A rotor bending vibration measurement system and method based on multi-stage blade tip clearance

Abstract

The application discloses a rotor bending vibration measurement system and method based on a multistage blade disc tip clearance, which comprises a sensor module, a tip clearance signal processing module, a tip clearance synchronous acquisition module, a same-stage blade disc shaft position inversion module for obtaining a shaft track of a stage blade disc, a same-stage blade disc amplitude extraction module for obtaining a vibration amplitude of a single-stage blade disc, a frequency and phase extraction module for obtaining a vibration frequency and a phase of a single-stage blade disc, a multistage joint space mode extraction module for obtaining a space mode function, and a bending vibration order extraction module for obtaining a bending vibration order, which are sequentially connected. The sensor module is composed of a plurality of tip clearance sensors. Each stage blade disc is provided with at least three tip clearance sensors. Each tip clearance sensor is sequentially connected with the tip clearance signal processing module and the tip clearance synchronous acquisition module to obtain tip clearance data.

Description

Technical Field

[0001] This invention relates to the field of non-contact rotor vibration measurement, and in particular to a rotor bending vibration measurement system and method based on the tip clearance of a multi-stage bladed disk. Background Technology

[0002] As a core component of large rotating machinery such as aero engines and gas turbines, the rotor system's operating status directly affects the safety and efficiency of the equipment. Rotor bending vibration is a key factor leading to blade fatigue fracture, bearing wear, and even overall machine failure. Traditional rotor bending vibration measurement methods mainly involve installing sensors (such as eddy current displacement sensors and accelerometers) at the rotor shaft end or near the bearing. However, these methods have the following limitations: (1) Installing sensors at the rotor shaft end or bearing requires intrusion into the rotor body or support structure, which may disrupt the rotor's dynamic balance. Furthermore, under high temperature and high pressure conditions, the sensors are prone to failure, threatening system safety. (2) Due to the limitations of the rotor structure, sensors can usually only be installed near the bearing, failing to reflect the actual bending deformation at the rotor mid-span or blade disk, resulting in insufficient vibration signal sensitivity. (3) Measurement data from a single location is insufficient to distinguish different orders of bending vibration modes (such as first-order and second-order bending), affecting the accuracy of fault diagnosis. Therefore, how to overcome these limitations and measure rotor bending vibration more safely and accurately is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a rotor bending vibration measurement system and method based on the tip clearance of multi-stage bladed disks, thereby addressing the deficiencies in safety and accuracy of current rotor bending vibration measurements. The system indirectly obtains rotor bending vibration signals by measuring the changes in tip clearance of multi-stage bladed disks, eliminating the need for sensors installed on the rotor itself. Utilizing the natural axial distribution of the multi-stage bladed disks along the rotor axis, tip clearance data at different locations are collected simultaneously, comprehensively capturing the bending deformation characteristics of each section of the rotor. By analyzing the phase difference and amplitude distribution of the multi-stage tip clearance changes, combined with an order decomposition algorithm, different orders of bending vibration (such as first-order and second-order) are separated and identified.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A rotor bending vibration measurement system based on multi-stage bladed disk tip clearance is applied to a rotor system under test including at least three stages of bladed disks. The system is characterized by comprising a sensor module, a tip clearance signal processing module, a tip clearance synchronous acquisition module, a same-stage bladed disk shaft center position inversion module, a same-stage bladed disk amplitude extraction module, a frequency and phase extraction module, a multi-stage joint spatial mode extraction module, and a bending vibration order extraction module connected in sequence.

[0006] The sensor module consists of several blade tip gap sensors; the blade tip gap sensors are installed on the casing, and at least three blade tip gap sensors are installed on each stage of the bladed disk to obtain blade tip gap data at different circumferential positions of the same stage of the bladed disk.

[0007] Each blade tip gap sensor is sequentially connected to the blade tip gap signal processing module and the blade tip gap synchronous acquisition module to obtain blade tip gap data;

[0008] The same-stage impeller shaft center position inversion module is used to obtain the shaft center trajectory of the same-stage impeller;

[0009] The same-stage bladed disk amplitude extraction module is used to obtain the vibration amplitude of a single-stage bladed disk;

[0010] The frequency and phase extraction module is used to obtain the vibration frequency and phase of a single-stage bladed disk;

[0011] The multi-level joint spatial mode extraction module is used to obtain spatial mode functions;

[0012] The bending vibration order extraction module is used to obtain the bending vibration order.

