CN110671155A - Self-adaptive variable working condition optimal positive pressure damping blade structure and design method - Google Patents

Self-adaptive variable working condition optimal positive pressure damping blade structure and design method Download PDF

Info

Publication number
CN110671155A
CN110671155A CN201910996209.0A CN201910996209A CN110671155A CN 110671155 A CN110671155 A CN 110671155A CN 201910996209 A CN201910996209 A CN 201910996209A CN 110671155 A CN110671155 A CN 110671155A
Authority
CN
China
Prior art keywords
positive pressure
blade
damping
shroud
design
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
CN201910996209.0A
Other languages
Chinese (zh)
Other versions
CN110671155B (en
Inventor
谢永慧
刘铸锋
赵伟
张荻
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.)
Xian Jiaotong University
Original Assignee
Xian Jiaotong University
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 Xian Jiaotong University filed Critical Xian Jiaotong University
Priority to CN201910996209.0A priority Critical patent/CN110671155B/en
Publication of CN110671155A publication Critical patent/CN110671155A/en
Application granted granted Critical
Publication of CN110671155B publication Critical patent/CN110671155B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

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
    • F01D5/12—Blades
    • F01D5/22—Blade-to-blade connections, e.g. for damping vibrations
    • F01D5/225—Blade-to-blade connections, e.g. for damping vibrations by shrouding
    • 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
    • F01D5/141—Shape, i.e. outer, aerodynamic form
    • 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
    • F01D5/147—Construction, i.e. structural features, e.g. of weight-saving hollow blades
    • 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
    • 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
    • F05D2250/00—Geometry
    • F05D2250/20—Three-dimensional
    • F05D2250/24—Three-dimensional ellipsoidal
    • F05D2250/241—Three-dimensional ellipsoidal spherical

Landscapes

  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Fluid Mechanics (AREA)
  • Architecture (AREA)
  • Turbine Rotor Nozzle Sealing (AREA)

Abstract

A self-adaptive variable working condition optimal positive pressure damping blade structure and a design method thereof are disclosed, wherein the damping blade structure comprises a blade root, a blade body, a shroud and a positive pressure adjusting ball; the shroud ring is integrally designed in a circumferential convex mode symmetrical along a median plane, grooves are correspondingly formed in the suction surface side and the pressure surface side in the direction, the grooves in the suction surface side of the shroud ring and the grooves in the pressure surface side of the adjacent shroud ring are oppositely arranged along the median plane of the shroud ring to form a complete installation groove, and the positive pressure adjusting balls are sequentially installed in the corresponding installation grooves. Under the design working condition, the optimal positive pressure is obtained by a positive pressure solving method, the design shape function of the contact surface of the shroud is obtained by combining the related parameter relation, and the parameterized flow design of the damping structure is completed. Under the variable working condition, the damping structure reaches a new design balance point according to the matching relation between the contact angle and the optimal positive pressure, the damping structure continues to operate under the new optimal positive pressure, the self-adaptive design of the optimal positive pressure optimization structure of the variable working condition damping is realized, and the damping performance is improved to enable the damping system to operate efficiently.

