EP3368748B1 - Verfahren zum absichtlichen verstimmen einer beschaufelten scheibe einer turbomaschine - Google Patents
Verfahren zum absichtlichen verstimmen einer beschaufelten scheibe einer turbomaschine Download PDFInfo
- Publication number
- EP3368748B1 EP3368748B1 EP16806240.4A EP16806240A EP3368748B1 EP 3368748 B1 EP3368748 B1 EP 3368748B1 EP 16806240 A EP16806240 A EP 16806240A EP 3368748 B1 EP3368748 B1 EP 3368748B1
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- EP
- European Patent Office
- Prior art keywords
- bladed wheel
- blades
- disc
- turbomachine
- notches
- Prior art date
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- 238000006073 displacement reaction Methods 0.000 claims description 14
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Images
Classifications
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
- F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
- F01D5/00—Blades; Blade-carrying members; Heating, heat-insulating, cooling or antivibration means on the blades or the members
- F01D5/02—Blade-carrying members, e.g. rotors
- F01D5/10—Anti- vibration means
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
- F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
- F01D25/00—Component parts, details, or accessories, not provided for in, or of interest apart from, other groups
- F01D25/04—Antivibration arrangements
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F01—MACHINES OR ENGINES IN GENERAL; ENGINE PLANTS IN GENERAL; STEAM ENGINES
- F01D—NON-POSITIVE DISPLACEMENT MACHINES OR ENGINES, e.g. STEAM TURBINES
- F01D5/00—Blades; Blade-carrying members; Heating, heat-insulating, cooling or antivibration means on the blades or the members
- F01D5/12—Blades
- F01D5/14—Form or construction
- F01D5/16—Form or construction for counteracting blade vibration
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
- F05D2220/00—Application
- F05D2220/30—Application in turbines
- F05D2220/32—Application in turbines in gas turbines
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01-F04
- F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NON-POSITIVE-DISPLACEMENT MACHINES OR ENGINES, GAS-TURBINES OR JET-PROPULSION PLANTS
- F05D2260/00—Function
- F05D2260/96—Preventing, counteracting or reducing vibration or noise
Definitions
- the present invention relates to a method for introducing a voluntary detuning in a bladed wheel of a turbomachine.
- a turbomachine generally comprises, from upstream to downstream, in the direction of gas flow, a fan, one or more stages of compressors, 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 stage of compressor or turbine is formed by a fixed blade or stator and a rotating blade or rotor around the main axis of the turbomachine.
- Each rotor conventionally comprises a disk extending around the main axis of the turbomachine and comprising an annular platform, and a plurality of blades distributed regularly around the main axis of the turbomachine and extending radially relative to this axis from an outer surface of the disc platform.
- bladed wheels we also speak of "bladed wheels”.
- the bladed wheels are the subject of multiple vibratory phenomena whose origins can be aerodynamic and / or mechanical.
- Voluntary detune is opposed to “involuntary detuning” which is the result of small geometric variations of the bladed wheels or small variations in the characteristics of the material constituting them, generally due to manufacturing and assembly tolerances, which may lead to to small variations of the natural frequencies of vibration from one blade to another.
- the document FR 2 869 069 describes for example a method for introducing a voluntary detuning in a bladed wheel of a turbomachine determined so as to reduce the vibratory levels of the wheel in forced response, characterized in that it consists in determining, according to the operating conditions of the wheel inside the turbomachine, an optimal value standard deviation of deviation from the maximum response in vibration amplitude wanted on the wheel, to have on said wheel, at least in part, blades of different eigenfrequencies so that the frequency distribution of all the blades has a standard deviation at least equal to said detuning value.
- This document also proposes several technological solutions for modifying the eigenfrequencies of vibration from one blade to the other, among which the fact of using different materials for the blades or the fact to act on their geometry, for example in using blades of different lengths.
- the present invention is intended in particular to overcome the disadvantages of the techniques of voluntary detuning of the prior art.
- the notches are made by countersinking or the projections are made by metallization.
- the disk comprises an annular platform from which the blades extend radially, the projections or notches being formed in the disk platform.
