requiring the implementation of friction elements added between the beads, with the advantage of reducing the overall mass of the bladed wheel.

Finally, the invention can be easily implemented without aerodynamically impacting the vein, in any case by generating less disturbance than with previous solutions consisting of adding friction elements to the interface between the beads, at the level of their circumferential faces which cooperate two by two.

The invention also preferably provides at least one of the following optional features, taken individually or in combination.

Preferably, the bladed wheel comprises another first angular wheel sector arranged so that the two first angular wheel sectors are located directly on either side of the second angular wheel sector, said dynamic damping device also comprising said at least one first friction surface of the other first angular wheel sector, intended to cooperate by friction with said at least one second friction surface of the second angular wheel sector. In other words, in this preferred embodiment of the invention, the production of the dynamic damping device by friction comes from the combined cooperation between on the one hand the movable heel of the second angular wheel sector, and on the other hand the fixed heel of each of the two first angular wheel sectors arranged on either side of the second sector. Nevertheless, a simple cooperation between a second angular wheel sector with a movable heel and a single first wheel sector with a fixed heel remains conceivable, without departing from the scope of the invention.

Preferably, the fixed heel comprises a first base and at least one sealing member projecting radially outward from the first base of the fixed heel. In addition, the movable heel comprises a second base, the first and second bases each having a radially internal surface for delimiting a gas circulation vein.

According to a first possibility, said at least one first friction surface of the fixed heel comprises at least one circumferential face of the first base of the fixed heel, and said at least one second friction surface of the movable heel comprises at least one circumferential face of the second base of the movable heel, the circumferential faces being intended to cooperate together by friction.

According to a second possibility, at least one sealing member of the fixed heel has a portion projecting circumferentially from the first base, and said at least one first friction surface of the fixed heel comprises a radially internal surface of the projecting portion of the sealing member, and said at least one second friction surface of the movable heel comprises at least a portion of a radially external surface of the second base of the movable heel, the radially internal surface of the projecting portion of the sealing member being intended to cooperate by friction with the portion of the radially external surface of the second base of the movable heel.

According to a third possibility, the second base of the mobile heel comprises at least one circumferential extension of reduced thickness, and said at least one second friction surface of the mobile heel comprises a radially external face of the circumferential extension, said at least one first friction surface of the fixed heel comprising a recess face on the radially internal surface delimiting the gas circulation vein, the radially external face of the circumferential extension being intended to cooperate by friction with the recess face of the radially internal surface delimiting the vein.

Of course, the first, second and third solutions mentioned above can be combined with each other.

Preferably, the movable heel is devoid of a sealing member projecting radially outwards from the second base. Consequently, the movable heel can be easily produced by a simple perforated plate, to allow the head of the blade(s) of the second angular sector of the wheel concerned to pass through.

Preferably, the bladed wheel is formed by alternating, in the circumferential direction, first and second angular wheel sectors.

Preferably, the first and second angular wheel sectors are made of ceramic matrix composite material, even if other materials can be envisaged, without departing from the scope of the invention.

Preferably, it is a fixed or mobile bladed wheel, compressor or turbine, and preferably a low pressure turbine mobile wheel.

Finally, the invention also relates to an aircraft turbomachine, such as a dual-flow, dual-body turbojet, comprising at least one such bladed wheel.

Other advantages and characteristics of the invention will appear in the detailed non-limiting description below.

This description will be made with regard to the attached drawings, among which:

represents a schematic view in longitudinal section of an aircraft turbomachine according to the invention;

represents a more detailed perspective view of a bladed wheel of a low pressure turbine of the turbomachine shown in the preceding figure, the bladed wheel being in the form of a preferred embodiment of the invention;

represents a partial and enlarged perspective view of a portion of the bladed wheel shown in the preceding figure;

represents an exploded perspective view of the bladed wheel portion shown in the preceding figure;

represents an exploded perspective view of the bladed wheel portion shown in the preceding figure, from another viewing angle; and

represents a schematic cross-sectional view of a portion of a bladed wheel in the form of another preferred embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

Referring first of all to the , there is shown an aircraft turbomachine 1, according to a preferred embodiment of the invention. This is a double-flow, double-spool turbojet. However, it could be a turbomachine of another type, for example a turboprop, without departing from the scope of the invention.

