CN110851963A - Casing circumferential arrangement method of blade end timing sensor - Google Patents

Casing circumferential arrangement method of blade end timing sensor Download PDF

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CN110851963A
CN110851963A CN201911028988.1A CN201911028988A CN110851963A CN 110851963 A CN110851963 A CN 110851963A CN 201911028988 A CN201911028988 A CN 201911028988A CN 110851963 A CN110851963 A CN 110851963A
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blade
vibration
matrix
iter
fitness
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陈雪峰
许敬晖
乔百杰
曹宏瑞
杨志勃
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Xian Jiaotong University
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Xian Jiaotong 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

Abstract

The invention discloses a circumferential arrangement method of casings of blade end timing sensors, which comprises the following steps: establishing a three-dimensional model of a single blade, calculating modal natural frequencies of the blade at different rotating speeds on the basis of the three-dimensional model, generating a Campbell diagram of blade vibration, and determining a resonance mode and a corresponding vibration order of the blade at a preset rotating speed on the basis of the Campbell diagram; determining a desired number of tip timing sensors based on said number of vibration orders; constructing a design matrix of a blade vibration model based on the circumferential installation angle of the blade end timing sensor and the vibration order; constructing a fitness function of an optimization process based on the design matrix, wherein a determinant of a product of the transpose of the design matrix and the determinant is calculated and used as the fitness function; and optimizing the fitness function to reach a maximum value so as to determine the circumferential installation angle of the blade end timing sensor.

Description

Casing circumferential arrangement method of blade end timing sensor
Technical Field
The invention belongs to the technical field of non-contact vibration testing of rotor blades of aeroengines and gas turbines, and particularly relates to a casing circumferential arrangement method of a blade end timing sensor.
Background
The rotor blade is an important part in an aircraft engine. When the aero-engine works, the blades can bear severe working conditions such as high temperature, high pressure, high rotating speed and the like. Moreover, the blade usually vibrates under the action of the alternating load, and high cycle fatigue of the blade is further caused, so that the blade is damaged by cracks and the like. Damage to the blade of an aircraft engine often results in changes in some vibration parameters of the blade, such as vibration frequency, amplitude, etc. In the operation process of the blade, the vibration parameter of the blade is accurately monitored, data support can be provided for blade health state assessment, blade residual life prediction and the like, and the blade vibration monitoring system plays an important role in reducing the operation and maintenance cost of an engine and guaranteeing the operation safety of an aeroengine.
The blade end timing technology can carry out non-contact measurement on the vibration of the rotating blade of the aircraft engine, and the characteristic plays an important role in long-term monitoring of the operating state of the blade. The blade end timing sensor is arranged on an engine casing, and the size of the vibration displacement of the blade top end is calculated and various parameters of the blade vibration are extracted from the blade top end vibration displacement by measuring the time when the blade reaches the sensor. However, the sensor is prone to generate large measurement errors under severe working conditions when the aircraft engine works, and the uncertain errors generated in the measurement process easily affect the subsequent blade tip amplitude and the calculation result of the blade vibration parameters, so that misjudgment on the blade fault degree and the residual life prediction may be caused. By analyzing the influence of the layout of the timing sensors at the blade end on the uncertainty of the identification result of the vibration parameters of the blade, the layout of the circumferential sensors of the casing can be optimized, the influence of the uncertainty of the measurement process on the subsequent calculation result is reduced as much as possible, and the reliability of the evaluation result of the running state of the blade is increased.
The above information disclosed in this background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a casing circumferential arrangement method of a blade end timing sensor, which reduces the uncertainty of the subsequent blade vibration parameter identification result caused by the uncertainty in the measurement process, and improves the signal reconstruction precision and the accuracy and reliability of the blade running state evaluation.
The invention aims to realize the purpose through the following technical scheme, and the casing circumferential arrangement method of the blade end timing sensor comprises the following steps:
a method of circumferentially arranging casings of tip timing sensors, the method comprising the steps of:
in the first step, a three-dimensional model of a single blade is established, modal natural frequencies of the blade in different orders at different rotating speeds are calculated based on the three-dimensional model, a Campbell diagram of blade vibration is generated, and a resonance mode and a corresponding vibration order of the blade at a preset rotating speed are determined based on the Campbell diagram;
in the second step, the required number of blade end timing sensors is determined based on the number of vibration orders;
in the third step, a design matrix of a blade vibration model is constructed based on the circumferential installation angle of the blade end timing sensor and the vibration order;
in the fourth step, a fitness function of an optimization process is constructed based on the design matrix, wherein a determinant of a product of the transpose of the design matrix and the design matrix is calculated and is used as the fitness function;
in the fifth step, the fitness function is optimized to reach a maximum value so as to determine the circumferential installation angle of the blade end timing sensor.
