CN113326647A - Water turbine shafting rotor dynamic modal calculation method - Google Patents

Water turbine shafting rotor dynamic modal calculation method Download PDF

Info

Publication number
CN113326647A
CN113326647A CN202110662625.4A CN202110662625A CN113326647A CN 113326647 A CN113326647 A CN 113326647A CN 202110662625 A CN202110662625 A CN 202110662625A CN 113326647 A CN113326647 A CN 113326647A
Authority
CN
China
Prior art keywords
equation
fluid
matrix
water
modal
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.)
Pending
Application number
CN202110662625.4A
Other languages
Chinese (zh)
Inventor
王正伟
曹景伟
田红
多文智
崔建华
赵国正
高海玉
陈林
王明明
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.)
Gansu Electric Power Investment Group Co ltd
Gansu Power Investment Bingling Hydropower Development Co ltd
Tsinghua University
Original Assignee
Gansu Electric Power Investment Group Co ltd
Gansu Power Investment Bingling Hydropower Development Co ltd
Tsinghua 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 Gansu Electric Power Investment Group Co ltd, Gansu Power Investment Bingling Hydropower Development Co ltd, Tsinghua University filed Critical Gansu Electric Power Investment Group Co ltd
Priority to CN202110662625.4A priority Critical patent/CN113326647A/en
Publication of CN113326647A publication Critical patent/CN113326647A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/12—Simultaneous equations, e.g. systems of linear equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
    • G06T17/205—Re-meshing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/08—Fluids
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Data Mining & Analysis (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Geometry (AREA)
  • Algebra (AREA)
  • Databases & Information Systems (AREA)
  • Operations Research (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Computer Graphics (AREA)
  • Hydraulic Turbines (AREA)

Abstract

The invention discloses a method for calculating the dynamic modal of a water turbine shafting rotor, which comprises the following steps of firstly, carrying out three-dimensional modeling on the water turbine shafting and a water body around a rotating wheel; then, carrying out mesh division on the model established in the step 1; secondly, setting boundary conditions of finite element analysis; then, based on ANSYS Mechanical APDL software, solving the wet modal characteristics; and finally, grouping the modal results solved in the step 4, and drawing a Campbell graph. The calculation method of the invention can simultaneously consider the influence of the rotating speed of the water turbine shafting and the additional mass of the surrounding water body, thereby greatly improving the calculation precision of the shafting mode.