- the projections or notches are formed in the disk so as to extend over an angular amplitude around the longitudinal axis of between 360 ° / N and 80 °.
- the present invention also relates to a bladed wheel of a turbomachine comprising a disk extending around a longitudinal axis and N vanes distributed regularly around said longitudinal axis and extending radially from the disk, N being a number non-zero natural integer, said bladed wheel further comprising a plurality of projections or notches formed in the disc facing each of the blades determined according to steps a) to c) of the method for introducing a voluntary detuning in a bladed wheel d a turbomachine as previously described.
- the detuning thus achieved is structurally different from a systematic detuning.
- the proposed method is particularly interesting in the case of detuning other than one blade out of two.
- the notches are made by countersinking or the projections are made by metallization.
- the disk comprises an annular platform from which the vanes extend radially, the projections or notches being formed in said platform of the disk.
- the projections or notches are formed in the disk so as to extend over an angular amplitude around the longitudinal axis of between 360 ° / N and 80 °.
- vibration nodes the points of a mechanical system that for a given vibration mode have a zero displacement. These points are not in motion.
- vibration bellies are the points of a mechanical system that for a given vibration mode have maximum displacement. These points therefore have a movement of maximum amplitude.
- the figure 1 illustrates a turbofan engine 10.
- the turbomachine 10 extends along a main axis 11 and comprises an air shaft 12 through which a flow of gas enters the turbine engine 10 and in which the flow of gas passes through a fan 13. Downstream of the blower 13, the flow of gas separates into a flow of primary gas flowing in a primary stream 14 and a flow of secondary gas flowing in a secondary vein 15.
- the primary stream passes, from upstream to downstream, a low-pressure compressor 16, a high-pressure compressor 17, a combustion chamber 18, a high-pressure turbine 19, a low-pressure turbine 20, and a casing exhaust gas which is connected to an exhaust nozzle 22.
- the secondary stream 15 the secondary flow passes through a fixed blade or fan rectifier 24, then mixes with the primary flow at the exhaust nozzle 22 .
- Each compressor 16, 17 of the turbomachine 10 comprises several stages, each stage being formed by a fixed blade or stator and a rotating blade or rotor 23 around the main axis 11 of the turbomachine 10.
- the rotating blade or rotor 23 is also called “bladed wheel”.
- FIGS. 2a and 2b respectively show a view upstream and downstream, with respect to the flow direction of the gases, of a bladed wheel 23 before the implementation of a method 100 for introducing a deliberate detuning into a turbomachine bladed wheel according to a method embodiment of the invention.
- the bladed wheel 23 comprises a disc 25 extending around a longitudinal axis 26 which, when the bladed wheel 23 is mounted in the turbomachine 10, coincides with the main axis 11 of said turbomachine 10.
- the bladed wheel 23 comprises in addition, an annular platform 27 arranged at the periphery of the disk 25.
- the platform 27 has an inner surface 28 facing the longitudinal axis 26 and an outer surface 29 opposite thereto.
- the platform 27 extends on either side of the disc 25 in the direction of the longitudinal axis 26.
- the bladed wheel 23 further comprises a plurality of vanes 30 uniformly distributed about the longitudinal axis 26 and extending radially with respect to this axis 26 from the outer surface 29 of the platform 27.
- the bladed wheel 23 comprises N vanes 30, N being a nonzero natural whole number.
- the blades 30 may be integral with the disc 25 or be reported on the disc 25 by means well known to those skilled in the art. In the example shown in Figures 2a and 2b , the bladed wheel 23 comprises thirty-four vanes 30 and are integral with the disc 25.
- Each blade 30 comprises a leading edge which is situated axially upstream in the direction of flow of the gases with respect to said blade 30, and a trailing edge which is situated axially downstream in the direction of flow of the gases through relative to said blade 30.
- the bladed wheels have a cyclic symmetry.
- the bladed wheels are composed of a series of geometrically identical sectors that repeat in a circular manner.
- the bladed wheel 23 comprises N identical sectors, a sector being associated with each of the blades 30.
- the eigenvalues obtained for each Fourier order k correspond to eigenvalues of the complete bladed wheel.