In the method, in the first step, the maximum rotation frequency of the blade is fωmaxFrom 0 to fωmaxSelecting N rotation speed points, wherein N is a natural number, and respectively calculating modal natural frequency of each order under each rotation speed point
Figure BDA0002248524300000021
Connecting different rotating speed points by taking the rotating speed of the blade as the abscissa and the vibration frequency of the blade as the ordinateNatural frequency point corresponding to the next same order modeTo generate a campbell diagram comprising a modal frequency line and a rotational speed multiplier line, wherein mbDenotes the b-th mode of the blade, b 1, 2aThe a-th speed point of the blade is shown, a being 1, 2.. N, M representing the calculated mode number.
In the method, any point on a straight line of the rotating speed frequency doubling line is a positive integer multiple of the corresponding rotating frequency.
In the method, based on the intersection point of the modal frequency line and the rotating speed frequency doubling line under the working rotating speed of the blade, the mode corresponding to the modal frequency line passing through the intersection point is a resonance mode, and the rotating frequency multiple corresponding to the rotating speed frequency doubling line passing through the intersection point is a vibration order.
In the method, in the second step, the relationship between the number S of the blade-end timing sensors circumferentially mounted on the casing and the number M of modes of blade vibration is as follows: s is more than or equal to 2M + 1.
In the method, in the third step, the blade vibration is the superposition of a plurality of sinusoidal vibrations, and the multi-modal vibration equation is as follows:
Figure BDA0002248524300000031
where i denotes the number of vibration orders, j denotes the number of sensors, yjRepresenting the tip vibration displacement measured by the jth sensor, M representing the number of modes of multi-modal vibration of the rotor blade, EOiRepresenting the ith order of vibration, θjShows the installation angle between the jth blade end timing sensor and the rotation speed sensor, Ai，Bi，CiAs the vibration parameters to be determined are,
Figure BDA0002248524300000032
accumulation of vibration equations representing M modes of the blade;
a certain blade displacement measured by the n blade tip timing sensors is expressed as y ═ Ψ x in a matrix-vector format, where the matrix is designed:
Figure BDA0002248524300000033
wherein, a multi-mode vibration parameter vector x is to be solveds×1＝[A1B1A2B2... C]TBlade displacement vector y measured by S blade tip timing sensorss×1＝[y1y2… ys]TThe superscript T is the transpose of the vector.
In the method, in the fourth step, a determinant | Ψ of the product of the transpose of the design matrix and itself is calculatedTΨ | and taking the determinant as a fitness function of the optimization process, fit ═ Ψ |TΨ |, where superscript T represents the transpose of the matrix and | | represents the determinant of the matrix.
In the method, the fifth step includes,
s501, generating installation angles of theta blade end timing sensors in a constraint range of a circumferential installation angle of a casing, generating a matrix phi of theta rows and 2M +1 columns based on the circumferential installation angles of the theta blade end timing sensors, wherein the matrix phi is a candidate set in which the sensors are circumferentially arranged, and elements in each row meet the form
[sin(EO1θj) cos(EO1θj) sin(EO2θj) … cos(EOMθj) 1]
In which EO isMRepresenting the Mth order of vibration, thetajThe installation angle between the jth blade end timing sensor and the rotating speed sensor is represented;
s502, at the initial moment, when the iteration number iter is equal to 0, randomly selecting S rows from the matrix phi to form an initial design matrix psiiter＝Ψ0；
S503, calculating the determinant of the product of the initial design matrix transpose and the determinant
Figure BDA0002248524300000041
As an adaptationA degree function;
s504, randomly selecting a row from the matrix phi and adding the row into the initial design matrix psiiterIn (1), it is changed to an s +1 row 2M +1 column matrix Ψiter+；
S505, calculating Ψiter+Transpose of (a) and determinant of its own product
Figure BDA0002248524300000052
If fitness+If < fitness, the newly added row is removed and a row of elements is selected from the matrix phi again for addition until fitness+＞fitness；
S506, from Ψiter+Removing a row of elements to become an S row 2M +1 column matrix Ψiter+-；
S507, calculating psiiter+-Transpose of (a) and determinant of its own product
Figure BDA0002248524300000051
If fitness+-< fit, the removed row of elements is added back to the matrix and the other row of elements is removed, after which Ψ is recalculatediter+-Transpose of determinant(s) multiplied by itself up to the fitness+-> fitness, and then fit+-The value of (1) is given to the fitness so that the fitness is equal to the fitness+-And will make Ψiter+-Redefining the result of (2) as Ψiter+1To represent the design matrix after one iteration;
s508, setting the maximum iteration number I, when the iteration number iter of the design matrix is less than I, iter +1 repeating the steps S503 to S507, and after the iteration is finished, psiiterAnd the circumferential installation angle of the sensor corresponding to each row in the middle is the circumferential installation angle of the optimized blade end timing sensor.
