CN109883380B - Rotor blade displacement field measuring method and system based on blade end timing - Google Patents
Rotor blade displacement field measuring method and system based on blade end timing Download PDFInfo
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Abstract
The invention discloses a rotor blade displacement field measuring method and system based on blade end timing, wherein the method comprises the following steps: establishing a three-dimensional finite element model of a rotor blade to be measured, and extracting modal parameters of the three-dimensional finite element model; determining the number and circumferential installation positions of timing sensors at the blade end; establishing a mapping relation between single-point displacement and full-field displacement of the blade; and acquiring single-point displacement of the blade end of the rotor blade based on the blade end timing sensor, wherein the single-point displacement is based on the mapping relation to obtain the displacement of the rotor blade at any position and in any direction. The method provided by the invention can realize the reconstruction of the whole displacement field of the rotor blade only by using the limited measuring points at the blade end, can realize the measurement of the displacements of all nodes on the surface and in the rotor blade under multi-mode vibration, has simple calculation process and is easy for on-line measurement.
Description
Technical Field
The invention belongs to the technical field of non-contact vibration testing of rotor blades of aero-engines, and particularly relates to a rotor blade displacement field measuring method and system based on blade end timing.
Background
The integrity of the blade directly influences the safe operation of the whole structure of the aeroengine, and is influenced by factors such as harsh working environment, strong load alternation and the like, and the blade is very easy to generate vibration fatigue cracks in the service process to cause serious accidents. High cycle fatigue caused by excessive blade vibration is the primary failure mode of an aircraft engine blade. The high cycle fatigue of the rotor blade is mainly caused by dynamic stress caused by various pneumatic loads and mechanical loads, a large number of cycles can be accumulated in a short time to generate fatigue cracks, and particularly, the dynamic stress is easy to cause the fatigue failure of the blade when the blade resonates. In the process of developing and producing an aircraft engine, blade vibration needs to be measured in order to master the vibration characteristics of the blades. For a long time, the aeroengine blade realizes dynamic strain measurement by sticking a strain gauge on the surface of a rotor blade, which can only measure the dynamic strain of limited blade at limited positions, and has low reliability and continuous working time, especially, the arrangement of a large number of strain gauges on the turbine blade under a high-temperature environment has only few strain gauges to obtain effective information, and the survival rate is extremely low. Due to the characteristic of high-speed rotation of the blades of the aero-engine, the non-contact measurement based on blade end timing becomes a development direction of research in the field of blade vibration testing. Tip vibration information is sensed with sensors mounted near the inside of the casing, referred to as "tip timing". The current leaf-end timing technology is a hot spot of great concern in manufacturing and testing of aircraft engines, for example, a Non-invasive Stress Measurement System (NSMS) of a leaf is introduced by the american air force arnold engineering research and development center (aecc).
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 rotor blade displacement field measurement method and system based on blade end timing, which solves the problem that the rotor blade end timing non-contact measurement technology is only suitable for dynamic strain estimation under single-mode vibration and has the advantage of reconstructing displacement fields of all nodes on the surface and in the rotor blade simultaneously.
Non-contact measurement based on Blade Tip Timing (BTT) becomes the most promising alternative method for contact strain measurement, and Blade Tip Timing can measure vibration information of all blades, such as vibration frequency, amplitude, excitation order, resonance region and the like. However, the blade tip senses the vibration information of the blade tip by using the sensor arranged close to the inner side of the casing at regular time, only the vibration of the limited position of the blade tip can be measured, and the reconstruction of a displacement field under multi-mode vibration at any moment cannot be realized. The current blade end timing vibration measurement method is only suitable for single-point displacement measurement of the blade under single-mode vibration, and cannot realize displacement variable-field reconstruction under multi-mode vibration at any moment. Therefore, the method has important significance in reconstructing the whole displacement field of the rotor blade through single-point vibration inversion of the blade end.
The invention aims to realize the technical scheme that a rotor blade displacement field measuring method based on blade end timing comprises the following steps:
in the first step, a three-dimensional finite element model of a rotor blade to be measured is established, and modal parameters of the three-dimensional finite element model are extracted;
in the second step, the number and the circumferential installation position of timing sensors at the blade end are determined;
in the third step, establishing a mapping relation between the single-point displacement of the blade and the full-field displacement;
in the fourth step, the single-point displacement of the blade end of the rotor blade is obtained based on the blade end timing sensor,
in the fifth step, the single-point displacement obtains the displacement of the rotor blade at any position and in any direction based on the mapping relation.
In the method, in the first step, the front n of the three-dimensional finite element model is extracted through modal analysismOrder mode parameter, mode frequency fiAnd a size of ndofX 1 displacement mode phiiConstructing a rotor blade full-field displacement modal shape matrix
Size ndof×nmWherein n ismRepresenting the number of vibration modes, i representing the order of the modes, ndofRepresenting the number of degrees of freedom, n, of a finite element model of a rotor bladedof＝3nn，nnRepresenting the number of nodes of the finite element model of the rotor blade.
