CN110309615A - A kind of prediction technique of rotating vane intrinsic frequency - Google Patents

A kind of prediction technique of rotating vane intrinsic frequency Download PDF

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CN110309615A
CN110309615A CN201910616285.4A CN201910616285A CN110309615A CN 110309615 A CN110309615 A CN 110309615A CN 201910616285 A CN201910616285 A CN 201910616285A CN 110309615 A CN110309615 A CN 110309615A
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李朝峰
佘厚鑫
唐千升
刘晓文
程昊
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Abstract

The present invention provides a kind of prediction technique of rotating vane intrinsic frequency, comprising: obtains turntable-blade coupled system mass matrix M, stiffness matrix Ke, rotational stiffness matrix KΩ, gyroscopic matrix G；Based on acquired data information and preset turntable-blade coupled system revolving speed Ω, the intrinsic frequency of rotating vane in the turntable-blade coupled system is obtained；Judge whether the intrinsic frequency of rotating vane falls into the range of driving frequency belonging to the turntable-blade coupled system, according to judging result, determines whether turntable-blade coupled system meets working condition；Because the present invention passes through the data parameters of acquisition, according to the calculating of rotating vane intrinsic frequency calculation formula, the intrinsic frequency of rotating vane can be predicted, and it is compared by rotating vane intrinsic frequency and driving frequency, it can be determined that being produced to the rotating vane for meeting actual production conditions, keep the rotating vane designed up-to-standard, and reduces production cost.

Description

A kind of prediction technique of rotating vane intrinsic frequency
Technical field
The invention belongs to mechanical kinetics technical field more particularly to a kind of prediction techniques of rotating vane intrinsic frequency.
Background technique
Currently, need to be designed rotating vane before turntable-blade coupled system actual production, and in work In the actual design of journey, thinks that the intrinsic frequency of rotating vane all on turntable is consistent, have ignored turntable flexibility pair The influence of rotating vane intrinsic frequency, therefore predict obtained rotating vane intrinsic frequency and practical rotating vane intrinsic frequency not Symbol, after carrying out actual production so as to cause the rotating vane designed, rotating vane is off quality, it is easy to and extraneous exciting Frequency is consistent and causes to resonate, and blade is made high cycle fatigue destruction occur.
Summary of the invention
(1) technical problems to be solved
The present invention is directed to occurring in the prior art because having ignored influence of the turntable flexibility to rotating vane intrinsic frequency Forecasting inaccuracy so as to cause the intrinsic frequency to rotating vane is true, and the rotating vane designed finally is made to carry out actual production Afterwards, rotating vane problem off quality provides a kind of prediction technique of rotating vane intrinsic frequency.
(2) technical solution
In order to achieve the above object, the present invention uses main technical schemes the following steps are included:
S1: turntable-blade coupled system mass matrix M, stiffness matrix K are obtainede, rotational stiffness matrix KΩ, gyro square Battle array G；
S2: the mass matrix M, stiffness matrix K are based one, rotational stiffness matrix KΩ, gyroscopic matrix G and preset Turntable-blade coupled system revolving speed Ω, obtain the intrinsic frequency of rotating vane in the turntable-blade coupled system；
S3: judge whether the intrinsic frequency of the rotating vane falls into excitation belonging to the turntable-blade coupled system In the range of frequency, according to judging result, determine whether the turntable-blade coupled system meets working condition.
Further, step S2 includes:
Based on the mass matrix M, stiffness matrix Ke, rotational stiffness matrix KΩ, gyroscopic matrix G and turntable-blade coupling The revolving speed Ω of collaboration system calculates the intrinsic frequency of the rotating vane according to formula one:
Formula one:
Wherein λ is the intrinsic frequency of turntable-blade coupled system rotating vane.
Further, before step S1 further include:
S0: according to current dial-blade coupled system static parameter and dynamic parameter, current dial-blade coupling is established The corresponding energy equation of collaboration system, the energy equation includes: turntable kinetic energy, turntable potential energy, blade kinetic energy and blade potential energy Equation；
Correspondingly, the step S1 includes:
Mode truncation and sliding-model control are carried out to the energy equation, and carry out dynamic analysis, obtains turntable-leaf Mass matrix M, the stiffness matrix K of piece coupled systeme, rotational stiffness matrix KΩ, gyroscopic matrix G.
