CN109408894A - A kind of consideration damping structure rubs the turbomachinery blade nonlinear vibration characteristics analysis method touched - Google Patents
A kind of consideration damping structure rubs the turbomachinery blade nonlinear vibration characteristics analysis method touched Download PDFInfo
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Abstract
It rubs the turbomachinery blade nonlinear vibration characteristics analysis method touched the invention proposes a kind of consideration damping structure, after obtaining the time domain linear finite element kinetics equation of turbomachinery bladed discs by finite element method, number of degrees of freedom, decrement is carried out using modal synthesis method, it obtains time domain linear and reduces finite element kinetics equation, further by multiple-harmonic balancing method, frequency-domain linear decrement finite element kinetics equation is obtained；The non-linear force vector generated on blade-wheel disc finite element model due to contact friction, it is determined by coulomb dry friction model, and it is converted into the non-linear force vector of all nodes of turbomachinery blade-wheel disc finite element model under frequency domain, to obtain the non-linear decrement finite element kinetics equation of turbomachinery blade-wheel disc frequency domain；It solves later and draws turbomachinery blade-wheel disc frequency response curve.We's invention, which considerably reduces, to be calculated the time and calculates cost, to greatly improve efficiency.
Description
Technical field
The invention belongs to turbomachinery design fields, and in particular to a kind of turbomachinery blade nonlinear vibration characteristics analysis
Method.
Background technique
Important equipment of the turbomachinery as energy conversion has consequence in modern society, guarantees turbine
The safe operation of tool is of great significance.Turbomachinery blade becomes turbomachinery failure as critical component, Problem of Failure
The main reason for.The working environment of turbomachinery blade is severe, and especially blade generates vibration under the action of Airflow Exciting-Vibration Force
Problem, high cycle fatigue caused by the biggish vibration stress in part are one of the main reason for causing blade failure.A kind of current row
The method for effectively reducing blade vibration level be exactly increase blade damping, and it is most widely used increase blade damping side
Method is to increase dry-friction damping, and basic functional principle is to be hindered by contact surface etc. between adjacent blades shroud contact surface, lacing wire
Friction-collision effect between Buddhist nun's structural friction face, formation, which rubs, touches phenomenon, converts vibrational energy into thermal energy consumption and dissipates, thus
Reduce blade vibration level.
It is directed to the dry-friction damping vibration characteristics of turbomachinery blade at present, common method is using linear etc. in engineering
It imitates model (mass-damper-spring) and replaces dry-friction damping, be equivalent to and only only account for being connect by turbomachinery blade damping structure
The single harmonic component of the non-linear force generated in contacting surface, accuracy is not high, when especially there is contact surface separate condition, while this
Kind of method in damping structure by fine motion sliding switchs to the transition region of macroslip, and usually error is larger, and is unsuitable for promoting.And it is sharp
The non-linear fortune of multiple-harmonic for being converted the turbomachinery Nonlinear Equations of Motion under former time domain under frequency domain with multiple-harmonic balancing method
Dynamic equation, i.e., it is contemplated that being acted on and the multiple harmonic component of the non-linear force of generation by turbomachinery blade dry-friction damping,
It can then guarantee that dry friction model used by turbomachinery blade has very high accuracy at this time.Further, it is possible to obtain
Vibration characteristics with Hi-Fi turbomachinery blade under steady stimulation (such as Airflow Exciting-Vibration Force).However, using more
When harmonic wave equilibrium method, the number of degrees of freedom, of former turbomachinery system can be expanded at double, institute according to selected harmonic component number
With if still carrying out equation of motion solution using the original number of degrees of freedom, of turbomachinery system, calculation amount is huge, is calculated as
This is excessively high.
Summary of the invention
It rubs the turbomachinery blade nonlinear vibration characteristics touched the purpose of the present invention is to provide a kind of consideration damping structure
Analysis method, it is above-mentioned existing to solve for calculation analysis on vibration of the turbomachinery blade under Non-linear dry friction damping
The problem for having computational efficiency existing for technology low.Present invention application multiple-harmonic balancing method improves the accuracy of dry friction model
And the fidelity of turbomachinery blade vibration characteristics under steady stimulation, meanwhile, reduce by using modal synthesis method
The number of degrees of freedom, of flat mechanical system, so that calculation amount be greatly lowered and calculate cost.
To achieve the goals above, the present invention uses following technical scheme.