In the method, in the second step, the number n of the blade-end timing sensors are circumferentially installed on the rotor blade casingbttAnd number n of vibration modesmThe relationship of (1) is: n isbtt≥2nm+1。
In the method, in the second step, a measuring point selection matrix S of circumferential layout of a multi-mode excitation lower blade end timing sensor casing is constructedbtt：
Wherein, the measuring point selection matrix SbttSize nbtt×(2nm+1)，nbttDenotes the j (j ═ 1.. n)btt) The total number of timed circumferential arrangements of the tips, EOiN denotes the excitation order of interest (i ═ 1.. times)m)，θjDenotes the j (j ═ 1.. n)btt) The installation angle of each blade end timing sensor in the circumferential direction of the casing; taking the position of the rotation speed sensor as a reference 0 DEG, excluding the limitation of the installation angle range of the casing, and randomly selecting n in the circumferential direction of the casingbttThe angle is used as the mounting position of the timing sensor at the blade end; calculating leaf end timing measuring point selection matrix SbttAnd (4) condition number kappa, repeating the random process R times and selecting the measuring point arrangement with the minimum matrix condition number kappa from the random process.
In the method, in the third step, a conversion matrix of the single-point displacement of the blade and the full-field displacement of the blade is constructed
Size ndof×nm(ii) a Wherein phi isbtt，iAnd (4) representing the ith order displacement mode shape of the blade end timing measuring point.
In the method, in the fourth step, n is usedbttBlade end multi-mode vibration signal u of Nth rotor blade rotation obtained by each blade end timing sensorbtt(t), further obtaining n by using a circumferential Fourier fitting algorithmmOrder vibration parameters:
wherein the content of the first and second substances,
amplitude AiModal frequency fiInitial phase of
Upper label
Representing the inverse of the matrix; superscript T represents the transpose of the vector; further, reconstructing to obtain a single-point multi-modal vibration signal of the leaf end:
wherein u isbtt，i(t) represents the i-th order modal vibration signal after decoupling, c represents the static deformation of the blade, and omegaiThe multi-mode vibration circumferential frequency of the blade is represented, and t represents the vibration moment of the blade.
In the method, in the fifth step, based on the conversion matrix T and the decoupled multi-modal vibration signal ubtt，i(t) calculating the displacement field of each rotating blade of the rotor blade in any direction of all nodes on the surface and in the interior of the rotating blade through a formula
wherein the content of the first and second substances,
According to another aspect of the invention, a measurement system for implementing the method comprises,
a plurality of tip timing sensors disposed on a casing of the rotor blade;
the blade end timing vibration measurement module is connected with the blade end timing sensor to measure multi-mode vibration signals of the circumferential blade end of the rotor blade;
a computing unit connected with the blade end timing vibration measurement module, wherein the computing unit comprises,
a modal analysis module configured to perform a modal analysis based on the three-dimensional finite element model of the rotor blade to be measured to obtain a rotor blade front nmOrder mode frequency fiOf displacement mode phiiAnd constructing the rotor bladeFull-field displacement modal shape matrix
A measurement point optimization module configured to optimize the number of measurement points of tip timing sensors arranged on the rotor blade, wherein a measurement point selection matrix S for a multi-modal excited tip timing sensor casing circumferential layout is constructedbttTaking the position of the rotating speed sensor as a reference 0 degree, excluding the limitation of the installation angle range of the casing, and randomly selecting n in the circumferential direction of the casingbttThe angle is used as the mounting position of the timing sensor at the blade end; calculating leaf end timing measuring point selection matrix SbttA condition number kappa, repeating the random process for R times and selecting the measuring point arrangement with the minimum matrix condition number kappa,
a transformation matrix calculation module configured to construct a transformation matrix of the single point displacements and the full field displacements of the blade,
a displacement field reconstruction module configured to calculate a displacement field of the rotor blade in any direction on the surface and inside of each rotor blade by a formula
wherein the content of the first and second substances,
In the measuring system, the blade end timing vibration measuring module comprises a plurality of blade end timing sensors, a rotating speed sensor, a time-displacement conversion module and a signal conditioning module, wherein the blade end timing sensors measure pulse signals of the blades; the rotating speed sensor measures the rotating speed of the blade; the time-displacement conversion module combines the pulse signal measured by the blade end timing sensor with the rotating speed signal to obtain the blade end vibration displacement of the blade; and the signal conditioning module is used for extracting blade vibration frequency and amplitude parameters from the vibration displacement.
In the measuring system, the measuring system further comprises a display unit and wireless communication equipment, and the wireless communication equipment comprises a 4G/GPRS or internet communication module.