In the fifth step, the fitness function is maximized by using a D optimization algorithm or a genetic algorithm or a particle swarm algorithm, so that the circumferential installation angle of the casing of the blade end timing sensor is determined.
In the method, in the first step, a three-dimensional model of a single blade is established, the three-dimensional model is subjected to grid division and constraint conditions are applied, a rotating speed preload of 0RPM to 8000RPM is applied to the blade, the modal frequencies of the first three orders of the blade at different rotating speeds are obtained through modal analysis, the rotating speed of the blade is taken as a horizontal coordinate, the vibration frequency of the blade is taken as a vertical coordinate, and a rotating speed frequency doubling line and a modal frequency line of blade vibration are drawn to obtain a Campbell diagram of the blade.
Advantageous effects
The method adopts the determinant of the product of the design matrix transposition and the determinant as the target function, and determines the installation position of the blade end timing sensor by optimizing the target function, thereby reducing the influence of uncertainty in the measurement process on the subsequent vibration parameter calculation result and increasing the reliability of the blade running state evaluation result. The determinant of the product of the design matrix transposition and the determinant replaces the traditional design matrix condition number to be used as a fitness function in the optimization process, the uncertainty in the measurement process is reduced to the maximum extent, the physical significance is more clear, and the subsequent parameter identification precision is improved.
Drawings
Various other advantages and benefits of the present invention will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. It is obvious that the drawings described below are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. Also, like parts are designated by like reference numerals throughout the drawings.
In the drawings:
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a single blade structural model;
FIG. 3 is a Campbell diagram of blade vibration;
FIG. 4 is a box plot of the relative error of 30 sets of optimized sensor layouts identifying 300 sets of noise signal vibration parameters;
FIG. 5 is a box plot of 30 sets of stochastic sensor layouts identifying 300 sets of relative errors of noise signal vibration parameters.
The invention is further explained below with reference to the figures and examples.
Detailed Description
Specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present invention is defined by the appended claims.
For the purpose of facilitating understanding of the embodiments of the present invention, the following description will be made by taking specific embodiments as examples with reference to the accompanying drawings, and the drawings are not to be construed as limiting the embodiments of the present invention.
For better understanding, fig. 1 is a flow chart of a method for circumferentially arranging a casing of a tip timing sensor, and as shown in fig. 1, the method for circumferentially arranging the casing of the tip timing sensor comprises the following steps:
a method of circumferentially arranging casings of tip timing sensors, the method comprising the steps of:
in a first step S1, establishing a three-dimensional model of a single blade, calculating modal natural frequencies of the blade at different rotation speeds in each order based on the three-dimensional model, generating a campbell diagram of blade vibration, and determining a resonance mode and a corresponding vibration order of the blade at a predetermined rotation speed based on the campbell diagram;
in a second step S2, determining a desired number of tip timing sensors based on said number of vibration orders;
in a third step S3, constructing a design matrix of a blade vibration model based on the circumferential installation angle of the blade end timing sensor and the vibration order;
in a fourth step S4, constructing a fitness function of an optimization process based on the design matrix, wherein a determinant of a product of the transpose of the design matrix and itself is calculated, and the determinant is used as the fitness function;
in a fifth step S5, the fitness function is optimized to a maximum value to determine the circumferential mounting angle of the tip timing sensor.
