CN-122021297-A - Rotating leaf disk dynamic response field reconstruction method based on tip timing test and Kalman filtering

CN122021297ACN 122021297 ACN122021297 ACN 122021297ACN-122021297-A

Abstract

The invention belongs to the field of impeller mechanical vibration analysis and response reconstruction, and provides a rotating impeller dynamic response field reconstruction method based on tip timing test and Kalman filtering. Firstly, establishing a leaf disc reduced order dynamics model, and utilizing leaf tip timing data to identify and update detuning parameters on line. And then constructing an augmentation state space model, reconstructing a global dynamic response field under unknown excitation by adopting augmentation Kalman filtering, and online estimating noise covariance by combining a moving window method to improve the anti-noise capability. Proved by experiments, the actual measurement strain error of the method is less than 10%, which indicates that the method can effectively inhibit noise and adapt to complex working conditions, and is suitable for leaf disc vibration monitoring and safety evaluation. The method can effectively solve the defect that the test only reflects the local vibration characteristic, realizes the reconstruction of the dynamic displacement field and the dynamic strain field, can effectively evaluate the vibration characteristic of the leaf disc from the angle of the integral leaf disc, and provides effective support for fatigue reliability and fault early warning of the leaf disc.

Inventors

CHEN YUGANG
LONG WEIFENG
MA XINLEI
WANG KUNPENG
LI HONGKUN

Assignees

大连理工大学

Dates

Publication Date: 20260512
Application Date: 20260128

Claims (5)