Advantageous effects
The rotor blade displacement field measurement method based on blade end timing can realize measurement of the whole displacement field of the rotor blade under multi-mode vibration by using single-point vibration of the blade. The method can realize measurement of the displacement field of the surface of the blade under multi-mode vibration and can also realize measurement of the displacement field of the node inside the blade. The limitation that the blade end timing non-contact measurement technology can only approximately reconstruct the displacement of a certain point of the blade under the single-mode vibration is broken through. The method provided by the invention is simple in calculation process and easy for on-line measurement. The multi-mode vibration coupling and decoupling are considered, the measurement precision is high, the process of a rotor blade displacement field reconstruction system is simple, and the description of the attached drawings is easy to realize
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 schematic flow chart of a preferred embodiment of a method for measuring a displacement field of a rotor blade based on tip timing according to the present invention;
2(a) to 2(b) are schematic structural diagrams of a rotor blade displacement field measurement system based on tip timing provided by the present invention, wherein FIG. 2(a) is a system for reconstructing a rotor blade displacement field; FIG. 2(b) is a schematic circumferential installation diagram of a blade tip timing vibration measurement module and a blade tip timing sensor;
FIG. 3 is a schematic representation of simulated rotor blade dynamic load excitation locations and tip timing sensor measurement point locations in one embodiment;
FIGS. 4(a) -4 (c) are displacement mode shapes of a rotor blade according to an embodiment, wherein FIG. 4(a) shows a bending mode shape and FIG. 4(b) shows a torsional mode shape; FIG. 4(c) shows a second bending mode;
FIG. 5 is a graph of tip displacement vibration signals measured by 7 Tip Timing Sensors (BTTs) in the circumferential direction of a rotor blade according to one embodiment;
FIG. 6 is a result of multi-modal decoupling of rotor blade displacement signals in one embodiment;
FIG. 7 is a comparison of the three displacement components of the blade body node number 748 with the true displacement in the reconstructed rotor blade displacement field in one embodiment;
FIG. 8 is a comparison of three displacement components of node 345 near the root of a blade in a reconstructed rotor blade displacement field with the true displacement according to one embodiment.
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 fig. 1 to 8. 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 flowchart of a method for measuring a displacement field of a rotor blade based on tip timing, and as shown in fig. 1, the method for measuring a displacement field of a rotor blade based on tip timing comprises the following steps:
in a first step S1, establishing a three-dimensional finite element model of a rotor blade to be measured, and extracting modal parameters of the three-dimensional finite element model;
in a second step S2, the number of tip timing sensors and the circumferential mounting position are determined;
in a third step S3, establishing a mapping relation between the single-point displacement of the blade and the full-field displacement;
in a fourth step S4, a single point displacement of the tip of the rotor blade is obtained based on the tip timing sensor,
in a fifth step S5, the single-point displacement is measured to obtain a displacement of the rotor blade at any position and in any direction based on the mapping relationship.
In one embodiment of the method, in a first step S1, the first n of the three-dimensional finite element model is extracted by modal analysismOrder mode parameter, mode frequency fiAnd a size of ndofX 1 displacement mode phiiConstructing a rotor blade full-field displacement modal shape matrix
Size ndof×nmWherein n ismRepresenting the number of vibration modes, i representing the order of the modes, ndofRepresenting the number of degrees of freedom, n, of a finite element model of a rotor bladedof＝3nn，nnRepresenting the number of nodes of the finite element model of the rotor blade.
In one embodiment of the method, in a second step S2, the number n of tip timing sensors is circumferentially mounted to the rotor blade casebttAnd number n of vibration modesmThe relationship of (1) is: n isbtt≥2nm+1。
In one embodiment of the method, in a second step S2, a station selection matrix S for a circumferential layout of a multimode excitation lower blade tip timing sensor casing is constructedbtt：
Wherein, the measuring point selection matrix SbttSize nbtt×(2nm+1)，EOiRepresenting the order of excitation of interest, thetajThe installation angle of a jth blade end timing sensor in the circumferential direction of the casing is shown; taking the position of the rotation speed sensor as a reference 0 DEG, excluding the limitation of the installation angle range of the casing, and randomly selecting n in the circumferential direction of the casingbttThe angle is used as the mounting position of the timing sensor at the blade end; calculating leaf end timing measuring point selection matrix SbttAnd (4) condition number kappa, repeating the random process R times and selecting the measuring point arrangement with the minimum matrix condition number kappa from the random process.
In one embodiment of the method, in the third step S3, a transformation matrix of the single-point displacement of the blade and the full-field displacement of the blade is constructed
Size ndof×nm(ii) a Wherein phi isbtt，iAnd (4) representing the ith order displacement mode shape of the blade end timing measuring point.
