Method for intentionally mistuning a turbine blade of a turbomachine

The present invention relates to a method (100) for intentionally mistuning a turbine blade of a turbomachine (10), by providing raised portions (31) or slots (32), the position of which is calculated on the basis of a vibration analysis of the disk (steps a) to d)).

GENERAL TECHNICAL FIELD

The present invention relates to a method for intentionally mistuning a bladed wheel of a turbomachine.

PRIOR ART

From upstream to downstream, in the direction of flow of gases, a turbomachine generally comprises a fan, one or more compressor stages, for example a low-pressure compressor and a high-pressure compressor, a combustion chamber, one or more turbine stages, for example a high-pressure turbine and a low-pressure turbine, and a gas exhaust nozzle.

Each compressor or turbine stage is formed by a stationary vane or stator and a rotating vane or rotor around the main axis of the turbomachine.

Each rotor conventionally comprises a disc extending around the main axis of the turbomachine and comprising an annular platform, as well as a plurality of blades distributed uniformly around the main axis of the turbomachine and extending radially relative to this axis from an outer surface of the platform of the disc. There are also “bladed wheels”.

The bladed wheels form the object of multiple vibratory phenomena whereof the origins can be aerodynamic and/or mechanical.

The particular focus here is floating, which is a vibratory phenomenon of aerodynamic origin. Floating is linked to the strong interaction between the blades and the fluid passing through them. In fact, when the turbomachine is operating, when fluid is passing through them, the blades modify its flow. In return, the effect of modification to the flow of fluid passing through the blades is to the excite them with vibrations. Now, when the blades are excited in the vicinity of one of their natural vibration frequencies, this coupling between the fluid and the blades can become unstable; this is the phenomenon of floating. This phenomenon materializes via oscillations of increasing amplitude of the blades which can lead to cracking or worse to destruction of the bladed wheel.

This phenomenon is therefore highly dangerous and it is vital to prevent the coupling between the fluid and the blades becoming unstable.

To rectify this problem, it is known to “intentionally mistune” the bladed wheels. The intentional mistuning of a bladed wheel consists of exploiting the cyclic symmetry of the bladed wheel, specifically the fact that the bladed wheels are generally composed of a series of geometrically identical sectors, and creating frequential disparity between all the blades of said bladed wheel. In other words, intentional mistuning of a bladed wheel consists of introducing variations between the natural vibration frequencies of the blades of said bladed wheel. Such frequential disparity stabilizes the bladed wheel vis-a-vis the floating by increasing its aeroelastic cushioning.

“Intentional mistuning” is opposed to “unintentional mistuning” which is the result of small geometric variations in bladed wheels, or small variations in the characteristics of the material constituting it, generally due to tolerances in manufacture and assembly, which can lead to small variations in natural vibration frequencies from one blade to another.

Several solutions have already been offered for intentional mistuning of a bladed wheel.

Document FR 2 869 069 describes for example a method for intentionally mistuning a bladed wheel of a turbomachine determined to reduce the vibratory levels of the wheel in forced response, characterized in that as a function of the operating conditions of the wheel inside the turbomachine, it consists of determining an optimum value of standard deviation of mistuning relative to the maximum response in amplitude of planned vibration on the wheel, fixing to said wheel, at least partly, blades of different natural frequencies such that the distribution of frequencies of all the blades has a standard deviation at least equal to said mistuning value. This document further proposes several technological solutions for modifying the natural vibration frequencies from one blade to the other, including the fact of using different materials for the blades or the fact of acting on their geometry, for example by using blades of different lengths.

The method described in this document however needs to be carried out during designing of the bladed wheel. Now, when the turbomachine is operating, the bladed wheels are subject to multiple and complex vibratory phenomena whereof the sources of excitation are variable and often difficult to predict. It can therefore eventuate that a bladed wheel mistuned according to the method described in this document is nevertheless subject to interfering vibratory phenomena which would not have been able to be foreseen, such as floating, when the turbomachine is operating.

Another example is described in document EP 2 463 481. This document describes a bladed wheel in which projections are provided every second blade over the entire circumference of an inner surface of the platform of the disc, in view of intentional mistuning of said bladed wheel.