- the solutions are double and with each proper pulse ⁇ k , we associate two orthogonal eigenvectors which form a basis for the eigen modes of vibration associated with these orders of Fourier, so that any linear combination of these vectors is also a proper vector.
- the modal deformations of the bladed wheel for all the natural modes of vibration associated with each of these Fourier orders correspond to a rotating wave of deformation which is the linear combination of two stationary deformation waves of the same frequency.
- the two stationary deformation waves are shifted by a quarter period.
- the modal deformations of a bladed wheel have nodal lines which extend radially with respect to the longitudinal axis of the bladed wheel. These nodal lines are commonly called “nodal diameters" and their number corresponds to the order of Fourier k.
- the method 100 makes it possible to modify one of the two stationary deformation waves O 1 and O 2 without impacting the other of said stationary deformation waves O 1 and O 2 , thus ensuring the frequency separation of said two standing waves of deformation O 1 and O 2.
- the method 100 takes advantage of the strong dynamic coupling between the blades 30 and the disc 25 to induce a frequency disparity between the blades 30 by changing the geometry of the disc 25.
- the method 100 is particularly advantageous because it allows to deliberately detune the bladed wheel 23 outside the design process of said bladed wheel 23 and without applying a systematic mismatch that would not necessarily be adapted to said bladed wheel 23.
- the bladed wheel 23 can indeed be detuned voluntarily once the bladed wheel 23 designed and manufactured to the extent that one does not directly modify the blades 30 but the disc 25. Moreover, by not modifying the geometry or the material of the blades 30, we avoid impacting their aerodynamics.
- Stage a) is for example carried out following wind tunnel tests of the turbomachine 10 and thus of the bladed wheel 23, having demonstrated troublesome vibratory phenomena, such as the floating in a clean mode of vibration of the turbine. Bladed wheel 23.
- These annoying vibratory phenomena can for example appear in the form of cracks at the foot of blades 30. These cracks can then be connected to a particular vibration phenomenon, for example floating, and the natural mode or modes of vibration for which or where this vibratory phenomenon appears can then be determined.
- Step b) is for example carried out by numerical simulation by means of a suitable software, such as the numerical simulation software proposed by ANSYS Inc which implements the finite element method.
- the displacement ⁇ of the blades 30 over the entire circumference of the bladed wheel 23 is for example determined at the top of the leading edge of the blades 30.
- the term "top of the leading edge” the point of the leading edge of the blades 30 which is furthest from the longitudinal axis 26.
- the Figures 5a to 5c illustrate step c) when the eigen mode selected in step a) is the first bending mode with two nodal diameters. It can be observed in these figures that the vibration bellies of the first stationary deformation wave O 1 coincide with the vibration nodes of the second stationary wave of deformation O 2 at the level of four vanes. These are the blades numbered here 6, 14, 23, and 31. These coincidences are referenced C 1 to C 4 on the Figures 5a to 5c .
- each vibration belly of the first deformation stationary wave O 1 may also coincide with a vibration node of the second stationary deformation wave O 2 at a plurality of adjacent blades 30.
- a protrusion 31 or notch 32 may be formed in the disk 25, facing each series of adjacent blades 30, over an angular amplitude around the longitudinal axis 26 at least equal to the number of blades 30 of each series multiplied by 360 ° / N.
- FIGS. 6a and 6b show the bladed wheel 23 after implementation of the method 100, and the Figures 7a and 7b show in more detail the notches 32 formed in the disc 25 in step d).
- the notches 32 are formed in the platform 27 of the disk 25.
- the notches 32 are thus formed in the disk 25 as close to the blades 30. This makes it possible to increase the effect of the geometric modification of the disk 25 on the frequency of the blades. 30.
- the notches 32 are preferably positioned on the platform 27 symmetrically with respect to said disc 25, to ensure the dynamic equilibrium of the bladed wheel 23.
- the notches 32 preferably extend over an angular amplitude around the longitudinal axis 26 between 360 ° / N and 80 °. In the example shown in Figures 6a and 6b , the notches 32 extend over an angular amplitude substantially of 40 ° around the longitudinal axis 26.
- substantially 40 ° means that the notches 32 extend over an angular amplitude of 40 ° around the longitudinal axis 26 to 5 °.