A kind of consideration damping structure rubs the turbomachinery blade nonlinear vibration characteristics analysis method touched, including following step
It is rapid:
1) according to the geometry of practical turbomachinery blade-wheel disc, turbomachinery blade-wheel disc threedimensional model is established
And generate finite element model；
2) it determines each damping structure contact interface of blade-wheel disc finite element model, rub and touch node pair, and carry out statics
Contact analysis；
3) blade-wheel disc finite element model stiffness matrix and mass matrix are solved；
4) damping matrix of turbomachinery blade-wheel disc is determined by testing；
5) aerodynamic analysis is carried out to blade-section, obtains turbomachinery blade-all nodes of wheel disc period flow induced vibrations
Force vector；
6) modal synthesis method is applied, turbomachinery blade-wheel disc time domain linear is obtained and reduces finite element kinetics equation；
7) turbomachinery blade-wheel disc frequency-domain linear is obtained by multiple-harmonic balancing method and reduces finite element dynamics side
Journey；
8) according to coulomb (Coulomb) dry friction model, obtain turbomachinery blade-each node of wheel disc finite element model by
The non-linear force vector arrived；
9) non-linear force vector under frequency domain is solved, and it is limited to obtain the non-linear decrement of turbomachinery blade-wheel disc frequency domain
First kinetics equation；
10) the non-linear decrement finite element kinetics equation of turbomachinery blade-wheel disc frequency domain is solved using arc-length methods；
11) frequency under time domain-displacement solution point is converted by the frequency under frequency domain-displacement solution point, and continues to seek next
The solution point of the non-linear decrement finite element kinetics equation of the frequency domain of a turbomachinery blade-wheel disc；
12) by the solution point under a series of time domain of obtained turbomachinery blade-wheel discs, turbomachinery blade-is drawn
The frequency response curve of wheel disc.
Further, further comprising the steps of:
13) turbomachinery blade-wheel disc frequency response curve is analyzed, obtains blade-wheeling disk structure design parameter
Influence to nonlinear vibration characteristics, to provide reference for turbomachinery blade-wheeling disk structure design.For to nonlinear vibration
One or several design parameters that dynamic characteristic is affected are adjusted, and turbomachinery blade Non-Linear Vibration is made to be in setting
Within the scope of.
Compared with the existing technology, the invention has the following advantages:
It rubs the turbomachinery blade nonlinear vibration characteristics analysis method touched the invention proposes a kind of consideration damping structure,
After obtaining the time domain linear finite element kinetics equation of turbomachinery bladed discs by finite element method, using mould
State synthesis carries out number of degrees of freedom, decrement to it, obtains turbomachinery blade-wheel disc time domain linear and reduces finite element dynamics
Equation obtains turbomachinery blade-wheel disc frequency-domain linear decrement finite element dynamics side further by multiple-harmonic balancing method
Journey.The non-linear force vector generated on blade-wheel disc finite element model due to contact friction, it is true by coulomb dry friction model
It is fixed, and the non-linear force vector for all nodes of turbomachinery blade-wheel disc finite element model being converted under frequency domain, to obtain
Obtain the non-linear decrement finite element kinetics equation of turbomachinery blade-wheel disc frequency domain.This equation is solved using arc-length methods later,
To draw turbomachinery blade-wheel disc frequency response curve, and can be further to turbomachinery blade nonlinear vibration characteristics
It is analyzed.It is possible to further study influence of blade-wheeling disk structure design parameter to vibration characteristics, to be turbine
Mechanical blade-wheeling disk structure design provides reference.
Compared to conventional method, the single harmonic method of the linear equivalence finite element model for the problem of touching of rubbing is extended to by the present invention
High-precision multiple-harmonic balance method, and by carrying out freedom degree decrement to finite element model, guaranteeing Nonlinear Vibration
When precision as a result, computational efficiency is greatly improved.
Detailed description of the invention
Fig. 1 is turbomachinery blade-disc vibration specificity analysis flow chart.
Fig. 2 rubs for turbomachinery blade-wheel disc to be touched a little to explanation schematic diagram.
Fig. 3 is turbomachinery blade vibration danger position node schematic diagram；Wherein Fig. 3 (a) is the air inlet of shroud damping vane
Side danger position schematic diagram；Fig. 3 (b) is that shroud damping vane goes out gas side danger position schematic diagram；Fig. 3 (c) be free blade into
Gas side danger position schematic diagram；Fig. 3 (d) is free blade air inlet side danger position schematic diagram.
Specific embodiment
It rubs the turbomachinery blade Non-Linear Vibration touched refering to Figure 1, the present invention provides a kind of consideration damping structure
Characteristic analysis method, comprising the following steps:
1) according to the geometry of practical turbomachinery blade-wheel disc, the three-dimensional mould of turbomachinery blade-wheel disc is established
Type, and grid dividing is carried out to threedimensional model, form turbomachinery blade-wheel disc global finite element model；
2) it determines each damping structure contact interface of blade-wheel disc finite element model, rub and touch node pair, and carry out statics
Contact analysis, specific steps are as follows:
(2.1) determine that rubbing for each damping structure contact interface of blade-wheel disc finite element model touches the quantity p of node pair,
Contact interface should include that contact surface between interface, including adjacent blades shroud contact surface, lashing wire is touched in all rubbing.
It please refers to shown in Fig. 2, remembers:
Rubbing and touching node is x to the displacement vector in each freedom degree direction of the node of sidebl；
Rubbing and touching node is x to the displacement vector in each freedom degree direction of the node of the other sidebr；
All displacement vectors touched in each freedom degree direction of node of rubbing are xb=[xbl T,xbr T]T；
Displacement vector in the non-each freedom degree direction of node for touching node of rubbing is xi；
Displacement vector in each freedom degree direction of all nodes of turbomachinery blade-wheel disc is x=[xi T,xb T]T。
(2.2) blade-wheel disc statics contact analysis is carried out, the normal direction pretightning force N between touching node pair that rubs is obtained0, and
To prestressing force field.