[0013] This invention also provides a method for measuring rotor bending vibration based on the tip clearance of a multi-stage bladed disk, and the rotor bending vibration measurement system described above includes:

[0014] S1. Synchronously acquire blade tip clearance data: Simultaneously acquire all blade tip clearance sensor signals at the same time for subsequent rotor bending vibration amplitude, frequency, phase extraction and rotor bending vibration order identification; S2. Establish rotor bending vibration geometric model;

[0015] S3. Invert the shaft center position of a single-stage bladed disk; use the tip clearance at different circumferential positions of the same stage bladed disk to obtain the shaft center trajectory of the corresponding section of the bladed disk, and obtain the rotor shaft center position of the current section through inversion;

[0016] S4. Extract the vibration amplitude at the single-stage bladed disk;

[0017] S5. Extract the vibration frequency and phase at the single-stage bladed disk;

[0018] S6. Multi-level joint spatial modal modeling and bending vibration order identification.

[0019] Furthermore, in step S2,

[0020] Assuming the impeller is rigidly connected to the rotor, and the change in blade tip clearance originates from the rotor shaft motion, the rotor is at multiple impeller positions z1, z2, ..., z n The vibration amplitude at a certain point exhibits an axial distribution, which can reflect the different orders of rotor bending vibration.

[0021] Establish a geometric model of rotor bending vibration, assuming that the rotor bending vibration is in simple harmonic form, expressed as follows:

[0022] x(z,t)=A(z)cos(ωt+φ(z))

[0023] y(z,t)=A(z)sin(ωt+φ(z))

[0024] Where A(z) is the amplitude distribution of the rotor bending vibration at the axial position z; ω=2πf is the angular frequency, f is the rotor bending vibration frequency; φ(z) is the phase at different axial positions.

[0025] Furthermore, in step S3,

[0026] Suppose that N tip clearance sensors are arranged on a certain stage of the rotor blade disk, distributed in the circumferential direction, with angles of θ1, θ2, ..., θ3. N The installation position of the OPR sensor used to measure the impeller rotation speed is defined as the reference direction 0°; the corresponding tip gaps measured by the tip gap sensor are c1(t), c2(t), ..., c N (t); These blade tip clearances are caused by the offset of the rotor shaft center relative to the center of the stationary casing. That is, at a certain time t, let the set of trajectory points of the rotor shaft center relative to the center of the casing on this cross section be r(t)=(x(t),y(t)), then the blade tip clearance measured at the blade tip clearance sensor n satisfies:

[0027] c n (t)=c0-x(t)cosθ n -y(t)sinθ n

[0028] Where c0 is the static gap without vibration, which is estimated by averaging; θ n y(t) represents the angle of the nth tip clearance sensor relative to the reference direction; x(t) and y(t) represent the axis center positions, i.e., the inverted target.

[0029] Assuming N≥3, the axis position is obtained by using least squares fitting, and a system of equations is constructed.

[0030]

[0031] make Therefore, the above equation is expressed as A·r(t)=b(t), and solving it yields...

[0032] r(t)=(A T A) -1 A T b(t)

[0033] That is, it is possible to reconstruct the motion trajectory of the axial cross section at every time t.

[0034] Furthermore, in step S4,

[0035] Plotting the x(t) and y(t) data points at different time points t as a trajectory yields the vibration trajectory of the rotor cross-section, which is elliptical. An ellipse fitting algorithm is used to obtain the principal axis direction and length, corresponding to the maximum / minimum vibration amplitude. The ellipse center corresponds to static eccentricity; variations in ellipse parameters correspond to multi-frequency components or modulation effects; the general equation for fitting the ellipse is:

[0036] a1x 2 +a2xy+a3y 2 +a4x+a5y+a6=0

[0037] Where a1-a6 are the fitting coefficients of the ellipse equation, by fitting this trajectory point set and extracting the lengths a and b of the main half-axis, the vibration amplitude at this stage of the bladed disk can be obtained.

