CN115062410A - Single-sensor rotor blade multi-modal strain field reconstruction method and measurement system - Google Patents

Single-sensor rotor blade multi-modal strain field reconstruction method and measurement system Download PDF

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CN115062410A
CN115062410A CN202210628623.8A CN202210628623A CN115062410A CN 115062410 A CN115062410 A CN 115062410A CN 202210628623 A CN202210628623 A CN 202210628623A CN 115062410 A CN115062410 A CN 115062410A
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strain
modal
rotor blade
blade
mode
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乔百杰
朱昱达
罗现强
符顺国
赵峻林
陈雪峰
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Xian Jiaotong University
AECC Sichuan Gas Turbine Research Institute
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AECC Sichuan Gas Turbine Research Institute
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Abstract

The method comprises the steps of establishing a three-dimensional finite element model of the rotor blade to be measured, drawing a Campbell diagram according to modal analysis at different rotating speeds, satisfying the multi-modal vibration of the blade, and extracting modal parameters of the finite element model of the blade; determining the installation position and direction of a single strain gauge sensor based on the blade modal parameters; respectively calculating the transfer ratio of the position strain of the single measuring point of the blade to the full-field strain according to different modal orders; after the rotor blade is provided with the strain gauge, a high-rotating-speed blade multi-mode test is carried out, and the limited dynamic strain measured by the strain gauge when the blade generates multi-mode vibration is obtained; carrying out Fourier transform on the measured dynamic strain response, and decoupling to obtain amplitude and phase corresponding to each order mode; and based on the transfer ratio of each order of mode and corresponding amplitude and phase information, performing inversion reconstruction to obtain the full-field dynamic strain of the rotor blade.

Description

Single-sensor rotor blade multi-modal strain field reconstruction method and measurement system
Technical Field
The invention belongs to the technical field of dynamic strain measurement of rotor blades of aero-engines and gas turbines, and particularly relates to a method and a system for reconstructing a multi-modal strain field of a rotor blade of a single sensor.
Background
The rotor blade is used as an important component of rotary machinery such as an aircraft engine, a gas turbine and the like, and the integrity of the high-speed rotary blade directly influences the safe operation of the whole structure of the rotary machinery. Under severe working environments such as high temperature, high pressure, high rotating speed and the like, the blades are subjected to alternating loads of flow field and rotor vibration in the service process, and large stress is easily generated to cause the vibration fatigue failure of the blades. In addition, when the excitation frequency coincides with the modal frequency of multiple orders (not less than 2 orders of modes) of the blade, the blade can generate multi-modal vibration, and the maximum stress point of the blade changes in two dimensions of space and time. In order to accurately predict the fatigue life of the blade, the full-field dynamic strain of the multi-mode vibration blade needs to be accurately obtained. At present, the most common method for measuring the stress/strain of the blades of the aeroengine in China is to adhere strain gauges to the surfaces of the blades, wherein the number of sensors is not less than the number of modes to be concerned, however, the measurement process of the strain gauges is easy to lose effectiveness and causes the limitation of mass addition, and the arrangement of too many strain gauges on the blades is inconvenient. Therefore, the real stress/strain level and the vibration parameters of the whole rotor blade under multi-mode vibration are obtained, the method plays an important role in design, manufacture and safety application of complex rotating machinery such as aeroengine blades, gas turbines and the like, and is a key technology for improving the working stability and reliability.
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 well known to those of ordinary skill in the art.
Disclosure of Invention
Aiming at the problem that the number of sensors is not lower than the number of modes to be paid attention to in the prior art, the invention provides a method and a system for reconstructing a multi-mode strain field of a single-sensor rotor blade.