Description

Self-adaptive variable working condition optimal positive pressure damping blade structure and design method
Technical Field
The invention relates to a moving blade of a steam turbine, in particular to a self-adaptive variable working condition optimal positive pressure damping blade structure and a design method thereof.
Background
The blades are important parts for converting the kinetic energy of steam into mechanical work in the steam turbine and are important for the safe operation of the steam turbine. The operating environment of the turbine blade is very complicated, and the turbine blade can be influenced by centrifugal force, stable airflow force and alternating exciting force during working, so that the blade is easy to vibrate. The vibration level of the blade is reduced, and the vibration stress is reduced to be within an allowable range, so that the safety and the reliability of the whole machine are guaranteed.
The blade that has damping shroud structure is adopted often in industry, takes place the friction effect through the contact between the blade shroud when vibration takes place, dissipates the mechanical energy conversion of blade structure vibration into heat energy, plays the effect of damping to thereby it changes the frictional damping to finely tune through the clearance between the shroud and change contact normal pressure. The positive pressure of the damping structure is a key parameter in the design of the damping structure, and directly influences the vibration reduction effect of the blade friction damping. When the positive pressure is small, the interaction between the blade shrouds is weak, the friction force is small, the friction contact surface is in a condition similar to shroud separation at the moment, the function of the friction damping piece for dissipating the vibration energy of the blades cannot be fully exerted, and therefore the resonance amplitude of the blades is large. Along with the increase of the positive pressure, the resonance frequency begins to increase, the interaction between the interfaces is enhanced, the vibration energy of the blade is dissipated by the friction damping part, and the vibration amplitude is reduced. However, when the positive pressure is further increased, the interaction between the blades is enhanced, the air flow exciting force under the normal working state is difficult to enable the friction contact surface to generate a macro slip phenomenon again, the friction node pair is in a micro slip state at the moment, the friction effect is blocked, and the blade vibration energy cannot be consumed through friction, so that the resonance amplitude of the blade is increased again, and the blade vibration is aggravated.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a self-adaptive variable working condition optimal positive pressure damping blade structure and a design method thereof. According to the invention, the contact positive pressure between the blade top shrouds is changed by designing the variable cross-section groove, so that the optimal solution of the positive pressure between the damping shrouds is obtained, the blade always works at the optimal positive pressure under different working conditions, the effect of a friction damping effect is effectively exerted, the response amplitude and the vibration level are reduced, and the safe operation of a unit is ensured.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
a self-adaptive variable working condition optimal positive pressure damping blade structure is subjected to pre-twisting treatment and comprises a positive pressure adjusting ball, a blade root platform, a blade root connected with the lower part of the blade root platform, a pre-twisted blade body connected with the upper part of the blade root platform and a blade shroud connected with the top of the pre-twisted blade body; wherein the content of the first and second substances,
the suction side and the pressure side of the blade shroud in the circumferential direction are correspondingly provided with grooves which are respectively a suction side groove and a pressure side groove, the suction side groove of each blade shroud and the pressure side groove of the adjacent blade shroud are oppositely arranged along the median plane of the shroud to form a complete mounting groove, and the positive pressure adjusting balls are sequentially mounted in the corresponding mounting grooves.
The invention has the further improvement that the shroud blade damping structure can be adjusted, and the contact surface and the angle between the ball and the blade shroud groove are adjusted by automatically adjusting the positive pressure when the working condition changes, so as to achieve a new design balance point, and the new design balance point is used for providing the optimal positive pressure under the adaptive variable working condition, so that the adaptive design of the damping structure under the variable working condition is realized.
The invention has the further improvement that the whole blade shroud adopts a circumferential convex design symmetrical along the bisection plane;
the included angle between the suction surface or the pressure surface of the blade shroud and the median plane is 60 degrees.
The invention has the further improvement that the circumferential section of the groove is in a right trapezoid shape, and the height ratio of the axial long side to the axial short side is 2: 1.
The invention is further improved in that the adjacent surfaces in the groove are in fillet transition.
The invention has the further improvement that the top surface, the two axial side surfaces and the bottom surface of the groove are planes which are determined by the size; the axial side surface is a curved surface and is determined by a shroud design shape function Q (phi, S); and the distance between the two axial side surfaces of the groove and the distance between the bottom surface and the end surface of the shroud ring are equal.
The invention is further improved in that the positive pressure adjusting ball is simultaneously contacted with the curved surfaces and the bottom surfaces of the grooves on the two sides in the groove channel and can generate rolling friction.
A design method of an adaptive variable working condition optimal positive pressure damping blade structure is a method for solving the optimal positive pressure of the damping structure under variable working conditions, and comprises the following steps:
(1) when the rotating speed of the blade with the structure is n, the exciting force F of the blade airflow is actually measureda；
(2) Applying positive pressure load N between the friction contact surfaces of the shroud ring groove and the positive pressure adjusting ball;
(3) applying a simple resonance exciting force F with exciting frequency omega and amplitude F to the surface of the bladeasinωt；
(4) Assuming that the initial value A of the displacement amplitude of the blade top motion is A0According to known parameters such as the friction coefficient mu between contact surfaces, the positive pressure load N, the vibration frequency omega and the relative movement displacement u, and by combining a micro-motion slip friction model, assuming that the contact surfaces do not slide integrally, the friction force in the initial loading process can be expressed as:
Figure BDA0002239780560000031
(5) by the harmonic balance method, when the system is excited by simple harmonic, the friction force is subjected to Fourier expansion, and the first harmonic is taken to obtain:
f(A,θ)＝fC(A)cosθ+fS(A)sinθ
in the formula fC(A) And fS(A) First order cosine and sine components of the friction force, respectively;
obtaining f by numerical integrationC(A) And fS(A) And the friction contact surface is simplified into a no-mass spring damping system, and the friction force can be obtained by adding the elastic force and the damping force:
f＝KeqA cosθ-CeqωA sinθ
combining the above equation and the integral property calculationObtaining the equivalent stiffness coefficient K between the friction contact surfaceseqAnd equivalent damping coefficient Ceq；
Figure BDA0002239780560000032
Figure BDA0002239780560000033
(6) Obtaining an updated value A' of the relative motion displacement amplitude between the friction contact surfaces under the working condition by adopting harmonic response analysis based on a modal superposition method;
(7) comparing the A ' obtained by calculation with the A of the previous time, if the error of the A ' and the A of the previous time is in an allowable range, the calculation is converged, otherwise, the A is equal to the A ', and returning to the step (4) until the calculation is converged;
(8) updating the excitation frequency omega, and repeating the steps (3) to (7) to obtain a forced response curve of the blade changing along with the excitation frequency;
(9) changing the positive pressure load value N, repeating the steps (2) to (8) to obtain a plurality of blade amplitude-frequency response curve families formed along with the change of the contact positive pressure, and obtaining a blade amplitude-frequency response curve function family through quadratic curve fitting;
(10) by solving the envelope curve of the amplitude-frequency response curve family, the positive pressure corresponding to the minimum value point on the envelope curve is found, namely the optimum positive pressure N found under the exciting force Fopt(ii) a The envelope equation is obtained by simultaneously solving a curve family function and a first derivative function thereof:
(11) updating the running rotating speed N and the corresponding simple harmonic excitation value F, and repeating the steps (1) to (10) to obtain different excitations and the optimal positive pressure N under variable working conditionsoptConstructing a library function L (F, N) forming the optimal positive pressure under variable working conditionsopt)。
A design method for an optimal positive pressure damping blade structure under a self-adaptive variable working condition can realize a parametric design method for a shroud friction damping structure, and comprises the following steps:
(1) designing a shroud damping structure according to the initial shape function Q (phi, S) to obtain shroud variable contact damping blade operation parameters under the design working condition;
(2) analyze stimulus conditions and call library functions L (F, N)opt) Obtaining the optimal positive pressure under the working condition;
(3) by introducing a function of contact angle phi (N, F, N)opt) Combining the shroud design parameter function to obtain a design shape function Q' (phi, S) of the shroud contact groove;
(4) if the damping structure meets the error range of the design value according to the design shape function Q' (phi, S), completing the parameterization process design of the damping structure; otherwise, repeating the steps (1) to (3) until the design condition is met.
A design method of an optimal positive pressure damping blade structure adaptive to variable working conditions is characterized in that under the condition that a shroud form is determined, optimal positive pressure and contact angles are matched according to actual working conditions; when the operation condition of the shroud damping structure blade changes, the positive pressure, the contact surface and the angle also change, and the change of the airflow exciting force is in the range of L (F, N)opt) Reaching new design balance point in the function, and reaching new balance position through the adjustment of contact surface and angle to make it always satisfy function phi (N, F, N)opt) And Q (phi, S) at the new optimum positive pressure No′ptAnd then continuously and stably running, and realizing the self-adaptive design of the optimal positive pressure optimization structure of variable working condition damping.
Compared with the prior art, the invention has at least the following beneficial technical effects:
the invention provides a self-adaptive variable working condition optimal positive pressure damping blade structure which is obtained by combining theoretical calculation derivation and actual engineering analysis (2) a shroud groove form function, wherein the design of a shroud groove variable section variable contact angle is adopted, and the self-adjustment of a contact surface and a contact angle between a ball and a shroud groove can be adjusted through positive pressure in variable working conditions, so that the optimal positive pressure adaptive to different working conditions is provided, and the shroud groove form function is obtained by combining theoretical calculation derivation and actual engineering analysis.
Furthermore, the whole vane shroud adopts a circumferential convex design symmetrical along a middle dividing plane, and the contact positive pressure is mainly provided by a damping structure, so that the mass of the shroud and the centrifugal force generated in the operation process are reduced.
Furthermore, the adjacent surfaces in the grooves are in fillet transition, so that stress concentration is reduced.