In one embodiment of the method, in the fifth step S5, the fitness function is maximized by using an optimization method, such as a particle swarm algorithm, a genetic algorithm, a D optimization algorithm, etc., so as to determine the circumferential installation angle of the casing of the tip timing sensor, where the D optimization method is taken as an example,
s501, initialization: generating the installation angle of theta blade end timing sensors in the constraint range of the circumferential installation angle of the casing, generating a matrix phi of theta rows and 2M +1 columns to represent a candidate set of a sensor arrangement scheme based on the circumferential installation angle of the casing of the theta blade end timing sensors, wherein elements of each row meet the form
[sin(EO1θj) cos(EO1θj) sin(EO2θj) … cos(EOMθj) 1]，
Wherein EO isMRepresenting the Mth order of vibration, thetajThe installation angle between the jth blade end timing sensor and the rotating speed sensor is represented;
s502, at the initial moment, when the iteration number iter is 0, selecting a candidate set from the sensor arrangement schemeRandomly selecting S rows from phi to form an initial design matrix psiiter＝Ψ0；
S503, calculating determinant of product of design matrix transposition and the determinantAs a fitness function;
s504, randomly selecting a row from the sensor arrangement scheme candidate set phi and adding the row into the initial design matrix psiiterIn (1), it is changed to an s +1 row 2M +1 column matrix Ψiter+：
S505, calculating psiiter+Transpose of (a) and determinant of its own product
Figure BDA0002248524300000082
If fitness+If < fitness, the newly added row of elements is removed and a row of elements from the candidate set is selected again for addition until fitness+＞fitness；
S506, from Ψiter+Removing a row of elements to become an S row 2M +1 column matrix Ψiter+-；
S507, calculating psiiter+-Transpose of (a) and determinant of its own product
Figure BDA0002248524300000091
If fitness+-< fit, the removed row of elements is added back to the matrix and the other row of elements is removed, after which Ψ is recalculatediter+-Transpose of determinant(s) multiplied by itself up to the fitness+-> fitness, and then fit+-The value of (2) is given to the fitness, i.e. let the fitness be the fitness+-And will make Ψiter+-Redefining the result of (2) as Ψiter+1I.e. representing the design matrix after one iteration;
s508, setting the maximum iteration number I, when the iteration number iter of the design matrix is less than I, iter +1, repeating the steps S503, S504, S505, S506 and S507, and after the iteration is finished, psiiterThe installation angle of the sensor corresponding to each row in the sensor array can be regarded as the preferable sensor arrangement scheme.
For further understanding of the present invention, the present invention is further described below with reference to fig. 1 to 5 and a specific embodiment, fig. 1 is a flowchart of a casing circumferential arrangement method of a blade end timing sensor, which is completed by the present invention, the method includes analyzing a three-dimensional model of a blade by finite elements, drawing a campbell diagram of blade vibration, determining a vibration order of the blade according to the campbell diagram, further determining the number of the required blade end timing sensors, taking a determinant of a product of a transpose of a design matrix of a blade vibration equation and itself as an objective function, taking a casing circumferential installation angle of the sensor as a design variable, and using an optimization algorithm to make the determinant reach a maximum value, further determining the casing circumferential installation angle of the blade end timing sensor, and the specific steps are as follows:
1) establishing a three-dimensional model of the straight blade shown in fig. 2, importing the model into ANSYS software, carrying out grid division on the blade model and applying constraint conditions, applying a rotating speed preload of 0-8000 RPM on the blade, obtaining the first three-order modal frequency of the blade under different rotating speeds through modal analysis, drawing a rotating speed frequency doubling line and a modal frequency line of blade vibration by taking the rotating speed of the blade as a horizontal coordinate and the vibration frequency of the blade as a vertical coordinate, and obtaining a Campbell diagram of the blade shown in fig. 3.
2) The vibration order of the blade that needs to be focused on is determined. Assuming that the rotation speed of interest is around 5500RPM, as can be seen from the campbell diagram of fig. 3, the first and second order modal frequency lines intersect the rotation speed doubling lines with vibration orders EO 4 and EO 19, respectively, thereby determining the vibration order of interest as EO1＝4，EO2＝19。
3) The number of tip timing sensors that need to be used is determined. Step 2) shows that the number of the vibration orders of the blade needing attention is two, so that the number s of the sensors needing to be used is more than or equal to 2 multiplied by 2+1 to 5, and 5 blade end timing sensors are selected for data acquisition.