In order to achieve the above purpose, the invention provides the following technical scheme:
the invention discloses a single-sensor rotor blade multi-modal strain field reconstruction method, which comprises the following steps:
in the first step, a three-dimensional finite element model of a rotor blade to be measured is established, a Campbell diagram is drawn through mode analysis under different rotating speeds, multi-mode vibration of the blade is met, and mode parameters of the three-dimensional finite element model are extracted;
in the second step, the position and the direction of a measuring point installed by a single strain gauge sensor are determined based on the modal parameters;
in the third step, respectively calculating the strain-strain response transfer ratio of the position of the measuring point of the rotor blade relative to the full field based on different modal orders;
in the fourth step, after the rotor blade is provided with the strain gauge sensor, a high-speed multi-mode test is carried out, and the dynamic strain measured by the strain gauge sensor when the rotor blade generates multi-mode vibration is obtained;
in the fifth step, Fourier transform is carried out on the dynamic strain, and amplitude and phase corresponding to each order of mode are obtained through decoupling;
and in the sixth step, based on the amplitude and the phase corresponding to the strain-strain response transfer ratio and each order of mode, carrying out inversion reconstruction to obtain the full-field dynamic strain of the rotor blade.
In the multi-modal strain field reconstruction method for the single-sensor rotor blade, in the first step, a three-dimensional geometric model of the rotor blade to be measured is established according to size parameters of the rotor blade, the three-dimensional finite element model of the rotor blade is established based on a finite element division grid of the three-dimensional geometric model, a Campbell diagram is drawn according to modal analysis of the three-dimensional finite element model at different rotating speeds, multi-modal vibration of the blade is determined through the Campbell diagram, modal parameters of the finite element model are extracted according to the multi-modal vibration parameters, and the frequency corresponding to the intersection point of excitation order EO and the natural frequency in the Campbell diagram is f i ＝EO*f r (ii) a The multi-modal blade vibration is represented in the Campbell diagram at the rotation speed f r There are two or more resonance intersections and the ratio of the excitation order corresponding to each resonance intersection is a rational number N, i.e. EO j /EO i ＝N，EO i For excitation order corresponding to i-th mode, EO j The excitation order corresponding to the j-th order mode.
In the multi-modal strain field reconstruction method for the single-sensor rotor blade, in the first step, the front N of the finite element model is extracted according to the multi-modal vibration parameters m Order modal parameters including modal frequency f i Size of N dof X 1 strain mode psi i ，N dof Is the number of degrees of freedom, and constructs the full-field strain mode vibration mode of the rotor blade
Figure BDA0003676906140000031
Having a size of N dof ×N m ，N dof ＝6*N n ，N m Representing modal order, N n Representing the total node number of the three-dimensional finite element model after meshing; the strain of each node comprises 3 principal strains epsilon x ，ε y ，ε z And 3 shear strains gamma xy ，γ yz ，γ xz For a total of 6 strain components.
In the multi-modal strain field reconstruction method for the single-sensor rotor blade, in the second step, the rotor blade to be measured is based onN before slice m The position and the direction of a measuring point pasted by a single strain gauge sensor are determined by the order full-field strain mode vibration mode, so that the measuring point response of the strain gauge sensor comprises multimode vibration modal components of each order of the blade and avoids the position of the maximum stress point of each order of the modal.
In the multi-modal strain field reconstruction method for the rotor blade with the single sensor, in the third step, a measuring point selection matrix is constructed from a full-field strain modal shape based on the position of a measuring point installed on the strain gauge sensor
Figure BDA0003676906140000032
Size of 1 XN m ，
Figure BDA0003676906140000033
Indicates the Nth after screening m Strain mode of order, and calculating the strain-strain transfer ratio between different positions of the blade according to different modal orders
Figure BDA0003676906140000041
Wherein
Figure BDA0003676906140000042
Indicating the use of Nth of a single sensor p m Order strain mode shape.
In the method for reconstructing the multi-modal strain field of the rotor blade with the single sensor, in the fourth step, a high-speed test of the rotor blade is carried out, and dynamic strain of a blade measuring point is obtained by combining a slip ring current inducer when the rotor blade generates multi-modal vibration
Figure BDA0003676906140000043
t represents the time until multi-modal vibration of the rotor blade occurs, q i (t) represents the modal engagement quantity of the ith order.
