EP1589191A1 - Method for intentionally mistuning a turbomachine bladed rotor and rotors with intentionally mistuned blades - Google Patents

Abstract

The method involves determining an optimal value of standard deviation of frequency variation with respect to a maximum amplitude response of desired vibration on wheel according to operating conditions of the wheel inside a turbine engine. Blades having different natural frequencies are arranged on the wheel such that frequency distribution of the blades has a standard deviation equal to a value of variation determined statistically. An independent claim is also included for an impeller wheel having blades.

Description

The present invention relates to turbomachine rotors, and in particularly the rotors comprising blades at their periphery which are subject to during the operation of the turbomachine to vibratory phenomena.

Turbomachine bladed wheels have a structure with a quasi-symmetry cyclic. They are usually composed of a series of sectors geometrically identical, with a tolerance that is related to the tolerances of manufacture of their various components and their assembly.

Although the tolerances generally used for the manufacture of bladed wheels are weak, they have significant effects on the dynamics of the structure. Small geometric variations, due for example to the manufacture of parts and their assembly, small variations in characteristics of the material that constitute them, such as their Young's modulus or their mass volume, can lead to small variations in the natural frequency of resonance from one dawn to another.

These variations are referred to as detuning and are very difficult to master; in this case the expression of detuning is used. involuntary. These small variations of dawn to dawn frequencies are enough to break the symmetry of the structure. The wheel is said to be out of tune. For the wheel to be detuned, it suffices to vary between the eigenfrequencies of the blades of 0.5% standard deviation or even less.

On a disordered bladed wheel, it can be seen that the vibratory energy is locate on one or a few blades instead of spreading over the entire wheel. The consequence of this location is an amplification of the forced response. We denotes by this expression the vibratory response to an external excitation. Sure a turbomachine including aeronautics, outdoor excitement finds its origin most often in a dissymmetry in the aerodynamic flow. She may be due for example to the upstream stators or the downstream stator, to a distortion, air sampling in the compressor, air reintroduction, combustion chamber or structural arms.

Dawn blade response levels can vary within a factor of 10 and the maximum on the bladed wheel can be double or triple the which would have been obtained on a perfectly symmetrical wheel.

The evolution of the response to a source of excitation according to the detuning follows a curve as shown in Figure 1. It represents the maximum response in vibration amplitude of the bladed wheel determined for different values of standard deviation of the eigenfrequencies of the blades distributed on the wheel. For 0% detuning, the response is standardized to 1. Standard deviation standard of detuning that is encountered on the wheels in use is to the order of 0.5%. We usually see on this graph that it corresponds to the case the most unfavorable. Trying to reduce it to get closer to the symmetry is very expensive because it implies in particular a reduction of the tolerances of manufacturing. This graph also shows that from a certain level of detuning b, the effect on the dynamics of the bladed wheel fades and the maximum levels observed on the wheel decrease.

The invention aims to introduce a voluntary detuning on the bladed wheel so as to reduce the maximum response on the wheel, and to no longer depend on involuntary disarray, weak, always present.

The method according to the invention for introducing a detuning voluntarily in a bladed wheel of a turbomachine, so as to reduce the vibratory levels of the wheel in forced response, is characterized by the fact that consists in determining, according to the operating conditions of the wheel to inside said turbomachine, an optimal value of detuning corresponding to a maximum response in the required amplitude of vibration, and disposing on said wheel, at least in part, blades of different frequencies so that the frequency distribution of all the vanes has a standard deviation at least equal to the said detuning value, detuning value being determined by a statistical calculation method.

The standard deviation discrepancy introduced is advantageously greater than this optimal value b.

The value b depends on the wheel studied, the stiffness of the disc and the value of damping present on the bladed wheel. We can consider that in most cases the value of b is of the order of 1 to 2% of standard deviation frequency. In these cases, the standard deviation of voluntary mismatch introduced is greater than 2%.