1. The rotating leaf disk dynamic response field reconstruction method based on the leaf tip timing test and the Kalman filtering is characterized by comprising the following steps of: Step 1, variable-rotation-speed rotation detuning order-reduction modeling method Firstly, fitting a quadratic polynomial of the rigidity matrix changing along with the rotation speed based on a harmonic leaf disc rigidity matrix at three characteristic rotation speeds to realize the rapid calculation of the rigidity matrix K 0 (omega) at any rotation speed, secondly, reducing the degree of freedom of a system to a modal coordinate through modal transformation, and interpolating the harmonic leaf disc characteristic value matrix lambda 0 at the three characteristic rotation speeds to obtain lambda 0 (omega) at any rotation speed so as to represent a rotation effect; Step 2, tip timing test and test parameter identification The tip timing test is carried out by firstly arranging a plurality of tip timing probes (BTT probes) in the circumferential direction of a casing of the aeroengine, and installing a key phase sensor on a rotating shaft as a time reference, after the tip timing system operates, calculating tip vibration displacement by collecting a time difference sequence of the actual time of each blade reaching each probe and the theoretical reaching time; step 3, detuning identification and model update Firstly, based on the rotational detuning blisk dynamics reduced order model which is established in the step 1 and is suitable for any rotating speed, by selecting excitation frequencies near two groups of resonance frequencies and constructing a differential equation, eliminating the influence of unknown excitation force, establishing a linear identification equation, namely a detuning identification equation, of the detuning parameters of mass and rigidity, and secondly, rewriting the detuning identification equation into a new equation Establishing a relation between the detuning parameters and the corresponding deviations, and carrying in the N groups of frequency response data measured in the step 2, so that the mass detuning parameters and the stiffness detuning parameters of all blades can be identified, thereby realizing the model updating of the dynamic reduced model of the rotary detuned blisk suitable for any rotating speed and the model updating of the dynamic equation of the blisk rotating at any rotating speed; Step 4, building an augmented state space model Firstly, reducing the degree of freedom of a system by using mode transformation of an updated dynamic equation of the blisk rotating at any rotating speed, and simplifying the system by using mode orthogonality, further representing a second-order equation into a state space form by defining a state vector, discretizing, combining the system state vector and an unknown load vector into an augmented state vector for solving the problem of unknown load in practice, thereby establishing an augmented state space model, and finally, calculating a time prediction step and a measurement update step based on an augmented Kalman filtering algorithm to provide core state input for the subsequent dynamic response field reconstruction; Step 5, dynamic response field reconstruction On the basis of the augmented state space model and the augmented Kalman filtering method established in the step 4, firstly, an augmented state vector under a modal coordinate is transformed to a physical coordinate, a displacement response state vector is extracted to reconstruct a leaf disc dynamic displacement field, then, based on a finite element strain-displacement relation, a unit strain is calculated and integrated into an integral strain field through a shape function and a jacobian matrix, finally, a moving window method is adopted to estimate and measure noise characteristics on line, and a fixed noise covariance is replaced in a Kalman filtering updating step, so that self-adaptive noise suppression is realized, and the response reconstruction precision is improved.
2. The method for reconstructing a dynamic response field of a rotary blade disk based on tip timing test and Kalman filtering according to claim 1, wherein in said step 1, the dynamic equation of the rotary blade disk rotating at an arbitrary rotation speed is expressed as ; Wherein D=C+G, C and G are respectively a damping matrix and a Kelvin matrix of the impeller, x (t) is the vibration displacement response of the impeller, 、 The second and first derivatives of x (t) are respectively, F (t) is exciting force acting on the impeller, and M and K are respectively a mass matrix and a rigidity matrix of the impeller; The mass matrix M, damping matrix C and stiffness matrix K of the rotating disk in the above description can be expressed as ; Wherein M 0 、C 0 、K 0 is a mass matrix, a damping matrix and a stiffness matrix of the tuning leaf disc respectively, and delta M, delta C and delta K respectively represent the variation of the mass matrix, the damping matrix and the stiffness matrix caused by detuning; For a blisk rotating at any rotational speed, stiffness matrix K 0 is represented as ; In the formula, 、 And For the coefficient matrix of the polynomial, Ω 1, Ω 2 and Ω 3 respectively represent 3 different rotational speeds of the blisk; Parameterizing the rotational stiffness matrix to obtain ; Wherein K is the rigidity matrix of the leaf disc, For the rotating impeller with the rotation speed between 0 and Omega max , selecting 3 different rotation speeds of Omega 0 、Ω 1 、Ω 2 , and making ; The parameterization method only needs to calculate the polynomial coefficient matrix by using the harmonic leaf disc stiffness matrix under 3 different rotating speeds 、 And Further obtaining a rigidity matrix K 0 of the harmonic leaf disc at any rotating speed; for small amount of detuning, a sub-structural mode detuning (Component Mode Mistuning, CMM) method is adopted to introduce detuning, the mode shape of the detuned impeller is approximately represented by linear superposition of the frequency-dense harmonic She Panmo mode shape, and for this purpose, the front r-order mode shape of the detuned impeller is selected The following conversion is performed ; Wherein x is a physical coordinate, and u is a modal coordinate; The above is brought into the above kinetic equation and the transpose of Φ 0 is multiplied by two sides of the equation simultaneously Obtaining a basic equation of the reduced order model: ; Wherein, lambda 0 (omega) is the eigenvalue matrix of the harmonic leaf disk, I is the identity matrix, 、、 And Representing a corresponding modal mass matrix, modal damping matrix, modal coriolis matrix, modal stiffness matrix, For the excitation force acting on the leaf disc in the modal coordinates, , Respectively is First and second derivatives of (a); let the mode shape be independent of the rotational speed, obtain Λ 0 (Ω) at any rotational speed by interpolation of the tuning disk eigenvalue matrix Λ 0 at three rotational speed points: ; wherein Λ 0 (0)、Λ 0 (Ω max /2)、Λ 0 (Ω max ) represents a harmonic disk eigenvalue matrix at rotational speeds of 0, Ω max /2, and Ω max , respectively; The rotation-induced Coriolis matrix G (omega) is ignored, and a final simplified rotation-detuned blisk dynamics reduced order model suitable for any rotation speed is further obtained: ; Where i is an imaginary unit, Omega represents exciting force frequency, namely the vibration frequency of the leaf disc, I is an identity matrix, alpha and beta are Rayleigh damping coefficients, And The stiffness mismatch parameter and the mass mismatch parameter of the nth blade are respectively, And Modal participation factors corresponding to mass and stiffness mismatch, And Representing a transpose thereof, And The modal stiffness contribution matrix and the modal mass contribution matrix of the nth blade under modal coordinates are respectively.