In one embodiment of the method, in the fourth step S4, n is usedbttBlade end multi-mode vibration signal u of Nth rotor blade rotation obtained by each blade end timing sensorbtt(t), further obtaining n by using a circumferential Fourier fitting algorithmmStep vibrationParameters are as follows:
wherein the content of the first and second substances,
amplitude AiModal frequency fiInitial phase of
Further, reconstructing to obtain a single-point multi-modal vibration signal of the leaf end:
wherein u isbtt，iAnd (t) represents an ith-order modal vibration signal after decoupling, and c represents static deformation of the blade.
In one embodiment of the method, in a fifth step S5, the displacement field of the rotor blade in any direction is calculated for all nodes on the surface and inside of each rotor blade according to the formula
wherein the content of the first and second substances,
For a further understanding of the present invention, reference is made to the following further description of the invention in conjunction with the accompanying fig. 1 to 8 and the specific embodiments, it being emphasized that the following description is given by way of example only and the invention is not limited in its application to the following examples.
In one embodiment, the method specifically comprises the following steps:
FIG. 1 is a schematic flow diagram of a method for measuring a rotor blade displacement field based on blade end timing, which is completed by the invention, and the method measures single-point vibration of a blade end by using a blade end timing sensor circumferentially installed on a casing, realizes multi-mode vibration decoupling by using a circumferential Fourier fitting method, constructs a conversion relation between a measurement point of the blade end displacement of the rotor blade and displacement of all nodes in a full field, and realizes reconstruction of the blade displacement field; 2(a) to 2(b) are schematic structural diagrams of a rotor blade displacement field measurement system based on tip timing provided by the present invention, wherein, 1-tip timing sensor; 2-a casing; 3-rotor blades; 4-a wheel disc; 5-a rotor; 6-rotating speed sensor. The method comprises the following specific steps:
1) extracting modal parameters of the three-dimensional finite element model of the blade: referring to FIG. 3, a three-dimensional finite element model was created using ANSYS finite element analysis software to simulate a straight blade of a rotor, wherein the material was aluminum and the density was 2700kg/m3Poisson's ratio 0.33, elastic modulus 72000 MPa; the length of the blade is 48mm, the thickness is 1mm, and the width is 20 mm; the finite element type is SOLID element SOLID185, and the total number of nodes is 3153; the two side surfaces of the blade root are fixedly constrained, and the actual working state of the rotor blade is simulated;
extracting the first 3 order modal parameters, namely n, by using ANSYS modal analysis modem3: modal frequency fiA size of ndofX 1 displacement mode phiiWherein the first three-order modal frequencies are respectively f1＝333.08Hz、f2＝1806.03Hz、f32076.52 Hz; constructing a rotor blade full-field displacement modal shape matrix
Size ndof×nmThe displacement mode is shown in fig. 4(a) to 4 (c); i denotes the order of the mode, ndof9459 denotes the number of degrees of freedom of the finite element model of the blade, the displacement of each node comprising three displacements ux、uy、uzComponent, i.e. 3 displacement mode modes per node, then ndof＝3nn，nn3153 the number of finite element model nodes of the blade is indicated.
2) Determining the number of timing sensors at the blade end and the circumferential installation position: number n of blade-end timing sensors circumferentially mounted on rotor blade casingbttAnd vibrate muchNumber of modes nmThe relationship of (1) is: n isbtt≥2nm+ 1; in this case, the vibration mode of the first three orders of the simulated rotor blade is focused, and n is takenm3; the minimum number of timing sensors at the circumferential blade end of the casing is nbtt＝7；
Measuring point selection matrix S for constructing circumferential layout of multi-mode excited lower blade end timing sensor casingbtt：
Wherein, the measuring point selection matrix SbttSize nbtt×(2nm+1)＝7×7，EOiRepresenting the order of excitation of interest, thetajThe installation angle of a jth blade end timing sensor in the circumferential direction of the casing is shown; the three excitation orders concerned in the case are 4, 18 and 23 respectively, and the front three-order vibration modes of the rotor blade are excited at the same rotating speed; taking the position of the rotation speed sensor as a reference 0 DEG, excluding the limitation of the installation angle range of the casing, and randomly selecting n in the circumferential direction of the casingbttTaking the angle of 7 degrees as the installation position of the timing sensor at the blade end; calculating leaf end timing measuring point selection matrix SbttA condition number κ; this random process was repeated 500 times R and the station placement scheme was chosen with the minimum condition number κ. The circumferential installation angles of the selected 7 blade end timing sensors are 3.12 degrees, 117.33 degrees, 183.42 degrees, 189.58 degrees, 303.71 degrees, 315.14 degrees and 351.08 degrees, and corresponding measuring point selection matrixes SbttThe condition number of (2) is 3.4694.
3) Establishing a mapping relation between single-point displacement and full-field displacement of the blade: constructing conversion matrix of single-point displacement and full-field displacement of blade
Size ndof×nm9459 × 3; wherein phi isbtt，iAnd (4) representing the ith order displacement mode shape of the blade end timing measuring point.
