CN115435894A - Blade tip timing vibration stress inversion method based on simulated annealing algorithm - Google Patents

Blade tip timing vibration stress inversion method based on simulated annealing algorithm Download PDF

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CN115435894A
CN115435894A CN202211079216.2A CN202211079216A CN115435894A CN 115435894 A CN115435894 A CN 115435894A CN 202211079216 A CN202211079216 A CN 202211079216A CN 115435894 A CN115435894 A CN 115435894A
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blade
amplitude
blade tip
measured
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张晓杰
胡殿印
王荣桥
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Beihang University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
    • G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M13/00—Testing of machine parts
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M15/00—Testing of engines
    • G01M15/02—Details or accessories of testing apparatus

Abstract

The invention provides a blade tip timing vibration stress inversion method based on a simulated annealing algorithm, which comprises the following steps of: establishing a blade tip installation angle model based on the axial coordinate, the circumferential coordinate, the measured displacement and the casing radius of the sensor; accurate reconstruction of the leaf tip timing undersampled signal is realized based on a compressed sensing theory, and amplitude and frequency are obtained; carrying out finite element modal analysis on the rotating blade to be measured, and establishing a sensor measuring point identification model by combining installation distance constraint of a sensor based on the actual measurement amplitude of the axial sensor and the virtual measurement amplitude of the blade tip node; and carrying out inversion of the vibration stress based on the identified sensor measuring points. The invention does not assume that the vibration direction is vertical to the chord direction of the blade, realizes the elimination of static deformation through the change of the mounting angle of the blade tip, integrates the layout information of the sensor, the actually measured displacement data and the finite element analysis result, can be applied to the identification of the measuring point of the sensor under any mode, and improves the inversion precision of the vibration stress.

Description

Blade tip timing vibration stress inversion method based on simulated annealing algorithm
Technical Field
The invention belongs to the technical field of vibration testing of rotating blades of aerospace engines, and particularly relates to a blade tip timing vibration stress inversion method based on a simulated annealing algorithm.
Background
The rotor blade is one of the key parts of an aeroengine, and high cycle fatigue failure is caused by flow-induced vibration. In order to ensure the safety and reliability of the aircraft engine, regulations/specifications represented by the American military Engine structural integrity outline, the Chinese aviation Engine airworthiness Specification and the like all provide clear requirements for vibration testing under the typical working conditions of the engine. The blade tip timing technology is a most promising vibration testing means because of non-contact and the realization of vibration monitoring of a full-period whole-stage blade. Three major aviation engine manufacturers, GE, rolls-Royce, P & W, all applied the tip timing testing technique to engine part tests and bench tests. Blade tip timing testing technology is also researched around 2000 years in China, and the technology is tried to be applied to vibration monitoring and fault diagnosis of aeroengines.
The vibration test mainly comprises the steps of obtaining the amplitude, the frequency and the vibration stress of the structure, and especially the monitoring of the vibration stress has important significance for evaluating the high-cycle fatigue resistance of the blade. However, the data obtained based on the tip timing test is limited to tip displacement. In order to obtain the vibration stress, a method of combining actual measurement and finite element analysis is generally adopted, and displacement-stress conversion is performed on the basis of the same measuring point (a finite element model and a sensor actual measuring point). However, the aero-engine blade is usually of a twisted blade type and has a large installation angle, so that a relatively significant axial component exists after the blade is deformed, and the relative position of the axial component and the casing is changed, so that the position of a blade measuring point swept by a sensor is different from the initial theoretical position. If the displacement-stress conversion is carried out based on 'wrong' measuring points, huge errors can be brought to the inversion of the vibration stress. The existing sensor measuring point identification method is mainly directed at simple motion forms, such as axial motion, chord motion perpendicular to the chord direction and torsional motion, and cannot be effectively applied to complex deformation conditions in engine cranked blades, and the specific conditions refer to document 1: zhang x.l., wang w.m., chen k., et al, five Dimensional motion Measurement Method for Tracking Blade Based on Blade Tip Tracking Point Position Tracking [ J ]. Mechanical Systems and Signal Processing,2021,161: mohamed M., bonello P., determination of singular and raw stages Using Blade Tip Timing Data [ J ]. Journal of visualization and Acoustics,2020,142 (1): 011017.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a blade tip timing vibration stress inversion method based on a simulated annealing algorithm, which is a blade tip timing vibration stress inversion method suitable for any mode and capable of considering measuring point deviation, provides a new research idea for accurately predicting vibration stress, and serves and supports an aeroengine blade tip timing vibration testing technology.