3) by linear finite method, according to blade-wheeling disk structure edge-restraint condition, and consider step (2.2)
The prestressing force field of middle acquisition and Spin softening effect obtain blade-wheel disc finite element model stiffness matrix K and mass matrix
M。
4) assume to meet proportional damping, then damping matrix C=α K+ β M.Test measurement is carried out to blade-wheeling disk structure, is obtained
The preceding two ranks resonant frequency of blade-wheeling disk structure and preceding two first order modes damping ratio are obtained, it is possible thereby to determine the value of factor alpha and β, from
And obtain blade-wheel disc finite element model damping matrix C.
5) aerodynamic analysis is carried out to blade-section: carries out unsteady Three-Dimensional Flow Field Analysis, obtains turbomachinery blade-wheel disc
The period fluid exciting force vector F of all nodese。
Obtain turbomachinery blade-all nodes of wheel disc period fluid exciting force vector FeSpecific steps are as follows:
(5.1) take movable vane by a static cascade time interval as a pneumatic period Δ T0=2 π/(ω n), wherein
ω represents the driving frequency determined by revolving speed, and n represents the stator blade number of blade.Time step takes a pneumatic period Δ T0'sCalculate a pneumatic period Δ T0Pressure field.
(5.2) and then a calculating cycle Δ T=n Δ T is calculated0Pressure field, wherein n represents the stator blade number of blade.
(5.3) pressure field is interpolated into blade surface, and calculated suffered by each node of blade surface contacted with fluid
Period fluid exciting force, the period fluid exciting force that each node not contacted with fluid is subject to are 0, thus obtain turbomachinery leaf
The period fluid exciting force vector f of all nodes of piece-wheel disce(t), wherein t represents the time.
6) it by turbomachinery blade-wheel disc time domain linear finite element kinetics equation, is carried out certainly using modal synthesis method
Reduced by degree, obtains turbomachinery blade-wheel disc time domain linear and reduce finite element kinetics equation.Specific steps are as follows:
(6.1) column write out turbomachinery blade-wheel disc time domain linear finite element kinetics equation:
Wherein,Subscript ii represents Fei Mo and touches a little,
Subscript bb representative, which rubs, touches a little, and subscript ib and bi represent cross term.Subscript i represents Fei Mo and touches a little, and subscript b representative, which rubs, touches a little.
(6.2) by the first row equation of time domain linear finite element kinetics equation in step (6.1), fixed turbomachinery leaf
Piece-wheel disc, which rubs, touches modal displacement, i.e. xb,WithIt is zero, obtains non-rub of turbomachinery blade-wheel disc and touch the mould of node
State equation:
The preceding k mode of the modal equations is sought, matrix Φ is formedik。
(6.3) turbomachinery blade-wheel disc is respectively rubbed and touches node and successively discharges one degree of freedom, and setting displacement is 1,
Remaining freedom degree is 0, obtain turbomachinery blade-wheel disc it is non-rub touch node modal matrix be Φib=-(Kii)-1Kib。
(6.4) modal matrix obtained according to step (6.2) and step (6.3), You Lizi (Ritz) method:
Wherein, ukAnd ubNon- rub represented under modal coordinate touches node and each freedom degree direction displacement arrow for touching node that rubs
Amount.U represents each freedom degree direction displacement vector of all nodes under modal coordinate.
(6.5) by turbomachinery blade-wheel disc time domain linear is limited in equation substitution step (6.1) in step (6.4)
In first kinetics equation, and premultiplicationIt is dynamic to obtain turbomachinery blade-wheel disc time domain linear decrement finite element
Mechanical equation:
Wherein,Subscript kk represents Fei Mo and touches
Point, subscript bb representative, which rubs, touches a little, and subscript kb and bk represent cross term.Subscript k represents Fei Mo and touches a little, and subscript b representative, which rubs, touches a little.
7) by multiple-harmonic balancing method, by the equation obtained in step (6.5) u andCarry out Fourier
(Fourier) it is unfolded, obtains turbomachinery blade-wheel disc frequency-domain linear decrement finite element kinetics equation.
Turbomachinery blade-wheel disc frequency-domain linear reduces the specific steps that finite element kinetics equation obtains are as follows:
(7.1) u in the equation obtained in step (6.5) is subjected to Fourier (Fourier) expansion:
Wherein:
D=[I, Icos (ω t), Isin (ω t) ..., Icos (Nkωt),Isin(Nkω t)], ω is excited frequency, Nk
To select harmonic component number；
In turn, it obtains
It (7.2) will be in step (6.5)Fourier (Fourier) expansion is carried out, is obtained:
Wherein:
D=[I, Icos (ω t), Isin (ω t) ..., Icos (Nkωt),Isin(Nkω t)], ω is excited frequency, Nk
To select harmonic component number；
In turn, it obtains
(7.3) by Fourier (Fourier) expansion after u andIn generation, returns the equation in step (6.5), obtains:
(7.4) according to step (7.1) to step (7.3), it is limited to obtain the decrement of turbomachinery blade-wheel disc frequency-domain linear
First kinetics equation:
Wherein, U is each freedom degree direction displacement harmonic component amplitude vector after decrement,For the finite element rigidity on frequency domain
Matrix, FeFor the fluid exciting force harmonic component amplitude vector on frequency domain.
