EP2787168A3 - Turbomachine and rotor for a turbomachine - Google Patents

Turbomachine and rotor for a turbomachine Download PDF

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Publication number
EP2787168A3
EP2787168A3 EP14002196.5A EP14002196A EP2787168A3 EP 2787168 A3 EP2787168 A3 EP 2787168A3 EP 14002196 A EP14002196 A EP 14002196A EP 2787168 A3 EP2787168 A3 EP 2787168A3
Authority
EP
European Patent Office
Prior art keywords
rotor
turbomachine
respect
hollow shaft
relates
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
EP14002196.5A
Other languages
German (de)
French (fr)
Other versions
EP2787168B1 (en
EP2787168A2 (en
Inventor
Harald Hoell
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Siemens AG
Original Assignee
Siemens AG
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Siemens AG filed Critical Siemens AG
Priority to EP14002196.5A priority Critical patent/EP2787168B1/en
Publication of EP2787168A2 publication Critical patent/EP2787168A2/en
Publication of EP2787168A3 publication Critical patent/EP2787168A3/en
Application granted granted Critical
Publication of EP2787168B1 publication Critical patent/EP2787168B1/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • 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
    • F01D5/026—Shaft to shaft connections
    • 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
    • F01D25/08—Cooling; Heating; Heat-insulation
    • F01D25/12—Cooling
    • 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
    • F01D5/04—Blade-carrying members, e.g. rotors for radial-flow machines or engines
    • F01D5/043—Blade-carrying members, e.g. rotors for radial-flow machines or engines of the axial inlet- radial outlet, or vice versa, type
    • F01D5/048—Form or construction
    • 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
    • F01D5/08—Heating, heat-insulating or cooling means
    • F01D5/085—Heating, heat-insulating or cooling means cooling fluid circulating inside the rotor
    • F01D5/088—Heating, heat-insulating or cooling means cooling fluid circulating inside the rotor in a closed cavity
    • 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
    • F05D2260/40—Transmission of power
    • F05D2260/403—Transmission of power through the shape of the drive components
    • F05D2260/4031—Transmission of power through the shape of the drive components as in toothed gearing

Landscapes

  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Structures Of Non-Positive Displacement Pumps (AREA)
  • Turbine Rotor Nozzle Sealing (AREA)

Abstract

Die Erfindung betrifft einen Rotor (3) für eine Strömungsmaschine,
mit einer zu seiner Drehachse koaxial angeordneten Hohlwelle (13), welche sich beidseitig stirnseitig an zwei axial gegenüberliegenden Abschnitten des Rotors (3) abstützt und einen inneren Hohlraum (51) umschließt. Um einen Rotor (3) für eine Strömungsmaschine anzugeben, der eine höhere Lebensdauer und eine geringere Anfälligkeit gegenüber mechanischen Defekten aufweist, wird vorgeschlagen, dass die Hohlwelle in Axialrichtung des Rotors (3) aus mehreren aneinanderliegenden Ringen (43) gebildet ist und dass die Ringe (43) gegeneinander und gegenüber den Abschnitten den Hohlraum (51) nach außen abdichten.The invention relates to a rotor (3) for a turbomachine,
with a hollow shaft (13) which is arranged coaxially with respect to its axis of rotation and which is supported on both sides on two axially opposite sections of the rotor (3) and encloses an inner cavity (51). In order to specify a rotor (3) for a turbomachine, which has a longer service life and a lower susceptibility to mechanical defects, it is proposed that the hollow shaft in the axial direction of the rotor (3) of several adjacent rings (43) is formed and that the rings (43) against each other and with respect to the portions of the cavity (51) to seal the outside.

Ferner betrifft die Erfindung eine Strömungsmaschine mit solch einem Rotor (3).

Figure imgaf001
Furthermore, the invention relates to a turbomachine with such a rotor (3).
Figure imgaf001
EP14002196.5A 2004-03-17 2005-03-10 Rotor for a turbomachine with hollow shaft Active EP2787168B1 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
EP14002196.5A EP2787168B1 (en) 2004-03-17 2005-03-10 Rotor for a turbomachine with hollow shaft

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
EP04006393A EP1577493A1 (en) 2004-03-17 2004-03-17 Turbomachine and rotor for a turbomachine
EP05715935.2A EP1725741B1 (en) 2004-03-17 2005-03-10 Rotor for a turbomachine
EP14002196.5A EP2787168B1 (en) 2004-03-17 2005-03-10 Rotor for a turbomachine with hollow shaft

Related Parent Applications (2)

Application Number Title Priority Date Filing Date
EP05715935.2A Division EP1725741B1 (en) 2004-03-17 2005-03-10 Rotor for a turbomachine
EP05715935.2A Division-Into EP1725741B1 (en) 2004-03-17 2005-03-10 Rotor for a turbomachine

Publications (3)

Publication Number Publication Date
EP2787168A2 EP2787168A2 (en) 2014-10-08
EP2787168A3 true EP2787168A3 (en) 2015-04-15
EP2787168B1 EP2787168B1 (en) 2016-01-06