Another example is described in document US 2015/0198047. This document describes a bladed wheel comprising alternatively blades formed from a first alloy of titanium and blades formed from a second alloy of titanium, the first and second alloys of titanium inducing natural vibration frequencies of a different blade.

Now, these two documents propose intentional systematic mistuning of the bladed wheels. In other words, irrespective of the bladed wheel concerned, it is mistuned in the same way by introducing a variation in natural vibration frequencies every second blade. It can therefore eventuate that a bladed wheel mistuned in this way is nevertheless subject to interfering vibratory phenomena, such as floating, when the turbomachine is operating.

PRESENTATION OF THE INVENTION

The aim of the present invention especially is to eliminate the drawbacks of the techniques of intentional mistuning of the prior art.

It proposes a method for intentionally mistuning a bladed wheel of a turbomachine to adapt mistuning applied to the geometry of said bladed wheel to be mistuned and therefore to interfering vibratory phenomena such as floating, to which said bladed wheel is subject when the turbomachine is operating.

More precisely, the aim of the present invention is a method for intentionally mistuning a bladed wheel of a turbomachine, said bladed wheel comprising a disc extending around a longitudinal axis and N blades distributed uniformly around said longitudinal axis and extending radially relative to this axis from the disc, N being a nonzero natural integer, said method comprising the following steps:

a) selecting a natural vibration mode of the bladed wheel with k nodal diameters, k being a natural integer different to zero and, when N is an even number, different to

N2,
said natural mode being a vibration mode in the operating range of the turbomachine;
b) determining the displacement of the blades over the entire circumference of the bladed wheel for each of the two standing deformation waves of the same frequency which combined generate the rotating mode shape of the bladed wheel in the selected natural vibration mode;
c) from the displacement of the blades thus determined for each of the two standing deformation waves, determining the blades for which a vibration antinode of a first of said standing deformation waves corresponds to a vibration node of the second standing deformation wave;
d) providing a projection or a notch in the disc of the bladed wheel facing each of the blades thus determined, so as to frequentially separate the two standing deformation waves and intentionally mistune the bladed wheel relative to the selected natural vibration mode.

Preferably, the notches are made by counterboring or the projections are made by metallization.

Preferably, the disc comprises an annular platform from which the blades extend radially, the projections or the notches being provided in the platform of the disc.

Preferably, the projections or the notches are provided in the disc so as to extend over an angular amplitude around the longitudinal axis of between 360°/N and 80°.

Another aim of the present invention is a bladed wheel of a turbomachine comprising a disc extending around a longitudinal axis and N blades distributed uniformly around said longitudinal axis and extending radially from the disc, N being a nonzero natural integer, said bladed wheel comprising also a plurality of projections or notches provided in the disc facing each of the blades determined according to steps a) to c) of the method for intentionally mistuning a bladed wheel of a turbomachine such as previously described.

The mistuning undertaken in this way is different structurally to systematic mistuning.

In particular, the method proposed is of particular interest in the case of mistuning other than one blade in two.

Preferably, the notches are made by counterboring or the projections are made by metallization.

Preferably, the disc comprises an annular platform from which the blades extend radially, the projections or the notches being provided in said platform of the disc.

Preferably, the projections or the notches are provided in the disc so as to extend over an angular amplitude around the longitudinal axis of between 360°/N and 80°.

DETAILED DESCRIPTION

As a preliminary issue, “vibration nodes” are called the points of a mechanical system which have zero displacement for a given vibration mode. These points are therefore not in motion. “Vibration antinodes” are called the points of a mechanical system which have maximum displacement for a given vibration mode. These points are therefore of maximum amplitude movement.

FIG. 1illustrates a bypass turbomachine10. The turbomachine10extends along a main axis11and comprises an air shaft12via which a gas flow enters the turbomachine10and in which the gas flow passes through a fan13. Downstream of the fan13, the gas flow is separated into a primary gas flow flowing into a primary airstream14and a secondary gas flow flowing in a secondary airstream15.