The Campbell diagram aims to determine the frequency situation of the structure with respect to possible excitations. It includes the frequencies of modes of vibration of the bladed wheel according to the speed of rotation of the wheel on the one hand, and the possible excitation frequencies on the other hand. The crossings between these two types of curves correspond to resonances.

An example of a source of excitations is constituted by an upstream stator having N vanes. Downstream of the stator, one is led to monitor the excitation of frequency f = Nω where ω is the rotation frequency of the rotor. As part of the turbomachine design, the geometrical parameters are determined and the relevant moving wheel so as to move the resonances out of the operating range with a margin of safety.

Le mode n° 1 est excité par l'ordre N1 en dehors de la plage de fonctionnement de la turbomachine avec une marge suffisante.

Le mode n°2 n'est pas excité par l'ordre N1 ; la marge est suffisante.

Le mode n°3 est excité par l'ordre N2 en dessous de la plage de fonctionnement de la turbomachine avec une marge suffisante.

Le mode n°4 est excité par l'ordre N2 dans la plage de fonctionnement de la roue. En fonction du type de mode, cette résonance peut ne pas être acceptable.

On constate donc qu'il est difficile de trouver un compromis acceptable.Consider, for example, the Campbell diagram of FIG. 2, which represents on the ordinate the vibration frequencies of the wheel under examination and on the abscissa the rotational frequencies of the wheel. The frequencies were reported for four vibratory modes and the lines corresponding to the excitation frequencies for two orders, N1 and N2, as a function of the rotation frequency

Mode No. 1 is excited by the order N1 outside the operating range of the turbomachine with a sufficient margin.

Mode No. 2 is not excited by the order N1; the margin is sufficient.

Mode No. 3 is excited by the order N2 below the operating range of the turbomachine with a sufficient margin.

Mode No. 4 is excited by the order N2 in the operating range of the wheel. Depending on the type of mode, this resonance may not be acceptable.

It is therefore difficult to find an acceptable compromise.

If one wishes for example to improve the situation for resonance Mode 4 / order N2, introducing a voluntary mismatch of b% goes lead to spread the frequencies of the bladed wheel around their value average. Instead of having one line per mode, we get one band per mode. The bandwidth depends on the mode: a voluntary detuning of b% for a frequency does not necessarily induce a variation of b% of the other frequencies.

This is much more constraining for sizing because the Possible resonance ranges are wider. For example, in the case preceding, the modes 1 to 3 which respected the frequency margins in the case granted no longer respect them.

The invention therefore also aims to determine the value of b minimum so that its effect on the vibratory levels is significant while spreading the modes of the structure as little as possible to facilitate their design.

Referring to Figure 1, the problem that the invention aims to solve consists for a given maximum amplitude value of vibration to be determined the corresponding value of b on the curve.

As has been reported above, said value of detuning by a statistical calculation method.

• on définit une première valeur σ_j d'écart type de désaccordage,
• on génère un nombre R, significatif statistiquement, de répartitions aléatoires de désaccordage dans cet écart type σ_j,
• on calcule pour chacune des R répartitions aléatoires, la réponse forcée désaccordée en fonction des conditions de fonctionnement de la roue dans la turbomachine,
• on en extrait la valeur maximale,
• on choisit une autre valeur de σ_j et on itère le calcul précédent, le nombre d'itérations étant suffisant pour effectuer un tracé des valeurs de réponse en fonction des valeurs σ_j.

This method includes the following steps:

• a first value σ _j of standard deviation of the detuning is defined,
• a statistically significant number R of random detuning distributions is generated in this standard deviation σ _j ,
• for each of the R random distributions, the forced response is detuned according to the operating conditions of the wheel in the turbomachine,
• we extract the maximum value,
• another value of σ _j is chosen and the previous calculation is iterated, the number of iterations being sufficient to plot the response values as a function of the values σ _j .

The subject of the invention is also a bladed wheel presenting a voluntary disconnection.