In order to achieve the purpose, the technical scheme adopted by the invention for solving the technical problems is as follows:
a method for inverting the timing vibration stress of a blade tip based on a simulated annealing algorithm comprises the steps of axially installing two sensors in a casing, and establishing a blade tip installation angle model based on sensor layout information and actual measurement displacement; determining vibration frequency and amplitude according to a compressed sensing theory and a vibration response equation; based on the installation distance constraint of the axial sensor, the measured data and the finite element modal information are fused, the measured point identification problem of the sensor is converted into the optimization problem of the virtual measured amplitude and the measured amplitude at different positions, and inversion of the vibration stress is carried out based on the identified measured points. The method comprises the following concrete steps:
the first step is as follows: and establishing a blade tip installation angle model. The method requires two sensors to be installed along the axial direction, a blade tip installation angle model is established through the axial coordinate, the circumferential coordinate, the measured displacement and the casing radius of the sensors, and the expression is as follows:
Figure BDA0003833054060000021
wherein, R is the radius of the casing,
Figure BDA0003833054060000028
and
Figure BDA0003833054060000029
representing the circumferential coordinates of the first and second sensors, respectively, d 1 And d 2 Is the measured displacement of the first and second sensors, P 1z And P 2z Axial coordinates of the first sensor and the second sensor.
The second step is that: and establishing a frequency amplitude reconstruction model. Accurate reconstruction of a timed undersampled signal of a blade tip is realized based on a compressed sensing theory, and actual measurement displacements of sensors at M different angle positions are expressed as
Figure BDA0003833054060000022
Wherein d is the measured displacement matrix of the sensor, A k And
Figure BDA0003833054060000023
respectively, the amplitude and phase of the response corresponding to the kth excitation, e is a natural constant, i is an imaginary unit,
Figure BDA0003833054060000024
N s is the nearest integer to the kth excitation frequency multiplication, beta 1 ～β M For a conversion angle related to the circumferential installation angle of the sensor, n represents the nth rotation period, C min To make N s Is the smallest integer of the integers, W is an amplification matrix that satisfies the Nyquist sampling theorem,
Figure BDA0003833054060000025
to characterize the blade vibration characteristics, the matrix is denoted by Θ. Because the blade is excited to a limited extent, Θ has only a few non-0 elements. Converting the solution of equation d = W · Θ into an optimization problem
Figure BDA0003833054060000026
s.t.||d-WΘ|| 2 =0. Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003833054060000027
for the optimal matrix, argminf (x) is solved for f: (x) ((x))x) a function of the value of the variable x when the minimum value is reached, | | | | non-conducting phosphor 1 Representing a first matrix norm, | | | calving 2 Representing a second matrix norm.
The third step: and establishing a sensor measuring point identification model. And carrying out finite element modal analysis on the blade to be tested to obtain modal parameters. Constructing virtual measurement amplitude through modal displacement, blade tip initial position, undetermined amplitude conversion factor and blade tip installation angle before and after deformation
Figure BDA0003833054060000031
Screening out node pairs (Q) meeting measurement accuracy by combining mounting distance constraint of axial sensor i ,Q j )＝find(|Δq ij -ΔP 12 And | is less than Tol (epsilon)), and establishing an optimization problem with the amplitude conversion factor as a parameter. Searching for node pairs (L) with minimal difference between measured sensor amplitude (related to measured data) and virtual measured amplitude (related to finite element modal analysis) by using simulated annealing algorithm 1 ,L 2 )＝min(|A′ im -A im |+|A′ jm -A jm And | percent), namely the actual measuring point of the sensor. The measured amplitudes are associated with measured data and the virtual measured amplitudes are associated with finite element modal analysis. Wherein (Q) i ,Q j ) For pairs of tip nodes that meet the axial sensor distance requirement, find () is a function of where the value that meets the condition is found, Δ q ij Is the distance, Δ P, between finite element tip nodes i and j 12 Tol (ε) is the distance error tolerance for the axial sensor distance. A' im For a virtual measured amplitude of the tip node i,
Figure BDA0003833054060000033
is the circumferential coordinate, O, of the intersection point of the deformed blade tip molded line and the deformed front node i i,ρ And
Figure BDA0003833054060000034
radial and circumferential coordinates, θ ', of finite element node i under column coordinates' B And theta B The mounting angles of the blade tips before and after deformation are respectively. (L) 1 ,L 2 ) For actual measurement of two axial transducersDot position, A' im And A' jm For virtual measurement of amplitude of axial sensor, A 1m And A 2m Is the measured amplitude of the first sensor and the second sensor.