- the notches 32 are for example made by countersinking.
- the counterbore applied on the disc 25, more precisely on the platform 27 of the disc 25, is illustrated in dashed line at the Figure 7c .
- the notches 32 made in the disk 25 of the bladed wheel 23 correspond, for example, to a removal of material from the bladed wheel 23 by approximately 5.5% of the mass of the bladed wheel 23 prior to the implementation of the method 100, and make it possible to obtain a separation frequency of substantially 4.1% in the first mode of bending of two nodal diameters between the blades 30 located opposite the notches 32 and the other blades 30.
- FIGS. 8a and 8b show the bladed wheel 23 after implementation of the method 100, and the Figures 9a and 9b show in more detail the projections 31 formed in the disc 25 in step d).
- the projections 31 are formed in the platform 27 of the disk 25.
- the projections 31 are thus formed in the disc 25 as close to the vanes 30. This makes it possible to increase the effect of the geometric modification of the disc 25 on the frequency of the vanes. 30.
- the projections 31 are preferably positioned on the platform 27 symmetrically with respect to said disk 25, to ensure the dynamic equilibrium of the bladed wheel 23.
- the projections 31 preferably extend radially from the inner surface 28 of the platform 27 of the disc 25. In other words, the projections 31 preferably extend radially from the platform 27 towards the longitudinal axis 26.
- the projections 31 extend radially from the platform 27 and along the longitudinal axis 26 from the disc 25.
- the platform 27 comprises at its end arranged upstream with respect to the direction of flow of the gas, a flange extending radially towards the longitudinal axis 26.
- the flange is provided with through openings arranged parallel to the longitudinal axis 26 and configured to receive weights, e.g., bolts, in order to rebalance the bladed wheel 23 as needed.
- the projections 31 are preferably arranged at a distance from the flange, in order to free a space between the projections 31 and the flange and thus not to prevent insertion of the weights into the openings.
- the projections 31 preferably extend over an angular amplitude around the longitudinal axis 26 between 360 ° / N and 80 °.
- the projections 31 extend over an angular amplitude substantially of 40 ° around the longitudinal axis 26.
- substantially 40 ° means that the notches 32 extend over an angular amplitude of 40 ° around the longitudinal axis 26 to 5 °.
- the projections 31 are for example made by metallization of the disk 25, that is to say by adding material to the disk 25.
- the projections 31 are made from a material which is the same as that to which from which the disc 25 is manufactured, in order to preserve the mechanical strength and the service life of the bladed wheel 23.
- the projections 31 can also be made from a material different from that from which the disc 25 is made.
- the present invention is described below with reference to a bladed wheel 23 of a turbomachine compressor 16, 17.
- the invention applies in the same way to a rotor 32 of a turbine 19, 20 or a blower 13, to the extent that these bladed wheels can also be confronted with annoying vibratory phenomena, such as floating.
- the proposed method is particularly interesting in the case of detuning other than one blade out of two.
Claims (8)
- Verfahren (100) zum Einführen einer absichtlichen Verstimmung in einem Laufrad (23) einer Turbomaschine (10), wobei das Laufrad (23) eine Scheibe (25), die sich um eine Längsachse (26) erstreckt, und N Radschaufeln (30) umfasst, die gleichmäßig um die Längsachse (26) verteilt sind und sich von der Scheibe (25) aus radial zu dieser Achse (26) erstrecken, wobei N eine natürliche ganze Zahl ungleich Null ist, wobei das Verfahren (100) die folgenden Schritte umfasst:a) Auswählen einer Eigenschwingung des Laufrads (23) bei k Knotendurchmessern, wobei k eine natürliche ganze Zahl ungleich Null ist und, wenn N eine gerade Zahl ist, sich vonb) Bestimmen der Verlagerung (δ) der Radschaufeln (30) über den gesamten Umkreis des Laufrads (23) für jede von den zwei stehenden Verformungswellen (O1, O2) mit der gleichen Frequenz (f), die kombiniert die Drehschwingungsverformung des Laufrads (23) bei der ausgewählten Eigenschwingungsart erzeugen;c) ausgehend von der so für jede von den zwei stehenden Verformungswellen (O1, O2) bestimmten Verlagerung (δ) der Radschaufeln (30), Bestimmen der Radschaufeln (30), für die ein Schwingungsbauch einer ersten von den stehenden Verformungswellen (O1, O2) einem Schwingungsknoten der zweiten stehenden Verformungswelle (O2, O1) entspricht;d) Anordnen eines Vorsprungs (31) oder einer Kerbe (32) in der Scheibe (25) des Laufrads (23) gegenüber jeder von den so bestimmten Radschaufeln (30), derart dass die zwei stehenden Verformungswellen (O1, O2) hinsichtlich der Frequenz getrennt werden und somit eine absichtliche Verstimmung in dem Laufrad (23) in Bezug zur ausgewählten Eigenschwingung eingeführt wird.