In the multi-modal strain field reconstruction method for the single-sensor rotor blade, in the fifth step, the dynamic strain of the measuring point is subjected to Fourier transform
Figure BDA0003676906140000044
Wherein, f isShowing frequency (Hz), and obtaining amplitude A corresponding to each order mode through decoupling calculation i | s (f) | and phase phi i ＝φ(2πf)。
In the multi-modal strain field reconstruction method for the single-sensor rotor blade, in the sixth step, based on the strain-strain transfer ratio T of each order mode and the amplitude A and the phase phi, all node strains on the surface and in the inner part of the blade are subjected to a formula when the rotating blade generates multi-modal vibration at the moment T
Figure BDA0003676906140000045
Inversion reconstruction is carried out to obtain the full-field dynamic strain of the rotor blade,
Figure BDA0003676906140000046
the reconstruction strain
Figure BDA0003676906140000051
Including positive and shear strains, where ε i，x Representing the strain in the x-direction of node i, gamma i，xy Represents the xy direction shear strain of the i-node.
A measuring system for implementing the multi-mode strain field reconstruction method of the single-sensor rotor blade comprises,
a finite element analysis module configured to construct a rotor blade finite element model and generate modal parameters and pitch diameter information for a rotor blade based on the rotor blade finite element model;
the dynamic strain vibration measurement module is connected with a strain gauge sensor and a slip ring current leading device to measure the dynamic strain of a blade measurement point when the rotor blade generates multi-mode vibration t
Figure BDA0003676906140000052
The amplitude and phase calculation module is connected with the dynamic strain vibration measurement module to decouple the dynamic strain to obtain amplitudes A corresponding to each order mode i And phase phi i ；
A computing unit connected with the dynamic strain vibration measurement module, the computing unit comprises,
finite element componentAn analysis module configured to construct a rotor blade finite element model and generate a Campbell diagram based on the rotor blade finite element model, the finite element analysis module extracting a rotor blade front N according to the multi-modal vibration parameters m Order mode frequency f i And strain mode vibration psi i Constructing a full-field strain mode vibration matrix of the rotor blade
Figure BDA0003676906140000053
A measurement point optimization module configured to optimize the measurement point based on the front N of the rotor blade to be measured m Determining the position and the direction of a measuring point pasted by a single strain gauge sensor according to the order full-field strain mode vibration mode;
each order modal transfer ratio calculation module is configured to calculate the strain-strain response transfer ratio of the position of the measuring point of the rotor blade relative to the whole field based on different modal orders;
and the strain field reconstruction module is connected with the transfer ratio calculation module of each order of modes and the amplitude and phase calculation module so as to perform inversion reconstruction to obtain the full-field dynamic strain of the rotor blade based on the amplitude and the phase corresponding to the strain-strain response transfer ratio and each order of modes.
In the technical scheme, the multimode strain field reconstruction method for the rotor blade of the single sensor and the electric card material have the following beneficial effects: the invention can realize the measurement of the integral dynamic strain field of the rotating blade under multi-mode vibration by only utilizing a single strain sensor. The method can realize measurement of dynamic strain on the surface of the blade and measurement of positive strain and shear strain of internal nodes of the blade. The method provided by the invention has high measurement precision, and the Campbell chart is drawn based on finite element modal analysis results of different rotating speeds to meet the requirement of multi-modal vibration of the blade; secondly, optimizing the mounting position of a single strain gauge based on multi-modal vibration parameters, and ensuring that the vibration response of the blade at the measuring point contains the modal participation of each order of multi-modal vibration; then respectively calculating the transfer ratio between different positions of the blade according to different modal orders; and then obtaining amplitude and phase information under multiple modes by decoupling response of the measuring points, and finally obtaining the full-field dynamic strain of the rotor blade by combining transfer ratio inversion reconstruction. The single-sensor rotor blade multi-mode dynamic strain field reconstruction system provided by the invention is simple in process and easy to realize.
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In order to more clearly illustrate the embodiments of the present application or technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present invention, and other drawings can be obtained by those skilled in the art according to the drawings.