4) And constructing a design matrix of the blade vibration model. Assuming that the mounting accuracy of the sensors is 0.01 °, 36000 sets of sensor placement solution candidates Φ are generated. Randomly selecting 5 groups of sensor installation angles from the candidate set, wherein if the initial randomly generated angles are as follows:
θ0＝(12.13°，83.75°，189.66°，303.71°，339.74°)
its corresponding design matrix:
Figure BDA0002248524300000101
5) computing determinant of the product of the design matrix transpose and itself [ psi ]TΨ|＝49.12
501 randomly selecting a row of data corresponding to the sensor installation angle theta from the candidate set phi of the sensor arrangement scheme+143.21. Adding the initial design matrix into the initial design matrix to obtain a new design matrix
Figure BDA0002248524300000111
502) Computing the design matrix Ψ0+Transpose and self product determinant
Figure BDA0002248524300000112
Due to the fact that+230.56 > fitness 49.12 satisfies the condition.
503) From Ψ0+Removing the first row of elements to obtain a new design matrix
Computing the design matrix Ψ0+-Transpose and self product determinant
Figure BDA0002248524300000114
Due to the fact that+-16.91 < fixness 49.12, so add the removal line to Ψ0+-And the other row elements are removed. When removing Ψ0+The third row of elements, the design matrix at this time
Figure BDA0002248524300000121
Computing the design matrix Ψ0+-Transpose and self product determinant
Figure BDA0002248524300000122
Due to the fact that+-103.01 > fitness 49.12, so will Ψ0+-The result of the first iteration is again denoted as Ψ1。
504) Set the maximum number of iterations I500, repeat steps 501), 502), 503), 504) when the number of iterations iter < I).
6) And after iteration is finished, obtaining an optimized sensor layout:
θopt＝[14.53°，67.48°，120.69°，268.38°，321.58°]
7) the tip timing sensor layout scheme provided by the present application is verified with reference to specific data.
701) Setting the blade rotation frequency to fωSetting the blade vibration parameters as 100 Hz:
A1＝2；B1＝3；A2＝4；B2＝5；C＝6
vibration equation of the blade:
y＝2sin(2πf1t)+3cos(2πf1t)+4sin(2πf2t)+5cos(2πf2t)+6
wherein
f1＝EO1×fω＝4×100＝400Hz、f2＝EO2×fω＝19×100＝1900Hz
702) Simulating uncertainty in the measurement process by using random white Gaussian noise, wherein the measurement uncertainty is measured by the signal-to-noise ratioQuantitative representation of, wherein Psignal、PnoiseThe effective power of the signal and noise is represented, and the SNR is 5 dB.
703) Because the adopted D optimization algorithm can only converge to the local optimal solution each time, 30 groups of optimized sensor layout schemes are calculated and generated, and each group of sensor layout scheme adopts 300 different groups of noise signals for inspection.
704) Using a circumferential Fourier method
Figure BDA0002248524300000135
The vibration parameters of the blade are calculated. Wherein y represents the conversion fωThe displacement vector measured by 5 leaf end timing sensors under the condition of 100Hz,the matrix is the inverse of the design matrix after I iterations, and X is the multi-modal vibration parameter vector to be solved. Calculating the relative error between the vibration parameter and the set parameter in 71):
Figure BDA0002248524300000133
wherein A is1，B1，A2，B2C represents the vibration parameter set in 71),
Figure BDA0002248524300000134
the vibration parameters obtained by the circumferential fourier method are shown. And adopting the magnitude of the relative error delta as a standard for evaluating the sensor layout scheme.
705) As a layout scheme of the sensors comparing 30 sets of random generation, a test was performed by applying 300 sets of the same noise signals as in step 73) to each set of random layout scheme.
706) The relative error of 300 groups of noise signal parameter identification results under each group of sensor layout is drawn as a box chart, and then a box chart of 30 groups of optimized sensor layout schemes is shown in figure 4, and a box chart of 30 groups of random sensor optimized layout schemes is shown in figure 5. Comparing fig. 4 and fig. 5, it can be seen that, in each sensor scheme with the optimized layout, for 300 different groups of noisy signal parameter identifications, the median of relative errors is about 5%, the average relative error of the optimized sensor layout of 30 groups is calculated to be 5.95%, and the variance is 0.0156, which indicates that the effect of parameter identification between different optimized sensor layout schemes is basically consistent, and the influence of measurement uncertainty on subsequent calculation results is small. As can be seen from fig. 5, the solutions of the sensors in the random layout have a large difference in parameter identification effect among the solutions of each group, and the same group of sensors has a large difference in parameter identification effect for different noise signals. The average relative error for the 30 random sensor layouts was calculated to be 38.9% with a variance of 3679.1.