[0038] Furthermore, in step S5,

[0039] Performing a Fast Fourier Transform (FFT) on the reconstructed x(t) and y(t) sequences yields:

[0040] X(f)=F[x(t)]

[0041] Y(f)=F[y(t)]

[0042] Where X(f) and Y(f) are the frequency domain representations of the x(t) and y(t) sequences obtained after FFT, respectively, the dominant frequency components of X(f) and Y(f) are taken as the rotor bending vibration frequency f. b ;

[0043] Alternatively, the least squares method can be used to fit the harmonic form of the function to obtain...

[0044] x(t)≈A x cos(2πf b t+φ x )

[0045] y(t)≈A y cos(2πf b t+φ y )

[0046] Among them, A x A y f represents the amplitudes of two vibrations in orthogonal directions. b Where φ is the vibration frequency. x φ y The phase is used for identifying the order of rotor bending vibration.

[0047] Furthermore, in step S6,

[0048] The axis center trajectory r at multiple axial positions i (t)=(x i (t),y i (t)), further establishing spatial mode functions

[0049]

[0050] Among them, A k (z) represents the spatial distribution of the bending vibration order, f k As the dominant frequency, φ k (z) represents the initial phase of the trajectory of the axis of each bladed disk; the different orders of bending vibrations such as the first and second orders can be identified by the above formula.

[0051] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0052] (1) This invention proposes a rotor bending vibration measurement method based on the tip gap of a multi-stage bladed disk, which replaces the traditional rotor end measurement and achieves safer and more accurate rotor bending vibration measurement.

[0053] (2) In this invention, the blade tip gap sensor only needs to be installed in the casing, which is a low-intervention measurement, avoiding structural damage to the rotor system and eliminating the safety hazards of invasive measurement.

[0054] (3) By synchronously measuring the blade tip gap of the multi-stage bladed disk, key bending sensitive areas such as the rotor mid-span and cantilever end can be covered, and the vibration status of the entire rotor length can be monitored.

[0055] (4) The present invention is applied to a rotor structure with multi-stage bladed disks. The change in the blade tip gap of different stages of bladed disks corresponds to different bending vibration orders. The separation and identification of multi-order bending vibrations can be achieved by characterizing the blade tip gap of different stages of bladed disks.

[0056] (5) The system and method of the present invention can directly reuse existing blade tip clearance measurement systems (such as capacitive, eddy current, microwave, etc.), without the need for additional sensor installation structure design, reducing modification costs and providing strong engineering compatibility. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the rotor bending vibration measurement system based on the tip clearance of a multi-stage bladed disk.

[0058] Figure 2 A simplified schematic diagram of the rotor system under test.

[0059] Figure 3a A three-dimensional schematic diagram of the layout of the blade tip gap sensor for the rotor system.

[0060] Figure 3b A two-dimensional schematic diagram of the installation of a single-stage blade disk tip gap sensor.

[0061] Figure 4 This is a flowchart of a rotor bending vibration measurement method based on the tip clearance of a multi-stage bladed disk.

[0062] Figure 5 This is a schematic diagram of the first-order bending vibration mode of the rotor. The dashed line represents the shape of the shaft and the position of the blade disk when no bending vibration occurs, and the solid line represents the shape of the shaft and the position of the blade disk when the first-order bending vibration occurs.

[0063] Figure 6 This is a schematic diagram of the second-order bending vibration mode of the rotor. The dashed line represents the shaft shape and blade disk position when no bending vibration occurs, and the solid line represents the shaft shape and blade disk position when second-order bending vibration occurs.