- Verfahren (100) nach Anspruch 1, wobei die Kerben (32) durch Senken ausgeführt werden oder die Vorsprünge (31) durch Metallisierung ausgeführt werden.
- Verfahren (100) nach Anspruch 1 oder Anspruch 2, wobei die Scheibe (25) eine ringförmige Plattform (27) umfasst, von der aus die Radschaufeln (30) sich radial erstrecken, wobei die Vorsprünge (31) oder die Kerben (32) in der Plattform (27) der Scheibe (25) angeordnet werden.
- Verfahren (100) nach einem der Ansprüche 1 bis 3, wobei die Vorsprünge (31) oder die Kerben (32) derart in der Scheibe (25) angeordnet sind, dass sie sich über eine Winkelamplitude um die Längsachse (26) erstrecken, die zwischen 360°/N und 80° enthalten ist.
- Laufrad (23) einer Turbomaschine (10), die eine Scheibe (25), die sich um eine Längsachse (26) erstreckt, und N Radschaufeln (30) umfasst, die gleichmäßig um die Längsachse (26) verteilt sind und sich von der Scheibe (25) aus radial erstrecken, wobei N eine natürliche ganze Zahl ungleich Null ist, wobei das Laufrad dadurch gekennzeichnet ist, dass es mehrere Vorsprünge (31) oder Kerben (32) umfasst, die in der Scheibe (25) jeder von den gemäß den Schritten a) bis c) des Verfahrens (100) bestimmten Radschaufeln (30) gegenüberstehend angeordnet sind, um eine absichtliche Verstimmung in dem Laufrad (23) einer Turbomaschine (10) nach einem der Ansprüche 1 bis 4 einzuführen.
- Laufrad (23) nach Anspruch 5, wobei die Kerben (32) durch Senken ausgeführt sind oder die Vorsprünge (31) durch Metallisierung ausgeführt sind.
- Laufrad (23) nach Anspruch 5 oder Anspruch 6, wobei die Scheibe (25) eine ringförmige Plattform (27) umfasst, von der aus die Radschaufeln (30) sich radial erstrecken, wobei die Vorsprünge (31) oder die Kerben (32) in der Plattform (27) der Scheibe (25) angeordnet sind.
- Laufrad (23) nach einem der Ansprüche 5 bis 7, wobei die Vorsprünge (31) oder die Kerben (32) derart in der Scheibe (25) angeordnet sind, dass sie sich über eine Winkelamplitude um die Längsachse (26) erstrecken, die zwischen 360°/N und 80° enthalten ist.