3. The method for reconstructing the dynamic response field of the rotary blisk based on the tip timing test and the Kalman filtering according to claim 2, wherein in the step 3, the rotary detuned blisk dynamics reduced order model suitable for any rotation speed, which is proposed in the step 1, is rewritten as ; Wherein the amount is unknown And The tuning-off parameters to be identified are; Two sets of excitation frequencies are taken near the resonance frequency to be omega j and omega k respectively, And Respectively substituting the corresponding modal coordinates into the above formula, and subtracting the two formulas to obtain a mismatch identification equation ; To simplify the expression, let ; ; The detuning identification equation is rewritten into the following form In the middle of ; ; ; Wherein L is a system matrix, T is a response vector, and the parameters in the above formula are the to-be-solved blisk detuning parameters, which are calculated by the following formula ; In the formula, the superscript '†' represents Moore-Penrose generalized inverse of the matrix, and the number of unknown quantity is N (the number of blades), so that the detuning parameters of the blisk can be obtained by solving only N groups of frequency response data measured in the step 2, and the model update of the dynamics equation of the blisk suitable for the dynamic reduced-order model update of the rotating detuned blisk at any rotating speed and the rotating blisk at any rotating speed is realized.
4. The method for reconstructing the dynamic response field of the rotary blisk based on the tip timing test and the Kalman filtering according to claim 3, wherein in the step 4, the updated dynamic equation of the rotary blisk at any rotation speed obtained in the step 3 is written as follows: ; In the formula M, D, K epsilon Respectively a system mass matrix, a damping matrix and a stiffness matrix, n s is a system freedom degree, and x (t) epsilon For the system vibration displacement vector, 、 First and second derivatives of x (t), F (t) ∈respectively Q (t) e for a load vector corresponding to all degrees of freedom of the system For a load vector corresponding to the degree of freedom of the excitation position, n p is the degree of freedom of the system excited, S p ε Selecting a matrix for excitation positions, wherein elements of the matrix consist of 0 and 1; Reducing system degrees of freedom using modal transformation, i.e Selecting the first n m -order mode of the leading system response The above updated dynamic equation of the blisk rotating at any rotational speed using the orthogonality of the system mode shape with respect to the mass matrix M is expressed as: ; Wherein p (t) ∈ For the vibration displacement vector of the system in the modal coordinates, In the form of a modal damping matrix, In the form of a modal stiffness matrix, Is a modal force vector; Defining a state vector The above equation is further expressed in the form of a state space, which is discretized to obtain a discrete model for filtering, i.e ; In the formula, And Respectively representing the measurement quantity and the system state quantity of the vibration displacement of the blade disc of the rotary blade disc blade tip timing measurement system; , W k is the model noise vector, the covariance matrix is V k is the measurement noise vector, the covariance matrix is The model noise and the measurement noise are uncorrelated Gaussian white noise processes, i.e ; Is a continuous time system matrix; t is the time step; inputting a matrix for continuous time; in order to measure the noise covariance matrix, A process noise covariance matrix; Combining the state vector z k and the load vector f k of the system in modal coordinates into an augmented state vector I.e. ; Representing the unknown load to which the system is subjected as an increment, i.e ; In the formula, Is a zero-mean random process, and the covariance matrix is , Random fluctuations of the first unknown parameter or detuned parameter; the state space model is augmented as ; In the formula, ; Augmentation of noise vectors Covariance matrix of (2) is ; In the formula, Covariance parameters corresponding to the first noise component; according to the augmented Kalman filtering method, the state estimation can be completed in two steps; Firstly, a time prediction step, namely: ; ; In the formula, A predicted value of the state at the k moment based on the information at the k-1 moment; Estimating an error covariance matrix for a priori; then the measurement update step, i.e ; ; ; In the formula, Is a Kalman gain matrix; And The error covariance matrix is updated for the state prediction error covariance matrix and the state.
5. The method for reconstructing the rotating leaf disk dynamic response field based on the tip timing test and the Kalman filtering according to claim 1, wherein in the step 5, the augmented state vector in the modal coordinate is calculated based on the solving result in the step 4 Transforming to a physical coordinate to obtain a displacement response state vector x k , and obtaining a dynamic displacement field of the rotary blade disc only by taking x k ; According to the finite element theory, the relation between the unit strain epsilon e and the node displacement delta e is that ; Wherein B is a strain-displacement matrix; b can be obtained based on the shape function and the jacobian matrix, the strain of each unit is calculated, and finally the strain field of the whole structure is obtained through integration; on-line estimation of measurement noise characteristics by using moving window method, and measurement noise covariance matrix of kth step Can be calculated by ; Wherein j represents a time step index within the moving window; In order to measure the noise substitution value, For a smooth estimation of the true value, y k is the measurement of the kth step, λ is the weighting factor, nr is the moving window length, And Respectively, measured noise substitution values A moving mean and a moving covariance matrix; In the Kalman filtering update step And the fixed measurement noise covariance R is replaced, the self-adaptive noise suppression is realized, and the reconstruction accuracy is improved.