Family

ID=34833623

Family Applications (3)

Application Number Title Priority Date Filing Date
EP04006393A Withdrawn EP1577493A1 (en) 2004-03-17 2004-03-17 Turbomachine and rotor for a turbomachine
EP14002196.5A Active EP2787168B1 (en) 2004-03-17 2005-03-10 Rotor for a turbomachine with hollow shaft
EP05715935.2A Active EP1725741B1 (en) 2004-03-17 2005-03-10 Rotor for a turbomachine

Family Applications Before (1)

Application Number Title Priority Date Filing Date
EP04006393A Withdrawn EP1577493A1 (en) 2004-03-17 2004-03-17 Turbomachine and rotor for a turbomachine

Family Applications After (1)

Application Number Title Priority Date Filing Date
EP05715935.2A Active EP1725741B1 (en) 2004-03-17 2005-03-10 Rotor for a turbomachine

Country Status (6)

Country Link
US (1) US7585148B2 (en)
EP (3) EP1577493A1 (en)
JP (1) JP4722120B2 (en)
CN (1) CN101010486B (en)
RU (1) RU2347912C2 (en)
WO (1) WO2005093219A1 (en)

Families Citing this family (26)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1970530A1 (en) * 2007-03-12 2008-09-17 Siemens Aktiengesellschaft Rotor of a thermal fluid flow engine and fluid flow engine
RU2482336C1 (en) * 2009-04-01 2013-05-20 Сименс Акциенгезелльшафт Rotor for hydraulic machine
IT1399904B1 (en) * 2010-04-21 2013-05-09 Nuovo Pignone Spa STACKED ROTOR WITH TIE AND BOLTED FLANGE AND METHOD
US9133729B1 (en) * 2011-06-08 2015-09-15 United Technologies Corporation Flexible support structure for a geared architecture gas turbine engine
US20130264779A1 (en) * 2012-04-10 2013-10-10 General Electric Company Segmented interstage seal system
US9032738B2 (en) * 2012-04-25 2015-05-19 Siemens Aktiengeselischaft Gas turbine compressor with bleed path
JP5865204B2 (en) * 2012-07-20 2016-02-17 株式会社東芝 Axial turbine and power plant
KR101665887B1 (en) * 2015-09-23 2016-10-12 두산중공업 주식회사 Cooling system of the gas turbine
KR101744411B1 (en) 2015-10-15 2017-06-20 두산중공업 주식회사 Cooling apparatus of the gas turbine
JP6554736B2 (en) * 2015-10-23 2019-08-07 三菱日立パワーシステムズ株式会社 Gas turbine rotor, gas turbine, and gas turbine equipment
KR101747550B1 (en) * 2015-12-01 2017-06-27 두산중공업 주식회사 Disk assembly and a turbine using the same
KR101788413B1 (en) 2015-12-01 2017-10-19 두산중공업 주식회사 Disk assembly and a turbine using the same
FR3047075B1 (en) * 2016-01-27 2018-02-23 Safran Aircraft Engines REVOLUTION PIECE FOR TURBINE TEST BENCH OR FOR TURBOMACHINE, TURBINE TESTING BENCH COMPRISING THE TURBINE, AND PROCESS USING THE SAME
EP3214266A1 (en) 2016-03-01 2017-09-06 Siemens Aktiengesellschaft Rotor of a gas turbine with cooling air path
KR102052029B1 (en) * 2016-03-01 2019-12-04 지멘스 악티엔게젤샤프트 Compressor bleed cooling system for mid-frame torque disks downstream from the compressor assembly in a gas turbine engine
EP3219911A1 (en) * 2016-03-17 2017-09-20 Siemens Aktiengesellschaft Gas turbine rotor with bolted rotor discs
US10024170B1 (en) * 2016-06-23 2018-07-17 Florida Turbine Technologies, Inc. Integrally bladed rotor with bore entry cooling holes
KR101772334B1 (en) 2016-07-07 2017-08-28 두산중공업 주식회사 Disk assembly and a turbine using the same
KR101794451B1 (en) 2016-07-07 2017-11-06 두산중공업 주식회사 Disk assembly and a turbine using the same
KR101834647B1 (en) * 2016-07-07 2018-04-13 두산중공업 주식회사 Disk assembly and a turbine using the same
EP3269926B1 (en) * 2016-07-07 2020-10-07 Doosan Heavy Industries & Construction Co., Ltd. Disk assembly and turbine including the same
KR101882107B1 (en) * 2016-12-22 2018-07-25 두산중공업 주식회사 Gas turbine
FR3063775B1 (en) * 2017-03-07 2022-05-06 Ifp Energies Now TURBOPUMP FOR A FLUID CIRCUIT, IN PARTICULAR FOR A CLOSED CIRCUIT IN PARTICULAR OF THE RANKINE CYCLE TYPE
WO2019162989A1 (en) * 2018-02-20 2019-08-29 三菱重工エンジン＆ターボチャージャ株式会社 Supercharger
US10794190B1 (en) 2018-07-30 2020-10-06 Florida Turbine Technologies, Inc. Cast integrally bladed rotor with bore entry cooling
US11428104B2 (en) 2019-07-29 2022-08-30 Pratt & Whitney Canada Corp. Partition arrangement for gas turbine engine and method