Further, the step S0 includes:
S0-1, the turntable-blade coupled system global coordinate system O-XYZ is established；
S0-2, it is based on the global coordinate system O-XYZ, establishes the turntable-corresponding energy equation of blade coupled system Include:
Turntable kinetic energy:
Turntable potential energy:
Blade kinetic energy:
Blade potential energy:
Wherein: ρD, hD, νD, RS, RDThe respectively density of turntable, thickness, Poisson's ratio, internal diameter and outer diameter；ρb, Ab, Lb, Eb, Gb, κbThe respectively density of rotating vane, area of section, length, Young's modulus, modulus of shearing, shearing factor；JpdFor turntable pole Rotary inertia；D is turntable bending stiffness；IbFor the cross sectional moment of inertia of rotating vane.
Further, the step S1 includes:
Corresponding turntable moment of mass caused by during discretization and mode truncation processing turntable blade energy equation Battle array MD1With turntable mass matrix MD2；Wherein, the matrix expression are as follows:
In the expression of the matrix, T is matrix transposition；
WithThe respectively Mode Shape of turntable；
The mass matrix M of single rotating vaneB；Wherein, the matrix expression are as follows:
Corresponding turntable caused by during energy equation described in mode truncation and sliding-model control and rotating vane Coupling mass matrix MDB1With the coupling mass matrix M of turntable and rotating vaneDB2；Wherein, the expression of the matrix Are as follows:
Discretization and mode truncation handle the stiffness matrix of generated corresponding turntable during the energy equationWith the stiffness matrix of turntableWherein, the expression of the matrix are as follows:
The stiffness matrix K of single rotating vanee B；Wherein, the matrix expression are as follows:
Discretization and mode truncation handle generated corresponding rotational stiffness matrix during the energy equationWith rotational stiffness matrixWherein, the expression of the matrix are as follows:
The rotational stiffness matrix of single rotating vane；Wherein, the expression of the matrix are as follows:
Discretization and mode truncation handle generated corresponding turntable and rotating vane during the energy equation Rotational stiffness matrixWith turntable and rotating vane rotational stiffness matrixWherein, the expression of the matrix Are as follows:
The gyroscopic matrix G of turntableD；Wherein, the expression of the matrix are as follows:
The gyroscopic matrix P of single rotating vaneB；Wherein, the expression of the matrix are as follows:
Wherein, the concrete form of the corresponding matrix of turntable-blade coupled system are as follows:
Wherein:
I indicates i-th of rotating vane on turntable；NbFor turntable complete cycle blade number.
(3) beneficial effect
The beneficial effects of the present invention are:
Because the present invention can be pre- according to the calculating of rotating vane intrinsic frequency calculation formula by the supplemental characteristic obtained The intrinsic frequency for considering the rotating vane of turntable flexibility is measured, and passes through rotating vane intrinsic frequency and preset excitation frequency Rate comparison, it is possible to which determination produces the rotating vane for meeting actual production conditions, makes the rotating vane matter designed Amount is qualified, and reduces production cost, shortens the blade design period.
Detailed description of the invention
Fig. 1 is that rotating vane intrinsic frequency of the present invention predicts flow chart；
Fig. 2 is the turntable-blade coupled system global coordinate system schematic diagram established according to the present invention；
Fig. 3 is the schematic diagram of local coordinate system before and after the turntable deformation established according to the present invention；
Fig. 4 is the schematic diagram for the rotating vane cross-sectional coordinates established according to the present invention.
[description of symbols]
1: turntable；
2: rotating vane.
Specific embodiment
In order to preferably explain the present invention, in order to understand, 1-4 with reference to the accompanying drawing, by specific embodiment, to this Invention is described in detail.
In this specific embodiment, it is assumed that in turntable-blade coupled system, the outer rim of turntable is uniformly distributed three identical rotations Rotating vane piece is respectively as follows: the first rotating vane, the second rotating vane and third rotating vane；Wherein, turntable is with rotating vane It is fixedly connected.