4) Acquiring single-point displacement of the blade end of the rotor blade by using a blade end timing sensor: transient analysis of simulated rotor blades in ANSYS finite element softwareThe mass damping coefficient is set to α -12.1380, and the stiffness damping coefficient is set to β -8.1986 × 10-8And the rotating speed is 15000RPM, multimode vibration of the rotor blade by aerodynamic load is simulated, and multifrequency simple harmonic excitation f (t) -cos (2 pi f) is applied to the X direction of a No. 1117 node of the rotor blade end1t)+10cos(2πf2t)+20cos(2πf3t) and taking the displacement field after transient analysis stabilization as a reference of a reconstruction result; using nbttObtaining blade end multi-mode vibration signals u of the Nth turn of the rotor blade by 7 blade end timing sensorsbtt(t), see fig. 5; the blade end timing sensor samples 7 data of No. 1122 node X-direction vibration signals of a blade end every time a rotor blade rotates for one circle, and 25 circles of 175 data are collected in total, so that the blade end timing signals are severely undersampled; also, fig. 5 shows the sampling frequency fsThe length of data of the leaf end 1122 node X-direction vibration signal under 25000Hz is N-2500, and the sampling time is t-N/fs＝0.1s。
Then n is obtained by utilizing a circumferential Fourier fitting algorithmmOrder vibration parameters:
wherein the content of the first and second substances,
amplitude AiModal frequency fiInitial phase of
Further, reconstructing to obtain a single-point multi-modal vibration signal of the leaf end:
wherein u isbtt，iAnd (t) represents an ith-order modal vibration signal after decoupling, and c represents static deformation of the blade. FIG. 6 shows the first three-order vibration mode decoupling results of the rotor blade displacement signals in the embodiment.
5) The displacement measurement of any position and direction of the rotor blade is realized: calculating the displacement field of each rotating blade surface and all internal nodes of the rotor blade in any direction:
wherein the content of the first and second substances,
Taking the No. 748 node of the rotor blade body and the No. 345 node near the blade root as typical representatives of the high-precision reconstruction of the displacement field (see FIG. 3), the conclusion is also applicable to other nodes, and in order to quantitatively evaluate the performance of the non-contact type displacement field reconstruction method of the rotor blade, the method is carried out in the t epsilon [0, 0.1 ∈]s interval, calculating the relative error between the reconstructed signal and the real displacement, and obtaining node u No. 748 of the leaf body in FIG. 7x、uy、uzThe relative errors of displacement in three directions are only 5.77%, 6.22% and 7.49%, respectively. Node u 345 near the leaf root in FIG. 8x、uy、uzThe relative errors of displacement in three directions are only 7.68%, 7.45% and 7.19%, respectively. Therefore, the rotor blade displacement field measuring method based on blade end timing can reconstruct the blade displacement field with high precision.
The method provided by the invention can realize the reconstruction of the whole displacement field of the rotor blade only by utilizing the limited measuring points at the blade end, can realize the measurement of the displacement of all nodes on the surface and in the rotor blade under multi-mode vibration, has simple calculation process and is easy for on-line measurement. The above description is only a preferred embodiment of the present invention, and can be applied to the vibration test of the fan/compressor/turbine blade of the rotating machinery such as an aircraft engine, a gas turbine, a steam turbine, etc., without limiting the present invention.
In another embodiment, the method comprises the steps of:
1) extracting modal parameters of the three-dimensional finite element model of the blade;
2) determining the number and circumferential installation positions of timing sensors at the blade end;
3) establishing a mapping relation between single-point displacement and full-field displacement of the blade;
4) acquiring single-point displacement of the blade end of a rotor blade by using a blade end timing sensor;
5) and the displacement measurement of any position and direction of the rotor blade is realized.
Further, step 1) establishing a three-dimensional finite element model of the rotor blade, and extracting the front n through modal analysismOrder modal parameters: modal frequency fiA size of ndofX 1 displacement mode phii(ii) a Constructing a rotor blade full-field displacement modal shape matrix
Size ndof×nm(ii) a i denotes the order of the mode, ndofRepresenting the number of degrees of freedom of the finite element model of the blade; the displacement of each node comprises 3 displacements ux、uy、uzComponent, i.e. 3 displacement mode modes per node, then ndof＝3nn，nnRepresenting the number of finite element model nodes of the blade.
Further, step 2) installing the number n of blade end timing sensors on the circumferential direction of the rotor blade casingbttAnd number n of vibration modesmThe relationship of (1) is: n isbtt≥2nm+ 1; measuring point selection matrix S for constructing circumferential layout of multi-mode excited lower blade end timing sensor casingbtt：
Wherein, the measuring point selection matrix SbttSize nbtt×(2nm+1)，EOiRepresenting an excitation order of interest; taking the position of the rotation speed sensor as a reference 0 DEG, excluding the limitation of the installation angle range of the casing, and randomly selecting n in the circumferential direction of the casingbttThe angle is used as the mounting position of the timing sensor at the blade end; calculating leaf end timing measuring point selection matrix SbttA condition number κ; this stochastic process is heavyRepeating the steps R times, and selecting a measuring point layout scheme with the minimum condition number kappa.