In one embodiment of the method, in the first step S1, the maximum blade rotation frequency is fωmaxFrom 0 to fωmaxSelecting N rotation speed points, wherein N is a natural number, and respectively calculating modal natural frequency of each order under each rotation speed point
Figure BDA0002248524300000141
The rotating speed of the blade is used as the abscissa, the vibration frequency of the blade is used as the ordinate, and the natural frequency points corresponding to the same-order mode at different rotating speed points are connected
Figure BDA0002248524300000142
To generate a campbell diagram comprising a modal frequency line and a rotational speed multiplier line, wherein mbDenotes the b-th mode of the blade, b 1, 2aThe a-th speed point of the blade is shown, a being 1, 2.. N, M representing the calculated mode number.
In one embodiment of the method, any point on the straight line of the rotational speed frequency doubling line is a positive integer multiple of the corresponding rotational frequency.
In one embodiment of the method, in the campbell diagram, based on an intersection point of a modal frequency line and a rotational speed frequency doubling line at a working rotational speed of the blade, a mode corresponding to the modal frequency line passing through the intersection point is a resonance mode, and a frequency conversion multiple corresponding to the rotational speed frequency doubling line passing through the intersection point is a vibration order.
In one embodiment of the method, in a second step S2, the relationship between the number S of circumferentially mounted tip timing sensors of the casing and the number M of modes of blade vibration is: s is more than or equal to 2M + 1.
In one embodiment of the method, in the third step S3, the blade vibration is a superposition of a plurality of sinusoidal vibrations, and the multi-modal vibration equation is:
Figure BDA0002248524300000151
where i denotes the number of vibration orders, j denotes the number of sensors, yjRepresenting the tip vibration displacement measured by the jth sensor, M representing the number of modes of multi-modal vibration of the rotor blade, EOiRepresenting the ith order of vibration, θjShows the installation angle between the jth blade end timing sensor and the rotation speed sensor, Ai，Bi，CiAs the vibration parameters to be determined are,
Figure BDA0002248524300000152
accumulation of vibration equations representing M modes of the blade;
a certain blade displacement measured by the n blade tip timing sensors is expressed as y ═ Ψ x in a matrix-vector format, where the matrix is designed:
Figure BDA0002248524300000153
wherein, a multi-mode vibration parameter vector x is to be solveds×1＝[A1B1A2B2... C]TBlade displacement vector y measured by s blade tip timing sensorss×1＝[y1y2… ys]TThe superscript T is the transpose of the vector.
In one embodiment of the method, in the fourth step S4, a determinant | Ψ of the product of the transpose of the design matrix and itself is calculatedTΨ | and taking the determinant as a fitness function of the optimization process, fit ═ Ψ |TΨ |, where superscript T represents the transpose of the matrix and | | represents the determinant of the matrix.
In one embodiment of the method, the fifth step S5 includes,
s501, generating installation angles of theta blade end timing sensors in a constraint range of a circumferential installation angle of a casing, generating a matrix phi of theta rows and 2M +1 columns based on the circumferential installation angles of the theta blade end timing sensors, wherein the matrix phi is a candidate set in which the sensors are circumferentially arranged, and elements in each row meet the form
[sin(EO1θj) cos(EO1θj) sin(EO2θj) … cos(EOMθj) 1]
In which EO isMRepresenting the Mth order of vibration, thetaiThe installation angle between the jth blade end timing sensor and the rotating speed sensor is represented;
s502, at the initial moment, when the iteration number iter is equal to 0, randomly selecting S rows from the matrix phi to form an initial design matrix psiiter＝Ψ0；
S503, calculating the determinant of the product of the initial design matrix transpose and the determinant
Figure BDA0002248524300000161
As a fitness function;
s504, randomly selecting a row from the matrix phi and adding the row into the initial design matrix psiiterIn (1), it is changed to an s +1 row 2M +1 column matrix Ψiter+；
S505, calculating Ψiter+Transpose of (a) and determinant of its own productIf fitness+If < fitness, the newly added row is removed and a row of elements is selected from the matrix phi again for addition until fitness+＞fitness；
S506, from Ψiter+Removing a row of elements to become an S row 2M +1 column matrix Ψiter+-；
S507, calculating psiiter+-Transpose of (a) and determinant of its own product
Figure BDA0002248524300000171
If fitness+-< fit, the removed row of elements is added back to the matrix and the other row of elements is removed, after which Ψ is recalculatediter+-Transpose of determinant(s) multiplied by itself up to the fitness+-> fitness, and then fit+-The value of (1) is given to the fitness so that the fitness is equal to the fitness+-And will make Ψiter+-Redefining the result of (2) as Ψiter+1To represent the design matrix after one iteration;
s508, setting the maximum iteration number I, when the iteration number iter of the design matrix is less than I, iter +1 repeating the steps S503 to S507, and after the iteration is finished, psiiterAnd the circumferential installation angle of the sensor corresponding to each row in the middle is the circumferential installation angle of the optimized blade end timing sensor.