FIG. 1 is a schematic flow diagram of a single-sensor rotor blade multi-modal strain field reconstruction method provided by the invention;
FIG. 2 is a schematic structural diagram of a multi-modal strain field reconstruction system for a single sensor rotor blade provided by the present invention;
3(a) -3 (b) are models of rotor blades built in one embodiment, wherein FIG. 3(a) is a three-dimensional geometric model of a rotor blade; FIG. 3(b) is a finite element meshing model;
FIG. 4 is a campbell diagram of a rotor blade according to an embodiment;
FIGS. 5(a) through 5(b) are front second order strain mode diagrams of the blade according to an embodiment, wherein FIG. 5(a) shows a first order strain mode and FIG. 5(b) shows a second order strain mode;
FIG. 6 is a schematic view of the installation position direction of the measuring points of the strain gauge of the rotor blade in one embodiment, wherein the measuring point A of the blade basin is the installation position of the strain gauge, and two positions of the measuring point B, C are reconstruction result reference points;
FIG. 7 is a phase frequency plot of a single strain sensor measurement dynamic strain response and its Fourier transform of a rotor blade according to one embodiment;
8(a) to 8(B) are comparison results of multi-modal dynamic strain reconstruction results of a single strain sensor of a rotor blade and experimental results in one embodiment, wherein FIG. 8(a) is comparison results of measurement point reconstruction and real strain of a rotor blade B, and FIG. 8(B) is comparison results of measurement point reconstruction and real strain of a rotor blade C.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
Thus, the following detailed description of the embodiments of the present invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
In the description of the present invention, it is to be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", and the like, indicate orientations and positional relationships based on those shown in the drawings, and are used only for convenience of description and simplicity of description, and do not indicate or imply that the equipment or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be considered as limiting the present invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.
In the present invention, unless otherwise explicitly stated or limited, the terms "mounted," "connected," "fixed," and the like are to be construed broadly, e.g., as being permanently connected, detachably connected, or integral; they may be directly connected or indirectly connected through intervening media, or may be connected through the use of two elements or the interaction of two elements. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the present invention, unless otherwise expressly stated or limited, "above" or "below" a first feature means that the first and second features are in direct contact, or that the first and second features are not in direct contact but are in contact with each other via another feature therebetween. Also, the first feature being "on," "above" and "over" the second feature includes the first feature being directly on and obliquely above the second feature, or merely indicating that the first feature is at a higher level than the second feature. "beneath," "under" and "beneath" a first feature includes the first feature being directly beneath and obliquely beneath the second feature, or simply indicating that the first feature is at a lesser elevation than the second feature.
In order to make the technical solutions of the present invention better understood, those skilled in the art will now describe the present invention in further detail with reference to the accompanying drawings.
In one embodiment, as shown in fig. 1 to 8(b), the method includes,
in the first step S1, a three-dimensional finite element model of the rotor blade to be tested is established, a Campbell diagram is drawn according to modal analysis results at different rotating speeds, multi-modal vibration of the blade is met, and modal parameters of the finite element model of the blade are extracted;
in a second step S2, the installation position and orientation of the single strain gauge sensor are determined based on the blade modal parameters;
in a third step S3, respectively calculating the strain-strain transfer ratio of the blade measuring point position relative to the whole field according to different modal orders;
in a fourth step S4, after mounting the strain gauge on the rotor blade, performing a high-speed multi-modal test to obtain the finite dynamic strain measured by the strain gauge when the blade generates multi-modal vibration;
in a fifth step S5, performing fourier transform on the measured dynamic strain response, and performing decoupling to obtain an amplitude and a phase corresponding to each order of mode;
in a sixth step S6, based on the transfer ratios of the modes of the above-mentioned orders and the corresponding amplitude and phase information, an inversion reconstruction is performed to obtain the full-field dynamic strain of the rotor blade.
In the method, in the first step, a three-dimensional geometric model of the rotor blade to be measured is established according to the size parameters of the rotor blade, finite element software is used for dividing grids to establish a finite element model of the rotor blade, a Campbell diagram is drawn according to the modal analysis result of the finite element model at different rotating speeds, the multi-modal vibration of the blade is determined through the Campbell diagram, and the modal parameters of the finite element model are extracted according to the multi-modal parameters. The intersection of the Excitation Order (EO) and the natural frequency in the Campbell diagram may be the blade reaching resonance, corresponding to a frequency f i ＝EO*f r (ii) a The multi-modal vibration of the blade is shown in the Campbell diagram at a certain rotation speed (f) r ) There are two or more resonance intersections and the ratio of the excitation order corresponding to each resonance intersection is a rational number N, i.e. EO j /EO i ＝N，EO i For excitation order corresponding to i-th mode, EO j The excitation order corresponding to the j-th order mode.
