A mechanism-data fusion-driven method for reconstructing the dynamic response field of a rotating bladed disk

Abstract

The present invention belongs to the field of structural vibration state monitoring, and proposes a mechanism-data fusion-driven method for reconstructing the dynamic response field of a rotating bladed disk. The steps of this method are as follows: extracting mechanism data, tip-timing measurement and vibration parameter identification, preprocessing of tip vibration signals, and evaluation of the dynamic response field. The present invention combines the tip vibration displacement, displacement mode shape, and strain mode shape obtained from tip-timing measurement to obtain the evaluation result of the entire bladed disk response field. The key lies in that the number of degrees of freedom of the measurement points should be greater than or equal to the number of intercepted mode shapes. It can effectively solve the drawback that experimental tests only reflect local vibration characteristics, realize the reconstruction of the dynamic displacement field and the dynamic strain field, and can effectively evaluate the vibration characteristics of the bladed disk from the perspective of the overall bladed disk, providing effective support for the fatigue reliability and fault warning of the bladed disk.

Description

Technical Field

[0001] The present invention relates to the field of structural vibration state monitoring, and particularly to a mechanism-data fusion-driven method for reconstructing the dynamic response field of a rotating bladed disk. Background Art

[0002] Rotating bladed disk structures are widely used in high-end equipment such as aeroengines, steam turbines, gas turbines, and large compressors, playing an important role in energy conversion. Due to the harsh operating environment of rotating bladed disks, which need to withstand high temperatures, high pressures, and other working conditions, after long-term service, they are extremely prone to high-cycle fatigue damage, resulting in microscopic cracks or even fractures on the blades or disks. Therefore, effective vibration monitoring and condition assessment during the operation of rotating bladed disks are important means to ensure the safe and reliable operation of equipment.

[0003] Since the rotating bladed disk is in a high-speed rotating state, the available testing methods are limited. Moreover, the testing environment has harsh conditions such as high temperature and oil contamination, further restricting the selection of sensing and testing methods. As described in patents such as "Online blade vibration monitoring method based on tip-timing technology without reference signal (CN109974849B)", "Dynamic calibration method and device for a tip-timing amplitude measurement system (CN111780858A)", "A method for real-time monitoring of tip clearance measurement (CN104515474A)", "A temperature compensation method for microwave testing of engine tip clearance (CN107044835A)", etc., the vibration testing methods for rotating bladed disks are mainly divided into contact testing and non-contact testing. Contact testing mainly uses the method of pasting strain gauges, and the strain signal is transmitted to the signal acquisition system through a slip ring or a wireless telemetry system, so as to evaluate the blade vibration state through the strain. Non-contact vibration testing mainly includes methods such as tip-timing testing, tip clearance testing, and microwave testing, and the vibration state of the blade end is evaluated by installing sensors on the casing or housing.

[0004] However, although the above strain testing method has a simple testing principle, its signal transmission is relatively complex, and there are problems of low reliability and poor signal quality in a harsh working environment. Moreover, affected by signal transmission and flow field performance, it can only be pasted at limited positions. For non-contact vibration testing methods, although non-invasive testing can be performed, due to the influence of the testing principle, the sensor can only sample once per revolution. Therefore, it is usually necessary to combine a specific vibration parameter identification algorithm for signal processing to obtain available monitoring information. Summary of the Invention

[0005] To solve the above problems, the present invention provides a mechanism-data fusion-driven method for reconstructing the dynamic response field of a rotating bladed disk. This method combines non-contact tip-timing measurement and mechanism data to evaluate the response field of the entire bladed disk, can solve the influence of the difficulty in measuring unsteady aerodynamic loads on the online evaluation of bladed disk vibration, and can conduct condition evaluation from the global perspective of the entire bladed disk.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A mechanism-data fusion-driven method for reconstructing the dynamic response field of a rotating bladed disk, comprising the following steps:

[0008] Step 1: Mechanism data extraction

[0009] Since only the vibration information of limited measuring points can be obtained by simply using the experimental test method, the prior knowledge of the mechanism model can be combined to expand the experimental test information. Since the vibration displacement response of the bladed disk under external load excitation can be expressed as a linear combination of multiple modal shapes, i.e.,

[0010] u = Φμ(1)

[0011] where u is the vibration response, Φ is the modal shape, and μ is the corresponding modal coefficient. Therefore, a certain number of displacement modal shapes can be used to approximate the response of the bladed disk. Similarly, there is a similar expression for the strain response of the structure, i.e.,

[0012] ε = Vμ (2)

[0013] where V is the modal strain shape and ε is the strain response of the structure.