A bladed wheel whose voluntary detuning was determined according to method of the invention has different blades of different frequencies, the number of different frequencies, excluding manufacturing tolerances, of not more than 3.

According to another characteristic, the blades are distributed according to patterns with blades of natural frequency f1 and frequency vanes own f2, f2 being different from f1. In particular, the successive motifs are identical or with a slight variation from one pattern to another.

According to another characteristic each pattern comprises (s1 + s2) blades, s1 blades of frequency f1 and s2 blades of frequency f2. In particular, s1 = s2 and s1 is at most equal to the total number N of blades of the wheel divided by 4. In particular, each pattern comprises (s1 + s2 +/- 1) vanes with (s1 +/- 1) vanes frequency f1 and (s2 +/- 1) blades of frequency f2.

According to another characteristic, the wheel being subjected to a harmonic excitation n less than the number N of vanes of the wheel divided by two (n <N / 2) blades are divided into n identical patterns or with a weak variation from one pattern to another.

According to another characteristic, the wheel being subjected to a harmonic excitation n, n being greater than the number N of vanes of the wheel divided by two (n> N / 2), the number of patterns is equal to the number of diameters of the concerned mode.

la figure 1 représente le tracé de la valeur de la réponse maximale en amplitude de vibration par rapport au désaccordage exprimé en écart type des fréquences propres,

la figure 2 représente un exemple de diagramme de Campbell,

la figure 3 représente un organigramme de calcul permettant de tracer la courbe de la réponse forcée en fonction de l'écart type des fréquences propres de vibration des aubes.

The invention will be described in more detail below with reference to the drawings in which

FIG. 1 represents the plot of the value of the maximum response in amplitude of vibration with respect to the detuning expressed in standard deviation of the eigenfrequencies,

FIG. 2 represents an example of a Campbell diagram,

FIG. 3 represents a calculation flowchart making it possible to draw the curve of the forced response as a function of the standard deviation of the eigen frequencies of vibration of the blades.

The statistical method for determine the minimum value to be used for detuning according to the characteristics of the bladed wheel that it is a question of treating and limiting the answer forced on a coincidence identified in the operating range.

In step 10, an initial value σ _j of the standard deviation in detuning frequencies is chosen. For a bladed wheel, it is, it is recalled, the average of the differences between the natural frequency of vibration of each blade and the average frequency. We observe that we take into account the variation of eigenfrequencies for the blades only. It is assumed that the modes for the discs remain cyclically symmetrical.

In step 20, a distribution R _{i is} randomly generated numerically. For a predefined value of standard deviation σ _j of a bladed wheel, there exists an infinity both of distributions R _i of the vanes on the wheel MR _i and of eigenfrequencies of the latter satisfying this condition of standard deviation σ _j .

In step 30, for this distribution R _i , the determination is made by a known numerical method to calculate the amplitude response to an excitation. For example, it may be for a turbojet compressor the response to distortions in the incident flow resulting from a side wind.

For the wheel having the distribution R _i , the response of each blade to the external disturbance is thus determined. We extract at 40 the maximum value R _i max σ _j that is expressed with respect to the response obtained on a blade of a perfectly tuned wheel. This value is greater than 1, and most often less than 3.

We loop at 42 on step 20 by determining a new distribution R _{i + 1} and we start the calculation to determine a new value R _{i + 1} max σ _j . The calculations are repeated for a number R of distributions. This number R is chosen to be statistically significant.

At 50 for all the R distributions, the maximum Mσ _j is extracted from the values R _i max σ _j . From the set of values R _i max, we determine the maximum value of the amplification which will not be statistically exceeded in a percentage of cases higher than a fixed rate, for example 99.99%. This result is achieved by plotting the values on a cumulative probability curve. The cloud of points is advantageously smoothed by a Weibull probability plot which makes it possible to reduce the number of prints required, for example to 150.