[0064] Reference numerals: 1- Tip gap sensor module, 2- Tip gap signal processing module, 3- Tip gap synchronous acquisition module, 4- Same-stage bladed disk shaft center position inversion module, 5- Same-stage bladed disk amplitude extraction module, 6- Frequency and phase extraction module, 7- Multi-stage joint spatial mode extraction module, 8- Bending vibration order extraction module, 9- Rotor system under test, 901- Shaft, 902, 903, 904- Bladed disk, 101, 102, 103, 104, 105, 106, 107, 108, 109- Tip gap sensor. Detailed Implementation

[0065] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0066] This embodiment provides a rotor bending vibration measurement system based on the tip clearance of a multi-stage bladed disk, see [link / reference]. Figure 1 The system comprises, in sequence, a blade tip gap sensor module 1, a blade tip gap signal processing module 2, a blade tip gap synchronous acquisition module 3, a same-level bladed disk axis center position inversion module 4, a same-level bladed disk amplitude extraction module 5, a frequency and phase extraction module 6, a multi-level joint spatial mode extraction module 7, and a bending vibration order extraction module 8. In this embodiment, the blade tip gap sensor module 1 consists of blade tip gap sensors 101, 102, 103, 104, 105, 106, 107, 108, and 109.

[0067] Since this invention utilizes the tip clearance of a multi-stage bladed disk to measure rotor bending vibration, the actual complex rotor system is simplified for ease of explanation. A simplified schematic diagram of the rotor system 9 under test is provided below. Figure 2 As shown, it includes a rotating shaft 901, an impeller 902, an impeller 903, and an impeller 904.

[0068] To ensure the implementation of the measurement method proposed in this invention, it is required to measure the tip clearance of at least three stages of impeller disks, and each stage of impeller disk should be equipped with at least three tip clearance sensors. Therefore, this embodiment takes a three-stage impeller disk with three tip clearance sensors per stage as an example. The layout of the tip clearance sensors 101-109 is as follows: Figure 3a As shown, the blade tip clearance sensor is mounted on the casing, and is... Figure 3b As shown, Figure 3b China is Figure 3a The leftmost single-stage bladed disk is shown as an example.

[0069] The blade tip clearance sensors 101-109 are installed on the casing. Each stage of the bladed disk has three blade tip clearance sensors installed to obtain blade tip clearance data at different circumferential positions of the same stage of the bladed disk.

[0070] Nine blade tip gap sensors 101-109, a blade tip gap signal processing module 2, and a blade tip gap synchronous acquisition module 3 are connected in sequence to obtain blade tip gap data.

[0071] The same-stage impeller shaft center position inversion module 4 is used to obtain the same-stage impeller shaft center trajectory.

[0072] The same-stage bladed disk amplitude extraction module 5 is used to obtain the vibration amplitude at a single-stage bladed disk.

[0073] The frequency and phase extraction module 6 is used to obtain the vibration frequency and phase at the single-stage bladed disk.

[0074] The multi-level joint spatial mode extraction module 7 is used to obtain spatial mode functions.

[0075] The bending vibration order extraction module 8 is used to obtain the bending vibration order.

[0076] Specifically, to measure rotor bending vibration, it is necessary to determine the physical relationship between blade tip clearance and rotor bending vibration. Blade tip clearance refers to the distance between the blade tip and the casing (blade tip clearance sensor end face) when the rotor rotates. When the rotor is in bending vibration (mainly first- or second-order bending vibration), its shaft trajectory will change periodically. For the blade tip, this is equivalent to the entire shaft vibrating over time, causing the blade tip to periodically shift radially, thus resulting in periodic changes in the blade tip clearance.

[0077] Tip clearances measured at different axial positions of the rotor (multi-stage impellers) and at different circumferential positions of the same stage impeller contain projection information of the rotor's bending vibration trajectory. Tip clearances of multi-stage impellers provide axial distribution information of rotor bending vibration; the phase difference between multiple stages along the axial direction reflects the rotor's bending vibration mode. Tip clearances at different circumferential positions provide radial distribution and phase information of rotor bending vibration; differences exist between multiple tip clearance sensor measurement points along the circumference, reflecting rotor bending vibration deflection eccentricity.

[0078] By considering these blade tip clearance variations as indirect observations of the rotor's bending modal response, the corresponding rotor modal parameters (frequency, amplitude, phase, and order) can be deduced.