The fourth step: and establishing a vibration stress inversion model. For the blade without the blade shroud, the vibration stress and the vibration amplitude satisfy the linear relation, and the inversion of the vibration stress is carried out on the basis of the sensor measuring point identified in the third step
Figure BDA0003833054060000032
The vibration stress distribution of the whole blade is obtained. Wherein, A' i, actual measurement And A i, mode of For the identified sensor measured amplitude and finite element modal displacement at the location i, S Mode of operation And S' Measured in fact The finite element modal stress and the actual vibratory stress distribution of the whole blade are shown.
Compared with the prior art, the invention has the advantages that:
(1) The frequency amplitude reconstruction model does not limit the vibration response to be in a single mode, can realize multi-mode vibration reconstruction of a blade tip timing signal based on the idea of sparse reconstruction in compressed sensing, and provides an analysis method for the blade tip timing applied to vibration monitoring of an aeroengine;
(2) The sensor measuring point identification model does not assume that the vibration direction is vertical to the chord direction of the blade (only suitable for the torsional mode), the static deformation is eliminated through the change of the installation angle of the blade tip, and the method is more universal and can be applied to the sensor measuring point identification of any mode;
(3) The sensor measuring point identification model can fully integrate sensor layout information, actually measured displacement data and finite element analysis results, realize the identification of the actual measuring point of the sensor under the measuring point deviation phenomenon, and improve the inversion precision of the vibration stress.
Drawings
FIG. 1 is a general flow chart of a blade tip timing vibration stress inversion method based on a simulated annealing algorithm;
FIG. 2 is a schematic view of a tip mount angle model;
FIG. 3 is a schematic diagram of virtual measurement amplitudes in a sensor station identification model;
FIG. 4a shows the positions of an initial measuring point and an actual measuring point of a sensor in a first-order bending mode of a certain compressor blade;
and fig. 4b shows the positions of the initial measuring point and the actual measuring point of the sensor in the first-order torsional mode of a certain compressor blade.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The technical scheme of the blade tip timing vibration stress inversion method based on the simulated annealing algorithm is further explained below by combining the attached drawings, and the related angles are all made of radians.
As shown in fig. 1, the blade tip timing vibration stress inversion method based on the simulated annealing algorithm specifically includes the following steps:
the first step is as follows: and establishing a blade tip installation angle model. The invention requires two sensors to be installed along the axial direction, and the axial coordinate, the circumferential coordinate, the measured displacement and the casing radius of the sensors are used as input to calculate the blade tip installation angle. The calculation method of the blade tip installation angle is illustrated by taking FIG. 2 as an example, l 1 Showing the initial position of the blade tip profile without blade deformation, l 2 Indicating the position of the blade tip profile after the blade has been deformed, l 3 Parallel to l 2 . When two sensors are mounted axially, the tip mounting angle can be expressed as:
Figure BDA0003833054060000041
d＝θR-tΩR (2)
in the formula (I), the compound is shown in the specification,
Figure BDA0003833054060000042
and
Figure BDA0003833054060000043
respectively representing the circumferential coordinates, P, of the first sensor 1 and the second sensor 2 1z And P 2z Is the axial coordinate of the first sensor 1 and the second sensor 2, R is the casing radius, d 1 And d 2 The measured displacements of the first sensor 1 and the second sensor 2 are obtained by equation (2). Theta is the circumferential angle of the sensor relative to the measured blade, t is the blade arrival time, omega is the rotor rotation angular frequency, and d is the measured displacement of the sensor.