Thus, for a standard deviation value σ _j , the corresponding point Mσ _j has been determined on the diagram of FIG.

In 52 we set a new value σ _{j + 1} from which we loop on step 10 to calculate a new value M σ _{j + 1}

At 60, there are a sufficient number of points to plot the curve of Figure 1 namely Mσ _j = f (σ _j )

Once the curve of Figure 1 has been drawn, it is easy to optimum value b of the standard deviation as a function of the maximum permitted amplitude.

Given the shape of the curve beyond the maximum, one could choose a value of b as large as possible. However the choice is limited by the fact that the introduction of a detuning as part of an improvement of the situation for a particular resonance amounts to widening the ranges of resonances for the other modes, as it appears on the diagram of Campbell of Figure 2.

According to another characteristic of the invention, it is verified that the introduction of a voluntary detuning improves the aeroelastic stability of wheel. The average of the damping coefficients corresponding to each possible phase angle between the blades, and it is verified that the mode affected by the float is below that average.

In other words, if the motor test indicates that the floating margins are insufficient, it may be interesting to introduce a detuning voluntary.

1- On fait l'hypothèse que la roue aubagée est accordée ;

2- pour chaque angle de phase possible entre les aubes, on fait un calcul aéroélastique de stabilité au moyen des outils numériques adaptés : Navier Stokes en subsonique ou éventuellement Euler en supersonique ; approche 2D ou 3D;

3- pour chaque angle de phase, on calcule le coefficient d'amortissement aéroélastique correspondant,

4- on calcule la moyenne des coefficients d'amortissement.

5- Si le coefficient d'amortissement du mode concerné par le flottement est en dessous de cette moyenne, l'introduction d'un désaccordage volontaire est bénéfique. On procède alors à la détermination du désaccordage optimal. Dans le cas contraire, il apparaít qu'il n'est pas nécessaire de procéder à un tel désaccordage puisque la roue présente une stabilité suffisante.

The method comprises the following steps:

1- It is assumed that the bladed wheel is tuned;

2- for each possible phase angle between the blades, aeroelastic stability calculation is done using the appropriate numerical tools: Navier Stokes in subsonic or possibly Euler in supersonic; 2D or 3D approach;

3- for each phase angle, calculate the corresponding aeroelastic damping coefficient,

4- the average of the damping coefficients is calculated.

5- If the damping coefficient of the mode concerned by the float is below this average, the introduction of a voluntary detuning is beneficial. This is followed by the determination of the optimal detuning. Otherwise, it appears that it is not necessary to perform such detuning since the wheel has sufficient stability.

In summary, we optimize the detuning to minimize the forced response on a resonance, making sure that the impact on the stability and the diagram of Campbell (for the other resonances) is acceptable or we optimize the detuning against stability by ensuring that the impact on the diagram from Campbell is acceptable.

The detuning reflects an asymmetry of the structure. The approaches classical analysis with cyclic symmetry, which allows us to model only one only sector of the structure and then reconstruct the behavior of the wheel complete are therefore not directly applicable.

Given the dissymmetry of the structure, a complete representation (360 °) is necessary.

The simplest but also the most expensive approach is to modelize the complete structure: the size of the model then becomes enormous and difficult to manage, especially for the statistical approaches of the detuning.

A) Le disque est supposé à symétrie cyclique : un seul secteur de disque est modélisé. Les calculs sont réalisés pour tous les angles de déphasages possibles applicable aux frontières de ce secteur.

A method of reducing the size of the models has therefore been developed. The simplified logic of this method is described below, knowing that many complexities, in particular related to the speed of rotation are also to be taken into account:

A) The disk is assumed to have cyclic symmetry: only one sector of disk is modeled. Calculations are made for all possible phase angle angles applicable to the boundaries of this sector.

• si N est pair : (N/2)+1 déphasages sont calculés,
• si N est impair : (N+1)/2 déphasages sont calculés.