Description

Water turbine shafting rotor dynamic modal calculation method
Technical Field
The invention belongs to the technical field of hydraulic machinery and engineering equipment, and particularly relates to a method for calculating the dynamic mode of a water turbine shafting rotor.
Background
Hydraulic turbines are important devices for the development of hydraulic resources, which have been plagued by resonance and fatigue problems. In order to avoid resonance and fatigue damage of the shafting structure caused by excessive dynamic stress, it is important to determine the dynamic response of the shafting structure, namely determine the modal response of the shafting structure. Since shafting is usually composed of shafts, wheels, alternators, bearings and seals, etc., the dynamic model is very complex and sometimes even non-linear, and it is very difficult to determine the modal response of these mechanical rotating components.
The runner of a water turbine is usually submerged in water, which has a great influence on the modal characteristics of the entire shafting. Therefore, it is important to study the "wet" rather than "dry" modal characteristics of the rotating structure. When determining the modal characteristics of the turbine shafting, the additional mass effect of the water around the runner must be considered. When the rotor is in water, the natural frequency of the shafting is lower than that of the air, which means that the shafting is more likely to be excited by low frequency to resonate. Currently, modal research on simple models (such as airfoils or discs) provides a theoretical basis for understanding the influence of fluid on the modal characteristics of the runner. Regarding the influence of the additional mass of the fluid on the modal characteristics of the water turbine, the current research is mainly focused on the runner mode of the francis turbine and the pump turbine.
In addition to considering the rotor and its additional mass effects, the influence of the shaft on the overall rotor dynamics must also be considered. For a water turbine, the modal characteristics of the runner are changed by the shaft. In addition, in a water turbine which usually has a long shaft, the gyroscopic effect plays an important role, namely, when analyzing the dynamic characteristics of a shafting, the rotating speed of the shafting cannot be ignored. The influence of the bearings and their loads affects the stability of the entire rotor. In the current research technology, when the modal characteristics of the whole shafting are analyzed, most of researches do not consider the influence of water around a rotating wheel, and the wet mode characteristics of the shafting of the water turbine are not deeply researched. The existing shafting modal calculation method cannot simultaneously consider the influence of the additional mass of the water body around the rotating wheel when the structure rotates, so that the calculated modal frequency is only the modal in the air, and the real situation cannot be reflected.
Object of the Invention
The invention aims to solve the defects in the prior art, provides a method for calculating the shafting wet mode of a water turbine, can simultaneously consider the influence of the shafting rotating speed and the additional mass of the surrounding water body, can improve the existing algorithm, and greatly improves the calculation precision of the shafting mode. The invention takes a turbine shaft system as a research object, takes a certain bulb through-flow turbine shaft system as an example, simultaneously considers the influence of the rotating speed of the shaft system and the additional mass of the surrounding water body, calculates the wet mode of the bulb through-flow turbine shaft system, and provides a Campbell diagram corrected by the bulb through-flow turbine shaft system. The method is not only suitable for calculating the dynamic mode of the shafting rotor of the bulb through-flow turbine, but also can be used for calculating the mode of the shafting of the hydraulic machinery, such as a mixed-flow turbine, an impulse turbine, a pump turbine and the like.
Disclosure of Invention
The invention provides a method for calculating the dynamic mode of a water turbine shafting rotor, which comprises the following steps:
step 1, three-dimensional modeling is conducted on a water turbine shafting and a water body around a rotating wheel, the water turbine comprises a bulb body, a stator, a generator rotor, a radial bearing, a thrust bearing, a main shaft and the rotating wheel, and water flow is formed outside a water turbine body and the rotating wheel;
step 2, carrying out mesh division on the model established in the step 1 so as to carry out finite element analysis;
step 3, setting boundary conditions of finite element analysis, including rigidity coefficients of a radial bearing and a thrust bearing, impedance boundary conditions of a water body, rotating speed and equivalent magnetic tension rigidity coefficients;