The turbomachine 1 has a longitudinal central axis 2 around which its various components extend. It comprises, from upstream to downstream along a main direction 5 of gas flow through this turbomachine, a fan 3, a low-pressure compressor 4, a high-pressure compressor 6, a combustion chamber 11, a high-pressure turbine 7 and a low-pressure turbine 8. The fan 3 can be driven directly by a low-pressure body comprising the compressor 4 and the turbine 8, or be driven indirectly by a reducer (not shown).

Conventionally, after passing through the blower 3, the air is divided into a central primary flow 12a and a secondary flow 12b which surrounds the primary flow. The primary flow 12a flows in a main gas circulation vein 14a passing through the compressors 4, 6, the combustion chamber 11 and the turbines 7, 8. The secondary flow 12b flows in a secondary vein 14b delimited radially outwards by an engine casing, surrounded by a nacelle 9.

Each turbine 7, 8 and each compressor 4, 6 comprises, in a conventional manner known to those skilled in the art, an alternation of mobile bladed wheels and fixed bladed wheels, centered on the axis 2. The invention lies in the design of these bladed wheels, and more particularly in the dynamic damping principle implemented therein.

There shows a mobile bladed wheel 20 according to a preferred embodiment of the invention, this wheel being preferentially intended to form a part of the low pressure turbine 8. Nevertheless, the invention can be applied to the high pressure turbine 7, or even to one of the two compressors 4, 6. In addition, it can be a fixed bladed wheel, without departing from the scope of the invention.

The bladed wheel 20 comprises a disk 22, centered on the axis 2 and on which are mounted, radially outwardly, a plurality of angular wheel sectors forming an annular row of blades. Indeed, in the invention, the bladed wheel has a sectorized/segmented character in the circumferential direction 24. In the preferred embodiment shown in the , each angular sector is in fact reduced to a single blade 26, comprising a vane 28 forming the aerodynamic part of the blade, as well as a foot 30 and a heel 32. In a known manner, the foot 30 is formed by a part of greater thickness, for example with a bulb-shaped section, which is engaged in a corresponding housing 34 formed on the periphery of the disk 22.

Opposite the foot 30, radially outwards, the blade 28 of the vane carries the heel 32, the latter therefore being arranged at the blade head.

Although this is not shown, each angular blade sector could alternatively integrate several adjacent blades in the circumferential direction 24, with the head of each of these blades associated with the same heel 32. In this case, each angular wheel sector can then be assimilated to a plurality of adjacent blades 26, integral with each other. Subsequently, only the solution with individual and distinct blades to form the angular wheel sectors will therefore be described in detail. Nevertheless, all of the characteristics and advantages that are described below also prove to be applicable to the solution of angular wheel sectors each comprising several circumferentially adjacent blades 28.

One of the particularities of the invention lies in the alternation, in the circumferential direction 24, of first and second angular wheel sectors of different designs, and forming at their interfaces dynamic damping devices by friction, as will be described later. Thus, in this preferred embodiment, it is an alternation between first blades and second blades of different designs, which will be described with reference to FIGS. 3 to 5.

In each of these figures, there is shown the alternation of two first blades 26a and two second blades 26b, which follow one another in the circumferential direction 24. Subsequently, the cooperation between one of the second blades 26b and the two first blades 26a which are arranged directly on either side of this second blade 26b will essentially be described. In this regard, it is noted that this cooperation between the blades 26a, 26b remains the same within the entire wheel, it being specified that a dynamic friction damping device 40 is associated with each of the second blades 26b of the wheel 20. In addition, all the first blades 26a have an identical or similar design, just as all the second blades 26b also have an identical or similar design, so that only a first blade 26a and a second blade 26b will be described below.