In one embodiment of the method, in the fifth step S5, the fitness function is maximized by using an optimization algorithm such as a D-optimization algorithm, a genetic algorithm, or a particle swarm algorithm, so as to determine the circumferential installation angle of the casing of the tip timing sensor.
In one embodiment of the method, in a first step S1, a three-dimensional model of a single blade is established, the three-dimensional model is subjected to meshing and constraint conditions are applied, a rotating speed preload of 0RPM to 8000RPM is applied to the blade, first three-order modal frequencies of the blade at different rotating speeds are obtained through modal analysis, the rotating speed of the blade is taken as an abscissa, the vibration frequency of the blade is taken as an ordinate, and a rotating speed frequency doubling line and a modal frequency line of blade vibration are drawn to obtain a campbell diagram of the blade.
Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments and application fields, and the above-described embodiments are illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto without departing from the scope of the invention as defined by the appended claims.

Claims (10)

1. A method of circumferentially arranging casings of tip timing sensors, the method comprising the steps of:
in the first step (S1), a three-dimensional model of a single blade is established, modal natural frequencies of the blade in various orders at different rotating speeds are calculated based on the three-dimensional model, a Campbell diagram of blade vibration is generated, and a resonance mode and a corresponding vibration order of the blade at a preset rotating speed are determined based on the Campbell diagram;
in a second step (S2), determining a desired number of tip timing sensors based on said number of vibration orders;
in the third step (S3), a design matrix of a blade vibration model is constructed based on the circumferential installation angle of the blade end timing sensor and the vibration order;
in a fourth step (S4), constructing a fitness function of an optimization process based on the design matrix, wherein a determinant of a product of the transpose of the design matrix and itself is calculated as the fitness function;
in a fifth step (S5), the fitness function is optimized to a maximum value to determine a circumferential mounting angle of the tip timing sensor.
2. The method according to claim 1, wherein preferably, in the first step (S1), the maximum rotation frequency of the blade is fωmaxFrom 0 to fωmaxSelecting N rotation speed points, wherein N is a natural number, and respectively calculating modal natural frequency of each order under each rotation speed point
Figure FDA0002248524290000011
The rotating speed of the blade is used as the abscissa, the vibration frequency of the blade is used as the ordinate, and the natural frequency points corresponding to the same-order mode at different rotating speed points are connected
Figure FDA0002248524290000012
To generate a campbell diagram comprising a modal frequency line and a rotational speed multiplier line, wherein mbDenotes the b-th mode of the blade, b 1, 2aThe a-th speed point of the blade is shown, a being 1, 2.. N, M representing the calculated mode number.
3. The method according to claim 2, wherein any point on the straight line of the rotational speed frequency doubling line is a positive integer multiple of the corresponding rotational frequency.
4. The method according to claim 2, wherein in the campbell diagram, based on the intersection point of the modal frequency line and the rotational speed frequency doubling line at the operating rotational speed of the blade, the mode corresponding to the modal frequency line passing through the intersection point is a resonance mode, and the rotational frequency multiple corresponding to the rotational speed frequency doubling line passing through the intersection point is a vibration order.
5. The method of claim 1, wherein in a second step (S2), the relationship between the number S of circumferentially mounted tip timing sensors of the casing and the number M of modes of blade vibration is: s is more than or equal to 2M + 1.