Select turntable-blade coupled system system geometric parameter and simulation parameter as follows:
1 turntable of table-blade coupled system material parameter and geometric parameter
According to the parameter provided in table 1, a kind of prediction technique of rotating vane intrinsic frequency of the invention, specific method is such as Under:
Step Q1 establishes turntable-blade coupled system coordinate system, comprising:
As shown in Fig. 2, establishing global coordinate system O-XYZ: in stationary state lower rotary table-blade coupled system turntable Heart point is that origin constructs global coordinate system, and the coordinate Z axis is perpendicular to the turntable-blade coupled system plane of rotor disc；
As shown in Fig. 2, establishing rotating coordinate system O-X1Y1Z1: with rotation status lower rotary table-blade coupled system turntable Central point is that origin constructs rotating coordinate system, coordinate Z1Axis is perpendicular to the turntable-blade coupled system plane of rotor disc； Coordinate system Y1Axis along rotor blade lengths direction；
As shown in figure 3, establishing the local coordinate system o of the rotating vane root before turntable deformationb-xbybzb: with disk shaped Coordinate system is constructed by origin of i-th of rotating vane root central point in turntable-blade coupled system before becoming, the coordinate system zbAxis is perpendicular to the turntable-blade coupled system plane of rotor disc；The y of the coordinate systembAxis along rotor blade lengths side To；
As shown in figure 3, establishing the local coordinate system o' of the rotating vane root after turntable deformationb-xb0yb0zb0: with turntable Coordinate system, the coordinate system are constructed by origin of i-th of rotating vane root central point in turntable-blade coupled system after deformation Zb0Axis is perpendicular to the turntable-blade coupled system plane of rotor disc；The y of the coordinate systemb0Axis is along rotor blade lengths Direction；
As shown in figure 4, establishing the local coordinate system o' in rotating vane sectionb-xb1yb1zb1: when being rotated with rotating vane Coordinate system, the y of the coordinate system are constructed by origin of i-th of rotating vane root central point in turntable-blade coupled systemb1Axis Along rotor blade lengths direction；The z of the coordinate systemb1Axis is along rotating vane width direction；
Wherein, the local coordinate system o of the rotating vane root before the turntable deformationb-xbybzbAfter the turntable deformation Rotating vane root local coordinate system o'b-xb1yb1zb1With the rotating coordinate system O-X1Y1Z1In parallel.
Step Q2 derives the energy equation of coupled system according to the coordinate system established in Q1, it is assumed that under local coordinate system, The displacement at any point is u in turntableDThe bending displacement of (r, θ, t), any rotating vane are v (x, t), then by local coordinate system Under data pass through local coordinate system ob-xbybzb, rotating coordinate system O-X1Y1Z1The number being transformed at global coordinate system O-XYZ According to expression,
At global coordinate system O-XYZ,
The motion vector at turntable any point are as follows:
The motion vector at any point on rotating vane are as follows:
Wherein, rDFor the motion vector at turntable any point, rQFor the motion vector at any point on rotating vane,For Rotation angle of i-th of rotating vane with respect to global coordinate system；uDFor the vibration displacement of turntable any position；U, v are respectively to rotate The radial direction and bending displacement of blade any position；β is rotating vane established angle；RDFor the outer diameter of turntable.
Step Q3: the coordinate system established according to Q1 establishes the turntable-blade coupled system by the data that Q2 is obtained Energy equation；The expression formula of the turntable-blade coupled system energy equation includes:
The kinetic energy expression of turntable:
The expression formula of the potential energy of turntable:
The expression formula of blade kinetic energy are as follows:
The expression formula of the potential energy of blade are as follows:
Wherein ρD, hD, νD, RS, RDThe respectively density of turntable, thickness, Poisson's ratio, internal diameter and outer diameter；ρb, Ab, Lb, Eb, Gb, κbThe respectively density of rotating vane, area of section, length, Young's modulus, modulus of shearing, shearing factor；JpdFor turntable pole Rotary inertia；D is turntable bending stiffness；IbFor the cross sectional moment of inertia of rotating vane.
Step Q4, at assuming vibration shape method and Galerkin method to the energy equation progress discretization and mode truncation of turntable Reason, then can indicate in the deformation of local coordinate system lower rotary table and rotating vane are as follows:
Wherein,WithThe respectively Mode Shape of turntable, U and V are respectively the Mode Shape of rotating vane；Qξ (t),Qη(t),qu(t),qvIt (t) is turntable after discretization, the generalized coordinates vector of rotating vane displacement；
The deformation expression formula of local coordinate system lower rotary table and rotating vane is updated to turntable-blade coupled system energy In equation, turntable-blade coupled system energy equation discretization expression formula is obtained:
Turntable-blade coupled system energy equation discretization expression formula are as follows:
Wherein, in above-mentioned turntable-blade coupled system energy equation discretization expression formula
Represent i-th of rotating vane rotational angle；
And it in turntable-blade energy equation discretization and mode truncation treatment process, also can be obtained: turntable moment of mass Battle array MD1With turntable mass matrix MD2；The mass matrix M of single rotating vaneB；The coupling mass matrix M of turntable and rotating vaneDB1 With the coupling mass matrix M of turntable and rotating vaneDB2；The stiffness matrix of turntableWith the stiffness matrix of turntableIt is single The stiffness matrix of a rotating vaneRotational stiffness matrixWith rotational stiffness matrixThe rotation of single rotating vane Stiffness matrixTurntable and rotating vane couple rotational stiffness matrixRotational stiffness square is coupled with turntable and rotating vane Battle arrayThe gyroscopic matrix G of turntableD；The gyroscopic matrix P of single rotating vaneB；
Wherein the expression formula of the matrix is respectively as follows:
Wherein, in the expression formula of above-mentioned matrix, T is matrix transposition.