With reference therefore jointly to FIGS. 3 to 5, each first blade 26a comprises a fixed heel 32a, integral with the head of the blade 28. This fixed heel 32a comprises a first base 36a as well as at least one sealing member 38 projecting radially outwards from the first base 36a. The first base 36a forms a radially external platform, the radially internal surface 37a of which delimits the main vein 14a. In a conventional manner, the first platform 36a can be extended axially upstream and downstream, respectively by two spoilers. From its radially external surface 39a, the first platform 36a of the fixed heel carries several sealing members 38, namely two members 38 in the form of lips which project from the surface 39a towards the outside, in a radial direction 35 of the blade in which the root 30 and the heel 32 are spaced apart from each other, with the root located further towards the inside. In the description, the terms internal/external and internal/external, associated with the radial direction 35, are defined in relation to each blade in its environment, and therefore in relation to the root of the blade which radially forms the innermost part of this blade.

As regards the aforementioned wipers 38, a slight axial inclination of these is possible, such as an inclination towards the upstream, without departing from the scope of the invention. The wipers 38, here two in number spaced axially from each other, have a distal end facing radially an inner surface of a turbine casing (not shown). They make it possible to control the sealing with this turbine casing, in the operating configuration of the turbojet. Indeed, these wipers 38 are intended to come as close as possible to the surface of the casing in order to provide a sealing function with respect to the primary flow 12a, which passes through the rotating bladed wheel 20.

The two lips 38 and the first platform 36a together delimit a cavity 45 open radially towards the outside, and usually called a “bathtub”.

Furthermore, each lip 38 has a portion 38a projecting circumferentially from the first base/platform 36a, and preferably two portions 38a projecting in opposite directions from the respective circumferential ends of the first base 36a. Each projecting lip portion 38a has a shape identical or similar to the lip body 38 which it extends in the circumferential direction 24.

The fixed heel 32a has the particularity of comprising several first friction surfaces, intended for the dynamic damping of the heels by friction.

These are first of all the two opposite circumferential faces 42a of the first base 36a, of low radial thickness. They then concern a radially internal surface 44a of each projecting lip portion 38a, namely four surfaces 44a for each first blade 26a.

In addition, each second blade 26b comprises a movable heel 32b, mounted radially movable on the head 46 of the blade 28. To do this, the movable heel 32b is here in the form of a simple second base 36b, preferably without lickers like those equipping the first base 36a of the fixed heels of the first blades 26a. As a result, the movable heel 32b can be produced using a simple plate pierced with an opening 48 of a shape complementary to that of the blade head 46 which it receives, and along which the heel 32b is able to move in operation, according to a limited radial amplitude.

The radially inward retention of the movable heel 32b is preferably carried out by one or more flats 50, made on the blade head 46. Alternatively, due to the twisting of the blade 28, the geometry of the latter can by itself prevent the movable heel 32b from sliding radially inward beyond a determined position relative to the blade head 46. The radially outward retention of the movable heel 32b is ensured by the projecting circumferential portions 38 of the fixed heels 32a of the first adjacent blades 26a, as will be explained later.

The second base 36b therefore also forms a radially external platform, the radially internal surface 37b of which delimits the main vein 14a. On the other hand, as indicated previously, its radially external surface 39b is devoid of a sealing member, and forms a free surface, preferably continuous. In this regard, it is nevertheless noted that the second bases 36b and/or the first bases 36a could be equipped, on their respective radially external surfaces 39b, 39a, with mechanical reinforcement ribs projecting radially outwards.

The mobile heel 32b has the particularity of comprising several second friction surfaces, intended for the dynamic damping of the heels by friction.

These are first of all the two opposite circumferential faces 42b of the second base 36b, of small radial thickness. These are then portions 44b of the radially external surface 39b of the second base 36b, namely four portions 44b for each second blade 26b, each of these portions 44b being in fact intended to cooperate by friction with the radially internal surface 44a of one of the projecting wiper portions 38a.