The second step is that: and establishing a frequency amplitude reconstruction model, and realizing accurate reconstruction of the blade tip timing undersampled signal based on a compressed sensing theory. For a multi-degree-of-freedom blade/disc structure, when K excitation types are applied, the vibration response d (t) can be expressed as:
Figure BDA0003833054060000044
in the formula, A k 、ω k And
Figure BDA0003833054060000045
respectively, the response amplitude, circular frequency and phase corresponding to the kth excitation, e is a natural constant, i is an imaginary unit,
Figure BDA0003833054060000046
according to the tip timing test principle, the time term in equation (3) is expressed as a function related to the sensor position, i.e.:
Figure BDA0003833054060000051
in the formula, N k ＝ω k And/Ω is the frequency multiplication of the kth excitation, and n represents the nth rotation period. For synchronous vibration, N k Is an integer number and is generally associated with forced vibration. For non-identityStep vibration, N k Are non-integers often associated with flutter and rotating stall.
Definition of N s ＝C min N k ，β＝θ/C min ，C min To make N s Being the smallest of the integers, equation (4) can be written as:
Figure BDA0003833054060000052
the measured displacements of the sensors at the M different angular positions may form a matrix d = [ d (θ =) 1 ),d(θ 2 ),…,d(θ M )] T It can be further written as:
Figure BDA0003833054060000053
wherein k = N s +p，
Figure BDA0003833054060000054
Expressed by theta, W is an amplification matrix satisfying the Nyquist sampling law, and N is required to be more than or equal to 2N s . When N is an even number, p =1-N/2; when N is an odd number, p = (1-N)/2. Because the blade is excited to a limited extent, Θ has only a few non-0 elements. According to the compressed sensing theory, the solution of equation d = W · Θ can be transformed into the following optimization problem:
Figure BDA0003833054060000055
in the formula (I), the compound is shown in the specification,
Figure BDA0003833054060000056
for the optimal matrix, argminf (x) is a function for solving the value of a variable x when f (x) reaches the minimum value, | | | calculation 1 Representing a first matrix norm, | | | calving 2 Representing a second matrix norm.
The third step: and establishing a sensor measuring point identification model. By arranging the two sensors in the axial direction, the mounting distance of the axial sensors is used as a constraint condition, and the problem of measuring point identification of the sensors is converted into an optimization problem of virtual measurement amplitude and actual measurement amplitude at different positions by combining finite element modal information. The method comprises the following specific steps:
(1) and establishing a three-dimensional finite element model of the rotating blade to be detected, developing finite element modal analysis, and extracting node coordinates and modal parameters of the three-dimensional finite element model of the blade.
(2) Determining a distance constraint condition: screening tip node pairs (Q) meeting axial sensor distance requirements i ,Q j ) The expression is:
(Q i ,Q j )＝find(|Δq ij -ΔP 12 |＜Tol(ε)) (8)
Figure BDA0003833054060000061
ΔP 12 ＝(P 2z -P 1z )/cosθ B (10)
where find () is a function of where the value satisfying the condition is located, Δ q ij Is the distance, Δ P, between finite element tip nodes i and j 12 For the distance of the axial sensor, tol (ε) is the distance error tolerance, here chosen as the mesh size of the tip section in the finite element model. O is x 、O y And O z Is the coordinate of three directions, P, under the rectangular coordinate system of the finite element node of the blade tip 1z And P 2z Axial coordinates, theta, of the first sensor 1 and the second sensor 2, respectively B And obtaining the blade tip installation angle from the formula (1).
(3) Calculating the difference between the virtual measured amplitude and the measured amplitude: defining virtual measurement amplitude as shown in fig. 3, and calculating a tip node coordinate O' (x, y, z) after virtual deformation according to the finite element node coordinate and modal displacement of the blade, where the expression is:
Figure BDA0003833054060000062
wherein μ' is the amplitude ratioFactor, A md (x, y, z) is the modal displacement of the blade.
Calculating a virtual measured amplitude A 'for the tip node pair in step (2)' im And removing the influence of static deformation through the relation of the mounting angles of the blade tips before and after deformation, namely:
Figure BDA0003833054060000063
in the formula, O i,ρ And
Figure BDA0003833054060000064
radial and circumferential coordinates, θ ', of finite element node i under column coordinates' B Setting angle of the tip before deformation, of known magnitude, theta B The deformed mounting angle is obtained by the formula (1).