In the primary airstream14, the primary flow passes through from upstream to downstream a low-pressure compressor16, a high-pressure compressor17, a combustion chamber18, a high-pressure turbine19, a low-pressure turbine20, and a gas discharge casing to which an exhaust nozzle22is connected. In the secondary airstream15, the secondary flow passes through a stationary vane or fan rectifier24, then mixes with the primary flow at the exhaust nozzle22.

Each compressor16,17of the turbomachine10comprises several stages, each stage being formed by a stationary vane or stator and a rotary vane or rotor23around the main axis11of the turbomachine10. The rotary vane or rotor23is also called “bladed wheel”.

FIGS. 2aand 2bshow respectively an upstream and downstream view, relative to the direction of flow of gases, of a bladed wheel23prior to implementation of a method100for intentionally mistuning a bladed wheel of a turbomachine according to an embodiment of the invention.

The bladed wheel23comprises a disc25extending around a longitudinal axis26which, when the bladed wheel23is mounted in the turbomachine10, is combined with the main axis11of said turbomachine10. The bladed wheel23further comprises an annular platform27arranged at the periphery of the disc25. The platform27has an inner surface28facing the longitudinal axis26and an outer surface29which is opposite it. The platform27extends on either side of the disc25in the direction of the longitudinal axis26.

The bladed wheel23further comprises a plurality of blades30distributed uniformly around the longitudinal axis26and extending radially relative to this axis26from the outer surface29of the platform27. The bladed wheel23comprises N blades30, N being a nonzero natural integer. The blades30can be one piece with the disc25or be attached to the disc25by means well known to the skilled person. In the example illustrated inFIGS. 2aand 2b, the bladed wheel23comprises thirty four blades30and are in a single piece with the disc25.

Each blade30comprises a leading edge which is located axially upstream in the direction of flow of gases relative to said blade30, and a trailing edge which is located axially downstream in the direction of flow of gases relative to said blade30.

In general, bladed wheels have a cyclic symmetry. In other words, bladed wheels are composed of a series of geometrically identical sectors repeated circularly. For example, the bladed wheel23comprises N identical sectors, one sector being associated with each of the blades30.

To achieve modal analysis of the bladed wheel, the aim is to resolve the eigenvalue problem: (K−ω2M)X=0, with K corresponding to the stiffness matrix of the bladed wheel, M corresponding to the mass matrix of the bladed wheel, X corresponding to the displacement vector of the bladed wheel and ω corresponding to the natural pulses of the bladed wheel.

Now, the cyclic symmetry of the bladed wheel performs modal analysis of the whole bladed wheel by taking on a single sector. For this, the viewpoint is the Fourier space and the eigenvalue problem mentioned hereinabove can be reformulated as follows: ({tilde over (K)}k−ω2{tilde over (M)}k){tilde over (X)}k=0, with k corresponding to the Fourier orders, {tilde over (K)}kcorresponding to the stiffness matrix of the sector in order k, {tilde over (M)}kcorresponding to the mass matrix of the sector in order k, {tilde over (X)}kcorresponding to the displacement vector of the sector in order k and ω corresponding to the natural pulses of the sector. The problem with eigenvalues reformulated in this way is resolved for each Fourier order k. Fourier orders k∈[0; K] are generally considered, with:

The eigenvalues obtained for each Fourier order k correspond to eigenvalues of the whole bladed wheel.

The solutions obtained for k=0 and, when N is even,

k=N2
correspond respectively to natural vibration modes where all the sectors are deformed in phase and at natural vibration modes where the adjacent sectors are deformed in phase opposition. The mode shapes of the bladed wheel for all the natural vibration modes associated with each of these two Fourier orders correspond to a standing deformation wave.

For the other Fourier orders k, the solutions are double and each natural pulse ωk, is associated with two natural orthogonal vectors which form a base for the natural vibration modes associated with these Fourier orders, such that any linear combination of these vectors is also a natural vector. The mode shapes of the bladed wheel for all the natural vibration modes associated with each of these Fourier orders corresponds to a rotary deformation wave which is the linear combination of two standing deformation waves of the same frequency. The two standing deformation waves are offset by a quarter period.

Apart from the mode shapes of the natural vibration modes corresponding to the Fourier order k=0, the mode shapes of a bladed wheel have nodal lines which extend radially relative to the longitudinal axis of the bladed wheel. These nodal lines are commonly called “nodal diameters” and their number corresponds to the Fourier order k.