Further, step 3) constructing a conversion matrix of single-point displacement and full-field displacement of the blade
Size ndof×nd(ii) a Wherein phi isbtt，iAnd (4) representing the ith order displacement mode shape of the blade end timing measuring point.
Further, step 4) utilizes nbttBlade end multi-mode vibration signal u of Nth rotor blade rotation obtained by each blade end timing sensorbtt(t), further obtaining n by using a circumferential Fourier fitting algorithmmOrder vibration parameters:
wherein the content of the first and second substances,
amplitude AiModal frequency fiInitial phase of
Further, reconstructing to obtain a single-point multi-modal vibration signal of the leaf end:
wherein u isbtt，iAnd (t) represents an ith-order modal vibration signal after decoupling, and c represents static deformation of the blade.
Further, step 5) calculates displacement fields of the rotor blades in any directions of all nodes on the surface and in the interior of each rotating blade, which are obtained through the formula
wherein the content of the first and second substances,
In another aspect, a measurement system for implementing the method includes,
a plurality of tip timing sensors disposed on a casing of the rotor blade;
the blade end timing vibration measurement module is connected with the blade end timing sensor to measure multi-mode vibration signals of the circumferential blade end of the rotor blade;
a computing unit connected with the blade end timing vibration measurement module, wherein the computing unit comprises,
a modal analysis module configured to perform a modal analysis based on the three-dimensional finite element model of the rotor blade to be measured to obtain a rotor blade front nmOrder mode frequency fiOf displacement mode phiiAnd constructing a full-field displacement modal shape matrix of the rotor blade
A measurement point optimization module configured to optimize the number of measurement points of tip timing sensors arranged on the rotor blade, wherein a measurement point selection matrix S for a multi-modal excited tip timing sensor casing circumferential layout is constructedbttTaking the position of the rotating speed sensor as a reference 0 degree, excluding the limitation of the installation angle range of the casing, and randomly selecting n in the circumferential direction of the casingbttThe angle is used as the mounting position of the timing sensor at the blade end; calculating leaf end timing measuring point selection matrix SbttA condition number kappa, repeating the random process for R times and selecting the measuring point arrangement with the minimum matrix condition number kappa,
a transformation matrix calculation module configured to construct a transformation matrix of the single point displacements and the full field displacements of the blade,
a displacement field reconstruction module configured to calculate a displacement field of the rotor blade in any direction on the surface and inside of each rotor blade by a formula
wherein the content of the first and second substances,
In one embodiment of the measuring system, the blade tip timing vibration measuring module comprises at least one rotating speed sensor, a signal conditioning module and a time-displacement conversion module.
In one embodiment, the measurement system further comprises a display unit and a wireless communication device comprising a 4G/GPRS or internet communication module.
In one embodiment, the modal analysis module, the measurement point optimization module, the transformation matrix calculation module or the displacement field reconstruction module is a general processor, a digital signal processor, an Application Specific Integrated Circuit (ASIC) or a Field Programmable Gate Array (FPGA),
in one embodiment the modal analysis module, the measurement point preference module, the transformation matrix calculation module or the displacement field reconstruction module comprises a memory comprising one or more of a read only memory ROM, a random access memory RAM, a flash memory or an electronically erasable programmable read only memory EEPROM.
In another aspect of the present invention, a system for measuring a displacement field of a rotor blade based on tip timing as described above includes:
a modal analysis module: for creating a three-dimensional finite element model of a rotor blade, extracting the top n by modal analysismOrder modal parameters: modal frequency fiSize of 2ndof X 1 displacement mode phii(ii) a Constructing a rotor blade full-field displacement modal shape matrix
Size ndof×nm(ii) a i denotes the order of the mode, ndofRepresenting the number of degrees of freedom of the finite element model of the blade; each nodeThe displacement of (a) comprises 3 displacements ux、uy、uzComponent, i.e. 3 displacement mode modes per node, then ndof＝3nn，nnRepresenting the number of finite element model nodes of the blade.
A measuring point optimization module: number n of blade-end timing sensors circumferentially mounted on rotor blade casingbttAnd number n of vibration modesmThe relationship of (1) is: n isbtt≥2nm+ 1; measuring point selection matrix S for constructing circumferential layout of multi-mode excited lower blade end timing sensor casingbtt：
Wherein, the measuring point selection matrix SbttSize nbtt×(2nm+1)，EOiRepresenting an excitation order of interest; taking the position of the rotation speed sensor as a reference 0 DEG, excluding the limitation of the installation angle range of the casing, and randomly selecting n in the circumferential direction of the casingbttThe angle is used as the mounting position of the timing sensor at the blade end; calculating leaf end timing measuring point selection matrix SbttA condition number κ; this random process was repeated R times and the station placement scheme was chosen with the minimum condition number κ.