In the method, in the first step, the front N of the finite element model is extracted according to multi-mode vibration parameters of the blade m Order modal parameters including modal frequency f i Size of N dof X 1 strain mode psi i ，N dof Is the number of degrees of freedom, constructs the full-field strain mode vibration matrix of the rotor blade
Figure BDA0003676906140000101
It is largeIs as small as N dof ×N m ，N dof ＝6*N n ，N n Representing the total number of nodes of the finite element model after meshing; the strain of each of the nodes comprises 3 principal strains epsilon x ，ε y ，ε z And 3 shear strains gamma xy ，γ yz ，γ xz For a total of 6 strain components.
In the method, in the second step, the front N of the rotor blade to be tested is based on m The sticking position and the sticking direction of a single strain gauge are determined by the order full-field strain mode vibration mode, so that the strain gauge measuring point is ensured to respond to each order mode component containing multi-mode vibration of the blade, and the position of the maximum stress point of each order mode is avoided.
In the method, in the third step, based on the position of a single strain gauge measuring point, a measuring point selection matrix is constructed from a full-field strain mode shape
Figure BDA0003676906140000102
Size of 1 XN m Respectively calculating the strain-strain transmission ratio between different positions of the blade according to different modal orders
Figure BDA0003676906140000111
Wherein
Figure BDA0003676906140000112
Indicating the use of Nth of a single sensor p m Order strain mode shape.
In the method, in the fourth step, a high-speed test of the rotor blade is carried out, and the dynamic strain of a blade measuring point is obtained by combining a single strain gauge of a slip ring current leading device when the blade generates multi-mode vibration
Figure BDA0003676906140000113
t represents the time until multi-modal vibration of the rotor blade occurs.
In the fifth step of the method, any periodic signal can be expanded into superposition of a plurality of simple harmonic signals according to the Fourier series theory
Figure BDA0003676906140000114
Fourier transform of the measured dynamic strain response
Figure BDA0003676906140000115
Wherein f represents frequency (Hz), and amplitude A corresponding to each order mode is obtained by decoupling calculation i | s (f) | and phase phi i ＝φ(2πf)。
In the method, in the sixth step, based on the transmission ratio T of each order mode and the corresponding amplitude A and phase phi information, all node strains on the surface and in the interior of the blade are processed by a formula when the rotating blade generates multi-mode vibration at the time T
Figure BDA0003676906140000116
Obtaining full-field dynamic strain of rotor blade by inversion reconstruction
Figure BDA0003676906140000117
The reconstruction strain
Figure BDA0003676906140000121
Including positive and shear strains.
For further understanding of the invention, in an embodiment, fig. 1 is a flowchart of a multi-modal edge field reconstruction method for a single-sensor rotor blade according to the invention, the method decouples multi-modal vibration strain responses of a blade measured at a single point, calculates to obtain amplitudes and phases corresponding to each order mode, and finally performs inversion reconstruction to obtain full-field dynamic strain of the rotor blade based on transfer ratios of different orders of the multi-modal and corresponding amplitude phase information; FIG. 2 is a schematic structural diagram of a single-sensor rotor blade multi-modal fringing field reconstruction system provided by the invention. The method comprises the following specific steps:
1) and establishing a three-dimensional geometric model of the rotor blade, importing finite element software to divide a grid, and establishing a finite element model of the rotor blade. Referring to FIG. 3(a), a CAD model was generated using three-dimensional modeling software based on the rotor blade geometry parameters, where the blade was 52.5mm long, 2mm thick and 20mm wide. Since the simulated rotor has a circularly symmetric structure, 1/5 sectors can be taken for analysis, and then the CAD model is imported into ANSYS finite element analysis software to build a three-dimensional finite element model of the rotor blade, as shown in FIG. 3(b), wherein the finite element type selects SOLID186 SOLID elements, and 2904 elements and 15301 nodes are counted after meshing. The rotor blade has a rotation radius of 82mm, and is made of high-temperature alloy GH4169, a density of 8240kg/m3, a Poisson ratio of 0.3 and an elastic modulus of 1.95 GPa.