8) according to coulomb (Coulomb) dry friction model, all on turbomachinery blade-wheel disc finite element model rub is obtained
The non-linear force vector being subject in a freedom degree direction is touched, and is further obtained on turbomachinery blade-wheel disc finite element model
The non-linear force vector f being subject on all degree of freedom on a node basis directionsn.Specific steps are as follows:
(8.1) it is rubbed and is touched a little to for by first turbomachinery blade-impeller, relative displacement vector is that Δ x is equal to vector
xbl-xbrFirst three component.
It (8.2) is that Δ x transforms to local coordinate system by the relative displacement vector in step (8.1)Under:
Wherein, R is that first turbomachinery blade-impeller rubs the local coordinate system transformation matrix touched a little pair.The direction λ is
It is flat mechanical axial this rub touch a little to projecting direction on the contact surface, the direction η rub for this touch a little on the contact surface
Normal direction,Direction is and the direction λ and the direction η vertical direction.
(8.3) it according to coulomb (Coulomb) dry friction model, obtains first turbomachinery blade-impeller and rubs and touch a little pair
The tangential friction force and normal direction normal pressure being subject under local coordinate system:
Wherein:
μ is coefficient of friction；
kλ、kηElastic properties of materials to be measured by test deforms tangential and normal stiffness coefficient；
N0(1)The normal direction pretightning force rubbed between touching a little pair for first turbomachinery, by step (2.2) blade-wheel disc statics
The normal direction pretightning force N that contact analysis obtains0In one-component obtain；
λ0=λ (τstick)、It rubs and is touched a little to the relatively tangential of one side gusset of static friction initial time for this
Displacement and frictional force, wherein τ=ω t；
It rubs and is touched a little to one side gusset relative velocity direction of sliding friction initial time depending on this；
Here, due toDirection position shifting is relatively small, neglects.
(8.4) first turbomachineries, which rub, to be touched a little pair, and a side gusset is by non-linear force vector under local coordinate systemIt converts back under former coordinate system and isTherefore, a side gusset
It is by non-linear force vector under turbomachinery blade-wheel disc original coordinate systemOther side section
It puts and is by non-linear force vector under turbomachinery blade-wheel disc original coordinate system
(8.5) successively traversal p touches a little pair each rub for touching a little pair of rubbing, repeatedly step (8.1) to step (8.4), acquisition
Each rub touches a side gusset a little pair and another side gusset under turbomachinery blade-wheel disc original coordinate system by non-linear force,
And then obtain all non-linear force vectors for rubbing and touching and being a little subject under turbomachinery blade-wheel disc original coordinate systemAt this point, whereinIndicate what all side gussets were subject to
Non-linear force vector,Indicate the non-linear force vector that all another side gussets are subject to.
(8.6) the non-non-linear force vector for touching and being a little subject to that rubs of turbomachinery blade-wheel discIt obtains saturating
The non-linear force vector of all nodes of flat mechanical blade-wheel disc finite element model
(8.7) by the relationship of practical former coordinate system and local coordinate system it follows that
Wherein,A little to be become to the global coordinate system that respective local coordinate system transformation matrix diagonally arranges by p to rubbing to touch
Change matrix.It is expressed by the tangential friction force and normal direction normal pressure of the coulomb dry friction model in step (8.3)
Formula, which calculates, to be determined.
9) by all nodes of turbomachinery blade-wheel disc finite element model under the time domain obtained in step (8.6)
Non-linear force vector fn, it is converted into all sections of turbomachinery blade-wheel disc finite element model under frequency domain after freedom degree decrement
The non-linear force vector F of pointn, and obtain the non-linear decrement finite element kinetics equation of turbomachinery blade-wheel disc frequency domain.Tool
Body step are as follows:
It (9.1) will be in step (8.6)PremultiplicationCarry out freedom degree
Decrement, obtains:
(9.2) by acquisition in step (9.1)By golden (Galerkin) method of gal the Liao Dynasty, obtain:
Wherein:
It is calculated by step (9.1)；
It is calculated by step (8.7).
(9.3) by all nodes of turbomachinery blade-wheel disc finite element model under the frequency domain obtained in step (9.2)
Non-linear force vector FnIt is added to the decrement finite element of turbomachinery blade-wheel disc frequency-domain linear obtained in step (7.4)
In kinetics equation, the non-linear decrement finite element kinetics equation of turbomachinery blade-wheel disc frequency domain is obtained:
10) the non-linear decrement of the turbomachinery blade-wheel disc frequency domain obtained using arc-length methods solution procedure (9.3) is limited
First kinetics equation.Specific steps are as follows:
(10.1) supplementary constraints equation:
(U-U*)T(U-U*)+(ω-ω*)2=(Δ l)2
ω is wherein introduced as variable, Δ l is selected arc-length methods iteration radius, ω*And U*Selection referring to step
(10.3)。
Combine constraint equation are as follows:
(10.2) equation that will be obtained in step (9.3)It is converted intoBy (U-U*)T(U-U*)+(ω-ω*)2=(Δ l)2It is converted into Υ=(U-U*)T(U-U*)+
(ω-ω*)2-(Δl)2。
(10.3) when first time iteration, turbomachinery blade-is obtained by Newton-Raphson (Newton-Raphson) method
The non-linear decrement finite element kinetics equation of the frequency domain of wheel discAn initial solution in small nonlinearity area
ω*And U*.Directly the Exact Solutions of previous step iteration are substituted into when iteration later, i.e. ω*=ω, U*=U.