By way of illustration,FIGS. 3ato 3dshow respectively:the mode shape of the first bending mode having two nodal diameters of the bladed wheel23, this mode shape being rotating;the mode shape corresponding to a first O1of the two standing deformation waves O1and O2which combined generate the mode shape of the bladed wheel23illustrated inFIG. 3a;the mode shape corresponding to a second O2of the two standing deformation waves O1and O2which combined generate the mode shape of the bladed wheel23illustrated inFIG. 3a;a graphic representing the first and second standing deformation waves O1and O2around the bladed wheel23; this graphic shows the displacement δ of the blades30over the entire circumference of the bladed wheel23, the blades30being numbered from 1 to N in order of appearance on the circumference of the bladed wheel23, corresponding to each of the standing deformation waves O1and O2; on the graphic, the displacement δ of the blades30corresponds to displacement of the blades30at the tip of their leading edge and it is standardized relative to the maximum displacement of said blades30; it is clear here that the two standing deformation waves O1and O2are offset by a quarter period.

FIG. 4shows the method100for intentionally mistuning the bladed wheel23, according to an embodiment of the invention. The method100comprises the following steps:

a) selecting a natural vibration mode of the bladed wheel23with k nodal diameters, k being a natural integer different to zero and, when N is an even number, different to

N2;
b) determining the displacement δ of the blades30over the entire circumference of the bladed wheel23for each of the two standing deformation waves O1and O2of the same frequency f which combined generate the rotating mode shape of the bladed wheel23in the selected natural vibration mode;
c) from the displacement δ of the blades30thus determined for each of the two standing deformation waves O1and O2, determining the blades30for which a vibration antinode of a first of said standing deformation waves O1, O2corresponds to a vibration node of the second standing deformation wave O2, O1;
d) providing a projection31or a notch32in the disc25of the bladed wheel23facing each of the blades30thus determined, so as to frequentially separate the two standing deformation waves O1and O2and intentionally mistune the bladed wheel23relative to the selected natural vibration mode.

The method100modifies one of the two standing deformation waves O1and O2without impacting the other of said standing deformation waves O1and O2, ensuring frequential separation of said two standing deformation waves O1and O2and therefore of the blades30arranged facing the notches31relative to the other blades30. The method100benefits from the strong dynamic coupling between the blades30and the disc25to induce frequential disparity between the blades30by modifying the geometry of the disc25.

The method100is particularly advantageous as it intentionally mistunes the bladed wheel23out of design process of said bladed wheel23and without applying systematic mistuning which would not necessarily be adapted to said bladed wheel23. The bladed wheel23can in effect be mistuned intentionally once the bladed wheel23is designed and produced to the extent where not the blades30but the disc25is modified directly. Also, not modifying as the geometry or the material of the blades30avoids impacting their aerodynamism.

Step a) is for example conducted following wind tunnel testing of the turbomachine10and therefore of the bladed wheel23, having revealed interfering vibratory phenomena, such as floating at a natural vibration mode of the bladed wheel23. These interfering vibratory phenomena can for example appear in the form of cracks at the root of the blades30. These cracks can then be connected to a particular vibratory phenomenon, for example floating, and the natural vibration mode(s) for which this vibratory phenomenon appears can then be determined.

Step b) is for example conducted via digital simulation by means of adapted software, such as the digital simulation software proposed by ANSYS Inc which implements the finite element method. The displacement δ of the blades30over the entire circumference of the bladed wheel23is for example determined at the tip of the leading edge of the blades30. “Tip of the leading edge” means the point of the leading edge of the blades30which is farthest from the longitudinal axis26.

FIGS. 5ato 5cillustrate step c) when the natural mode selected at step a) is the first bending mode having two nodal diameters. These figures show that the vibration antinodes of the first standing deformation wave O1coincide with the vibration nodes of the second standing deformation wave O2at the four blades. These are blades here numbered6,14,23, and31. These coincidences are referenced C1to C4inFIGS. 5ato5c.