step 4, solving the wet modal characteristics, wherein the wet modal characteristics are relative to the dry modal characteristics, namely the modal analysis of the runner when running in water, and the influence of the quality of the surrounding water body needs to be considered; the solution is based on ANSYS Mechanical APDL software, and is embedded into a written program language considering the additional mass of the water body; determining a rotating speed range to be solved and an order to be solved according to the actual running condition of the hydraulic turbine set, and selecting a certain interval to carry out solving;
and 5, grouping the modal results solved in the step 4, and drawing a Campbell graph.
Preferably, the turbine is a bulb turbine set.
Preferably, when the solution is performed in the step 4, the structure dynamic balance equation, the acoustic control equation and the acoustic fluid-solid coupling equation which are based on the consideration of the rotating speed influence are used;
wherein, when the influence of the surrounding medium on the structure is neglected, the structural dynamic balance equation considering the influence of the rotating speed is expressed as a discretized linear structural dynamic equation shown in formula (1):
Figure BDA0003115695260000041
in the formula [ Ms]、[Cs]And [ K ]s]Respectively n x n mass matrix, n x n damping matrix andn × n stiffness matrix, n being a degree of freedom; { u }, (u) },
Figure BDA0003115695260000042
{ u } acceleration, velocity, and displacement, respectively; the rotor dynamics equation is expressed as a rotational structure control equation shown in formula (2):
Figure BDA0003115695260000043
wherein [ G ]s]Is a gyro matrix, which depends on the rotation speed;
Figure BDA0003115695260000044
wherein [ K ]c]Is a spin softening matrix, also dependent on the rotation speed;
the derivation process of the acoustic control equation is that, assuming that the pressure disturbance of the fluid is small, the linearized continuity equation is expressed as shown in equation (3):
Figure BDA0003115695260000051
in the formula, vaIs the speed of sound, paIs the pressure, p0Is the average fluid density, Q is the source of mass,
Figure BDA0003115695260000052
is the speed of sound in the fluid medium, K is the bulk modulus of the fluid;
the linearized Navier-Stokes equation is expressed as shown in equation (4):
Figure BDA0003115695260000053
and (3) combining the linearized continuity equation (3) and the linearized Navier-Stokes equation (4) to obtain the sound wave equation shown in the formula (5):
Figure BDA0003115695260000054
discretizing the sound wave equation (5), and discretizing the wave equation by a matrix representation method as shown in the formula (6): :
Figure BDA0003115695260000055
in the formula [ MF],[CF]And [ K ]F]Respectively an n multiplied by n acoustic fluid mass matrix, an n multiplied by n acoustic fluid damping matrix and an n multiplied by n acoustic fluid stiffness matrix, wherein n is a degree of freedom; { peIs the node pressure vector, [ R ]]In the form of an acoustic fluid boundary matrix,
Figure BDA0003115695260000056
acoustic fluid mass density constant, { fF-is the acoustic fluid load vector;
the sound fluid-solid coupling equation is obtained by simultaneously solving a rotating structure control equation (2) and an acoustic control equation (6), and is expressed as shown in a formula (7):
Figure BDA0003115695260000061
drawings
FIG. 1 is a flow chart of the present invention for performing the calculation of the dynamic mode of the water turbine shafting rotor.
FIG. 2 is a schematic diagram of a model obtained by three-dimensional modeling of a bulb turbine shafting and a solid around a shaft body.
FIG. 3 is a schematic diagram of mechanical boundary conditions of a bulb turbine shaft system and a water body around the shaft body after three-dimensional modeling;
FIG. 4 is a Campbell diagram of a turbine shafting for a prior art calculation method (comparative) without regard to the added mass of the surrounding water;
FIG. 5 is a schematic view of the shape of the rotor and wheel at nominal speed;
FIG. 6 is a Campbell diagram of a water turbine shafting at rated speed in an embodiment of the present invention;
Detailed Description
The invention is explained in detail below with reference to the drawings. The embodiments are merely illustrative of the present invention and should not be construed as limiting the scope of the invention.
First, the theory underlying the calculations includes:
(1) structural dynamic balance equation considering rotating speed influence
The existing linear structure dynamic balance equation usually ignores the influence of surrounding media on the structure, and the discretized linear structure dynamic equation is expressed as follows:
Figure BDA0003115695260000071
in the formula [ Ms]、[Cs]And [ K ]s]Respectively a mass matrix, a damping matrix and a rigidity matrix (n multiplied by n matrix, n is degree of freedom); { u }, (u) },
Figure BDA0003115695260000072
{ u } are acceleration, velocity, and displacement, respectively.
The rotating machine not only introduces gyroscopic effects, but also introduces rotational softening and other effects. Neglecting the rotational damping effect, the general rotor dynamics equation can be expressed as a rotational structure control equation as shown in equation (2):
Figure BDA0003115695260000073
wherein [ G ]s]Is a gyro matrix, which depends on the rotation speed;
Figure BDA0003115695260000074
[Kc]is a spin softening matrix, which also depends on the rotation speed.
(2) Acoustic control equation
For mechanical structures, such as hydraulic machines, which are typically immersed in a medium that is much denser than air, the influence of the fluid must be considered in analyzing the dynamic characteristics of the structure. That is, the vibration of the underwater structure is greatly affected by the surrounding fluid. Therefore, methods based on the theory of acoustic structures are often employed to obtain the dynamic properties of the structure.
The Navier-Stokes equation is a very complex and difficult to solve problem, especially when it needs to be solved simultaneously with the structural control equations. Thus, the assumption is that the fluid is compressible, non-rotational, free of external forces, and free of mean flow, simplifying the fluid momentum and flow continuity equations. In addition, it is assumed that the pressure disturbance of the fluid is small. The linearized continuity equation may then be expressed as shown in equation (3):
Figure BDA0003115695260000081
in the formula, vaIs the speed of sound, paIs the pressure, p0Is the average fluid density, Q is the source of mass,
Figure BDA0003115695260000082
is the speed of sound in the fluid medium and K is the bulk modulus of the fluid.
The linearized Navier-Stokes equation is shown in equation (4):
Figure BDA0003115695260000083
by using the linearized continuity equation (3) and the linearized Navier-Stokes equation (4), an acoustic wave equation is obtained in a simultaneous manner, and is shown in the formula (5):
Figure BDA0003115695260000084
to obtain a finite element equation in discrete form, equation (5) needs to be discretized, and due to the difficulty of coupling the fluid equation with the solid equation using equation (5), the wave equation discretized by the matrix representation is as shown in equation (6): :
Figure BDA0003115695260000085
in the formula [ MF],[CF]And [ K ]F]Respectively, an acoustic fluid mass matrix, an acoustic fluid damping matrix, and an acoustic fluid stiffness matrix (n × n matrix, n is a degree of freedom) { p }eIs the node pressure vector, [ R ]]In the form of an acoustic fluid boundary matrix,
Figure BDA0003115695260000086
acoustic fluid mass density constant, { fFIs the acoustic fluid load vector.
(3) Acoustic fluid-solid coupling equation
The rotating structure control equation (2) and the acoustic control equation (6) must be solved simultaneously, and the combination form is shown in the formula (7):
Figure BDA0003115695260000091
fig. 1 is a flow chart of calculation of a dynamic mode of a water turbine shafting rotor provided by the present invention, and it can be seen that the calculation method of the present invention includes the following steps:
step 1, three-dimensional modeling is conducted on a water turbine shafting and a water body around a rotating wheel, the water turbine comprises a bulb body, a stator, a generator rotor, a radial bearing, a thrust bearing, a main shaft and the rotating wheel, and water flow is formed outside a water turbine body and the rotating wheel;
step 2, carrying out mesh division on the model established in the step 1 so as to carry out finite element analysis;
step 3, setting boundary conditions of finite element analysis, including rigidity coefficients of a radial bearing and a thrust bearing, impedance boundary conditions of a water body, rotating speed and equivalent magnetic tension rigidity coefficients;
step 4, solving the wet modal characteristics, wherein the wet modal characteristics are relative to the dry modal characteristics, namely the modal analysis of the runner when running in water, and the influence of the quality of the surrounding water body needs to be considered; the solution is based on ANSYS Mechanical APDL software, and is embedded into a written program language considering the additional mass of the water body; determining a rotating speed range to be solved and an order to be solved according to the actual running condition of the hydraulic turbine set, and selecting a certain interval to carry out solving;
and 5, grouping the modal results solved in the step 4, and drawing a Campbell graph.