A conversion matrix calculation module: transformation matrix for single-point displacement and full-field displacement of blade
Size ndof×nm(ii) a Wherein phi isbtt，iAnd (4) representing the ith order displacement mode shape of the blade end timing measuring point.
The blade end timing vibration measurement module: the system comprises a plurality of leaf end timing sensors, at least one rotating speed sensor, a signal conditioning module and a time-displacement conversion module; using nbttBlade end multi-mode vibration signal u of Nth rotor blade rotation obtained by each blade end timing sensorbtt(t), further obtaining n by using a circumferential Fourier fitting algorithmmOrder vibration parameters:
wherein the content of the first and second substances,
amplitude AiModal frequency fiInitial phase of
Further, reconstructing to obtain a single-point multi-modal vibration signal of the leaf end:
wherein u isbtt，iAnd (t) represents an ith-order modal vibration signal after decoupling, and c represents static deformation of the blade.
A displacement field reconstruction module: calculating the displacement field of each rotating blade surface and all internal nodes of the rotor blade in any direction through a formula
wherein the content of the first and second substances,
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 (9)
1. A method of rotor blade displacement field measurement based on tip timing, the method comprising the steps of:
in the first step (S1), a three-dimensional finite element model of a rotor blade to be measured is established, and modal parameters of the three-dimensional finite element model are extracted;
in a second step (S2), the number of tip timing sensors and the circumferential mounting position are determined, wherein a site selection matrix S for a multi-modal excited tip timing sensor casing circumferential layout is constructedbtt：
Wherein, the measuring point selection matrix SbttSize nbtt×(2nm+1)，nbttIndicating the number of circumferentially mounted tip timing sensors, EO, of a rotor blade caseiN denotes the excitation order of interest (i ═ 1.. times)m)，θjDenotes the j (j ═ 1.. n)btt) The installation angle of each blade end timing sensor in the circumferential direction of the casing; taking the position of the rotation speed sensor as a reference 0 DEG, excluding the limitation of the installation angle range of the casing, and randomly selecting n in the circumferential direction of the casingbttThe angle is used as the mounting position of the timing sensor at the blade end; calculating a measurement point selection matrix SbttA condition number kappa, repeating the random process for R times and selecting the measuring point arrangement with the minimum matrix condition number kappa from the random process;
in the third step (S3), a mapping relation between the single-point displacement of the blade and the full-field displacement is established;
in a fourth step (S4), a rotor blade tip single-point displacement is acquired based on the tip timing sensor;
in the fifth step (S5), the single-point displacement is obtained as a displacement of the rotor blade at an arbitrary position and in an arbitrary direction based on the mapping relationship.
2. The method according to claim 1, wherein in a first step (S1), the three-dimensional finite element model front n is extracted by modal analysismOrder mode parameter, mode frequency fiAnd a size of ndofX 1 displacement mode phiiConstructing the full-field displacement mode of the rotor bladeVibration mode matrix
Size ndof×nmWherein n ismRepresenting the number of vibration modes, i representing the order of the modes, ndofRepresenting the number of degrees of freedom, n, of a finite element model of a rotor bladedof＝3nn，nnRepresenting the number of nodes of the finite element model of the rotor blade.
3. The method of claim 1, wherein in a second step (S2), the rotor blade case is circumferentially mounted with a tip timing sensor number nbttAnd number n of vibration modesmThe relationship of (1) is: n isbtt≥2nm+1。
4. The method according to claim 2, wherein in the third step (S3), a transformation matrix of single point displacement of the blade and full field displacement of the blade is constructed
Size ndof×nm(ii) a Wherein phi isbtt，iAnd (4) representing the ith order displacement mode shape of the blade end timing measuring point.
5. The method of claim 4, wherein in the fourth step (S4), n is utilizedbttBlade end multi-mode vibration signal u of Nth rotor blade rotation obtained by each blade end timing sensorbtt(t), further obtaining n by using a circumferential Fourier fitting algorithmmOrder vibration parameters:
wherein the content of the first and second substances,
amplitude AiModal frequency fiInitial phase of
Upper label
Representing the inverse of the matrix; superscript T represents the transpose of the vector; further, reconstructing to obtain a single-point multi-modal vibration signal of the leaf end:
wherein u isbtt，i(t) represents the i-th order modal vibration signal after decoupling, c represents the static deformation of the blade, and omegaiThe multi-mode vibration circumferential frequency of the blade is represented, and t represents the vibration moment of the blade.