In step c), each vibration antinode of the first standing deformation wave O1can also coincide with a vibration node of the second standing deformation wave O2at several adjacent blades30. In this case, a projection31or notch32can be provided in the disc25, facing each series of adjacent blades30, over an angular amplitude around the longitudinal axis26at least equal to the number of blades30of each series multiplied by 360°/N.

FIGS. 6aand 6bshow the bladed wheel23after implementation of the method100, andFIGS. 7aand 7bshow the notches32provided in the disc25in step d) in more detail.

The notches32are provided in the platform27of the disc25. The notches32are provided in the disc25as closely as possible to the blades30, effectively heightening the effect of modification geometric of the disc25on the frequency of the blades30.

The notches32are preferably positioned on the platform27symmetrically relative to said disc25to ensure the dynamic equilibrium of the bladed wheel23.

The notches32extend preferably over an angular amplitude around the longitudinal axis26between 360°/N and 80°. In the example illustrated inFIGS. 6aand 6b, the notches32extend over an angular amplitude substantially of 40° around the longitudinal axis26. “Substantially of 40°” means the fact that the notches32extend over an angular amplitude of 40° around the longitudinal axis26to within 5°.

The notches32are for example made by counterboring. The counterboring applied to the disc25, more precisely to the platform27of the disc25, is illustrated in dotted lines inFIG. 7c.

In the example illustrated inFIGS. 6aand 6b, the notches32provided in the disc25of the bladed wheel23correspond for example to a removal of material from the bladed wheel23of about 5.5% of the mass of the bladed wheel23prior to implementation of the method100, and create frequential separation substantially of 4.1% in the first bending mode of two nodal diameters between the blades30located facing the notches32and the other blades30.

FIGS. 8aand 8bshow the bladed wheel23after implementation of the method100, and theFIGS. 9aand 9bshow the projections31provided in the disc25at step d) in more detail.

The projections31are provided in the platform27of the disc25. The projections31are provided in the disc25as closely as possible to the blades30, effectively heightening the effect of geometric modification of the disc25on the frequency of the blades30.

The projections31are preferably positioned on the platform27symmetrically relative to said disc25to ensure dynamic equilibrium of the bladed wheel23.

The projections31extend preferably radially from the inner surface28of the platform27of the disc25. In other words, the projections31extend preferably radially from the platform27to the longitudinal axis26.

In the example illustrated inFIGS. 9aand 9b, the projections31extend radially from the platform27and along the longitudinal axis26from the disc25.

In the example illustrated inFIGS. 9aand 9b, at its end arranged upstream relative to the direction of flow of gases, the platform27comprises a flange extending radially towards the longitudinal axis26. The flange is provided with through openings arranged parallel to the longitudinal axis26and configured to receive weights, for example bolts, so that they can rebalance the bladed wheel23, if needed. In this case, the projections31are preferably arranged at a distance from the flange so as to free up a space between the projections31and the flange and accordingly not prevent the insertion of weights into the openings.

The projections31extend preferably over an angular amplitude around the longitudinal axis26between 360°/N and 80°. In the example illustrated inFIGS. 8aand 8b, the projections31extend over an angular amplitude substantially of 40° around the longitudinal axis26. “Substantially of 40°” means the fact that the notches32extend over an angular amplitude of 40° around the longitudinal axis26to within 5°.

The projections31are for example made by metallization of the disc25, that is, by addition of material to the disc25. Preferably, the projections31are made from material which is the same as that from which the disc25is made to preserve the mechanical performance and the service life of the bladed wheel23. However, the projections31can also be made from material different to that from which the disc25is manufactured.

It will be clear that with his general knowledge the skilled person will know how much material to remove from or add to the disc25relative to the mass of the bladed wheel23prior to implementation of the method100so as to obtain preferred frequential separation for the selected natural vibration mode between the blades30located facing the projections31or the notches32and that of the other blades30.

The present invention is described hereinbelow by making reference to a bladed wheel23of a compressor16,17of a turbomachine10. But, the invention applies in the same way to a rotor32of a turbine19,20or to a fan13, to the extent where these bladed wheels can be also confronted by interfering vibratory phenomena, such as floating. As will have been clear, the proposed method is particularly interesting in the case of mistuning other than one blade in two.