The invention provides a design method of an adaptive variable working condition optimal positive pressure damping blade structure, which comprises the following steps of (1) providing a solving algorithm of the optimal positive pressure of a damping structure under a certain excitation force to obtain a library function of the optimal positive pressure under a variable working condition; (2) the contact angle function and the shroud band shape function are accessed through the obtained optimal positive pressure, so that a parameterized design algorithm for a shroud band friction damping structure can be realized; (3) the positive pressure and the contact angle can be matched according to the actual working condition, a new design balance point is reached through the autonomous adjustment of the contact angle of the damping structure when the working condition changes, and the adaptive design of the optimal positive pressure optimization structure of the variable working condition damping is realized.
In conclusion, on the basis of fully researching the vibration damping structure of the moving blade, the shroud contact damping structure is improved, a structure of a shroud groove positive pressure adjusting ball variable contact surface and contact angle is designed, a complete shroud damping structure parametric design flow is formed by combining a positive pressure solving algorithm with a contact angle function and a shroud shape function, quick balance optimization of the optimal positive pressure can be completed under the condition of variable working conditions, the self-adaptive design of the damping structure is realized, the blade structure always keeps the excellent vibration damping performance and efficient operation of the system, and the safety and stable operation of a unit is guaranteed to have certain significance. In addition, the invention has better universality, simple structure and easy processing, and can be suitable for blades in different shroud forms.
Drawings
FIGS. 1 and 2 are schematic views of a blade embodying the present invention from two different perspectives;
FIG. 3 is an enlarged view taken at a in FIG. 2;
FIG. 4 is a schematic structural view of the present invention;
FIG. 5 is a top view of the structure of the present invention;
FIG. 6 is a schematic diagram of a real working section and a simplified stress analysis of a damping structure;
FIG. 7 is a flow chart of a solving algorithm for optimal positive pressure of the damping structure;
FIG. 8 is a flow chart of a parametric design of a shroud frictional damping structure;
FIG. 9 is a variable-operating-condition adaptive flow chart of the shroud friction damping structure.
Reference numbers and symbols in the drawings mean:
1-a blade root; 2-a blade root platform; 3-leaf body; 4, a blade shroud; 41-shroud suction side; 42-shroud pressure face side; 5-positive pressure adjusting ball; 6-groove; 61-suction side grooves; 62-pressure face side groove; 7-median plane division of the shroud ring; a-the height of the axially longer side of the mounting groove; b-length of bottom edge of the mounting groove; c, the height of the axial shorter side of the mounting groove is increased; d-the distance between the two end surfaces of the steam inlet side or the steam outlet side of the shroud band; h, the distance between the side edge and the bottom edge of the groove and the end surface of the shroud ring, and the distance between the end surface of the shroud ring and the bottom surface of the shroud ring are respectively; l-total length of shroud; w-total width of the shroud; s-shroud convex portion length; t-shroud convex portion height; the r-positive pressure adjusts the ball radius.
QcPositive pressure regulates the centrifugal force to which the ball is subjected; supporting reaction force of each node of the Z-shroud damping structure; f-positive pressure adjusts the airflow exciting force applied to the ball; the N-positive pressure adjusts the pressure of the contact surface of the shroud, which is applied to the ball; phi-positive pressure adjusts the included angle between the positive pressures of the groove curved surfaces on the two sides of the ball, namely the contact angle.
Detailed Description
The invention will be further described below with reference to the accompanying drawings by taking a fir tree root as an example.
Referring to fig. 1 to 3, the optimal positive pressure damping blade structure with adaptive variable working conditions provided by the invention comprises a blade root 1, a blade root platform 2, a blade body 3, a shroud 4 and a positive pressure adjusting ball 5, wherein the blade is subjected to pre-twisting treatment; the suction surface side 41 and the pressure surface side 42 of each blade shroud band 4 in the circumferential direction of the shroud band are correspondingly provided with grooves 6, the suction surface side groove 61 of each blade shroud band 4 and the pressure surface side groove 62 of the adjacent blade shroud band are oppositely arranged along the shroud band split surface 7 to form a complete installation groove, the positive pressure adjusting ball 5 is sequentially installed in the corresponding installation groove, and the form of the installation groove is determined by a design function and the form of the shroud band.
Referring to fig. 4, specific parameters of the structure of the invention are given by taking a 350mm blade as an example: the total length l of the shroud ring is 84 +/-0.1 mm; the total width w of the shroud ring is 68 plus or minus 0.3 mm; the height a of the axial longer side of the mounting groove is 12.0 +/-0.1 mm; the height c of the axial shorter side of the mounting groove is 6.0 +/-0.1 mm; the length b of the bottom edge of the mounting groove is 47.0 +/-0.5 mm; the distance d between the two end surfaces of the steam inlet side or the steam outlet side of the shroud band is 6.0 +/-0.1 mm; the distance h between the axial side surface and the bottom surface of the groove and the end surface of the shroud ring is 4.50 +/-0.05 mm; the distance h between the end surface of the shroud ring and the bottom surface of the shroud ring is 4.50 +/-0.05 mm; the length s of the convex part of the shroud band is 56.0 +/-0.1 mm; the height t of the convex part of the shroud band is 15.0 +/-0.1 mm; the radius r of the ball is adjusted to be 4mm under positive pressure; the round angle R is 1.0-2.0 mm.