6. The method according to claim 1, wherein in the third step (S3), the blade vibration is a superposition of a plurality of sinusoidal vibrations, the multi-modal vibration equation of which is:
Figure FDA0002248524290000021
where i denotes the number of vibration orders, j denotes the number of sensors, yjRepresenting the tip vibration displacement measured by the jth sensor, M representing the number of modes of multi-modal vibration of the rotor blade, EOiRepresenting the ith order of vibration, θjShows the installation angle between the jth blade end timing sensor and the rotation speed sensor, Ai，Bi，CiAs the vibration parameters to be determined are,accumulation of vibration equations representing M modes of the blade;
a certain blade displacement measured by the n blade tip timing sensors is expressed as y ═ Ψ x in a matrix-vector format, where the matrix is designed:
Figure FDA0002248524290000023
wherein, a multi-mode vibration parameter vector x is to be solveds×1＝[A1B1A2B2...C]TBlade displacement vector y measured by S blade tip timing sensorss×1＝[y1y2…ys]TThe superscript T is the transpose of the vector.
7. The method according to claim 6, wherein in the fourth step (S4), the determinant | Ψ of the product of the transpose of the design matrix and itself is calculatedTΨ | and taking the determinant as a fitness function of the optimization process, fit ═ Ψ |TΨ |, where superscript T represents the transpose of the matrix and | | represents the determinant of the matrix.
8. The method according to claim 6, wherein the fifth step (S5) includes,
s501, generating installation angles of theta blade end timing sensors in a constraint range of a circumferential installation angle of a casing, generating a matrix phi of theta rows and 2M +1 columns based on the circumferential installation angles of the theta blade end timing sensors, wherein the matrix phi is a candidate set in which the sensors are circumferentially arranged, and elements in each row meet the form
[sin(EO1θj) cos(EO1θj) sin(EO2θj)…cos(EOMθj) 1]
In which EO isMRepresenting the Mth order of vibration, thetajThe installation angle between the jth blade end timing sensor and the rotating speed sensor is represented;
s502, at the initial moment, when the iteration number iter is equal to 0, randomly selecting S rows from the matrix phi to form an initial design matrix psiiter＝Ψ0；
S503, calculating the determinant of the product of the initial design matrix transpose and the determinant
Figure FDA0002248524290000031
As a fitness function;
s504, randomly selecting a row from the matrix phi and adding the row into the initial design matrix psiiterIn (2), it is changed to an S +1 row 2M +1 column matrix Ψiter+；
S505, calculating Ψiter+Transpose of (a) and determinant of its own productIf fitness+If < fitness, the newly added row is removed and a row of elements is selected from the matrix phi again for addition until fitness+＞fitness；
S506, from Ψiter+Removing a row of elements to become an S row 2M +1 column matrix Ψiter+-；
S507, calculating psiiter+-Transpose of (a) and determinant of its own productIf fitness+-< fit, the removed row of elements is added back to the matrix and the other row of elements is removed, after which Ψ is recalculatediter+-Transpose of determinant(s) multiplied by itself up to the fitness+-> fitness, and then fit+-The value of (1) is given to the fitness so that the fitness is equal to the fitness+-And will make Ψiter+-Redefining the result of (2) as Ψiter+1To represent the design matrix after one iteration;
s508, setting the maximum iteration number I, when the iteration number iter of the design matrix is less than I, iter +1 repeating the steps S503 to S507, and after the iteration is finished, psiiterAnd the circumferential installation angle of the sensor corresponding to each row in the middle is the circumferential installation angle of the optimized blade end timing sensor.
9. The method according to claim 1, wherein in a fifth step (S5), the fitness function is maximized using a D-optimization algorithm, a genetic algorithm or a particle swarm algorithm to determine a casing circumferential installation angle of the tip timing sensor.
10. The method of claim 1, wherein in the first step (S1), a three-dimensional model of a single blade is established, the three-dimensional model is gridded and constrained, a rotational speed preload of 0-8000 RPM is applied to the blade, the first three modal frequencies of the blade at different rotational speeds are obtained through modal analysis, the rotational speed of the blade is taken as the abscissa, the vibration frequency of the blade is taken as the ordinate, and a rotational speed frequency doubling line and a modal frequency line of blade vibration are drawn to obtain a Campbell diagram of the blade.
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