The effect of the method of the present invention is demonstrated by comparative examples and an embodiment of the present invention, specifically, a bulb flow turbine shafting is used as an analysis example.
FIG. 2 is a schematic view of a bulb turbine assembly. As can be seen from the figure, the bulb tubular turbine includes a bulb body, a stator, a generator rotor, a radial bearing, a thrust bearing, a main shaft, a runner, and the like, and water flows outside the bulb body and the runner.
FIG. 3 is a schematic diagram of mechanical boundary conditions of a bulb turbine shaft system and a water body around the shaft body after three-dimensional modeling. The figure shows a schematic diagram of the generator rotor, radial bearings, thrust bearing main shaft and rotor, as well as calculated boundary conditions, including the boundary conditions of the impedance of the water body and the equivalent magnetic pull of the motor rotor.
Although the actual rotor comprises a runner submerged in water, the existing calculation method cannot simultaneously consider the influence of the additional mass of the water body around the runner when considering the influence of the rotating speed of the shafting. Therefore, firstly, by using the existing calculation method, the modal frequency and the mode shape of the shafting at 22 rotating speeds (0-200rpm) are calculated under the condition that the additional mass of the water body around the rotating wheel is not considered.
Comparative example
In the comparative example, without considering the additional mass influence of the surrounding water body, a Campbell diagram of the axis system is shown in fig. 4, and each line represents the change of modal frequency with the rotation speed under the same modal shape. Under the rated rotating speed, each order mode of the shaft system is respectively the mode frequency and the mode shape corresponding to the points A-H. When considering the influence of the rotating speed, the transverse whirling mode of the shafting is divided into two types: forward swirl and reverse swirl. Wherein, the positive whirl indicates that the whirl direction of the shafting is the same as the rotation direction, and the modal frequency of the shafting is increased along with the increase of the rotation speed; reverse whirl means that the whirl direction of the shaft system is opposite to the rotation direction, and the modal frequency of the shaft system is reduced along with the increase of the rotation speed.
Fig. 5 is a schematic view of the shape of the rotor and wheel at nominal speed.
Examples
Firstly, three-dimensional modeling is performed on a bulb turbine shaft system and fluid around a rotating wheel, as shown in fig. 2 and 3, the three-dimensional modeling comprises a generator rotor, a radial bearing, a thrust bearing, a main shaft, the rotating wheel, water around the rotating wheel and the like.
The created model is then gridded for finite element analysis, as shown in FIG. 3.
And then setting boundary conditions of finite element analysis, including rigidity coefficients of the radial bearing and the thrust bearing, impedance boundary conditions of the water body, rotating speed, equivalent magnetic tension rigidity coefficients and the like.
And then, solving the characteristic of a wet mode, wherein the influence of the quality of the surrounding water body needs to be considered in comparison with a dry mode, namely mode analysis of the runner running in water. When the rotor is in water, the natural frequency of the shafting is lower than that of the air, which means that the shafting is more likely to be excited by low frequency to resonate. The solving software is based on ANSYS Mechanical APDL software, and is embedded into a written program language considering the additional mass of the water body. The rotating speed range to be solved and the order to be solved are determined according to the actual running condition of the unit, and a proper interval is selected for solving.
Finally, grouping the modes and drawing a Campbell graph
FIG. 6 is a graph of the natural frequency of the shafting at the rated speed in the calculation method of the present invention. As can be seen from the figure, in water, the change of each order modal frequency of the shafting with the rotating speed shows the same trend as that in air. Due to the influence of the additional mass of the water body, the modal frequency of the shafting at different rotating speeds is lower than that of the shafting in the air. The influence of the additional mass of the water body on the modal frequency of the shafting under the actual operation condition of the unit is fully considered, and the method has important engineering significance for accurately determining the modal frequency of the unit and avoiding the problems of resonance of the unit and the like.