(10.4) step is estimated.U=U*+ Δ U, ω=ω*+Δω.Δ U and Δ ω represents the difference of this step solution and initial solution.
Wherein:
In calculating processItem is obtained by step (9.2)；
In Δ ω expression formula ± selection sign (Δ ω)=sign is determined by the determinant of kt* | kt*|。
(10.5) correction step.
UsingExpansion, and it is assigned a value of 0:
Wherein:
In calculating processItem is obtained by step (9.2)；
Ψ=Ψ (U, ω)；
δ U and δ ω represents the difference of this step solution and solution in next step.
Further,
Wherein,δUt=-(kt)-1q。
Then
Reapply Υ=(U-U*)T(U-U*)+(ω-ω*)2-(Δl)2It is assigned a value of 0:
(ΔU+δU)T(ΔU+δU)+(Δω+δω)2=(Δ l)2
It willAbove formula is substituted into, can be obtained:
a(δω)2+ b δ ω+c=0
Wherein:
A=(δ Ut)T(δUt)+1；
Two δ ω can be solved by radical formula:
To solve two Δ U+ δ U:
Calculate twoValue, take Δ U+ δ U corresponding to big cos θ, thus obtain δ ω,
δU。
(10.6) if judging, δ ω, δ U are unsatisfactory for both less than giving residual values, U=U+ δ U, ω=ω+δ ω, Δ U=Δ
U+ δ U, Δ ω=Δ ω+δ ω, return to step (10.5), continue iteration, until δ ω, δ U, which are all satisfied, is less than given residual error
Value.
If judging, δ ω, δ U are respectively less than given residual values, and it is non-linear to obtain new turbomachinery blade-wheel disc frequency domain
Reduce the solution point of finite element kinetics equation, U*=U+ δ U, ω*=ω+δ ω.Then, U=U*, ω=ω*,
11) the non-linear decrement finite element dynamics of turbomachinery blade-wheel disc frequency domain that will be obtained by step (10.6)
The new solution point (ω, U) of equation is converted into the solution point (ω, x) under time domain, and continues to seek next turbomachinery blade-wheel
The solution point of the non-linear decrement finite element kinetics equation of the frequency domain of disk.Specific steps are as follows:
(11.1) u value is obtained by U value:
(11.2) x value is obtained by u value:
(11.3) solution point (ω, x) under step (10.6) and the time domain of step (11.2) acquisition is returned into step 7),
Seek the solution point of the non-linear decrement finite element kinetics equation of frequency domain of next turbomachinery blade-wheel disc.
12) solution point under a series of time domain of the turbomachinery blade-wheel discs obtained by step (11.3), draws turbine
Mechanical blade-wheel disc frequency response curve, and further turbomachinery blade nonlinear vibration characteristics can be analyzed.With reference to
Fig. 3, specific steps are as follows:
(12.1) for the solution point under each time domain, by the position of each freedom degree of turbomachinery bladed discs
Move the total displacement vector x that vector x is converted to each node of turbomachinery bladed discss。
(12.2) it chooses under each solution point, total displacement vector xsThe component x of middle maximum absolute values mIt is corresponding with the solution point to swash
Each point that frequencies omega forms the turbomachinery bladed discs frequency response curve is encouraged, all points being calculated are fitted, from
And obtain turbomachinery bladed discs frequency response curve.Alternatively, some danger position nodes are selected, it is general to choose shown in Fig. 3
Blade position risk symptoms node (such as blade air inlet side and in the Ye Ding, leaf of gas side and blade lower part is connected with platform out
Fillet at), under each solution point, find out total displacement vector xsIn the displacement component of these risk symptoms nodes and corresponding with the solution point
Driving frequency ω form several frequency response curve points, be the turbomachinery bladed discs in these risk symptoms node positions
A point on every line of several frequency response curves, all frequencies being calculated being fitted on these risk symptoms node positions respectively
Curve point is rung, to obtain several frequency response curves of these risk symptoms node positions of turbomachinery bladed discs.
(12.3) the turbomachinery bladed discs frequency response curve obtained by analytical procedure (12.2), to the turbine
Mechanical blade-blade disk system nonlinear vibration characteristics carry out accurate quantitative study.
13) turbomachinery blade-wheel disc frequency response curve is analyzed, obtains blade-wheeling disk structure design parameter
Influence to nonlinear vibration characteristics, to provide reference for turbomachinery blade-wheeling disk structure design.For to nonlinear vibration
Dynamic characteristic influences one or several maximum design parameters and is adjusted, and turbomachinery blade Non-Linear Vibration is made to be in setting
Within the scope of.