Referring to fig. 5, a top view of the damping structure is shown, and the included angle between the suction surface or the pressure surface of the shroud and the median plane (7) is 60 degrees.
Referring to FIG. 6, the support reaction force Z of each node of the shroud damping structure and the centrifugal force Q at the central plane of the damping structure under the operating condition are obtained by a finite element analysis and calculation methodcAnd measuring the simple resonance exciting force F of the blade through an experiment: by force balance analysis:
Figure BDA0002239780560000071
obtaining a functional relation phi (N, F, N) between the contact angle and the positive pressureopt)。
Referring to fig. 7, a method for solving the optimal positive pressure of the damping structure under variable working conditions is provided, which comprises the following steps:
(1) when the rotating speed of the blade with the structure is n, the exciting force F of the blade airflow is actually measureda；
(2) Applying positive pressure load N between the friction contact surfaces of the shroud ring groove and the positive pressure adjusting ball;
(3) applying a simple resonance exciting force F with exciting frequency omega and amplitude F to the surface of the bladeasinωt；
(4) Assuming that the initial value A of the displacement amplitude of the blade top motion is A0According to known parameters such as the friction coefficient mu between contact surfaces, the positive pressure load N, the vibration frequency omega and the relative movement displacement u, and by combining a micro-motion slip friction model, assuming that the contact surfaces do not slide integrally, the friction force in the initial loading process can be expressed as:
Figure BDA0002239780560000081
(5) by the harmonic balance method, when the system is excited by simple harmonic, the friction force is subjected to Fourier expansion, and the first harmonic is taken to obtain:
f(A,θ)＝fC(A)cosθ+fS(A)sinθ
in the formula fC(A) And fS(A) First order cosine and sine components of the friction force, respectively;
obtaining f by numerical integrationC(A) And fS(A) And the friction contact surface is simplified into a no-mass spring damping system, and the friction force can be obtained by adding the elastic force and the damping force:
f＝KeqA cosθ-CeqωA sinθ
calculating to obtain the equivalent stiffness coefficient K between the friction contact surfaces by combining the upper formula and the integral propertyeqAnd equivalent damping coefficient Ceq；
Figure BDA0002239780560000082
Figure BDA0002239780560000083
(6) Obtaining an updated value A' of the relative motion displacement amplitude between the friction contact surfaces under the working condition by adopting harmonic response analysis based on a modal superposition method;
(7) comparing the A ' obtained by calculation with the A of the previous time, if the error of the A ' and the A of the previous time is in an allowable range, the calculation is converged, otherwise, the A is equal to the A ', and returning to the step (4) until the calculation is converged;
(8) updating the excitation frequency omega, and repeating the steps (3) to (7) to obtain a forced response curve of the blade changing along with the excitation frequency;
(9) changing the positive pressure load value N, repeating the steps (2) to (8) to obtain a plurality of blade amplitude-frequency response curve families formed along with the change of the contact positive pressure, and obtaining a blade amplitude-frequency response curve function family through quadratic curve fitting;
(10) by solving the envelope curve of the amplitude-frequency response curve family, the positive pressure corresponding to the minimum value point on the envelope curve is found, namely the optimum positive pressure N found under the exciting force Fopt(ii) a The envelope equation is obtained by simultaneously solving a curve family function and a first derivative function thereof:
(11) updating the running rotating speed N and the corresponding simple harmonic excitation value F, and repeating the steps (1) to (10) to obtain different excitations and the optimal positive pressure N under variable working conditionsoptConstructing a library function L (F, N) forming the optimal positive pressure under variable working conditionsopt)。
Referring to fig. 8, a parametric design of the shroud frictional damping structure may be achieved. The specific calculation process comprises the following steps:
(1) designing a shroud according to the initial shape function Q (phi, S) to obtain the operating parameters of the shroud variable contact damping blade under the design working condition;
(2) analyze stimulus conditions and call library functions L (F, N)opt) Obtaining the optimal positive pressure under the working condition;
(3) by introducing a function of contact angle phi (N, F, N)opt) Combining the shroud design parameter function to obtain a design shape function Q' (phi, S) of the shroud contact groove;
(4) if the damping structure meets the error range of the design value according to the design shape function Q' (phi, S), completing the parameterization process design of the damping structure; otherwise, repeating the steps (1) to (3) until the design condition is met.
Referring to fig. 9, under the condition that the shroud form is determined, matching is performed on the optimal positive pressure and the contact angle according to the actual working condition; when the operation condition of the shroud damping structure blade changes, the positive pressure, the contact surface and the angleAnd the change is also carried out according to the change of the airflow exciting force in L (F, N)opt) Reaching new design balance point in the function, and reaching new balance position through the adjustment of contact surface and angle to make it always satisfy function phi (N, F, N)opt) And Q (phi, S) at a new optimum positive pressure N'optAnd then continuously and stably running, and realizing the self-adaptive design of the optimal positive pressure optimization structure of variable working condition damping.
In conclusion, the invention designs the structure for regulating the variable contact surface and the contact angle of the ball under the positive pressure of the shroud groove, provides a complete parameterization design flow of the shroud damping structure, and can realize the self-adaptive design of the optimal positive pressure structure under the variable working condition damping, thereby meeting the requirements of excellent vibration damping performance and efficient operation of the system.