Figure BDA0003833054060000069
For the circumferential coordinate of the intersection point of the deformed blade tip molded line and the deformed front node i, the solving process is as follows: performing polynomial curve fitting on the deformed blade tip molded line, and solving the circumferential coordinate of a point with the same blade tip fitting curve and the axial coordinate of the node i on the basis
Figure BDA0003833054060000065
The expression is as follows:
Figure BDA0003833054060000066
Figure BDA0003833054060000067
in the formula (I), the compound is shown in the specification,
Figure BDA0003833054060000068
and O' z Respectively the circumferential and axial coordinates of the deformed cusp nodes, a 0 ～a n As a polynomial fitting parameter, O i,z Axial seat of node i before deformationAnd (4) marking.
(4) Determining an optimal measuring point: when the amplitude scaling factor mu' is determined, the optimization problem of the virtual measurement amplitude and the actual measurement amplitude at different positions is converted, as shown in formula (15). Solving by adopting a simulated annealing algorithm mu' opt The corresponding virtual deformation position of the blade is an actual deformation position, and the intersection point of the blade and the sensor is an actual measuring point (L) of the sensor 1 ,L 2 ) The expression is:
Figure BDA0003833054060000071
in the formula (II), A' im And A' jm For virtual measurement of amplitude of axial sensor, A 1m And A 2m Which is the measured amplitude of the first sensor 1 and the second sensor 2, is obtained from the second step.
If a plurality of sensors are arranged in the axial direction, a plurality of sets of relationships are restricted to each other, and accordingly, the equations (8) and (15) need to be modified.
The fourth step: and establishing a vibration stress inversion model. For the blade without the blade tip, the blade tip part is far away from dry friction dampers such as the edge plate, the damping ring and the like and the tenon connection structure, the nonlinear degree is weak, and the vibration stress and the vibration amplitude satisfy the linear relation. The sensor measures the amplitude A 'at position i when the blade is vibrating in natural mode' i, actual measurement With finite element modal displacement A at the corresponding position i, mode And stress S Mode of operation Satisfying the formula (16), and performing vibration stress inversion based on the actual measuring point of the sensor identified in the third step to obtain a stress conversion proportion eta and vibration stress distribution S 'of the whole blade' Measured actually 。
Figure BDA0003833054060000072
Fig. 4a and 4b show the initial (conventional) and actual (inventive) measurement point positions of the first and second sensors 1, 2 in the first-order bending and first-order torsional modes, respectively, of a typical compressor blade. The inversion results of the vibrational stress obtained based on the two station locations are shown in table 1.
Table 1 shows the results of performing vibratory stress inversion based on the initial measured points and the identified actual measured points
Figure BDA0003833054060000073
The above embodiments are provided only for the purpose of describing the present invention, and are not intended to limit the scope of the present invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications can be made without departing from the spirit and principles of the invention, and are intended to be within the scope of the invention.

Claims (5)

1. A method for inverting the timing vibration stress of a blade tip based on a simulated annealing algorithm is characterized in that two sensors are mounted at different axial positions of a casing and used for measuring a blade tip timing signal of the same blade row, and a blade tip mounting angle model and a frequency amplitude reconstruction model are respectively built based on sensor layout information and actual measurement displacement; a sensor measuring point identification model is established through distance constraint, virtual measurement amplitude and actual measurement amplitude of the sensor, displacement-stress conversion is carried out on the basis of the identified sensor measuring point, and the inversion precision of the vibration stress is improved; the method specifically comprises the following steps:
step (1), establishing a blade tip installation angle model based on the axial coordinate, the circumferential coordinate, the actually measured displacement and the casing radius of the sensor, and expressing the blade tip installation angle as
Figure FDA0003833054050000011
Wherein R is the radius of the casing,
Figure FDA0003833054050000012
and
Figure FDA0003833054050000013
representing the circumferential coordinates of the first and second sensors, respectively, d 1 And d 2 Is a first transmissionMeasured displacement, P, of the sensor and the second sensor 1z And P 2z Axial coordinates of the first sensor and the second sensor;
accurately reconstructing a timed undersampled signal of the blade tip based on a compressive sensing theory, carrying out sparse representation on multi-modal vibration response of a blade/disc structure, establishing an equation of actually measured displacement and the position, amplitude, frequency and phase of a sensor, and converting the solution of the equation into an optimization problem by using the compressive sensing theory;
step (3), carrying out finite element modal analysis on the blade to be tested to obtain modal parameters; based on the steps (1) and (2), acquiring the actual measurement amplitude of the sensor at different axial positions and the virtual measurement amplitude of the blade tip node, and establishing a sensor measuring point identification model by combining the installation distance constraint of the sensor;
and (4) carrying out inversion of the vibration stress on the basis of the sensor measuring point identified in the step (3).