Turntable-blade coupled system energy equation that discretization indicates is updated in Lagrange's equation by step Q5, Obtain turntable-blade coupled system kinetics equation；
Wherein, Lagrange's equation are as follows:
Turntable-blade coupled system kinetics equation are as follows:
Wherein, M is turntable-blade system mass matrix；KeFor turntable-blade system stiffness matrix；KΩFor turntable- The rotational stiffness matrix of blade system；G turntable-blade system gyroscopic matrix；
Wherein, the concrete form of the corresponding matrix of turntable-blade coupled system are as follows:
Wherein:
I indicates i-th of rotating vane on turntable；NbFor turntable complete cycle blade number.
Step Q6, based on mass matrix M, the stiffness matrix K obtained in Q5e, rotational stiffness matrix KΩ, gyroscopic matrix G with And turntable-blade coupled system revolving speed Ω of setting, it is calculated and turns according to turntable-Natural Frequency of Blade calculation formula Disk-blade coupled system rotating vane intrinsic frequency λ；
Wherein, the consolidating when intrinsic frequency in turntable-blade coupled system when rotating vane static state and rotating vane rotate Have frequency calculation formula difference as follows:
Wherein, λ is the intrinsic frequency of turntable-blade coupled system rotating vane.
At this point, according to the parameter provided in table 1, when the turntable set-blade coupled system revolving speed Ω is 0rad/s, Then obtain the intrinsic frequency of the first rotating vane, the intrinsic frequency of the second rotating vane, the intrinsic frequency of third rotating vane point Not are as follows: 80.960Hz, 80.960Hz, 81.139Hz；
When the turntable set-blade coupled system revolving speed Ω is 500rad/s, then consolidating for the first rotating vane is obtained Have frequency, the intrinsic frequency of the second rotating vane, the intrinsic frequency of third rotating vane be respectively as follows: 154.693Hz, 154.958Hz、154.991Hz。
Step Q7: the comparison of driving frequency belonging to turntable-blade coupled system with setting judges consolidating for rotating vane Have whether frequency falls within the scope of driving frequency belonging to turntable-blade coupled system, the turntable in the present embodiment-blade coupling Driving frequency belonging to system is set as 180Hz, according to judging result, when turntable-blade coupled system revolving speed Ω is 0rad/s and Rotating vane intrinsic frequency when revolving speed Ω is 500rad/s does not have overlapping range with driving frequency, so turntable-blade coupling Collaboration system meets working condition.
Influence of the turntable to rotating vane intrinsic frequency is considered in the present embodiment, is coupled by establishing turntable-blade Data needed for system dynamics equation obtains rotating vane intrinsic frequency calculation formula are realized to rotating vane intrinsic frequency Prediction, and according to prediction obtained rotating vane intrinsic frequency λ and turntable-blade system belonging to driving frequency compare, judgement Whether driving frequency and the rotating vane intrinsic frequency predicted have overlapping range, according to judging result, determine the turntable- Whether blade coupled system meets working condition, and final determination produces the rotating vane for meeting actual production conditions, makes The rotating vane produced is up-to-standard.
The technical principle of the invention is described above in combination with a specific embodiment, these descriptions are intended merely to explain of the invention Principle shall not be construed in any way as a limitation of the scope of protection of the invention.Based on explaining herein, those skilled in the art It can associate with other specific embodiments of the invention without creative labor, these modes fall within this hair Within bright protection scope.