[0014] Therefore, in this step, modal analysis is performed on the entire bladed disk, and the corresponding modal displacement shapes and strain shapes are intercepted within a certain frequency range as mechanism data. Based on the finite element method, a finite element model of the rotating bladed disk is constructed, fixed constraints are applied at the installation surface of the rotating bladed disk, and the Block Lanczos method eigenvalue solver is used for modal analysis of the rotating bladed disk, including modal displacement and modal strain, and the modal vectors are extracted using APDL code; within the set frequency range, the modal displacement shape Φn and the modal strain shape V characterizing the vibration displacement and vibration strain characteristics are respectively intercepted as mechanism data;

[0015] Step 2: Tip-timing measurement and vibration parameter identification

[0016] Tip timing test is an effective means for rotating blade vibration analysis. By installing tip timing probes on the casing or housing, the arrival time of each blade at the probe during rotation is recorded, and a keyphasor probe is installed near the rotating shaft as the time reference for each revolution. Based on the tip timing test principle, p tip timing probes are arranged circumferentially on the rotating bladed disk to record the arrival time of the rotating blades at the tip timing probes;

[0017] One keyphasor probe is installed near the rotating shaft of the rotating bladed disk as the time reference; gas nozzles are evenly arranged at the front end of the rotating bladed disk, and continuous gas excitation is applied to the rotating bladed disk through compressed gas; when the rotating bladed disk runs at a constant speed, the NI data acquisition platform is used to collect the vibration of the rotating blades, and the vibration displacement of the rotating blades at this rotational speed is identified by combining the circumferential Fourier fitting method;

[0018] By subtracting the actual arrival time of the rotating blade from the theoretical time and combining the rotational speed at the tip of the rotating blade, the vibration displacement at the tip position of the rotating blade is obtained:

[0019] d = (t 实际 - t 理论 ) × Ω × R (3)

[0020] where t 实际 is the actual arrival time of the tip of the rotating blade at the tip timing probe, t 理论 is the theoretical arrival time of the tip of the rotating blade at the tip timing probe, Ω is the rotational angular velocity of the rotating blade, and R is the radius of the tip trajectory of the rotating blade;

[0021] Through the above method, the vibration displacement at the tip of the blade during blade rotation can be calculated. However, due to the characteristics of non-uniform undersampling of the tip timing sampling data, therefore, certain vibration parameter identification methods need to be combined to obtain the vibration parameters of the blade. Therefore, in the implementation process of the present invention, the circumferential Fourier fitting method is used for vibration parameter identification at a constant rotational speed.

[0022] When the blades vibrate synchronously at a constant speed, the vibration frequency of the blades is an integer multiple of the disk rotation frequency, that is, ω = N e × Ω, N e is the multiple frequency value. n probes are arbitrarily installed on the casing, and the relative angles of each probe are θ0, θ1,..., θ n-1 (where θ0 = 0°). Considering the synchronous vibration component dominated by a single frequency, different constant displacement values are sampled for different tip probes of a single blade

[0023]

[0024] Equation (4) can be rewritten after trigonometric transformation as

[0025]

[0026] It can be expressed in matrix form as

[0027] Y = BX (6)

[0028] where

[0029]

[0030]

[0031] Y = [y0…y n-1 T (9)

[0032] Combining the frequency doubling traversal method and the least squares method, we can obtain

[0033] X = (B T B) -1 B T Y (10)

[0034] Thus, parameters such as the blade vibration frequency, vibration amplitude, vibration phase, and vibration constant offset can be further obtained.

[0035] Step 3: Preprocessing of the tip vibration signal

[0036] For the system equivalent reduction / expansion theory, the test data needs to be the data values at the same moment. However, although the tip-timing probe can measure the circumferential vibration displacements of all tips, they are not collected at the same moment. Therefore, it is necessary to phase-shift the circumferential vibration displacements of different rotating blades after vibration parameter identification based on the vibration value of one rotating blade, and convert the tip vibration of the rotating blade into the vibration result at the same moment. The vibration phases of different rotating blades are mainly affected by two factors, namely the phase difference between the traveling wave loads and the phase difference caused by the circumferential distribution angle of the rotating blades.