Claims (10)
- A kind of turbomachinery blade nonlinear vibration characteristics analysis method touched 1. consideration damping structure rubs, which is characterized in that packet Include following steps:1) according to the geometry of practical turbomachinery blade-wheel disc, turbomachinery blade-wheel disc threedimensional model and life are established At finite element model；2) it determines each damping structure contact interface of blade-wheel disc finite element model, rub and touch node pair, and carry out statics contact Analysis；3) blade-wheel disc finite element model stiffness matrix and mass matrix are solved；4) damping matrix of turbomachinery blade-wheel disc is determined by testing；5) aerodynamic analysis is carried out to blade-section, obtains turbomachinery blade-all nodes of wheel disc period fluid exciting force arrow Amount；6) modal synthesis method is applied, turbomachinery blade-wheel disc time domain linear is obtained and reduces finite element kinetics equation；7) turbomachinery blade-wheel disc frequency-domain linear is obtained by multiple-harmonic balancing method and reduces finite element kinetics equation；8) according to Coulomb friction model response, the non-linear force that turbomachinery blade-each node of wheel disc finite element model is subject to is obtained Vector；9) non-linear force vector under frequency domain is solved, and it is dynamic to obtain the non-linear decrement finite element of turbomachinery blade-wheel disc frequency domain Mechanical equation；10) the non-linear decrement finite element kinetics equation of turbomachinery blade-wheel disc frequency domain is solved using arc-length methods；11) frequency under time domain-displacement solution point is converted by the frequency under frequency domain-displacement solution point, and continues to seek next The solution point of the non-linear decrement finite element kinetics equation of the frequency domain of flat mechanical blade-wheel disc；12) by the solution point under a series of time domain of obtained turbomachinery blade-wheel discs, turbomachinery blade-wheel disc is drawn Frequency response curve.
- The turbomachinery blade nonlinear vibration characteristics analysis touched 2. a kind of consideration damping structure according to claim 1 rubs Method, which is characterized in that further comprising the steps of:13) turbomachinery blade-wheel disc frequency response curve is analyzed, obtains blade-wheeling disk structure design parameter to non- The influence of linear oscillator characteristic, to provide reference for turbomachinery blade-wheeling disk structure design；For to Non-Linear Vibration spy Property influence maximally related one or several design parameters and be adjusted, so that turbomachinery blade Non-Linear Vibration is in setting model Within enclosing.
- The turbomachinery blade nonlinear vibration characteristics analysis touched 3. a kind of consideration damping structure according to claim 1 rubs Method, which is characterized in that step 2) specifically includes:(2.1) it determines that rubbing for each damping structure contact interface of blade-wheel disc finite element model touches the quantity p of node pair, contacts Interface includes that interface is touched in all rubbing；Rubbing and touching node is x to the displacement vector in each freedom degree direction of the node of sidebl；Rubbing and touching node is x to the displacement vector in each freedom degree direction of the node of the other sidebr；All displacement vectors touched in each freedom degree direction of node of rubbing are xb=[xbl T,xbr T]T；Displacement vector in the non-each freedom degree direction of node for touching node of rubbing is xi；Displacement vector in each freedom degree direction of all nodes of turbomachinery blade-wheel disc is x=[xi T,xb T]T；(2.2) blade-wheel disc statics contact analysis is carried out, the normal direction pretightning force N between touching node pair that rubs is obtained0, and obtain pre- answer The field of force；Step 3) according to blade-wheeling disk structure edge-restraint condition, and considers step (2.2) by linear finite method The prestressing force field of middle acquisition and Spin softening effect obtain blade-wheel disc finite element model stiffness matrix K and mass matrix M；Step 4) hypothesis meets proportional damping, then damping matrix C=α K+ β M；Test measurement is carried out to blade-wheeling disk structure, is obtained The preceding two ranks resonant frequency of blade-wheeling disk structure and preceding two first order modes damping ratio are obtained, it is possible thereby to determine the value of factor alpha and β, from And obtain blade-wheel disc finite element model damping matrix C.
- The turbomachinery blade nonlinear vibration characteristics analysis touched 4. a kind of consideration damping structure according to claim 1 rubs Method, which is characterized in that step 5) specifically includes:(5.1) take movable vane by a static cascade time interval as a pneumatic period Δ T0=2 π/(ω n), wherein ω is represented The driving frequency determined by revolving speed, n represent the stator blade number of blade；Time step takes a pneumatic period Δ T0'sIt calculates A pneumatic period Δ T out0Pressure field；(5.2) and then a calculating cycle Δ T=n Δ T is calculated0Pressure field；(5.3) pressure field is interpolated into blade surface, and calculates the period suffered by each node of blade surface contacted with fluid Fluid exciting force, the period fluid exciting force that each node not contacted with fluid is subject to are 0, thus obtain turbomachinery blade- The period fluid exciting force vector f of all nodes of wheel disce(t), wherein t represents the time.