Claims (3)

1. A method for calculating the dynamic mode of a water turbine shafting rotor is characterized by comprising the following steps:
step 1, three-dimensional modeling is conducted on a water turbine shafting and a water body around a rotating wheel, the water turbine comprises a bulb body, a stator, a generator rotor, a radial bearing, a thrust bearing, a main shaft and the rotating wheel, and water flow is formed outside a water turbine body and the rotating wheel;
step 2, carrying out mesh division on the three-dimensional model established in the step 1 so as to carry out finite element analysis;
step 3, setting boundary conditions of finite element analysis, including rigidity coefficients of a radial bearing and a thrust bearing, impedance boundary conditions of a water body, rotating speed and equivalent magnetic tension rigidity coefficients;
step 4, solving the wet modal characteristics, wherein the wet modal characteristics refer to modal analysis of the runner when the runner runs in water, and the influence of the quality of the surrounding water body needs to be considered; the solution is based on ANSYS Mechanical APDL software, and is embedded into a written program language considering the additional mass of the water body; determining a rotating speed range to be solved and an order to be solved according to the actual running condition of the hydraulic turbine set, and selecting a certain interval to carry out solving;
and 5, grouping the modal results solved in the step 4, and drawing a Campbell graph.
2. The method of claim 1, wherein the turbine is a bulb turbine set.
3. The method for calculating the dynamic modal of the water turbine shafting rotor is characterized in that when the solution is carried out in the step 4, the structural dynamic balance equation, the acoustic control equation and the acoustic fluid-structure interaction equation which take the rotating speed influence into consideration are used as the basis;
wherein, when the influence of the surrounding medium on the structure is neglected, the structural dynamic balance equation considering the influence of the rotating speed is expressed as a discretized linear structural dynamic equation shown in formula (1):
Figure FDA0003115695250000021
in the formula [ MS]、[CS]And [ K ]S]Respectively are a mass matrix of n multiplied by n, a damping matrix of n multiplied by n and a rigidity matrix of n multiplied by n, wherein n is a degree of freedom;
Figure FDA0003115695250000022
{ u } acceleration, velocity, and displacement, respectively; the rotor dynamics equation is expressed as a rotational structure control equation shown in formula (2):
Figure FDA0003115695250000023
wherein [ G ]S]Is a gyro matrix, which depends on the rotation speed;
Figure FDA0003115695250000024
wherein [ K ]C]Is a spin softening matrix, also dependent on the rotation speed;
the derivation process of the acoustic control equation is that, assuming that the pressure disturbance of the fluid is small, the linearized continuity equation is expressed as shown in equation (3):
Figure FDA0003115695250000025
in the formula, vaIs the speed of sound, paIs the pressure, p0Is the average fluid density, Q is the source of mass,
Figure FDA0003115695250000026
is the speed of sound in the fluid medium, K is the bulk modulus of the fluid;
the linearized Navier-Stokes equation is expressed as shown in equation (4):
Figure FDA0003115695250000031
and (3) combining the linearized continuity equation (3) and the linearized Navier-Stokes equation (4) to obtain the sound wave equation shown in the formula (5):
Figure FDA0003115695250000032
discretizing the sound wave equation (5), and discretizing the wave equation by a matrix representation method as shown in the formula (6): :
Figure FDA0003115695250000033
in the formula [ MF]，[CF]And [ K ]F]Respectively an n multiplied by n acoustic fluid mass matrix, an n multiplied by n acoustic fluid damping matrix and an n multiplied by n acoustic fluid stiffness matrix, wherein n is a degree of freedom; { peIs the node pressure vector, [ R ]]In the form of an acoustic fluid boundary matrix,
Figure FDA0003115695250000034
acoustic fluid mass density constant, { fF-is the acoustic fluid load vector;
the sound fluid-solid coupling equation is obtained by simultaneously solving a rotating structure control equation (2) and an acoustic control equation (6), and is expressed as shown in a formula (7):
Figure FDA0003115695250000035
CN202110662625.4A 2021-06-15 2021-06-15 Water turbine shafting rotor dynamic modal calculation method Pending CN113326647A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110662625.4A CN113326647A (en) 2021-06-15 2021-06-15 Water turbine shafting rotor dynamic modal calculation method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110662625.4A CN113326647A (en) 2021-06-15 2021-06-15 Water turbine shafting rotor dynamic modal calculation method