[0079] See Figure 4 The specific steps of the measurement method based on the above rotor bending vibration measurement system provided in this embodiment are as follows:

[0080] S1. Synchronously acquire blade tip gap data:

[0081] Simultaneously acquire all blade tip clearance sensor signals for subsequent rotor bending vibration amplitude, frequency, phase extraction, and vibration order identification. An example of the blade tip clearance sensor layout is shown in Figure 3. S2. Establish the rotor bending vibration geometric model:

[0082] Assuming the impeller is rigidly connected to the rotor, and the change in blade tip clearance originates from the rotor shaft motion, the rotor is at multiple impeller positions z1, z2, ..., z n The vibration amplitude at a certain point exhibits an axial distribution, which can be used to characterize different orders of rotor bending vibration.

[0083] Establish a spatial position model of the rotor shaft, assuming that the rotor bending vibration is of simple harmonic form, and its simple harmonic motion equation can be expressed as follows:

[0084] x(z,t)=A(z)cos(ωt+φ(z))

[0085] y(z,t)=A(z)sin(ωt+φ(z))

[0086] Where A(z) is the amplitude distribution at axial position z; ω=2πf is the angular frequency, t represents time, f is the frequency of rotor bending vibration; φ(z) is the phase at different axial positions.

[0087] S3. Invert the axis position of the single-stage bladed disk:

[0088] By using the tip clearance at different circumferential positions of the same stage impeller, the axis center trajectory of the corresponding section of the impeller is obtained. The rotor axis center position at the current section is then obtained through inversion. Assume that N tip clearance sensors are arranged on a certain stage of the rotor impeller, distributed circumferentially with angles θ1, θ2, ..., θ... N The installation position of the OPR sensor used to measure the impeller rotation speed is defined as the reference direction 0°; the corresponding tip gaps measured by the tip gap sensor are c1(t), c2(t), ..., c N (t). These blade tip clearances are caused by the offset of the rotor shaft center relative to the center of the stationary casing. That is, at a certain time t, let the set of trajectory points of the rotor shaft center relative to the center of the casing on this cross section be r(t)=(x(t),y(t)), then the blade tip clearance measured at the blade tip clearance sensor n satisfies:

[0089] c n (t)=c0-x(t)cosθ n -y(t)sinθ n

[0090] Where c0 is the static gap without vibration (which can be estimated by averaging); θ n Let t be the angle of the nth tip clearance sensor relative to the reference direction, where n = 1, 2, ..., N; x(t) and y(t) are the axis center positions (i.e., the inverted target).

[0091] Assuming N ≥ 3, the axis position can be obtained by least squares fitting, and a system of equations can be constructed.

[0092]

[0093] make Therefore, the above equation can be expressed as A·r(t)=b(t), and solving for it yields...

[0094] r(t)=(A T A) -1 A T b(t)

[0095] This allows for the reconstruction of the trajectory of the axial cross section at each time t.

[0096] S4. Extract the vibration amplitude at the single-stage bladed disk:

[0097] Plotting the x(t) and y(t) data points at different time points t as a trajectory yields the vibration trajectory of the rotor cross-section, typically elliptical. An ellipse fitting algorithm (such as least squares fitting) can then be used to obtain the principal axis direction and length, corresponding to the maximum / minimum vibration amplitude; the ellipse center, corresponding to static eccentricity; and the variations in ellipse parameters, corresponding to multi-frequency components or modulation effects. The general equation for fitting an ellipse is:

[0098] a1x 2 +a2xy+a3y 2 +a4x+a5y+a6=0

[0099] Where a1-a6 are the fitting coefficients of the ellipse equation. By fitting this trajectory point set and extracting the lengths a and b of the principal half-axis, the vibration amplitude at this stage of the bladed disk can be obtained.

[0100] S5. Extract the vibration frequency and phase at the single-stage bladed disk:

[0101] Performing a Fast Fourier Transform (FFT) on the reconstructed x(t) and y(t) sequences yields...

[0102] X(f)=F[x(t)]

[0103] Y(f)=F[y(t)]

[0104] X(f) and Y(f) are the frequency domain representations of the x(t) and y(t) sequences obtained after FFT, respectively. The dominant frequency components of X(f) and Y(f) are taken as the rotor bending vibration frequency f. b .