Modal analysis of the blade at different speeds, considering the centrifugal effect, the natural frequency increases with increasing speed, the Campbell chart is drawn according to the natural frequency at different speeds as shown in FIG. 4. the example rotor blade has two intersections of first order-EO 4 and second order-EO 12 at a speed of about 9840RPM, and the blade generates multi-modal resonance at the same time, and the corresponding frequencies are f 1 ＝656Hz，f 2 1968Hz, and f 2 ÷f 1 Satisfying the multimodal frequency ratio as rational number 3.
Extracting modal parameters of multi-modal generation of rotor blade, namely N, by using ANSYS modal analysis m 2: modal frequency f i Size of N dof X 1 strain mode psi i Wherein the first N m Fig. 5(a) and 5(b) show 2-section strain mode vibration members, and a rotor blade full-field strain mode vibration matrix is constructed
Figure BDA0003676906140000131
Having a size of N dof ×N m ，N dof ＝6*N n ，N n Representing the total number of nodes of the finite element model after meshing; the strain of each of the nodes comprises 3 principal strains epsilon x ，ε y ，ε z And 3 shear strains gamma xy ，γ yz ，γ xz For a total of 6 strain components.
2) And determining the position and the direction of a strain measuring point of the rotor blade according to the strain vibration mode distribution of the rotor blade modal analysis, and ensuring that the strain gauge measuring point responds to each order of modal components including multi-modal vibration of the blade. According to the first N of interest of the rotor blade m In the present case, the mounting position of the single strain gage on the rotor blade is determined as shown in fig. 6, wherein the strain is 2-order modal parametersThe pasting position of the strain gauge should avoid the maximum strain distribution gradient area, namely the position A of the position where the strain gauge is pasted on the blade root is usually selected to be pasted on the next largest strain point, and the rest points B and C are used as reference points for reconstruction result evaluation.
3) Respectively calculating the transmission ratio between different positions of the blade according to different modal orders: selecting a matrix psi from a measuring point of a full-field strain mode shape structure based on a rotor blade finite element model node number 1772 corresponding to the position of the A point p ＝[-0.51786 -1.05550]Calculating the transfer ratios T with respect to the points B and C, respectively B ＝[-1.29800 0.01869]，T C ＝[-0.22056 0.14838]。
4) After the rotor blade is provided with the strain gauge, a high-speed multi-mode test is carried out, and the dynamic strain of a blade measuring point is obtained by combining the single strain of a slip ring current leading device when the blade generates multi-mode vibration
Figure BDA0003676906140000132
Wherein the sampling frequency fs is 16384, and the sampling time interval t epsilon [0, 0.6]s, then Fourier transforming the measured dynamic strain response
Figure BDA0003676906140000133
Wherein f represents frequency (Hz), and amplitude A corresponding to each order mode is obtained by decoupling calculation i And phase phi i As shown in fig. 7.
5) Based on the transmission ratio of each order mode and corresponding amplitude and phase information, inversion reconstruction is carried out to obtain the full-field dynamic strain of the rotor blade: based on the transmission ratio T ═ T [ T ] of the reference point B, C corresponding to the previous two-order mode at the point a strain gage installation position B ，T C ]And corresponding amplitude A and phase phi information, when the rotating blade generates multi-mode vibration at the moment T, all node strains on the surface and the inner part of the blade are changed into T & s through a formula s A (t), obtaining the full-field dynamic strain s (t) of the rotor blade by inversion reconstruction B ，s C ]As shown in fig. 8(a) to 8(b), the reconstructed dynamic strain signal highly coincides with the true dynamic strain, and is hardly distinguishable. Therefore, the method for measuring the dynamic strain field of the rotating blade provided by the invention can be used for measuring the dynamic strain field of the rotating blade with high precisionAnd reconstructing a dynamic strain field of the blade.
The multi-mode dynamic strain field reconstruction method of the rotor blade provided by the invention can realize measurement of the whole dynamic strain field of the rotating blade under multi-mode vibration by only using a single strain sensor. The method can realize measurement of dynamic strain on the surface of the blade and measurement of positive strain and shear strain of internal nodes of the blade. The method provided by the invention has high measurement precision and saves a large number of strain gauges. The single-sensor rotor blade multi-mode dynamic strain field reconstruction system provided by the invention is simple in process and easy to realize. 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.