[0037] The phase difference caused by the exciting load of the rotating blade is:

[0038]

[0039] where ND is the nodal diameter of the rotating blade; i refers to the current number of rotating blades, and N is the total number of rotating blades;

[0040] The phase difference caused by the distribution angle of the rotating blades on the rotating disk is:

[0041]

[0042] where N e is the excitation multiple frequency; ​

[0043] The vibration displacement equations of different rotating blades at the same moment are obtained as follows:

[0044]

[0045] Where, A i is the amplitude of the rotating blade; ω is the excitation frequency; is the initial phase; C i is the constant vibration offset;

[0046] Step 4: Dynamic response field evaluation

[0047] Since the response of the structure to the excitation can be expressed as a linear combination of multiple modal shapes. Then all degrees of freedom can be divided into tested degrees of freedom (subscript a) and untested degrees of freedom (subscript d). That is

[0048]

[0049] Where, Φ a is the modal shape subset of the tested degrees of freedom of the structure, and Φ d is the modal shape subset of the untested degrees of freedom of the structure.

[0050] Equation (14) can be expressed as the equation of the tested degrees of freedom

[0051] u a = Φ a μ (15)

[0052] Then, there is

[0053]

[0054] Where, the superscript g represents the generalized inverse matrix of the matrix. In order to obtain the response of all degrees of freedom, substituting μ obtained in formula (16) into formula (1) gives

[0055]

[0056] Combining formula (17) with formula (2) can obtain the conversion relationship from the tip displacement to the strain field as

[0057]

[0058] Through the above steps, that is, combining the tip vibration displacement, displacement modal shape and modal strain shape obtained by tip timing measurement, the evaluation result of the entire bladed disk response field is obtained. The key lies in that the number of measured degrees of freedom should be greater than or equal to the number of intercepted modal shapes.

[0059] Advantages of the present invention: The mechanism-data fusion-driven dynamic response field reconstruction method for rotating bladed disks proposed by the present invention can effectively solve the drawback that test measurements only reflect local vibration characteristics, realize the reconstruction of the dynamic displacement field and the dynamic strain field, and can effectively evaluate the vibration characteristics of the bladed disk from the perspective of the overall bladed disk, providing effective support for the fatigue reliability and fault warning of the bladed disk. Brief Description of the Drawings

[0060] Figure 1 is a schematic flow chart of the mechanism-data fusion-driven dynamic response field reconstruction method for rotating bladed disks;

[0061] Figure 2 is a diagram of the bladed disk model;

[0062] Fig. 3(a) shows the result before the tip vibration phase shift;

[0063] Fig. 3(b) shows the result after the tip vibration phase shift;

[0064] Figure 4 is the evaluation result of the dynamic displacement field;

[0065] Figure 5 is the evaluation result of the dynamic strain field. Detailed Embodiment

[0066] The following describes in detail the detailed embodiment of the present invention in combination with the technical solution and the drawings.

[0067] Step 1: Mechanism data extraction

[0068] In a specific embodiment, a rotating bladed disk with 9 sectors is taken as an example to illustrate the method, as Figure 2 shown. A finite element model of the bladed disk is constructed using finite element software, and fixed constraints are applied to the mounting surface of the bladed disk according to the actual constraint conditions. The Block Lanczos method eigenvalue solver is used to extract the modes of the rotating bladed disk, and the modal displacement mode vectors and modal strain mode vectors are output and saved as text files in combination with APDL code. The modal displacement mode vectors and modal strain mode vectors are shown in Table 1.

[0069] Table 1 Modal displacement and strain

[0070]

[0071] Step 2: Tip-timing measurement and vibration parameter identification

[0072] Based on the tip-timing measurement principle, five tip-timing probes are arranged circumferentially on the rotating bladed disk to record the moments when the rotating blades reach the probes. The relative angles of the probes are 0°, 36°, 54°, 72°, and 108° respectively. One key-phase probe is installed near the rotating shaft as the time reference. Ten gas nozzles are evenly arranged at the front end of the rotating bladed disk, and continuous gas excitation is applied to the rotating bladed disk by compressed gas with an air pressure of 0.7 MPa. When the rotating frequency of the bladed disk is 44.58 Hz, the vibration of the rotating blade is collected through the NI vibration signal acquisition platform, and the vibration displacement of the blade at this rotational speed is identified by combining the circumferential Fourier fitting method.