[0105] Alternatively, the least squares method can be used to fit the harmonic form of the function, resulting in x(t)≈A. x cos(2πf b t+φ x )

[0106] y(t)≈A y cos(2πf b t+φ y )

[0107] Among them, A x A y f represents the amplitudes of two vibrations in orthogonal directions. b Where φ is the vibration frequency. x φ y It represents the phase (which can be used to identify the order of bending vibrations).

[0108] S6. Multi-level joint spatial modal modeling and bending vibration order identification:

[0109] The axis center trajectory r at multiple axial positions i (t)=(x i (t),y i (t)) can be further used to establish spatial mode functions.

[0110]

[0111] Among them, A k(z) represents the spatial distribution of the bending modes, f k As the dominant frequency, φ k (z) represents the initial phase of the trajectory of the axis of each impeller. Figure 5 , 6 The diagrams show the first and second order mode shapes of bending vibration. Figure 5 , 6 It can be seen that there are differences in the vibration modes under different orders. Therefore, the different orders of bending vibrations such as first order and second order can be identified by equation (8).

[0112] This invention is not limited to the embodiments described above. The above description of specific embodiments is intended to illustrate and explain the technical solutions of this invention. The specific embodiments described above are merely illustrative and not restrictive. Without departing from the spirit and scope of the claims, those skilled in the art can make many specific modifications based on the teachings of this invention, and these modifications all fall within the scope of protection of this invention.

Claims

1. A rotor bending vibration measurement method based on multi-stage bladed disk tip clearance, based on a rotor bending vibration measurement system, comprising a sensor module (1), a tip clearance signal processing module (2), a tip clearance synchronous acquisition module (3), a same-stage bladed disk shaft center position inversion module (4), a same-stage bladed disk amplitude extraction module (5), a frequency and phase extraction module (6), a multi-stage joint spatial mode extraction module (7), and a bending vibration order extraction module (8) connected in sequence; the sensor module (1) consists of several tip clearance sensors; the tip clearance sensors are installed on the casing, and at least three tip clearance sensors are installed for each stage of the bladed disk, so as to... Acquire tip gap data at different circumferential positions of the same-stage bladed disk; each tip gap sensor is sequentially connected to the tip gap signal processing module (2) and the tip gap synchronous acquisition module (3) to obtain tip gap data; the same-stage bladed disk axis center position inversion module (4) is used to obtain the axis center trajectory of the same-stage bladed disk; the same-stage bladed disk amplitude extraction module (5) is used to obtain the vibration amplitude of a single-stage bladed disk; the frequency and phase extraction module (6) is used to obtain the vibration frequency and phase of a single-stage bladed disk; the multi-stage joint spatial mode extraction module (7) is used to obtain the spatial mode function; the bending vibration order extraction module (8) is used to obtain the bending vibration order; characterized in that, include: S1. Synchronously acquire blade tip clearance data: Simultaneously acquire all blade tip clearance sensor signals at the same time for subsequent rotor bending vibration amplitude, frequency, phase extraction, and rotor bending vibration order identification; S2. Establish rotor bending vibration geometric model; S3. Invert the shaft center position of a single-stage bladed disk; use the tip clearance at different circumferential positions of the same stage bladed disk to obtain the shaft center trajectory of the corresponding section of the bladed disk, and obtain the rotor shaft center position of the current section through inversion; S4. Extract the vibration amplitude at the single-stage bladed disk; S5. Extract the vibration frequency and phase at the single-stage bladed disk; S6. Multi-level joint spatial modal modeling and bending vibration order identification.

2. The rotor bending vibration measurement method based on the tip clearance of a multi-stage bladed disk according to claim 1, characterized in that, In step S2, Assuming the impeller is rigidly connected to the rotor, the change in blade tip clearance originates from the rotor shaft motion, and the rotor is positioned in multiple stages of the impeller. z 1, z 2, ..., z n The vibration amplitude at a certain point exhibits an axial distribution, which reflects the different orders of the rotor's bending vibration. Establish a geometric model of rotor bending vibration, assuming that the rotor bending vibration is in simple harmonic form, expressed as follows: x ( z , t )= A ( z )cos( ωt + φ ( z )) y ( z , t )= A ( z )sin( ωt + φ ( z )) in, A ( z ( ) represents the amplitude distribution of the rotor bending vibration at the axial position z; ω =2 πf Angular frequency, f This is the frequency of rotor bending vibration; φ ( z ) represents the phase at different axial positions.