For a bladed wheel of N vanes, according to the principle of cyclic symmetry,

• if N is even: (N / 2) +1 phase shifts are calculated,
• if N is odd: (N + 1) / 2 phase shifts are calculated.

B) Pour les aubes, les modes d'une aube nominale, isolés du disque sont calculés.

C) Un vecteur de désaccordage qui représente la variation de fréquence d'une aube à l'autre, est ensuite introduit de façon à perturber les modes de l'aube nominale calculée en B) ci-dessus.

D) La roue aubagée désaccordée est ensuite représentée par une combinaison des modes de disques calculés en A) ci-dessus et des modes d'aubes désaccordés calculés en C) (projection sur une base de représentation).

This makes it possible to obtain all the modes of the symmetrical disk.

B) For the blades, the modes of a nominal blade, isolated from the disk are calculated.

C) A detuning vector which represents the variation of frequency from one blade to another, is then introduced so as to disturb the modes of the nominal blade calculated in B) above.

D) The detuned bladed wheel is then represented by a combination of the disk modes calculated in A) above and detuned blade modes calculated in C) (projection on a basis of representation).

Steps A) and B) are long enough to calculate but the calculation is not done only once. On the other hand, steps C) and D) are very fast, which allows fast analyzes for different detuning vectors. This method is therefore particularly well suited to statistical approaches.

The greater the number of modes calculated in steps A) and B), the greater the representation base is rich, the more precise the result, but the more the calculation is expensive.

For the forced answer

An aerodynamic force is calculated (unsteady analysis). different methods exist. The calculation is quite simple and inexpensive because decorrelated mode (detuned) of the structure. A force calculation is sufficient, this force being then applied to the detuned structure from step D).

For stability

This case is more complex because the unsteady aerodynamic forces depend on the detuned mode. For simplicity, aeroelastic efforts "to base "are calculated for each mode of the representation database.

The total aeroelastic "out of tune" effort is obtained by combining the "basic" efforts, according to the same rule of overlap as used in step D). (The representation base is the same).

The stability calculation therefore requires a large number of calculations unsteady aerodynamics that are quite expensive. However, once aeroelastic model built, the detuned analyzes are very fast.

When the value of detuning to be introduced into the wheel has been determined blurred, this detuning is achieved advantageously in one of the ways following.

Once the value of b is determined, a blade distribution is selected on the wheel whose eigenfrequencies satisfy the standard deviation condition b.

Advantageously all the blades are positioned so symmetrical on the disc notably in terms of angle, step and position axial. The wheel is asymmetrical from the point of view of frequencies only.

Preferably, the number of different blades is limited to two or three types.

Consider that we have three types of blades whose frequencies are respectively: f0, f1, f2. For example, the nominal frequency of the blades is f0, f1 the natural frequency of the blades with increased frequency compared to f0 and f2 la eigenfrequency of the vanes with reduced frequency.

According to a first embodiment, the vanes are distributed according to the pattern: [f1 f1 f2 f2] is a distribution f1f1f2f2 f1 f1 f2 f2 etc .; on the rotor, two blades of frequency f1 are alternately arranged, then two blades of frequency f2, or
according to the pattern [f1 f1 f1 f2 f2 f2]; alternation is three blades. etc.

More generally, we define a pattern of (s1 + s2) vanes with s1 vanes frequency f1 and s2 blades of frequency f2 that is repeated on the wheel. Even more generally the successive patterns vary slightly from one pattern to another, in particular of +/- 1 blades or +/- 2 blades. For example, 36 blades may be distributed in successive patterns: (4f1 4f2) (5f1 5f2) (4f1 4f2) (5f1 5f2) or well according to the patterns (4f1 Sf2) (4f1 Sf2) (5f1 5f2) (4f1 4f2). other solutions are possible.

According to a particular distribution mode, s1 = s2 and s1 is at most N / 4.