Claims (10)

1. A self-adaptive variable working condition optimal positive pressure damping blade structure is characterized in that the damping blade structure is subjected to pre-twisting treatment and comprises a positive pressure adjusting ball (5), a blade root platform (2), a blade root (1) connected with the lower part of the blade root platform (2), a pre-twisting blade body (3) connected with the upper part of the blade root platform (2) and a blade shroud (4) connected with the top of the pre-twisting blade body (3); wherein the content of the first and second substances,
the suction surface side (41) and the pressure surface side (42) of each blade shroud band (4) in the circumferential direction are correspondingly provided with grooves (6) which are respectively a suction surface side groove (61) and a pressure surface side groove (62), the suction surface side groove (61) of each blade shroud band (4) and the pressure surface side groove (62) of the adjacent blade shroud band (4) are oppositely arranged along the shroud band bisection surface (7) to form a complete installation groove, and positive pressure adjusting balls (5) are sequentially installed in the corresponding installation grooves.
2. The adaptive variable-working-condition optimal positive pressure damping blade structure according to claim 1, wherein the shroud blade damping structure can be adjusted, and when the working condition changes, a new design balance point is reached by automatically adjusting the contact surface and the angle of the positive pressure adjusting ball (5) and the groove (6) of the blade shroud (4) so as to provide the optimal positive pressure under the adaptive variable working condition, so that the adaptive design of the damping structure under the variable working condition is realized.
3. The structure of the self-adaptive variable-working-condition optimal positive pressure damping blade as claimed in claim 1, wherein the whole blade shroud (4) adopts a circumferential convex design symmetrical along a bisection plane (7);
the included angle between the suction surface or the pressure surface of the blade shroud ring (4) and the median plane (7) is 60 degrees.
4. The structure of the self-adaptive variable-working-condition optimal positive pressure damping blade as claimed in claim 1, wherein the circumferential section of the groove is a right trapezoid, and the height ratio of the axial long side to the axial short side is 2: 1.
5. The adaptive variable working condition optimal positive pressure damping blade structure as claimed in claim 1, wherein adjacent surfaces inside the groove are in fillet transition.
6. The structure of the adaptive variable working condition optimal positive pressure damping blade as claimed in claim 1, wherein the top surface, the two axial side surfaces and the bottom surface of the groove are planes, and are determined by size; the axial side surface is a curved surface and is determined by a shroud design shape function Q (phi, S); and the distance between the two axial side surfaces of the groove and the distance between the bottom surface and the end surface of the shroud ring are equal.
7. The adaptive variable working condition optimal positive pressure damping blade structure as claimed in claim 1, wherein the positive pressure adjusting ball is in contact with the curved surfaces and the bottom surfaces of the grooves on two sides simultaneously in the groove channel and can generate rolling friction.
8. The design method of the adaptive variable-working-condition optimal positive pressure damping blade structure as claimed in any one of claims 1 to 7, wherein the method for solving the optimal positive pressure of the damping structure under the variable working conditions comprises the following steps:
(1) when the rotating speed of the blade with the structure is n, the exciting force F of the blade airflow is actually measureda；
(2) Applying positive pressure load N between the friction contact surfaces of the shroud ring groove and the positive pressure adjusting ball;
(3) applying a simple resonance exciting force F with exciting frequency omega and amplitude F to the surface of the bladeasinωt；
(4) Assuming that the initial value A of the displacement amplitude of the blade top motion is A0According to known parameters such as the friction coefficient mu between contact surfaces, the positive pressure load N, the vibration frequency omega and the relative movement displacement u, and by combining a micro-motion slip friction model, assuming that the contact surfaces do not slide integrally, the friction force in the initial loading process can be expressed as:
Figure FDA0002239780550000021
(5) by the harmonic balance method, when the system is excited by simple harmonic, the friction force is subjected to Fourier expansion, and the first harmonic is taken to obtain:
f(A,θ)＝fC(A)cosθ+fS(A)sinθ
in the formula fC(A) And fS(A) First order cosine and sine components of the friction force, respectively;
obtaining f by numerical integrationC(A) And fS(A) And the friction contact surface is simplified into a no-mass spring damping system, and the friction force can be obtained by adding the elastic force and the damping force:
f＝KeqA cosθ-CeqωA sinθ
calculating to obtain the equivalent stiffness coefficient K between the friction contact surfaces by combining the upper formula and the integral propertyeqAnd equivalent damping coefficient Ceq；
Figure FDA0002239780550000022
Figure FDA0002239780550000023
(6) Obtaining an updated value A' of the relative motion displacement amplitude between the friction contact surfaces under the working condition by adopting harmonic response analysis based on a modal superposition method;
(7) comparing the A ' obtained by calculation with the A of the previous time, if the error of the A ' and the A of the previous time is in an allowable range, the calculation is converged, otherwise, the A is equal to the A ', and returning to the step (4) until the calculation is converged;
(8) updating the excitation frequency omega, and repeating the steps (3) to (7) to obtain a forced response curve of the blade changing along with the excitation frequency;
(9) changing the positive pressure load value N, repeating the steps (2) to (8) to obtain a plurality of blade amplitude-frequency response curve families formed along with the change of the contact positive pressure, and obtaining a blade amplitude-frequency response curve function family through quadratic curve fitting;
(10) by solving the envelope curve of the amplitude-frequency response curve family, the positive pressure corresponding to the minimum value point on the envelope curve is found, namely the optimum positive pressure N found under the exciting force Fopt(ii) a The envelope equation is obtained by simultaneously solving a curve family function and a first derivative function thereof:
Figure FDA0002239780550000031
(11) updating the running rotating speed N and the corresponding simple harmonic excitation value F, and repeating the steps (1) to (10) to obtain different excitations and the optimal positive pressure N under variable working conditionsoptConstructing a library function L (F, N) forming the optimal positive pressure under variable working conditionsopt)。
9. The design method of the self-adaptive variable-working-condition optimal positive pressure damping blade structure as claimed in any one of claims 1 to 7, wherein the parameterized design method of the shroud friction damping structure can be realized, and the method comprises the following steps:
(1) designing a shroud damping structure according to the initial shape function Q (phi, S) to obtain shroud variable contact damping blade operation parameters under the design working condition;
(2) analyze stimulus conditions and call library functions L (F, N)opt) Obtaining the optimal positive pressure under the working condition;
(3) by introducing a function of contact angle phi (N, F, N)opt) And combined with the design parameter letter of the shroudCounting to obtain a design shape function Q' (phi, S) of the shroud band contact groove;
(4) if the damping structure meets the error range of the design value according to the design shape function Q' (phi, S), completing the parameterization process design of the damping structure; otherwise, repeating the steps (1) to (3) until the design condition is met.
10. The design method of the optimal positive pressure damping blade structure with the self-adaptive variable working conditions according to any one of claims 1 to 7 is characterized in that under the condition of determining the shroud form, the optimal positive pressure and the contact angle are matched according to the actual working conditions; when the operation condition of the shroud damping structure blade changes, the positive pressure, the contact surface and the angle also change, and the change of the airflow exciting force is in the range of L (F, N)opt) Reaching new design balance point in the function, and reaching new balance position through the adjustment of contact surface and angle to make it always satisfy function phi (N, F, N)opt) And Q (phi, S) at a new optimum positive pressure N'optAnd then continuously and stably running, and realizing the self-adaptive design of the optimal positive pressure optimization structure of variable working condition damping.
CN201910996209.0A 2019-10-18 2019-10-18 Self-adaptive variable working condition optimal positive pressure damping blade structure and design method Active CN110671155B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910996209.0A CN110671155B (en) 2019-10-18 2019-10-18 Self-adaptive variable working condition optimal positive pressure damping blade structure and design method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910996209.0A CN110671155B (en) 2019-10-18 2019-10-18 Self-adaptive variable working condition optimal positive pressure damping blade structure and design method