Finally, it should be noted that: the described embodiments are only some of the present application, not all embodiments, and all other embodiments that can be obtained by one skilled in the art without inventive efforts based on the embodiments in the present application are within the scope of protection of the present application.
While certain exemplary embodiments of the present invention have been described above by way of illustration only, it will be apparent to those of ordinary skill in the art that the described embodiments may be modified in various different ways without departing from the spirit and scope of the present invention. Accordingly, the drawings and description are illustrative in nature and should not be construed as limiting the scope of the invention.

Claims (9)

1. A single-sensor rotor blade multi-modal strain field reconstruction method is characterized by comprising the following steps:
in the first step (S1), a three-dimensional finite element model of a rotor blade to be tested is established, mode analysis is carried out at different rotating speeds so as to draw a Campbell diagram and meet multi-mode vibration of the blade, and mode parameters of the three-dimensional finite element model are extracted;
in a second step (S2), determining the position and the direction of a measuring point of a single strain gauge sensor installation based on the modal parameters;
in the third step (S3), respectively calculating the strain-strain response transfer ratio of the position of the measuring point of the rotor blade relative to the full field based on different modal orders;
in the fourth step (S4), a high-speed multi-modal test is performed after the rotor blade is mounted with the strain gauge sensor, and the dynamic strain measured by the strain gauge sensor when the rotor blade generates multi-modal vibration is obtained;
in the fifth step (S5), Fourier transform is carried out on the dynamic strain, and amplitude and phase corresponding to each order of mode are obtained through decoupling;
in the sixth step (S6), based on the amplitude and phase of the strain-strain response transfer ratio corresponding to each order mode, the full-field dynamic strain of the rotor blade is obtained through inversion reconstruction.
2. The method for reconstructing the multi-modal strain field of a single-sensor rotor blade as claimed in claim 1, wherein in the first step (S1), preferably, a three-dimensional geometric model of the rotor blade to be measured is established according to the dimensional parameters of the rotor blade, a three-dimensional finite element model of the rotor blade is established based on the finite element mesh division of the three-dimensional geometric model, a campbell diagram is drawn according to the modal analysis result of the three-dimensional finite element model at different rotation speeds, multi-modal vibration of the blade is determined through the campbell diagram, the modal parameters of the finite element model are extracted according to the multi-modal vibration parameters, and the frequency corresponding to the intersection point of excitation order EO and the natural frequency in the campbell diagram is f i ＝EO*f r (ii) a The multi-modal blade vibration is represented in the Campbell diagram at the rotation speed f r There are two or more resonance intersections and the ratio of the excitation order corresponding to each resonance intersection is a rational number N, i.e. EO j /EO i ＝N，EO i For excitation order corresponding to i-th mode, EO j The excitation order corresponding to the j-th order mode.
3. The method of claim 2, wherein in the first step (S1), the first N of the finite element model is extracted according to the multi-modal vibration parameters m Order modal parameters including modal frequency f i Size of N dof X 1 strain mode psi i ，N dof Is the number of degrees of freedom, and constructs the full-field strain mode vibration mode of the rotor blade
Figure FDA0003676906130000021
With a size of N dof ×N m ，N dof ＝6*N n ，N m Representing modal order, N n Representing the total number of nodes of the three-dimensional finite element model after meshing; the strain of each node comprises 3 principal strains epsilon x ，ε y ，ε z And 3 shear strains gamma xy ，γ yz ，γ xz For a total of 6 strain components.
4. The method for reconstructing the multi-modal strain field of a single sensor rotor blade as claimed in claim 3, wherein in the second step (S2), the method is based on the front N of the rotor blade to be measured m The position and the direction of a measuring point pasted by a single strain gauge sensor are determined by the order full-field strain mode vibration mode, so that the measuring point response of the strain gauge sensor comprises multimode vibration modal components of each order of the blade and avoids the position of the maximum stress point of each order of the modal.
5. The method for reconstructing the multi-modal strain field of the single-sensor rotor blade according to claim 4, wherein in the third step (S3), a measurement point selection matrix is constructed from a full-field strain modal shape based on the measurement point positions where the strain gauge sensors are installed
Figure FDA0003676906130000022
Size of 1 XN m ，
Figure FDA0003676906130000023
Indicates the Nth after screening m Strain mode of order, and calculating the strain-strain transfer ratio between different positions of the blade according to different modal orders
Figure FDA0003676906130000031
Wherein
Figure FDA0003676906130000032
Indicating the use of Nth of a single sensor p m Order strain mode shape.