Preferably, the wheel being subjected to harmonic excitation n, either n perturbations per revolution, n being smaller than the number N of vanes of the divided wheel by two (n <N / 2), the blades are arranged in a distribution that tends to have the same order of symmetry as the excitation on the wheel. They are divided into n identical or distribution groups that vary little from one group to another.

4 fois le motif f1 f1 f1 f1 f2 f2 f2 f2 ou bien

4 fois le motif f2 f1 f1 f2 f2 f2 f1 f1 ou bien

4 fois le motif f1 f1 f2 f2 f1 f1 f2 f2 ou bien

4 fois le motif f1 f2 f2 f2 f2 f1 f1 f1.

In particular, if the number of vanes is divisible by n, the vanes are divided into n repetitive frequency distribution patterns. Thus, for a wheel of 32 blades excited by 4 disturbances per revolution, the vanes are, for example, arranged in four identical patterns:

4 times the pattern f1 f1 f1 f1 f2 f2 f2 f2 or

4 times the pattern f2 f1 f1 f2 f2 f2 f1 f1 or else

4 times the pattern f1 f1 f2 f2 f1 f1 f2 f2 or

4 times the pattern f1 f2 f2 f2 f2 f1 f1 f1.

Preferably the average frequency is f0 or close to f0.

If the number N of vanes is not divisible by the number n of disturbances one chooses patterns that give a distribution that approximates the most of a distribution where N is divisible by n. So for a wheel of 36 blades excited by 5 perturbations per turn, the blades are arranged according to patterns nearly identical: 4 groups of 7 blades and a group of 8 blades such as example (4f1 3f2) (3f1 4f2) (4f1 3f2) (3f1 4f2) and (4f1 4f2). Other distributions are possible.

According to another embodiment, if the wheel is subjected to a harmonic excitation n, n being greater than the number N of vanes of the wheel divided by two (n> N / 2), we divide the blades according to a number of reasons repetitive equals the number of diameters of the mode concerned. For example 24 excitations per turn on a moving wheel of 32 blades involve an answer dynamic of the so-called 8-diameter bladed wheel. So we use a distribution of detuning with 8 repetitive patterns.

To modify the natural vibration frequency of a dawn, there exists various technological solutions.

The frequency can be modified by acting on the material constituting dawn. This solution makes it possible to produce the identical blades geometrically to manufacturing tolerances and not to change the flow stationary aerodynamics. For example, for metal blades dawn from materials with Young's Modules or different densities. The frequencies being linked to the stiffness ratio on mass, the simple change of material has an impact on the frequencies. For composite blades, the texture of the zone composite is affected.

Another range of solutions consists in modifying the foot of the dawn without affect the blade; we can modify the length or the thickness of the stilt, the shape of the underside of the platform its thickness. In particular a punctual addition of masses under the platform allows to shift the frequencies of the first vibration modes.

Evidement de l'aube par micro-perçage puis reconstitution de la veine avec un matériau plus ou moins raide ou plus ou moins lourd.

Remplissage de cavités d'aubes creuses.

Emploi de revêtements locaux tels que des céramiques de faible épaisseur de façon à ajouter localement de la masse dans les zones à forte énergie cinétique de déformation pour décaler les fréquences.

Modification locale de l'état de surface.

Modification de la tête d'aube par usinage d'une « langue de chat »

Modification de la tête d'aube par usinage d'une cavité dite en forme de baignoire.

Modification des lois d'empilage des coupes de l'aube selon une direction perpendiculaire à son axe.

Utilisation de pales de longueurs différentes.

Modification du raccord pale / plate forme au niveau du congé de raccordement en utilisant des rayons de raccordement différents. On constate que l'impact sur les premières fréquences de l'aube est sensible tout en présentant un effet limité sur l'aérodynamique stationnaire.

Other solutions relate to geometric modifications of the blade:

Evidence of dawn by micro-drilling and reconstitution of the vein with a more or less stiff material or more or less heavy.

Filling of hollow blade cavities.