Description

Rotating leaf disk dynamic response field reconstruction method based on tip timing test and Kalman filtering Technical Field The invention belongs to the field of impeller mechanical vibration analysis and response reconstruction, and particularly relates to a rotating impeller dynamic response field reconstruction method based on tip timing test and Kalman filtering. Background In the field of structural dynamics and state monitoring, accurate acquisition of full-field dynamic response of complex structures is a key challenge. And the response reconstruction technology constructs a mapping from local to global by fusing the finite-point data and the high-fidelity finite-element model, so as to realize high-fidelity virtual reproduction of the structure dynamic behavior. With the progress of sensing and computing technologies, the method has wide application prospects in health monitoring, vibration control and fatigue evaluation in the fields of aerospace and the like. The modal expansion method is used as a classical reconstruction method, and depends on modal coordinate recognition and vibration mode expansion, and the effect is limited by model precision and measurement signal to noise ratio. However, in the high-speed rotating machinery monitoring of aeroengine blades, etc., the method faces double challenges that firstly, the structural dynamics characteristic is changed due to the 'detuning' of blades caused by manufacturing and abrasion, the vibration localization and the frequency deviation are caused, so that the finite element analysis based on an ideal model has inherent errors and is directly used for reconstruction to generate distortion, secondly, the blade tip timing measurement is easily interfered by the fluctuation of the rotating speed and the signal noise under the actual working condition, the modal coordinate estimation precision is influenced, the reconstruction accuracy is further reduced, and even the detuning characteristic is covered after the errors are amplified by a vibration mode matrix, so that the reliability of fault diagnosis and service life prediction is seriously influenced. Therefore, it is difficult for the conventional mode expansion method to satisfy engineering accuracy requirements under the dual influence of model mismatch and measurement noise. Development of a response reconstruction method capable of simultaneously correcting model errors, suppressing noise interference and adapting to a complex operating environment has become an urgent requirement for improving the monitoring capability of the state of a rotating machine. Disclosure of Invention The invention provides a rotating leaf disk dynamic response field reconstruction method based on inter-leaf timing test and Kalman filtering, which solves the problem that the dynamic response field reconstruction precision is insufficient under multiple complex working conditions of variable rotation speed, detuning and strong noise. The invention comprises the following technical scheme: a rotating leaf disk dynamic response field reconstruction method based on a leaf tip timing test and Kalman filtering comprises the following steps: Step 1, variable-rotation-speed rotation detuning order-reduction modeling method And the vibration analysis requirement under the comprehensive action of the rotation effect and the detuning effect is considered, and a parameterization method and a substructure modal detuning method are combined to establish a rotation detuning blisk dynamics reduced order model applicable to any rotation speed. Firstly, fitting a quadratic polynomial of the rigidity matrix changing along with the rotating speed based on the rigidity matrix of the harmonic leaf disk under three characteristic rotating speeds, and realizing the rapid calculation of the rigidity matrix K 0 (omega) under any rotating speed. Secondly, the degree of freedom of the system is reduced to a modal coordinate through modal transformation, and the lambda 0 (omega) at any rotating speed is obtained through interpolation of a harmonic leaf disk eigenvalue matrix lambda 0 at three characteristic rotating speeds so as to represent the rotating effect. And finally, after ignoring the Kerr matrix, establishing a steady-state vibration equation containing the rotation rigidity change, the detuning effect and the Rayleigh damping in a reduced-order mode space to form a rotation detuned blisk dynamics reduced-order model suitable for any rotation speed. Further, in the step 1, the dynamic equation of the blisk rotating at any rotation speed can be expressed as Wherein D=C+G, C and G are respectively a damping matrix and a Kelvin matrix of the impeller, x (t) is the vibration displacement response of the impeller,、The second and first derivatives of x (t) are respectively, F (t) is the exciting force acting on the impeller, and M and K are respectively the mass matrix and the stiffness matrix of the impeller. The mass matrix M, damping