More specifically, a dynamic damping device 40 is associated with each second blade 26b, at its movable heel 32b. For the second blade 26b located furthest to the left in FIGS. 3 to 5, on either side of which two first blades 26a are arranged, the dynamic damping device 40 is formed by the frictional cooperation of the following surfaces, in the event of vibration excitations during operation of the turbojet:

- on the first blade 26a on the left, the two radially internal surfaces 44a of the two wiper portions 38a projecting towards the second blade 26b considered, respectively with two portions 44b of the radially external surface 39b of the second base 36b of the movable heel 32b, these surfaces being opposite/in contact two by two;

- on the other first blade 26a, namely the one on the right, the two radially internal surfaces 44a of the two wiper portions 38a projecting towards the second blade 26b considered, respectively with the two other portions 44b of the radially external surface 39b of the second base 36b of the movable heel 32b, these surfaces being opposite/in contact two by two;

- on the first blade 26a on the left, the circumferential face 42a of the first base 36a, with the circumferential face 42b of the second base 36b which is located opposite it/in contact in the circumferential direction 24; and

- on the first blade 26a on the right, the circumferential face 42a of the first base 36a, with the circumferential face 42b of the second base 36b which is located opposite it/in contact in the circumferential direction 24.

In operation, it is the two-by-two friction of the surfaces mentioned above which provides the desired damping.

In the invention, the dynamic damping capacity is advantageously reinforced by the mobile nature of the second heel 32b, according to a preferably limited radial amplitude, and whose external radial stop is formed by the four projecting circumferential lip portions 38a which cover it. Moreover, it is noted that the four projecting portions 38a concerned can be in contact two by two circumferentially, to further reinforce the dynamic damping effect conferred by the device 40, in the event of vibration excitations.

The preferred embodiment relates to a mobile turbine or compressor wheel 20, such that the radial plating of the second heel 32b, against the four projecting circumferential lip portions 38a, is carried out under the effect of centrifugal force during operation of the turbojet. In another preferred embodiment where the wheel 20 is a fixed compressor or turbine wheel, this radial plating can be simply obtained due to the pressure difference observed on either side of the second heel 32b, in the radial direction 35.

It is noted that it is the same type of material that is here preferentially envisaged for the manufacture of the first and second blades 26a, 26b, namely a CMC material. It is in fact this type of material that is preferred for all the constituent parts of these blades 26a, 26b, in particular the fixed and mobile heels 32a, 32b.

Furthermore, the fixed and movable heels 32a, 32b are preferably made so that the first bases 36a have a circumferential length strictly greater than the circumferential length of the second bases 36b. The ratio between these lengths may exceed the value of two, or even be even greater.

Also, the invention provides a simple and efficient damping solution, responding to cases of vibration excitation of the blades generating on them one or more axial bending modes, one or more tangential/circumferential bending modes, as well as one or more radial torsion modes around the radial direction of these blades.

According to another preferred embodiment of the invention shown in the , the damping device 40 associated with the second blade 26b located in the center, is completed by the cooperation by friction two by two of other surfaces of the heels 32a, 32b. Indeed, the second base 36b of the movable heel 32b comprises on either side of this base 36b a circumferential extension 54 of reduced thickness, coming to be housed in a recess made on the radially internal surface 37a, at a circumferential end thereof. Consequently, among the second friction surfaces of the movable heel, the damping device 40 also comprises a radially external face 52b of the left circumferential extension, cooperating by friction with a recess face 52a provided on the radially internal surface 37a of the left blade, this recess face 52a then forming an integral part of the first friction surfaces of the device 40.

Similarly, among the second friction surfaces of the movable heel, the damping device 40 also comprises a radially external face 52b of the right circumferential extension, cooperating by friction with a recess face 52a provided on the radially internal surface 37a of the right blade, this recess face 52a also forming an integral part of the first friction surfaces of the device 40.

Of course, various modifications may be made by those skilled in the art to the invention which has just been described, solely by way of non-limiting examples and within the scope of the appended claims.