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
FR1560326A FR3043131B1 (fr) | 2015-10-28 | 2015-10-28 | Procede pour introduire un desaccordage volontaire dans une roue aubagee de turbomachine |
PCT/FR2016/052819 WO2017072469A1 (fr) | 2015-10-28 | 2016-10-28 | Procede pour introduire un desaccordage volontaire dans une roue aubagee de turbomachine |
Publications (2)
Publication Number | Publication Date |
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EP3368748A1 EP3368748A1 (de) | 2018-09-05 |
EP3368748B1 true EP3368748B1 (de) | 2019-09-11 |
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EP16806240.4A Active EP3368748B1 (de) | 2015-10-28 | 2016-10-28 | Verfahren zum absichtlichen verstimmen einer beschaufelten scheibe einer turbomaschine |
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US (1) | US10267155B2 (de) |
EP (1) | EP3368748B1 (de) |
JP (1) | JP6438630B1 (de) |
CN (1) | CN108350744B (de) |
BR (1) | BR112018008624B1 (de) |
CA (1) | CA3003396C (de) |
FR (1) | FR3043131B1 (de) |
RU (1) | RU2689489C1 (de) |
WO (1) | WO2017072469A1 (de) |
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CN109583063B (zh) * | 2018-11-20 | 2023-04-18 | 东北大学 | 一种风扇转子试验模型的动力学特性相似设计方法 |
US11959395B2 (en) | 2022-05-03 | 2024-04-16 | General Electric Company | Rotor blade system of turbine engines |
Citations (1)
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US20150292337A1 (en) * | 2014-04-11 | 2015-10-15 | Honeywell International Inc. | Components resistant to traveling wave vibration and methods for manufacturing the same |
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JP3940937B2 (ja) * | 1996-08-07 | 2007-07-04 | 石川島播磨重工業株式会社 | タービン動翼の配列方法 |
US6471482B2 (en) * | 2000-11-30 | 2002-10-29 | United Technologies Corporation | Frequency-mistuned light-weight turbomachinery blade rows for increased flutter stability |
FR2869069B1 (fr) * | 2004-04-20 | 2008-11-21 | Snecma Moteurs Sa | Procede pour introduire un desaccordage volontaire sur une roue aubagee de turbomachine roue aubagee presentant un desaccordage volontaire |
US8757979B2 (en) * | 2006-10-05 | 2014-06-24 | Volvo Aero Corporation | Rotor element and method for producing the rotor element |
US8342804B2 (en) * | 2008-09-30 | 2013-01-01 | Pratt & Whitney Canada Corp. | Rotor disc and method of balancing |
WO2012035658A1 (ja) * | 2010-09-17 | 2012-03-22 | 株式会社日立製作所 | 翼の配列方法 |
CA2761208C (en) * | 2010-12-08 | 2019-03-05 | Pratt & Whitney Canada Corp. | Blade disk arrangement for blade frequency tuning |
US8926290B2 (en) * | 2012-01-04 | 2015-01-06 | General Electric Company | Impeller tube assembly |
EP2762678A1 (de) * | 2013-02-05 | 2014-08-06 | Siemens Aktiengesellschaft | Verfahren zum Verstimmen eines Laufschaufelgitters |
JP5519835B1 (ja) * | 2013-06-18 | 2014-06-11 | 川崎重工業株式会社 | 翼を備える回転体 |
US10400606B2 (en) | 2014-01-15 | 2019-09-03 | United Technologies Corporation | Mistuned airfoil assemblies |
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2015
- 2015-10-28 FR FR1560326A patent/FR3043131B1/fr not_active Expired - Fee Related
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2016
- 2016-10-28 WO PCT/FR2016/052819 patent/WO2017072469A1/fr active Application Filing
- 2016-10-28 CA CA3003396A patent/CA3003396C/en active Active
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Patent Citations (1)
Publication number | Priority date | Publication date | Assignee | Title |
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US20150292337A1 (en) * | 2014-04-11 | 2015-10-15 | Honeywell International Inc. | Components resistant to traveling wave vibration and methods for manufacturing the same |
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BR112018008624B1 (pt) | 2022-11-22 |
JP2019500531A (ja) | 2019-01-10 |
US20180313216A1 (en) | 2018-11-01 |
US10267155B2 (en) | 2019-04-23 |
CA3003396A1 (en) | 2017-05-04 |
RU2689489C1 (ru) | 2019-05-28 |
JP6438630B1 (ja) | 2018-12-19 |
FR3043131B1 (fr) | 2017-11-03 |
BR112018008624A2 (pt) | 2018-10-30 |
EP3368748A1 (de) | 2018-09-05 |
WO2017072469A1 (fr) | 2017-05-04 |
CN108350744A (zh) | 2018-07-31 |
CN108350744B (zh) | 2019-04-12 |
CA3003396C (en) | 2018-07-31 |
FR3043131A1 (fr) | 2017-05-05 |
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