[0073] Step 3: Preprocessing of the tip vibration signal

[0074] Since the system equivalence / reduction method requires that the vibration test results be obtained at the same moment. Therefore, it is necessary to perform phase shift on the results obtained from the tip-timing test by combining formulas (11) - (13) to convert the tip vibration into the vibration results at the same moment. The phase shift results shown in Figure 3 are obtained.

[0075] Step 4: Evaluation of the dynamic response field

[0076] By combining the above phase-shifted vibration displacement results with the system equivalence reduction / expansion theory to expand the test results, the evaluation results of the dynamic displacement field and dynamic strain field of the bladed disk under the current excitation state can be obtained, as Figure 4 、 Figure 5 shown.

[0077] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are only used to illustrate the technical solutions of the present invention and cannot be construed as limitations on the present invention. Those of ordinary skill in the art can modify and replace the above embodiments within the scope of the present invention without departing from the principles and purposes of the present invention.

Claims

1. A mechanism-data fusion-driven method for reconstructing the dynamic response field of a rotating bladed disk, characterized in that, It includes the following steps: Step 1: Mechanism data extraction Based on the finite element method, a finite element model of the rotating bladed disk is constructed. A fixed constraint is applied at the mounting surface of the rotating bladed disk. The Block Lanczos method eigenvalue solver is used for the modal analysis of the rotating bladed disk, including modal displacement and modal strain, and the modal vectors are extracted using APDL code. The corresponding modal displacement mode shape Φn and strain modal mode shape V are intercepted within the set frequency range as mechanism data; Step 2: Tip-timing test and vibration parameter identification Based on the tip-timing test principle, p tip-timing probes are arranged circumferentially on the rotating bladed disk to record the moments when the rotating blades reach the tip-timing probes; One key-phase probe is installed near the rotating axis of the rotating bladed disk as a time reference. Gas nozzles are evenly arranged at the front end of the rotating bladed disk, and continuous gas excitation is applied to the rotating bladed disk through compressed gas. When the rotating bladed disk runs at a constant speed, the NI data acquisition platform is used to collect the vibration of the rotating blades, and the vibration displacement of the rotating blades at this rotational speed is identified by combining the circumferential Fourier fitting method; By subtracting the actual arrival time of the rotating blade from the theoretical time and combining the rotational speed of the tip of the rotating blade, the vibration displacement at the tip position of the rotating blade is obtained: d=(t 实际 -t 理论 )×Ω×R (1) where t 实际 is the moment when the tip of the rotating blade actually reaches the tip timing probe, and t 理论 is the moment when the tip of the rotating blade theoretically reaches the tip timing probe, Ω is the rotational angular velocity of the rotating blade, and R is the radius of the tip trajectory of the rotating blade; Step 3: Preprocessing of tip vibration signals The circumferential vibration displacements of different rotating blades are phase-shifted with the vibration value of one rotating blade as a reference, and the tip vibration of the rotating blade is converted into the vibration result at the same moment; The phase difference caused by the excitation load of the rotating blade is: where ND is the nodal diameter of the rotating blade; i refers to the current number of rotating blades, and N is the total number of rotating blades; The phase difference caused by the distribution angle of the rotating blades on the rotating bladed disk is: Among them, N e is the excitation frequency doubling; The vibration displacement equations of different rotating blades at the same moment are obtained as: Among them, A i is the amplitude of the rotating blade; ω is the excitation frequency; is the initial phase; C i is the constant vibration offset; Step 4: Dynamic response field evaluation Combining the above phase-shifted vibration displacement results, the test results are extended using the system equivalent reduction / expansion theory, and the evaluation results of the dynamic displacement field and dynamic strain field of the rotating bladed disk under the current excitation state are obtained according to formula (5) and formula (7); u a = Φ a μ where, Φ a is the mode subset of the structural test degrees of freedom; is the generalized inverse matrix of Φ a ; u is the vibration response; μ is the corresponding modal coefficient; Φ n is the modal displacement mode; ε = Vμ (6) Combining formula (5) and formula (6) to obtain the conversion relationship from tip displacement to strain field as: where V is the strain modal mode shape, and ε is the strain response of the structure;

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