3. The rotor bending vibration measurement method based on the tip clearance of a multi-stage bladed disk according to claim 1, characterized in that, In step S3, Suppose that a certain stage of the rotor has blades arranged on it. N Several blade tip clearance sensors are distributed circumferentially, with angles of [missing information]. θ 1, θ 2,..., θ N The installation position of the OPR sensor used to measure the impeller rotation speed is defined as the reference direction 0°; the corresponding tip gaps measured by the tip gap sensor are respectively c 1( t ), c 2( t ), ..., c N ( t These blade tip clearances are caused by the offset of the rotor shaft center relative to the center of the stationary casing, i.e., at a certain time... t Let the set of trajectory points of the rotor shaft center relative to the center of the casing on this cross section be... r ( t )=( x ( t ), y ( t Then the blade tip gap sensor n The tip clearance measured at the point satisfies: c n ( t )= c 0- x ( t )cos θ n - y ( t )without θ n in, c 0 represents the static clearance when there is no vibration, which is estimated by averaging. θ n For the first n The angle of each blade tip gap sensor relative to the reference direction; x ( t ), y ( t The axis position is the inversion target. set up N ≥3, use least squares fitting to obtain the axis position, and construct a system of equations. make , , Therefore, the above formula is expressed as A·r( t )=b( t Solving for the given information yields the following results: r( t )=( A T A ) -1 A T b( t ) That is, able to at every moment t Reconstruct the motion trajectory of the axial cross section.

4. The rotor bending vibration measurement method based on the tip clearance of a multi-stage bladed disk according to claim 1, characterized in that, In step S4, Different time points t of x ( t ), y ( t The data points are plotted as a trajectory, which is the vibration trajectory of the rotor cross-section, and is elliptical. The direction and length of the principal shaft are obtained through an ellipse fitting algorithm, corresponding to the maximum / minimum amplitude of the vibration; the center of the ellipse corresponds to static eccentricity; the changes in the ellipse parameters correspond to multi-frequency components or modulation effects; the equation of the fitted ellipse is: a 1 x 2 + a 2 xy + a 3 y 2 + a 4 x + a 5 y + a 6=0 in a 1- a 6 represents the fitting coefficient for the ellipse equation. By fitting this trajectory point set, the length of the principal semi-axis is extracted. a and b This gives the vibration amplitude at that stage of the bladed disk.

5. The rotor bending vibration measurement method based on the tip clearance of a multi-stage bladed disk according to claim 1, characterized in that, In step S5, For reconstruction x ( t ), y ( t Performing a Fast Fourier Transform (FFT) on the sequence yields: X ( f )= F [ x ( t )] Y ( f )= F [ y ( t )] in X ( f )and Y ( f ) are respectively x ( t ), y ( t The frequency domain representation of the sequence obtained after FFT is taken as follows: X ( f )and Y ( f The dominant frequency component is the rotor bending vibration frequency. f b ; Alternatively, the least squares method can be used to fit the harmonic form of the function to obtain... x ( t )≈ A x cos(2 πf b t + φ x ) y ( t )≈ A y cos(2 πf b t + φ y ) in, A x , A y These are the two vibration amplitudes in orthogonal directions. f b The vibration frequency, φ x , φ y The phase is used for identifying the order of rotor bending vibration.

6. The rotor bending vibration measurement method based on the tip clearance of a multi-stage bladed disk according to claim 1, characterized in that, In step S6, Axis center trajectory for multiple axial positions r i ( t )=( x i ( t ), y i ( t Further establish spatial mode functions in, A k ( z ( ) represents the spatial distribution of bending vibration orders. f k As the dominant frequency, φ k ( z ) represents the initial phase of the trajectory of the axis of each bladed disk; the different orders of bending vibration can be identified by the above formula.

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