Use of local coatings such as thin ceramics to locally add mass in areas of high kinetic strain energy to shift frequencies.

Local modification of the surface condition.

Modification of the blade head by machining a "cat tongue"

Modification of the blade head by machining a so-called bathtub-shaped cavity.

Modification of the laws of stacking the sections of the dawn in a direction perpendicular to its axis.

Use of blades of different lengths.

Modification of the blade / platform connection at the connection fillet using different connecting radii. It is noted that the impact on the first frequencies of the dawn is sensitive while having a limited effect on stationary aerodynamics.

Claims (16)

Method for introducing a deliberate detuning in a bladed wheel of a specific turbomachine, so as to reduce the vibratory levels of the wheel in forced response, characterized in that it consists in determining, as a function of the operating conditions of the wheel inside the turbomachine, an optimum value of the standard deviation of the detuning relative to the maximum response in desired amplitude of vibration on the wheel, to have on said wheel, at least in part, blades of eigenfrequencies different from such so that the frequency distribution of all the blades has a standard deviation at least equal to said detuning value, said detuning value being determined statistically. Method according to the preceding claim, according to which a first value σ _j of standard deviation of the detuning is defined, a statistically significant number R of random detuning distributions is generated in this standard deviation σ _j , for each of the R random distributions, the forced response is detuned according to the operating conditions of the wheel inside the turbomachine, we extract the maximum value, another value of σ _j is chosen and the previous calculation is iterated, the number of iterations being sufficient to plot the response values as a function of the values σ _j . Method according to one of the preceding claims, according to which determine beforehand whether the introduction of a voluntary detuning improves the aeroelastic stability by calculating the average of the coefficients amortization corresponding to each possible phase angle between paddles, and verifying that the aero-elastic damping of the mode affected by the float is below that average. Bladed wheel obtained according to the method of one of claims 1 to 2 whose number of eigenfrequencies of different blades, out of tolerances of manufacture, is at most three. A bladed wheel according to claim 4, the blades of which are distributed according to patterns with vanes of natural frequency f1 and vanishing vanes natural frequency f2, f2 being different from f1. A bladed wheel according to claim 5, the successive patterns of which are identical or with a slight variation from one pattern to another. Bladed wheel according to the preceding claim, each pattern comprises (s1 + s2) blades, s1 blades of frequency f1 and s2 vanes frequency f2. Bladed wheel according to the preceding claim, wherein s1 = s2 and s1 is at more equal to the total number N of blades of the wheel divided by 4. A bladed wheel according to claim 6, wherein each pattern comprises (s1 + s2 +/- 2) vanes with (s1 +/- 1) blades of frequency f1 and (s2 +/- 1) vanes frequency f2. Bladed wheel according to one of claims 4 to 8, the wheel being subjected to a harmonic excitation n less than the number N of vanes of the wheel divided by two (n <N / 2) whose vanes are divided into n patterns identical or with a slight variation from one pattern to another. A bladed wheel obtained according to the method of one of claims 1 to 2, the wheel being subjected to a harmonic excitation n, n being greater the number N of vanes of the wheel divided by two (n> N / 2), whose number of patterns is equal to the number of diameters of the mode concerned. Bladed wheel according to one of claims 4 to 11, the frequency of which resonance of the blades is modified by modification, in particular geometric, of their pale. Bladed wheel according to one of Claims 4 to 11, whose frequency of resonance of the blades are modified by modification, in particular geometrically, their foot, the blade not being modified, so as to modify the stiffness. Bladed wheel according to one of claims 4 to 11, whose frequencies resonant blades are modified by mass modifications or of material constituting the dawn. Bladed wheel according to the preceding claim, the blades being hollow or hollowed out, the modification being induced by filling a part of the cavities with a material of suitable density. Monobloc type bladed wheel according to one of Claims 5 to 12, whose connection fillet between the blade and the hub is changed by one pale to the other.

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