2. The simulated annealing algorithm-based blade tip timing vibration stress inversion method according to claim 1, wherein in the step (2), the measured displacements of the sensors at the M different angular positions are expressed as the measured displacements of the sensors in consideration of multi-modal vibration responses
Figure FDA0003833054050000014
Wherein d is the measured displacement matrix of the sensor, A k And
Figure FDA0003833054050000015
respectively, the amplitude and phase of the response corresponding to the kth excitation, e is a natural constant, i is an imaginary unit,
Figure FDA0003833054050000016
N s is the nearest integer to the kth excitation frequency multiplication, beta 1 ～β M For a conversion angle related to the circumferential installation angle of the sensor, n represents the nth rotation period, C min To make N s Is the smallest integer of the integers, W is an amplification matrix that satisfies the Nyquist sampling theorem,
Figure FDA0003833054050000017
to characterize the blade vibration characteristics, the matrix is denoted by Θ, which has only a few non-0 elements due to the limited excitation to which the blade is subjected.
3. The simulated annealing algorithm-based blade tip timing vibration stress inversion method according to claim 2, wherein in the step (2), the optimization problem is as follows:
Figure FDA0003833054050000018
s.t.||d-WΘ|| 2 =0, wherein,
Figure FDA0003833054050000021
for the optimal matrix, argminf (x) is a function for solving the value of variable x when f (x) reaches the minimum value, | | | | | sweet potato 1 Representing a first matrix norm, | | | | | non-conducting phosphor 2 Representing a second matrix norm.
4. The simulated annealing algorithm-based blade tip timing vibration stress inversion method according to claim 3, wherein the step (3) specifically comprises: finite element tip node pairs (Q) meeting precision requirements are screened out by utilizing sensor installation distance constraint i ,Q j )＝find(|Δq ij -ΔP 12 L < Tol (epsilon)), and constructing virtual measurement amplitude through modal displacement, blade tip initial position, undetermined amplitude conversion factor and blade tip installation angle before and after deformation
Figure FDA0003833054050000022
Establishing an optimization problem with the amplitude conversion factor as a parameter, and searching a node pair (L) with the minimum difference between the actually measured amplitude and the virtually measured amplitude of the sensor by using a simulated annealing algorithm 1 ,L 2 )＝min(|A′ im -A im |+|A′ jm -A jm I), namely the actual measuring point of the sensor; the measured amplitude is correlated with measured data, the virtual measured amplitude is correlated with a finite elementThe modal analysis is relevant; wherein (Q) i ,Q j ) For pairs of tip nodes that meet the axial sensor distance requirement, find () is a function of where the value that meets the condition is found, Δ q ij Is the distance, Δ P, between finite element tip nodes i and j 12 Tol (ε) is the distance of the axial sensor, distance error margin, A' im For a virtual measured amplitude of the tip node i,
Figure FDA0003833054050000023
is the circumferential coordinate, O, of the intersection point of the deformed blade tip molded line and the deformed front node i i,ρ And
Figure FDA0003833054050000024
radial and circumferential coordinates of finite element node i, θ ', under column coordinates' B And theta B The mounting angles of the blade tips before and after deformation (L) 1 ,L 2 ) Is the actual measuring point positions of two axial sensors, A' im And A' jm For virtual measurement of amplitude of axial sensor, A 1m And A 2m Is the measured amplitude of the first sensor and the second sensor.
5. The simulated annealing algorithm-based blade tip timing vibration stress inversion method according to claim 4, wherein the step (4) specifically comprises: for the blade without the blade crown, the vibration stress and the vibration amplitude satisfy a linear relation, and the inversion of the vibration stress is carried out on the basis of the actual measuring point of the sensor identified in the step (3)
Figure FDA0003833054050000025
Obtaining the vibration stress distribution of the whole blade, wherein, A' i, actual measurement And A i, mode For the identified sensor measured amplitude and finite element modal displacement at the location i, S Modality And S' Measured in fact The finite element modal stress and the actual vibratory stress distribution of the whole blade are shown.
CN202211079216.2A 2022-09-05 2022-09-05 Blade tip timing vibration stress inversion method based on simulated annealing algorithm Pending CN115435894A (en)

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