6. The method according to claim 5, wherein in a fifth step (S5), based on the transformation matrix T and the decoupled multi-modal vibration signal ubtt，i(t) calculating the displacement field of each rotating blade of the rotor blade in any direction of all nodes on the surface and in the interior of the rotating blade through a formula
wherein the content of the first and second substances,
7. A measurement system for carrying out the method of any one of claims 1 to 6, the measurement system comprising,
a plurality of tip timing sensors disposed on a casing of the rotor blade;
the blade end timing vibration measurement module is connected with the blade end timing sensor to measure multi-mode vibration signals of the circumferential blade end of the rotor blade;
a computing unit connected with the blade end timing vibration measurement module, wherein the computing unit comprises,
a modal analysis module configured to perform a modal analysis based on the three-dimensional finite element model of the rotor blade to be measured to obtain a rotor blade front nmOrder mode frequency fiOf displacement mode phiiAnd constructing a full-field displacement modal shape matrix of the rotor blade
A measurement point optimization module configured to optimize the number of measurement points of tip timing sensors arranged on the rotor blade, wherein a measurement point selection matrix S for a multi-modal excited tip timing sensor casing circumferential layout is constructedbttTaking the position of the rotating speed sensor as a reference 0 degree, excluding the limitation of the installation angle range of the casing, and randomly selecting n in the circumferential direction of the casingbttThe angle is used as the mounting position of the timing sensor at the blade end; calculating a measurement point selection matrix SbttA condition number kappa, repeating the random process for R times and selecting the measuring point arrangement with the minimum matrix condition number kappa,
a transformation matrix calculation module configured to construct a transformation matrix of the single point displacements and the full field displacements of the blade,
a displacement field reconstruction module configured to calculate a displacement field of the rotor blade in any direction on the surface and inside of each rotor blade by a formula
wherein the content of the first and second substances,
representing displacement of the surface and all internal nodes of the blade in three directions at the moment t; wherein u isi，x(t) represents the displacement of the i-th node of the finite element model of the blade in the x direction at the moment t, ui，y(t) represents the displacement of the i-th node of the finite element model of the blade in the y direction at the moment t, ui，z(t) represents the displacement of the blade finite element model in the z direction at the ith node t.
8. The measuring system of claim 7, wherein the tip timing vibration measuring module comprises a plurality of tip timing sensors, a rotational speed sensor, a time-displacement conversion module and a signal conditioning module, wherein the tip timing sensors measure blade reaching pulse signals; the rotating speed sensor measures the rotating speed of the blade; the time-displacement conversion module combines the pulse signal measured by the blade end timing sensor with the rotating speed signal to obtain the blade end vibration displacement of the blade; and the signal conditioning module is used for extracting blade vibration frequency and amplitude parameters from the vibration displacement.
9. The measurement system of claim 7, wherein the measurement system further comprises a display unit and a wireless communication device, the wireless communication device comprising a 4G/GPRS or internet communication module.
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| CN110851963A (en) * | 2019-10-25 | 2020-02-28 | 西安交通大学 | Casing circumferential arrangement method of blade end timing sensor |
| CN111174903B (en) * | 2019-12-31 | 2021-10-01 | 北京化工大学 | Method for diagnosing faults of turbomachinery |
| CN111353129B (en) * | 2020-02-10 | 2021-12-28 | 西安交通大学 | Leaf-end timing data storage matrixing processing method |
| CN111507043A (en) * | 2020-04-29 | 2020-08-07 | 西安交通大学 | Rotor blade dynamic stress field measuring method and system based on blade end timing |
| CN112179480B (en) * | 2020-08-26 | 2021-11-19 | 西安交通大学 | Method and system for identifying timing vibration parameters of harmonic superposition fitting blade tip and electronic equipment |
| CN112507576B (en) * | 2020-11-05 | 2022-12-06 | 西安交通大学 | Rotor blade crack damage identification method based on blade end displacement-displacement transfer ratio |
| CN112541283B (en) * | 2020-11-05 | 2022-12-06 | 西安交通大学 | Rotor blade crack damage identification method based on displacement-strain transfer ratio |
| CN113029481B (en) * | 2021-02-25 | 2023-03-03 | 中国人民解放军国防科技大学 | Method for measuring torsional vibration of blade |
| CN113008362B (en) * | 2021-03-01 | 2022-01-18 | 南京航空航天大学 | Blade tip timing sensor circumferential position optimization method |
| CN113404555B (en) * | 2021-05-18 | 2022-06-21 | 西安交通大学 | Blade natural frequency identification method based on multiple blade end timing sensors |
| CN114033732A (en) * | 2021-11-10 | 2022-02-11 | 中国航发沈阳发动机研究所 | Rotor blade during operation twists reverse angle measurement system |
| CN115081271B (en) * | 2022-06-02 | 2024-04-05 | 西安交通大学 | Leaf end timing system checking method and checking system based on digital simulator |
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