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB661078A (en) * 1948-07-27 1951-11-14 Westinghouse Electric Int Co Improvements in or relating to gas turbine power plants
DE1023933B (en) * 1954-03-08 1958-02-06 Canadian Patents Dev Shaft coupling, especially for gas turbine engines
GB836920A (en) * 1957-05-15 1960-06-09 Napier & Son Ltd Rotors for multi-stage axial flow compressors or turbines

Family Cites Families (25)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB599809A (en) 1945-01-15 1948-03-22 Bristol Aeroplane Co Ltd Improvements in axial flow compressors, turbines and the like
US2452782A (en) * 1945-01-16 1948-11-02 Power Jets Res & Dev Ltd Construction of rotors for compressors and like machines
BE534314A (en) * 1953-12-24
US2858101A (en) * 1954-01-28 1958-10-28 Gen Electric Cooling of turbine wheels
US2741454A (en) * 1954-09-28 1956-04-10 Clifford R Eppley Elastic fluid machine
US3059901A (en) * 1958-04-01 1962-10-23 Carrier Corp Rotor construction
DE2250484A1 (en) * 1972-10-14 1974-04-18 Bulawin STATOR OF THE MULTISTAGE FLOW MACHINE
US4173120A (en) * 1977-09-09 1979-11-06 International Harvester Company Turbine nozzle and rotor cooling systems
US4292008A (en) * 1977-09-09 1981-09-29 International Harvester Company Gas turbine cooling systems
US4184797A (en) * 1977-10-17 1980-01-22 General Electric Company Liquid-cooled turbine rotor
DE3606597C1 (en) * 1986-02-28 1987-02-19 Mtu Muenchen Gmbh Blade and sealing gap optimization device for compressors of gas turbine engines
JPS63253125A (en) * 1987-04-08 1988-10-20 Hitachi Ltd Cooling air centrifugal accelerator for gas turbine
US5054996A (en) * 1990-07-27 1991-10-08 General Electric Company Thermal linear actuator for rotor air flow control in a gas turbine
FR2685936A1 (en) * 1992-01-08 1993-07-09 Snecma DEVICE FOR CONTROLLING THE GAMES OF A TURBOMACHINE COMPRESSOR HOUSING.
JP3149774B2 (en) * 1996-03-19 2001-03-26 株式会社日立製作所 Gas turbine rotor
US5755556A (en) * 1996-05-17 1998-05-26 Westinghouse Electric Corporation Turbomachine rotor with improved cooling
JP3621523B2 (en) * 1996-09-25 2005-02-16 株式会社東芝 Gas turbine rotor blade cooling system
EP0965726B1 (en) * 1996-11-29 2004-06-30 Hitachi, Ltd. Refrigerant recovery type gas turbine
US6053701A (en) * 1997-01-23 2000-04-25 Mitsubishi Heavy Industries, Ltd. Gas turbine rotor for steam cooling
DE69934570T2 (en) * 1999-01-06 2007-10-04 General Electric Co. Cover plate for a turbine rotor
EP1079069B1 (en) * 1999-08-24 2006-03-01 General Electric Company Steam cooling system for a gas turbine
US6287079B1 (en) * 1999-12-03 2001-09-11 Siemens Westinghouse Power Corporation Shear pin with locking cam
JP3361501B2 (en) * 2000-03-02 2003-01-07 株式会社日立製作所 Closed-circuit blade cooling turbine
JP3762661B2 (en) * 2001-05-31 2006-04-05 株式会社日立製作所 Turbine rotor
JP2003206701A (en) * 2002-01-11 2003-07-25 Mitsubishi Heavy Ind Ltd Turbine rotor for gas turbine, and gas turbine

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB661078A (en) * 1948-07-27 1951-11-14 Westinghouse Electric Int Co Improvements in or relating to gas turbine power plants
DE1023933B (en) * 1954-03-08 1958-02-06 Canadian Patents Dev Shaft coupling, especially for gas turbine engines
GB836920A (en) * 1957-05-15 1960-06-09 Napier & Son Ltd Rotors for multi-stage axial flow compressors or turbines

Also Published As

Publication number Publication date
JP4722120B2 (en) 2011-07-13
EP2787168B1 (en) 2016-01-06
EP1725741B1 (en) 2014-09-24
US20080159864A1 (en) 2008-07-03
EP1725741A1 (en) 2006-11-29
JP2007529668A (en) 2007-10-25
US7585148B2 (en) 2009-09-08
WO2005093219A1 (en) 2005-10-06
CN101010486A (en) 2007-08-01
EP2787168A2 (en) 2014-10-08
EP1577493A1 (en) 2005-09-21
CN101010486B (en) 2011-06-01
RU2006136413A (en) 2008-04-27
RU2347912C2 (en) 2009-02-27

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