Claims (5)

1. a kind of prediction technique of rotating vane intrinsic frequency, the rotating vane is used in turntable-blade coupled system, special Sign is, comprising the following steps:
S1: turntable-blade coupled system mass matrix M, stiffness matrix K are obtainede, rotational stiffness matrix KΩ, gyroscopic matrix G；
S2: the mass matrix M, stiffness matrix K are based one, rotational stiffness matrix KΩ, gyroscopic matrix G and preset turn Disk-blade coupled system revolving speed Ω, obtains the intrinsic frequency of rotating vane in the turntable-blade coupled system；
S3: judge whether the intrinsic frequency of the rotating vane falls into driving frequency belonging to the turntable-blade coupled system In the range of, according to judging result, determine whether the turntable-blade coupled system meets working condition.
2. the prediction technique of rotating vane intrinsic frequency according to claim 1, which is characterized in that the step S2 packet It includes:
Based on the mass matrix M, stiffness matrix Ke, rotational stiffness matrix KΩ, gyroscopic matrix G and turntable-blade coupled system Revolving speed Ω the intrinsic frequency of the rotating vane is calculated according to formula one:
Formula one:
Wherein λ is the intrinsic frequency of turntable-blade coupled system rotating vane.
3. the prediction technique of rotating vane intrinsic frequency according to claim 1, which is characterized in that also wrapped before step S1 It includes:
S0: according to current dial-blade coupled system static parameter and dynamic parameter, current dial-blade coupled systemes are established It unites corresponding energy equation, the energy equation includes: the equation of turntable kinetic energy, turntable potential energy, blade kinetic energy and blade potential energy；
Correspondingly, the step S1 includes:
Discretization and mode truncation processing are carried out to the energy equation, and carry out dynamic analysis, obtains turntable-blade coupling Mass matrix M, the stiffness matrix K of collaboration systeme, rotational stiffness matrix KΩ, gyroscopic matrix G.
4. the prediction technique of rotating vane intrinsic frequency according to claim 3, which is characterized in that the step S0 packet It includes:
S0-1, the turntable-blade coupled system global coordinate system O-XYZ is established；
S0-2, it is based on the global coordinate system O-XYZ, establishing the turntable-corresponding energy equation of blade coupled system includes:
Turntable kinetic energy:
Turntable potential energy:
Blade kinetic energy:
Blade potential energy:
Wherein: ρD, hD, νD, RS, RDThe respectively density of turntable, thickness, Poisson's ratio, internal diameter and outer diameter；ρb, Ab, Lb, Eb, Gb, κb The respectively density of rotating vane, area of section, length, Young's modulus, modulus of shearing, shearing factor；JpdFor the rotation of turntable pole Inertia；D is turntable bending stiffness；IbFor the cross sectional moment of inertia of rotating vane.
5. the prediction technique of rotating vane intrinsic frequency according to claim 4, which is characterized in that the step S1 packet It includes:
Corresponding turntable mass matrix M caused by during discretization and mode truncation processing turntable blade energy equationD1 With turntable mass matrix MD2；Wherein, the matrix expression are as follows:
In the expression of the matrix, T is matrix transposition；
WithThe respectively Mode Shape of turntable；
The mass matrix M of single rotating vaneB；Wherein, the matrix expression are as follows:
Discretization and mode truncation handle the coupling of generated corresponding turntable and rotating vane during the energy equation Close mass matrix MDB1With the coupling mass matrix M of turntable and rotating vaneDB2；Wherein, the expression of the matrix are as follows:
Discretization and mode truncation handle the stiffness matrix of generated corresponding turntable during the energy equationWith The stiffness matrix of turntableWherein, the expression of the matrix are as follows:
The stiffness matrix of single bladeWherein, the matrix expression are as follows:
Discretization and mode truncation handle generated corresponding rotational stiffness matrix during the energy equationAnd rotation Turn stiffness matrixWherein, the expression of the matrix are as follows:
The rotational stiffness matrix of single blade；Wherein, the expression of the matrix are as follows:
Discretization and mode truncation handle generated corresponding turntable and rotating vane rotation during the energy equation Stiffness matrixWith turntable and rotating vane rotational stiffness matrixWherein, the expression of the matrix are as follows:
The gyroscopic matrix G of turntableD；Wherein, the expression of the matrix are as follows:
The gyroscopic matrix P of single bladeB；Wherein, the expression of the matrix are as follows:
Wherein, the concrete form of the corresponding matrix of turntable-blade coupled system are as follows:
Wherein,
I indicates i-th of rotating vane on turntable；NbFor complete cycle blade number on turntable.
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