Claims (10)

Bladed wheel (20) for an aircraft turbomachine, the wheel being formed by several angular wheel sectors (26a, 26b) succeeding one another in a circumferential direction (24) of the wheel, each angular wheel sector comprising one or more blades (28) as well as a heel (32a, 32b) arranged at the head of said one or more blades,
characterized in that the wheel comprises a first angular wheel sector (26a) and a second angular wheel sector (26b) adjacent to the first, the first angular wheel sector having a fixed heel (32a) secured to the head of said one or more blades of this first sector, while the second angular wheel sector (26b) has a movable heel (32b) mounted radially movable on the head (46) of said one or more blades of this second wheel sector,
the fixed heel (32a) comprising at least one first friction surface (42a, 44a, 52a), and the movable heel (32b) comprising at least one second friction surface (42b, 44b, 52b) intended to cooperate by friction with said at least one first friction surface, so as to form a dynamic damping device (40). Bladed wheel according to claim 1, characterized in that it comprises another first angular wheel sector (26a) arranged so that the two first angular wheel sectors (26a) are located directly on either side of the second angular wheel sector (26b), said dynamic damping device (40) also comprising said at least one first friction surface (42a, 44a, 52a) of the other first angular wheel sector (26a), intended to cooperate by friction with said at least one second friction surface (42b, 44b, 52b) of the second angular wheel sector (26b). Bladed wheel according to claim 1 or claim 2, characterized in that the fixed heel (32a) comprises a first base (36a) and at least one sealing member (38) projecting radially outwards from the first base (36a) of the fixed heel, in that the movable heel (32b) comprises a second base (36b), the first and second bases (36a, 36b) each having a radially internal surface (37a, 37b) for delimiting a gas circulation vein (14a). Bladed wheel according to claim 3, characterized in that said at least one first friction surface of the fixed heel (32a) comprises at least one circumferential face (42a) of the first base (36a) of the fixed heel, and in that said at least one second friction surface of the movable heel (32b) comprises at least one circumferential face (42b) of the second base (36b) of the movable heel, the circumferential faces (42a, 42b) being intended to cooperate together by friction. Bladed wheel according to claim 3 or claim 4, characterized in that at least one sealing member (38) of the fixed heel (32a) has a portion (38a) projecting circumferentially from the first base (36a), in that said at least one first friction surface of the fixed heel comprises a radially internal surface (44a) of the projecting portion (38a) of the sealing member (38), and in that said at least one second friction surface of the movable heel (32b) comprises at least one portion (44b) of a radially external surface (39b) of the second base (36b) of the movable heel, the radially internal surface (44a) of the projecting portion (38a) of the sealing member (38) being intended to cooperate by friction with the portion (44b) of the radially external surface (39b) of the second base (36b) of the heel mobile. Bladed wheel according to any one of claims 3 to 5, characterized in that the second base (36b) of the movable heel (32b) comprises at least one circumferential extension (54) of reduced thickness, and in that said at least one second friction surface of the movable heel (32b) comprises a radially external face (52b) of the circumferential extension, said at least one first friction surface of the fixed heel (32a) comprising a recess face (52a) on the radially internal surface (37a) delimiting the gas circulation vein (14a), the radially external face (52b) of the circumferential extension (54) being intended to cooperate by friction with the recess face (52a) of the radially internal surface (37a) delimiting the vein. Bladed wheel according to any one of the preceding claims, combined with claim 3, characterized in that the movable heel (32b) is devoid of a sealing member projecting radially outwards from the second base (36b). Bladed wheel according to any one of the preceding claims, characterized in that it is formed by the alternation, in the circumferential direction (24), of first and second angular wheel sectors (26a, 26b). Bladed wheel according to any one of the preceding claims, characterized in that the first and second angular wheel sectors (26a, 26b) are made of ceramic matrix composite material. Aircraft turbomachine (1) comprising at least one bladed wheel (20) according to any one of the preceding claims.