6. The method for reconstructing the multi-modal strain field of the single-sensor rotor blade as claimed in claim 5, wherein in the fourth step (S4), a high-speed test of the rotor blade is carried out, and a slip ring current-guiding device is combined to obtain the dynamic strain of the blade measuring point when the multi-modal vibration of the rotor blade occurs
Figure FDA0003676906130000033
t represents the time until multi-modal vibration of the rotor blade occurs, q i (t) represents the modal engagement quantity of the ith order.
7. The method for reconstructing the multi-modal strain field of the single-sensor rotor blade as claimed in claim 6, wherein in the fifth step (S5), the dynamic strain of the measuring point is Fourier transformed
Figure FDA0003676906130000034
Wherein f represents frequency (Hz), and amplitude A corresponding to each order mode is obtained by decoupling calculation i | s (f) | and phase phi i ＝φ(2πf)。
8. The method for reconstructing the multi-modal strain field of the single-sensor rotor blade as claimed in claim 7, wherein in the sixth step (S6), based on the strain-strain transfer ratio T of each order mode and the amplitude A and the phase phi, all the node strains on the surface and inside of the blade when the multi-modal vibration occurs on the rotating blade at the time T are represented by the formula
Figure FDA0003676906130000035
Inversion reconstruction is carried out to obtain the full-field dynamic strain of the rotor blade,
Figure FDA0003676906130000036
the reconstruction strain
Figure FDA0003676906130000041
Including positive and shear strains, where ε i，x Representing the strain in the x-direction of node i, gamma i，xy Represents the xy direction shear strain of the i-node.
9. A measurement system implementing the method of single sensor rotor blade multi-modal strain field reconstruction of any of claims 1-8, comprising,
a finite element analysis module configured to construct a rotor blade finite element model and generate modal parameters and pitch diameter information for a rotor blade based on the rotor blade finite element model;
the dynamic strain vibration measurement module is connected with a strain gauge sensor and a slip ring current leading device to measure the dynamic strain of a blade measurement point when the rotor blade generates multi-mode vibration t
Figure FDA0003676906130000042
The amplitude and phase calculation module is connected with the dynamic strain vibration measurement module to decouple the dynamic strain to obtain amplitudes A corresponding to each order mode i And phase phi i ；
A computing unit connected with the dynamic strain vibration measurement module, the computing unit comprising,
a finite element analysis module configured to construct a rotor blade finite element model and generate a Campbell diagram based on the rotor blade finite element model, the finite element analysis module extracting a rotor blade front N according to the multi-modal vibration parameters m Modal frequency f of order i And strain mode vibration psi i Constructing a rotor blade full-field strain mode vibration matrix
Figure FDA0003676906130000043
A measurement point optimization module configured to optimize the measurement point based on the front N of the rotor blade to be measured m Determining the position and direction of a measuring point stuck to a single strain gauge sensor by the order full-field strain mode vibration mode;
each order modal transfer ratio calculation module is configured to calculate the strain-strain response transfer ratio of the position of the measuring point of the rotor blade relative to the whole field based on different modal orders;
and the strain field reconstruction module is connected with the transfer ratio calculation module of each order of modes and the amplitude and phase calculation module so as to perform inversion reconstruction to obtain the full-field dynamic strain of the rotor blade based on the amplitude and the phase corresponding to the strain-strain response transfer ratio and each order of modes.
CN202210628623.8A 2022-06-02 2022-06-02 Single-sensor rotor blade multi-modal strain field reconstruction method and measurement system Pending CN115062410A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115840139A (en) * 2023-02-14 2023-03-24 济宁矿业集团海纳科技机电股份有限公司 Rotor production quality detection system for motor

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115840139A (en) * 2023-02-14 2023-03-24 济宁矿业集团海纳科技机电股份有限公司 Rotor production quality detection system for motor
CN115840139B (en) * 2023-02-14 2023-05-26 山东海纳智能装备科技股份有限公司 Rotor production quality detection system for motor

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