- The turbomachinery blade nonlinear vibration characteristics analysis touched 5. a kind of consideration damping structure according to claim 1 rubs Method, which is characterized in that step 6) specifically includes:(6.1) column write out turbomachinery blade-wheel disc time domain linear finite element kinetics equation:Wherein,Subscript ii represents Fei Mo and touches a little, subscript Bb representative, which rubs, touches a little, and subscript ib and bi represent cross term； Subscript i represents Fei Mo and touches a little, and subscript b representative, which rubs, touches a little；(6.2) by the first row equation of time domain linear finite element kinetics equation in step (6.1), fixed turbomachinery blade- Modal displacement is touched in rubbing for wheel disc, i.e. xb,WithIt is zero, obtains non-rub of turbomachinery blade-wheel disc and touch the mode of node Equation:The preceding k mode of the modal equations is sought, matrix Φ is formedik；(6.3) turbomachinery blade-wheel disc is respectively rubbed and touches node and successively discharges one degree of freedom, and setting displacement is 1, remaining Freedom degree is 0, obtain turbomachinery blade-wheel disc it is non-rub touch node modal matrix be Φib=-(Kii)-1Kib；(6.4) modal matrix obtained according to step (6.2) and step (6.3), by Ritz method:Wherein, ukAnd ubIt represents non-under modal coordinate and rubs to touch node and rub and touch each freedom degree direction displacement vector of node；u Represent each freedom degree direction displacement vector of all nodes under modal coordinate；(6.5) equation in step (6.4) turbomachinery blade-wheel disc time domain linear finite element in step (6.1) is substituted into move In mechanical equation, and premultiplicationIt obtains turbomachinery blade-wheel disc time domain linear and reduces finite element dynamics Equation:Wherein,Subscript kk represents Fei Mo and touches a little, under Mark bb representative, which rubs, touches a little, and subscript kb and bk represent cross term； Subscript k represents Fei Mo and touches a little, and subscript b representative, which rubs, touches a little.
- The turbomachinery blade nonlinear vibration characteristics analysis touched 6. a kind of consideration damping structure according to claim 5 rubs Method, which is characterized in that step 7) specifically includes:(7.1) u in the equation obtained in step (6.5) is subjected to Fourier expansion:Wherein:D=[I, Icos (ω t), Isin (ω t) ..., Icos (Nkωt),Isin(Nkω t)], ω is excited frequency, NkFor choosing Determine harmonic component number；In turn, it obtainsIt (7.2) will be in step (6.5)Fourier expansion is carried out, is obtained:Wherein:D=[I, Icos (ω t), Isin (ω t) ..., Icos (Nkωt),Isin(Nkω t)], ω is excited frequency, NkFor choosing Determine harmonic component number；In turn, it obtains(7.3) by after Fourier expansion u andIn generation, returns the equation in step (6.5), obtains:(7.4) according to step (7.1) to step (7.3), it is dynamic to obtain turbomachinery blade-wheel disc frequency-domain linear decrement finite element Mechanical equation:Wherein, U is each freedom degree direction displacement harmonic component amplitude vector after decrement,For the finite element matrix on frequency domain, FeFor the fluid exciting force harmonic component amplitude vector on frequency domain.
- The turbomachinery blade nonlinear vibration characteristics analysis touched 7. a kind of consideration damping structure according to claim 1 rubs Method, which is characterized in that step 8) specifically includes:(8.1) first turbomachinery blade-impellers, which rub, to be touched relative displacement vector Δ x a little and is equal to vector xbl-xbrFirst three Component；It (8.2) is that Δ x transforms to local coordinate system by the relative displacement vector in step (8.1)Under:Wherein, R is that first turbomachinery blade-impeller rubs the local coordinate system transformation matrix touched a little pair；The direction λ is turbine Tool it is axial this rub touch a little to projecting direction on the contact surface, the direction η rub for this touch a little to normal on the contact surface Direction,Direction is and the direction λ and the direction η vertical direction；(8.3) it according to Coulomb friction model response, obtains first turbomachinery blade-impeller and rubs and touch a little under local coordinate system The tangential friction force and normal direction normal pressure being subject to:Wherein:μ is coefficient of friction；kλ、kηElastic properties of materials to be measured by test deforms tangential and normal stiffness coefficient；N0(1)The normal direction pretightning force rubbed between touching a little pair for first turbomachinery is contacted by step (2.2) blade-wheel disc statics Analyze obtained normal direction pretightning force N0In one-component obtain；λ0=λ (τstick)、Rub for this touch a little to the opposite tangential displacement of one side gusset of static friction initial time and Frictional force, wherein τ=ω t；It rubs and is touched a little to one side gusset relative velocity direction of sliding friction initial time depending on this；(8.4) first turbomachineries, which rub, to be touched a little pair, and a side gusset is by non-linear force vector under local coordinate systemIt converts back under former coordinate system and isTherefore, a side gusset It is by non-linear force vector under turbomachinery blade-wheel disc original coordinate systemOther side section It puts and is by non-linear force vector under turbomachinery blade-wheel disc original coordinate system(8.5) successively traversal p touches a little pair each rub for touching a little pair of rubbing, and repeatedly step (8.1) to step (8.4), acquisition is each It rubs and touches a side gusset a little pair and another side gusset under turbomachinery blade-wheel disc original coordinate system by non-linear force, in turn Obtain all non-linear force vectors for rubbing and touching and being a little subject under turbomachinery blade-wheel disc original coordinate systemWhereinIt is non-linear to indicate that all side gussets are subject to Force vector,Indicate the non-linear force vector that all another side gussets are subject to；(8.6) the non-non-linear force vector for touching and being a little subject to that rubs of turbomachinery blade-wheel discObtain turbine The non-linear force vector of all nodes of tool blade-wheel disc finite element model(8.7) it is obtained by the relationship of practical former coordinate system and local coordinate system:Wherein,A little to convert square to the global coordinate system that respective local coordinate system transformation matrix diagonally arranges to rubbing to touch by p Battle array；By the tangential friction force and normal direction normal pressure expression formula meter of the coulomb dry friction model in step (8.3) It calculates and determines.