Publications (1)

Publication Number Publication Date
CN113326647A true CN113326647A (en) 2021-08-31

Family

ID=77420963

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110662625.4A Pending CN113326647A (en) 2021-06-15 2021-06-15 Water turbine shafting rotor dynamic modal calculation method

Country Status (1)

Country Link
CN (1) CN113326647A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117554498A (en) * 2023-11-13 2024-02-13 昆明理工大学 Frequency multiplication-based turbine runner blade crack identification method

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110083937A (en) * 2019-04-26 2019-08-02 南京理工大学 A kind of breakwater blade modal analysis method based on Navier-Stokes equation
CN111141518A (en) * 2019-12-16 2020-05-12 西安交通大学 Model-based asymmetric rotor bearing system unbalance identification method
CN111159950A (en) * 2019-12-30 2020-05-15 北京理工大学 Acoustic-solid coupling-based composite propeller prestress wet mode prediction method
WO2020152646A1 (en) * 2019-01-24 2020-07-30 Romax Technology Limited Rotor dynamics

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2020152646A1 (en) * 2019-01-24 2020-07-30 Romax Technology Limited Rotor dynamics
CN110083937A (en) * 2019-04-26 2019-08-02 南京理工大学 A kind of breakwater blade modal analysis method based on Navier-Stokes equation
CN111141518A (en) * 2019-12-16 2020-05-12 西安交通大学 Model-based asymmetric rotor bearing system unbalance identification method
CN111159950A (en) * 2019-12-30 2020-05-15 北京理工大学 Acoustic-solid coupling-based composite propeller prestress wet mode prediction method

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
蔡克伦等: ""刚-液-柔耦合结构湿模态试验与仿真分析"", 《振动与冲击》 *

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117554498A (en) * 2023-11-13 2024-02-13 昆明理工大学 Frequency multiplication-based turbine runner blade crack identification method

Similar Documents

Publication Publication Date Title
CN107341288B (en) Optimization method for controlling vibration of combined cycle unit by adjusting elevation of bearing
Yu et al. Frequency-dependent nonlinear dynamic stiffness of aerostatic bearings subjected to external perturbations
Arias-Montiel et al. Active vibration control in a rotor system by an active suspension with linear actuators
CN113326647A (en) Water turbine shafting rotor dynamic modal calculation method
Zhang et al. Dynamic analysis of active magnetic bearing rotor system considering Alford force
Yang et al. Dynamic analysis of flexible shaft and elastic disk rotor system based on the effect of Alford force
Cao et al. Coupled lateral and torsional nonlinear transient rotor–bearing system analysis with applications
Rao et al. Dynamics of asymmetric rotors using solid models
CN116629053A (en) Analysis method, system, equipment and medium for wet mode of water turbine shafting
CN104614161B (en) A kind of rotating machinery rotatable parts come off weight and location recognition method
Wei et al. A simplified analysis method and suppression of the modalities of a magnetic levitation turbo rotor system
Wang et al. The research on temperature effect for dynamic performance of high-speed permanent-magnet synchronous machines rotors
Uslu et al. Innovative computational modal analysis of a marine propeller
Yong et al. Modal analysis on impeller rotor of the axial flow pump based on fluid-structure interaction
Jensen et al. Numerical simulation of gyroscopic effects in Ansys
Ogbonnaya et al. Analysis of gas turbine blade vibration due to random excitation
Schmied et al. Application of MADYN 2000 to rotordynamic problems of industrial machinery
Lyu et al. Research on Rotor Dynamics of a 60000rpm 200KW High Speed Motor
Guoying et al. Study on vibration of the anisotropically rotor system with different sections based on the improved riccati transfer matrix method
Szasz et al. Hub-based vibration control of multiple rotating airfoils
Parikyan et al. Turbocharger dynamic analysis: Concept-phase simulation in frequency domain
Pandya et al. Vibration Analysis of Pump Shaft Using Finite Element Analysis Software: A Review
Hsu et al. Rotor dynamics analysis and testing of a turbomolecular pump rotor-bearing system
Eling et al. Dynamics of rotors on hydrodynamic bearings
Wang et al. Wind-tunnel experimental study on identification of modal aerodynamic damping matrix for operating wind turbines

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
RJ01 Rejection of invention patent application after publication
RJ01 Rejection of invention patent application after publication

Application publication date: 20210831