Publications (2)

Publication Number Publication Date
CN110671155A true CN110671155A (en) 2020-01-10
CN110671155B CN110671155B (en) 2021-01-19

Family

ID=69083133

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910996209.0A Active CN110671155B (en) 2019-10-18 2019-10-18 Self-adaptive variable working condition optimal positive pressure damping blade structure and design method

Country Status (1)

Country Link
CN (1) CN110671155B (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113404547A (en) * 2021-07-09 2021-09-17 中国联合重型燃气轮机技术有限公司 Turbine blade and gas turbine
FR3137121A1 (en) * 2022-06-22 2023-12-29 Safran Aircraft Engines Bladed assembly with inter-platform connection by interposed rolling element

Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB561897A (en) * 1941-03-08 1944-06-09 Westinghouse Electric Int Co Improvements in or relating to vibration damping means for turbine blades
FR2522364A1 (en) * 1982-03-01 1983-09-02 Snecma DEVICE FOR DAMPENING THE VIBRATION OF BLADES OF TURBOMACHINES
GB2223277A (en) * 1988-09-30 1990-04-04 Rolls Royce Plc Aerofoil blade damping
US6827551B1 (en) * 2000-02-01 2004-12-07 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Self-tuning impact damper for rotating blades
CN101158290A (en) * 2007-10-30 2008-04-09 西安交通大学 Bucket root platform double wedge shape blocks damping structure of turbine bucket
DE102010051529A1 (en) * 2010-11-16 2012-05-16 Mtu Aero Engines Gmbh Rotor blade arrangement for turbo machine, particularly gas turbine, has rotor blade and hollow space, in which vocal mass is mobile arranged
CN106528982A (en) * 2016-10-26 2017-03-22 西安交通大学 Vibration analysis method for dry frictional damping mistuned blades with tendons and shroud bands
CN206419068U (en) * 2017-02-08 2017-08-18 景德镇明兴航空锻压有限公司 A kind of large steam turbine blade
CN209444376U (en) * 2018-10-25 2019-09-27 中国科学院工程热物理研究所 Using the blade of adaptive Condar jet