- The turbomachinery blade nonlinear vibration characteristics analysis touched 8. a kind of consideration damping structure according to claim 7 rubs Method, which is characterized in that step 9) specifically includes:It (9.1) will be in step (8.6)PremultiplicationFreedom degree decrement is carried out, It obtains:(9.2) by acquisition in step (9.1)By the golden method of gal the Liao Dynasty, obtain:Wherein:It is calculated by step (9.1)；It is calculated by step (8.7)；(9.3) by the non-of all nodes of turbomachinery blade-wheel disc finite element model under the frequency domain obtained in step (9.2) Linear force vector FnIt is added in turbomachinery blade-wheel disc frequency-domain linear decrement finite element kinetics equation, obtains turbine The non-linear decrement finite element kinetics equation of mechanical blade-wheel disc frequency domain:
- The turbomachinery blade nonlinear vibration characteristics analysis touched 9. a kind of consideration damping structure according to claim 8 rubs Method, which is characterized in that step 10) specifically includes:(10.1) supplementary constraints equation:(U-U*)T(U-U*)+(ω-ω*)2=(Δ l)2ω is wherein introduced as variable, Δ l is selected arc-length methods iteration radius；；Combine constraint equation are as follows:(10.2) equation that will be obtained in step (9.3)It is converted intoIt will (U-U*)T(U-U*)+(ω-ω*)2=(Δ l)2It is converted into Υ=(U-U*)T(U-U*)+(ω-ω*)2-(Δl)2；(10.3) when first time iteration, the non-linear decrement of turbomachinery blade-wheel disc frequency domain is obtained by Newton-Raphson method Finite element kinetics equationAn initial solution ω in small nonlinearity area*And U*；When iteration later Directly the Exact Solutions of previous step iteration are substituted into, i.e. ω*=ω, U*=U；(10.4) step: U=U is estimated*+ Δ U, ω=ω*+Δω；Δ U and Δ ω represents the difference of this step solution and initial solution；Wherein:In calculating processItem is obtained by step (9.2)；In Δ ω expression formula ± selection by kt*Determinant determine sign (Δ ω)=sign | kt*|；(10.5) correction step:UsingExpansion, and it is assigned a value of 0:Wherein:In calculating processItem is obtained by step (9.2)；Ψ=Ψ (U, ω)；δ U and δ ω represents the difference of this step solution and solution in next step；Wherein,ThenReapply Υ=(U-U*)T(U-U*)+(ω-ω*)2-(Δl)2It is assigned a value of 0:(ΔU+δU)T(ΔU+δU)+(Δω+δω)2=(Δ l)2It willAbove formula is substituted into, is obtained:a(δω)2+ b δ ω+c=0Wherein:A=(δ Ut)T(δUt)+1；Two δ ω can be solved by radical formula:To solve two Δ U+ δ U:Calculate twoValue, takes Δ U+ δ U corresponding to big cos θ, to obtain δ ω, δ U；(10.6) if judging, δ ω, δ U are unsatisfactory for both less than giving residual values, U=U+ δ U, ω=ω+δ ω, Δ U=Δ U+ δ U, Δ ω=Δ ω+δ ω, return to step (10.5), continue iteration, until δ ω, δ U, which are all satisfied, is less than given residual values；If judging, δ ω, δ U are respectively less than given residual values, obtain the new non-linear decrement of turbomachinery blade-wheel disc frequency domain The solution point of finite element kinetics equation, U*=U+ δ U, ω*=ω+δ ω；Then, U=U*, ω=ω*。
- The turbomachinery blade nonlinear vibration characteristics point touched 10. a kind of consideration damping structure according to claim 9 rubs Analysis method, which is characterized in that step 11) and step 12) specifically include:Step 11) specifically includes:(11.1) u value is obtained by U value:(11.2) x value is obtained by u value:(11.3) solution point (ω, x) under step (10.6) and the time domain of step (11.2) acquisition is returned into step 7), sought The solution point of the non-linear decrement finite element kinetics equation of the frequency domain of next turbomachinery blade-wheel disc；Step 12) specifically includes:(12.1) for the solution point under each time domain, by the displacement of turbomachinery bladed discs each freedom degrees to Amount x is converted to the total displacement vector x of each node of turbomachinery bladed discss；(12.2) it chooses under each solution point, total displacement vector xsThe component x of middle maximum absolute values mExcitation frequency corresponding with the solution point Rate ω forms each point of the turbomachinery bladed discs frequency response curve, is fitted all points being calculated, and obtains saturating Flat mechanical blade-blade disk system frequency response curve；Alternatively, some danger position nodes is selected to find out total displacement under each solution point Vector xsIn these risk symptoms nodes displacement component and driving frequency ω corresponding with the solution point form several frequency response curve points, be A point of the turbomachinery bladed discs on every line of several frequency response curves of these risk symptoms node positions, All frequency response curve points being calculated being fitted on these risk symptoms node positions respectively, to obtain turbomachinery blade-wheel Several frequency response curves of these risk symptoms node positions of disc system.
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| CN114154363B (en) * | 2021-11-09 | 2024-05-28 | 北京航空航天大学 | Vibration damping characteristic analysis method for high-pressure turbine blade edge plate damper |
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