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB561897A (en) * 1941-03-08 1944-06-09 Westinghouse Electric Int Co Improvements in or relating to vibration damping means for turbine blades
FR2522364A1 (en) * 1982-03-01 1983-09-02 Snecma DEVICE FOR DAMPENING THE VIBRATION OF BLADES OF TURBOMACHINES
GB2223277A (en) * 1988-09-30 1990-04-04 Rolls Royce Plc Aerofoil blade damping
US6827551B1 (en) * 2000-02-01 2004-12-07 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Self-tuning impact damper for rotating blades
CN101158290A (en) * 2007-10-30 2008-04-09 西安交通大学 Bucket root platform double wedge shape blocks damping structure of turbine bucket
DE102010051529A1 (en) * 2010-11-16 2012-05-16 Mtu Aero Engines Gmbh Rotor blade arrangement for turbo machine, particularly gas turbine, has rotor blade and hollow space, in which vocal mass is mobile arranged
CN106528982A (en) * 2016-10-26 2017-03-22 西安交通大学 Vibration analysis method for dry frictional damping mistuned blades with tendons and shroud bands
CN206419068U (en) * 2017-02-08 2017-08-18 景德镇明兴航空锻压有限公司 A kind of large steam turbine blade
CN209444376U (en) * 2018-10-25 2019-09-27 中国科学院工程热物理研究所 Using the blade of adaptive Condar jet

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
季葆华等: "现代汽轮机叶片阻尼结构形式设计方法的研究", 《西安交通大学学报》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113404547A (en) * 2021-07-09 2021-09-17 中国联合重型燃气轮机技术有限公司 Turbine blade and gas turbine
FR3137121A1 (en) * 2022-06-22 2023-12-29 Safran Aircraft Engines Bladed assembly with inter-platform connection by interposed rolling element

Also Published As

Publication number Publication date
CN110671155B (en) 2021-01-19

Similar Documents

Publication Publication Date Title
JP5314851B2 (en) Rotor blade for the second phase of the compressor
CN110671155B (en) Self-adaptive variable working condition optimal positive pressure damping blade structure and design method
US9963974B2 (en) Reduction of equally spaced turbine nozzle vane excitation
JP4765882B2 (en) Steam turbine blades
US10401161B2 (en) Method for dimensioning a turbomachine
Florea et al. Reduced-order modeling of unsteady viscous flow in a compressor cascade
JP5462225B2 (en) Turbine design method and turbine manufacturing method
Muszyńska et al. On tuned bladed disk dynamics: Some aspects of friction related mistuning
CN106089314B (en) Leaving area 3.2m2The low-pressure stage group final stage moving blade of efficient industrial steam turbine
US20140017089A1 (en) Airfoil
Gnesin et al. A coupled fluid–structure analysis for 3-D inviscid flutter of IV standard configuration
KR100340699B1 (en) Design method for axial fan blade and a blade manufactured thereby
Myoren et al. Multi-objective optimization of three-dimensional blade shape for an axial compressor rotor in transonic stage
JP6807950B2 (en) Methods for contouring the blades of axial turbomachinery
Pust et al. Blades forced vibration under aero-elastic excitation modeled by Van der Pol
CN114154363B (en) Vibration damping characteristic analysis method for high-pressure turbine blade edge plate damper
Willeke et al. Reduced order modeling of mistuned bladed disks considering aerodynamic coupling and mode family interaction
CN112943699B (en) Compressor stator blade vibration reduction optimization design method based on corner design
Waite et al. Physical Understanding and Sensitivities of LPT Flutter
Frey et al. Oscillating airfoil aerodynamics of a rotating compressor blade row
Vedeneev et al. Numerical analysis of compressor blade flutter in modern gas turbine engines
Pesek et al. Modal synthesis method for inter-blade dry-friction surface angle design of turbine wheel for vibration suppression
JPH05187203A (en) Drum rotor of axial-flow turbomachinery
KR101346085B1 (en) Transonic Compressor Rotor Design Method, And Transonic Compressor Rotor
Van der Spuy The design of a low-noise rotor-only axial flow fan series

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant