CN109883379B - Blade displacement strain measurement method based on modal shape - Google Patents
Blade displacement strain measurement method based on modal shape Download PDFInfo
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Abstract
The invention discloses a blade displacement strain measurement method based on modal shape, which comprises the following steps: establishing a three-dimensional finite element model of the blade to be measured, and generating a displacement mode vibration mode and a strain mode vibration mode based on the three-dimensional finite element model; arranging a measuring unit at a predetermined measuring point of the blade, measuring blade displacement u (t) and/or strain s (t), and determining the vibration mode order of the blade; and establishing a mapping relation between the displacement u (t) of the measuring points and the full-field strain and displacement and/or a mapping relation between the strain s (t) of the measuring points and the full-field strain and displacement to obtain a strain-displacement conversion coefficient matrix so as to measure the full-field strain or displacement of the blade.
Description
Technical Field
The invention belongs to the technical field of blade vibration testing of aero-engines and gas turbines, and particularly relates to a blade displacement strain measurement method based on modal vibration modes.
Background
The integrality of the high-speed rotating blade directly influences the safe operation of the whole structure of the aircraft engine, and is influenced by factors such as harsh working environment, strong load alternation and the like, and the high-speed rotating blade is very easy to generate vibration fatigue cracks in the service process to cause serious accidents. High cycle fatigue caused by excessive blade vibration is the primary failure mode of an aircraft engine blade. The high cycle fatigue of the blade is mainly caused by dynamic stress caused by various pneumatic loads and mechanical loads, a large number of cycles can be accumulated in a short time to generate fatigue cracks, and particularly, the dynamic stress is easy to cause fatigue failure of the blade when the blade resonates. In the process of developing and producing an aircraft engine, blade vibration needs to be measured in order to master the vibration characteristics of the blades. For a long time, the aeroengine blade realizes dynamic strain measurement by sticking a strain gauge on the surface of a rotating blade, which can only measure the dynamic strain of limited blade at limited position, and has low reliability and continuous working time, especially, a large number of strain gauges are arranged on the turbine blade under high temperature environment, and only few strain gauges can obtain effective information, the survival rate is extremely low, and the vibration information of other measuring points needs to be calculated or predicted by using the actually measured data of the strain gauges. Meanwhile, when a high-cycle fatigue test is carried out on the blade, the strain gauge is very easy to fail under the conditions of large load and resonance, at this time, the non-contact laser displacement sensor is required to be used for measuring the vibration of the blade end and calculating the dynamic strain of the key point of the blade, and the conversion relation between the displacement of the blade end and the maximum stress point is required to be established.
Due to the characteristic of high-speed rotation of the blades of the aero-engine, the non-contact measurement based on blade end timing becomes a development direction of research in the field of blade vibration testing. The sensor arranged close to the inner side of the casing is used for sensing the vibration information of the blade tip, and the estimation of the dynamic strain of the specific position of the blade under the specific modal vibration can be realized by means of a finite element model. The blisk lacks a damping suppression mechanism, and a high-order mode is easy to excite while a low-order mode of the blade is excited. The working environment of the rotating blade is harsh, the vibration of the blade under the excitation of complex load is the result of superposition of a plurality of modes, the position of the maximum dynamic stress point is not fixed at the moment, and the displacement-strain has no fixed conversion relation; the current common calculation method of the displacement-strain conversion coefficient is to establish a finite element model of the blade, calculate the conversion coefficient of the blade tip displacement and the maximum dynamic strain under single-order modal frequency through harmonic response analysis, not comprehensively utilize information superposed by multi-modal vibration, and cannot realize the dynamic strain field reconstruction under multi-modal vibration at any moment.
The above information disclosed in this background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a blade displacement strain measurement method based on a modal shape, which establishes a conversion relation between non-contact (such as blade end timing) or contact (such as a strain gauge) vibration measurement test data and full-field vibration of a blade, and obtains a blade displacement-strain conversion coefficient measurement method based on the modal shape.
The invention aims to realize the following technical scheme, and the blade displacement strain measurement method based on the modal shape comprises the following steps:
in the first step, a three-dimensional finite element model of the blade to be measured is established, and a displacement mode vibration mode and a strain mode vibration mode are generated based on the three-dimensional finite element model;
in the second step, a measuring unit is arranged at a preset measuring point of the blade, the blade displacement u (t) and/or the strain s (t) are/is measured, and the vibration mode order of the blade is determined;
in the third step, a mapping relation between the displacement u (t) of the measuring point and the full-field strain and displacement and/or a mapping relation between the strain s (t) of the measuring point and the full-field strain and displacement are established to obtain a strain-displacement conversion coefficient matrix so as to measure the full-field strain or displacement of the blade.
In the method, in the first step, the front n of the three-dimensional finite element model is extracted through modal analysismOrder mode shape including size ndof× 1 displacement mode shape phiiAnd a size of 2ndof× 1 strain mode psiiConstructing a blade full-field displacement modal shape matrix
Size ndof×nm(ii) a Constructing blade full-field strain mode vibration matrix
Size of 2ndof×nm(ii) a Wherein n ismRepresenting the number of modes, i representing the order of the modes, ndofRepresenting the number of degrees of freedom of the finite element model of the blade, the strain of each finite element model node of the blade comprises 3 positive strainsx、y、zAnd 3 shear strains gammaxy、γyz、γxz6 strain components in total, in the second step, the measuring unit comprises a blade end timing sensor, a strain gauge, a laser vibration meter, a high-speed camera, a laser displacement sensor or an eddy current sensor, and the number n of the measuring unitsdNumber n of modes or moremThe positions and directions of the measuring points of the sensors correspond to the degrees of freedom of the nodes in the finite element model one by one, and the mode shape matrix phi of the full-field displacement mode or the full-field strain is selected fromExtracting the modal shape matrix psi to obtain the measuring point displacement modal shape phidOr gauge point strain mode psidAll sizes are nd×nm。
In the third step, a mapping relation S (T) T of the finite measuring point displacement u (T) and the strain S (T) of all nodes in the whole field under multi-modal excitation is establisheddsu (t); wherein, the calculation formula of the displacement-strain conversion coefficient matrix is
Size of 2ndof×nd；
Modal shape matrix phi for representing displacement of measuring pointdThe inverse of (c).
In the third step, a mapping relation U (T) T between the displacement u (T) of the finite measuring point and the displacement U (T) of all nodes in the whole field under the multi-modal excitation is establishedddu (t); wherein, the matrix calculation formula of the displacement-displacement conversion coefficient is as follows
Size ndof×nd。
In the method, in the third step, a mapping relation U (T) ═ T between the strain s (T) of the finite measuring points under the multi-modal excitation and the displacement U (T) of all nodes in the whole field is establishedsds (t); wherein the strain-displacement conversion coefficient matrix is calculated by the following formula
Size ndof×nd；
Modal shape matrix for representing displacement of measuring point
The inverse of (c).
In the method, in the third step, strain of the limited measuring point under multi-modal excitation is establishedu (T) and the mapping relation S (T) T of all node strains U (T) in the whole fieldsss (t); wherein the strain-strain conversion coefficient matrix calculation formula is
Size of 2ndof×nd。
In the method, in the third step, the displacement u of the measuring point j under the ith order modal excitation is establishedj(T) mapping relation S (T) with all-field node strain S (T)dsuj(t); wherein the vector calculation formula of the displacement-strain conversion coefficient is as follows
Size of 2ndof× 1, wherein phij，iThe i-th order displacement mode shape of the measuring point j is shown.
In the method, in the third step, the displacement u of the measuring point j under the ith order modal excitation is establishedj(T) mapping relation U (T) to total node displacement U (T)dduj(t); wherein the vector calculation formula of the displacement-displacement conversion coefficient is as follows
Size ndof×1。
In the method, in the third step, the strain s of the lower measuring point j under the i-th order modal excitation is establishedj(T) mapping relation U (T) to total node displacement U (T)sdsj(t); wherein the vector calculation formula of the strain-displacement conversion coefficient is as follows
Size ndof× 1 where phij，iAnd the ith order strain mode shape of the measuring point j is shown.
In the method, in the third step, the strain s of the lower measuring point j under the i-th order modal excitation is establishedj(T) mapping relation S (T) with all-field node strain S (T)sssj(t); wherein the vector calculation formula of the strain-strain conversion coefficient is as follows
Size of 2ndof×1。
Advantageous effects
The blade dynamic strain field reconstruction method provided by the invention provides calculation formulas of four conversion coefficient matrixes of displacement-strain, displacement-displacement, strain-displacement and strain-strain under multi-modal excitation, provides calculation formulas of four conversion coefficient matrixes of displacement-strain, displacement-displacement, strain-displacement and strain-strain under single-modal excitation, and overcomes the limitation that the conversion coefficient of displacement-strain under multi-modal vibration is difficult to calculate based on a harmonic response analysis method. The displacement-strain conversion coefficient matrix constructed by the method is constant and independent of frequency, time and stress conditions. The invention can be applied to timing non-contact vibration measurement of the blade end of the blade, strain gauge measurement and high cycle fatigue test, and is easy to realize.
Drawings
Various other advantages and benefits of the present invention will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. It is obvious that the drawings described below are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort. Also, like parts are designated by like reference numerals throughout the drawings.
In the drawings:
FIG. 1 is a schematic flow chart of a preferred embodiment of a blade displacement-strain conversion coefficient calculation method based on a mode shape according to the present invention;
FIG. 2 is a simulated rotating blade finite element model in one embodiment;
FIGS. 3(a) -3 (f) are displacement mode shapes and strain mode shapes of a rotor blade according to an embodiment, wherein FIG. 3(a) is a bending displacement mode shape; FIG. 3(b) a flexural strain mode; FIG. 3(c) a torsional displacement mode; FIG. 3(d) torsional strain mode; FIG. 3(e) two bending displacement vibration modes; FIG. 3(f) second bending strain mode;
the invention is further explained below with reference to the figures and examples.
Detailed Description
Specific embodiments of the present invention will be described in more detail below with reference to fig. 1 to 3 (f). While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be embodied in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
It should be noted that certain terms are used throughout the description and claims to refer to particular components. As one skilled in the art will appreciate, various names may be used to refer to a component. This specification and claims do not intend to distinguish between components that differ in name but not function. In the following description and in the claims, the terms "include" and "comprise" are used in an open-ended fashion, and thus should be interpreted to mean "include, but not limited to. The description which follows is a preferred embodiment of the invention, but is made for the purpose of illustrating the general principles of the invention and not for the purpose of limiting the scope of the invention. The scope of the present invention is defined by the appended claims.
For the purpose of facilitating understanding of the embodiments of the present invention, the following description will be made by taking specific embodiments as examples with reference to the accompanying drawings, and the drawings are not to be construed as limiting the embodiments of the present invention.
For better understanding, fig. 1 is a working flow chart of a blade displacement strain measurement method based on a mode shape, and as shown in fig. 1, the blade displacement strain measurement method based on the mode shape comprises the following steps:
in a first step S1, establishing a three-dimensional finite element model of the blade to be measured, and generating a displacement mode shape and a strain mode shape based on the three-dimensional finite element model;
in a second step S2, arranging a measuring unit at a predetermined measuring point of the blade, measuring blade displacement u (t) and/or strain S (t), and determining the vibration mode order of the blade;
in the third step S3, a mapping relation between the displacement u (t) of the measuring point and the full-field strain and displacement and/or a mapping relation between the strain S (t) of the measuring point and the full-field strain and displacement are/is established to obtain a strain-displacement conversion coefficient matrix for measuring the full-field strain or displacement of the blade.
In one embodiment of the method, in a first step S1, the first n of the three-dimensional finite element model is extracted by modal analysismOrder mode shape including size ndof× 1 displacement mode shape phiiAnd a size of 2ndof× 1 strain mode psiiConstructing a blade full-field displacement modal shape matrix
Size ndof×nm(ii) a Constructing blade full-field strain mode vibration matrix
Size of 2ndof×nm(ii) a Wherein n ismRepresenting the number of modes, i representing the order of the modes, ndofRepresenting the number of degrees of freedom of the finite element model of the blade, the strain of each finite element model node of the blade comprises 3 positive strainsx、y、zAnd 3 shear strains gammaxy、γyz、γxz6 strain components in total, in the second step S2, the measuring units comprise a blade end timing sensor, a strain gauge, a laser vibration meter, a high-speed camera, a laser displacement sensor or an eddy current sensor, and the number n of the measuring unitsdNumber n of modes or moremWherein, the positions and the directions of the measuring points of the sensor are in one-to-one correspondence with the degrees of freedom of the nodes in the finite element model, and the measuring point displacement modal shape phi is obtained by extracting from the full-field displacement modal shape matrix phi or the full-field strain modal shape matrix psidOr gauge point strain mode psidAll sizes are nd×nm。
In one embodiment of the method, in the third step S3, a mapping relation S (T) ═ T between the finite point displacement u (T) under the multi-modal excitation and the strain S (T) of all nodes in the full field is establisheddsu (t); wherein, the calculation formula of the displacement-strain conversion coefficient matrix is
Size of 2ndof×nd；
Modal shape matrix phi for representing displacement of measuring pointdThe inverse of (c).
In one embodiment of the method, in the third step S3, a mapping relationship u (T) ═ T between the finite measurement point displacement u (T) and the displacement u (T) of all nodes in the full field under the multi-modal excitation is establishedddu (t); wherein, the matrix calculation formula of the displacement-displacement conversion coefficient is as follows
Size ndof×nd。
In one embodiment of the method, in the third step S3, a mapping relationship u (T) ═ T between the finite point strain S (T) under the multi-modal excitation and the displacement u (T) of all nodes in the full field is establishedsds (t); wherein the strain-displacement conversion coefficient matrix is calculated by the following formula
Size ndof×nd；
Modal shape matrix for representing displacement of measuring point
The inverse of (c).
In one embodiment of the method, in the third step S3, a mapping relation between the finite measuring point strain u (t) under multi-modal excitation and all node strains u (t) in the whole field is establishedS(t)＝Tsss (t); wherein the strain-strain conversion coefficient matrix calculation formula is
Size of 2ndof×nd。
In one embodiment of the method, in a third step S3, a displacement u of a lower point j of an i-th order modal excitation is establishedj(T) mapping relation S (T) with all-field node strain S (T)dsuj(t); wherein the vector calculation formula of the displacement-strain conversion coefficient is as follows
Size of 2ndof× 1, wherein phij，iThe i-th order displacement mode shape of the measuring point j is shown.
In one embodiment of the method, in a third step S3, a displacement u of a lower point j of an i-th order modal excitation is establishedj(T) mapping relation U (T) to total node displacement U (T)dduj(t); wherein the vector calculation formula of the displacement-displacement conversion coefficient is as follows
Size ndof×1。
In one embodiment of the method, in a third step S3, strain S at ith-order modal excitation lower point j is establishedj(T) mapping relation U (T) to total node displacement U (T)sdsj(t); wherein the vector calculation formula of the strain-displacement conversion coefficient is as follows
Size ndof× 1 where phij，iAnd the ith order strain mode shape of the measuring point j is shown.
In one embodiment of the method, in a third step S3, strain S at ith-order modal excitation lower point j is establishedj(T) mapping relation S (T) with all-field node strain S (T)sssj(t); wherein the strain-strain conversion coefficient vectorIs calculated by the formula
Size of 2ndof×1。
For a further understanding of the present invention, in one embodiment, the present invention is further described with reference to fig. 1 to 3(f) and a specific embodiment, and it should be emphasized that the following description is merely exemplary and the application of the present invention is not limited to the following examples.
In one embodiment, the method specifically comprises the following steps:
FIG. 1 is a schematic flow chart of a blade displacement-strain conversion coefficient calculation method based on modal shape, which is implemented by the method and is used for constructing a conversion relation between a blade end limited displacement measurement point of a rotating blade and all node strains in a full field based on a modal superposition principle. FIG. 2 is a diagram of node numbers of excitation application points, displacement and strain extraction points and corresponding positions on a blade selected in a three-dimensional finite element model of the blade in a specific embodiment.
The method comprises the following specific steps:
1, extracting a displacement modal vibration mode and a strain modal vibration mode of a three-dimensional finite element model of a blade, namely, referring to fig. 2, establishing the three-dimensional finite element model simulating a straight blade of a rotor by using ANSYS finite element analysis software, wherein the material is aluminum, the density is 2700kg/m3, the Poisson ratio is 0.33, the elastic modulus is 72000MPa, the length of the blade is 48mm, the thickness is 1mm, and the width is 20mm, the type of the finite element is an entity unit SO L ID185, the total number of nodes is 3153, and the two side surfaces of the blade root are fixedly restrained to simulate the actual working state of;
extracting the first 3 order modal parameters, namely n, by using ANSYS modal analysis modem3: modal frequency fiA size of ndof× 1 displacement mode shape phiiSize of 2ndof× 1 strain mode psiiWherein the first three-order modal frequencies are respectively f1＝333.08Hz、f2＝1806.03Hz、f32076.52 Hz; constructing a rotor blade full-field displacement modal shape matrix
Size ndof×nm(ii) a Constructing a rotor blade full-field strain mode vibration mode matrix
Size of 2ndof×nmThe mode shapes are shown in fig. 3(a) to 3 (f); i denotes the order of the mode, ndof9459 represents the number of degrees of freedom of the finite element model of the blade; the displacement of each node comprises three displacements ux、uy、uzComponent, i.e. 3 displacement mode modes per node, then ndof＝3nn， nn3153, the number of nodes of the finite element model of the blade is represented; strain comprises 3 positive strainsx、y、zAnd 3 shear strains gammaxy、γyz、γxzThere are 6 strain components in total, i.e. 6 strain mode shapes per node. Note that: the displacement is in mm and the mass is in tonne in this example.
2, determining the vibration mode order of the blade, the number and the positions of sensors: the blade vibration measuring sensor is a contact type or non-contact type sensor such as a blade tip timing sensor, a strain gauge, a laser vibration meter, a high-speed camera DIC, a laser displacement sensor or an eddy current sensor and the like, and can measure blade displacement or strain; number of sensors ndMust not be less than the number of modalities n of interestmI.e. nd≥nm(ii) a In this case, the vibration mode of the first three orders of the simulated rotor blade is focused, and n is takenm3; taking minimum n corresponding sensor measuring points d3; the positions and the directions of the measuring points of the sensors correspond to the degrees of freedom of the nodes in the finite element model one by one, and the measuring point displacement modal shape phi is obtained by extracting from the full-field displacement modal shape matrix phi or the full-field strain modal shape matrix psidOr gauge point strain mode psidAll sizes are nd×nm＝3×3。
3, calculating a blade displacement-strain conversion coefficient:
step 3.1, calculating a displacement-strain conversion coefficient under multi-modal vibration:
3.1.1 establishing multiple modesMapping relation S (T) of finite point displacement u (T) and all-field node strain S (T) under state excitationdsu (t); wherein, the calculation formula of the displacement-strain conversion coefficient matrix is
Size of 2ndof×nd；
Modal shape matrix phi for representing displacement of measuring pointdThe inverse of (1); in the embodiment, a conversion coefficient matrix of displacement of three nodes at a leaf end and strain of three nodes at a leaf body is calculated; extracting the X-direction displacement mode vibration patterns of the front three-order of node No. 1136, 1125 and 1119 of the blade end and the Y-direction mode vibration patterns of the front three-order strain of node No. 158, 166 and 47 of the blade root, and calculating to obtain a displacement-strain conversion coefficient matrix Tds：
3.1.2 establishing a mapping relation U (T) ═ T between the displacement u (T) of the limited measuring points and the displacement U (T) of all nodes in the whole field under the multi-mode excitationddu (t); wherein, the matrix calculation formula of the displacement-displacement conversion coefficient is as follows
Size ndof×nd(ii) a In the embodiment, a conversion coefficient matrix of displacement of three nodes at a leaf end and displacement of three nodes at a leaf body is calculated; extracting the X-direction modal shape of the first three-order displacement of nodes No. 1136, 1125 and 1119 of the leaf tip and the X-direction modal shape of the first three-order displacement of nodes No. 481, 491 and 498 of the leaf body, and calculating to obtain a displacement-displacement conversion coefficient matrix Tdd：
3.1.3 establishing a mapping relation U (T) ═ T between the strain s (T) of the finite measuring point under the multi-mode excitation and the displacement U (T) of all nodes in the whole fieldsds (t); wherein, the strain-displacement conversion coefficient matrixIs calculated by the formula
Size ndof×nd；
Modal shape matrix for representing displacement of measuring point
The inverse of (1); in the embodiment, a conversion coefficient matrix of the strain of three nodes of the blade body and the displacement of three nodes of the blade end is calculated; extracting Y-direction modal shape of strain of the first three orders of nodes of No. 158, 166 and 47 root and X-direction modal shape of displacement of the first three orders of measuring points of No. 1136, 1125 and 1119 leaf end, and calculating to obtain a strain-displacement conversion coefficient matrix Tsd：
3.1.4 establishing a mapping relation S (T) ═ T between the strain u (T) of the finite measuring point and the strain U (T) of all nodes in the whole field under the multi-mode excitationsss (t); wherein the strain-strain conversion coefficient matrix calculation formula is
Size of 2ndof×nd(ii) a In the embodiment, a conversion coefficient matrix of the strain of three nodes of the blade body and the strain of three nodes of the blade end is calculated; extracting the Y-direction modal shape of the strain of the first three orders of the No. 158, 166 and 47 node and the Y-direction modal shape of the strain of the first three orders of the No. 481, 491 and 498 measuring points of the blade, and calculating to obtain a strain-strain conversion coefficient matrix Tss：
Step 3.2 displacement-strain conversion coefficient under single mode vibration:
3.2.1 establishing displacement u of measuring point j under ith order modal excitationj(t) mapping relation with all-node strain S (t) in full fieldS(t)＝Tdsuj(t); wherein the vector calculation formula of the displacement-strain conversion coefficient is as follows
Size of 2ndof× 1, in the embodiment, calculating the conversion coefficient vector of the displacement of the No. 1136 node of the blade end and the maximum stress point, and extracting the X-direction modal shape of the displacement of the No. 1136 node of the blade end and the Y-direction modal shape of the strain of the No. 47 node of the maximum stress point to obtain the displacement-strain conversion coefficient vector TsdTable 1 shows the conversion coefficients of the displacement of all the nodes at the front three-order blade end and the strain at the maximum strain point, and the conversion coefficients are compared with the harmonic response analysis result, wherein when the harmonic response analysis is carried out by using ANSYS finite element software, the mass damping coefficient is set to be α -12.1380, and the stiffness damping coefficient is set to be β -8.1986 × 10-8(ii) a In this embodiment, the maximum strain point of the first three orders is the same node, i.e., node 47. As can be seen from Table 1, the displacement-strain conversion coefficients obtained by the calculation method and the harmonic response analysis method are very close, and the relative errors of the first three orders do not exceed 1%.
TABLE 1 conversion factor of displacement-strain under monomodal vibration
| Order of the order | First order | Second order | Third order |
| Modal method | -0.000546 | 0.002194 | 0.002717 |
| Harmonic response | -0.000545 | 0.002193 | 0.002716 |
| Relative error% | 0.006061 | 0.016806 | 0.032471 |
3.2.2 establishing displacement u of measuring point j under ith order modal excitationj(T) mapping relation U (T) to total node displacement U (T)dduj(t); wherein the vector calculation formula of the displacement-displacement conversion coefficient is as follows
Size ndof× 1, extracting the front three-order X-direction displacement mode vibration patterns of 1136 node at leaf end and 481 node at leaf body to obtain the vector T of displacement-displacement conversion coefficientdd(ii) a Table 2 lists the scaling factors and relative errors of the first third harmonic response analysis and the modal analysis of the present invention. As can be seen from Table 2, the displacement-displacement conversion coefficient obtained by the calculation method of the invention is very close to that obtained by the harmonic response analysis method, and the relative error of the first three orders is not more than 1%.
TABLE 2 conversion factor of unimodal vibration displacement to displacement
| Order of the order | First order | Second order | Third order |
| Modal method | 0.210388 | 0.422356 | -0.633746 |
| Harmonic response | 0.210387 | 0.421768 | -0.632415 |
| Relative error% | 0.000641 | 0.001392 | 0.002105 |
3.2.3 establishing the strain s of the ith-order modal excitation lower measuring point jj(T) mapping relation U (T) to total node displacement U (T)sdsj (t); wherein the vector calculation formula of the strain-displacement conversion coefficient is as follows
Size ndof× 1, extracting the Y-direction strain mode shape of the first three-order of No. 47 blade root node and the X-direction displacement mode shape of No. 1136 blade end node to obtain the strain-displacement conversion coefficient vector Tsd(ii) a Table 3 lists the scaling factor and relative error for the first third harmonic response analysis and the modal analysis. As can be seen from Table 3, the strain-displacement conversion coefficients obtained by the calculation method and the harmonic response analysis method are very close, and the relative errors of the first three orders are not more than 1%.
TABLE 3 conversion factor of strain to displacement for single mode vibration
| Order of the order | First order | Second order | Third order |
| Modal method | -1831.711229 | 455.749755 | 368.028146 |
| Harmonic response | -1831.711228 | 455.828682 | 368.155544 |
| Relative error% | 0.002946 | 0.017315 | 0.034604 |
3.2.4 establishing strain s of i-th order modal excitation lower measuring point jj(T) mapping relation S (T) with all-field node strain U (T)ssSj(t); wherein the vector calculation formula of the strain-strain conversion coefficient is as follows
Size of 2ndof× 1, extracting the Y-direction strain mode shapes of the first three orders of the No. 47 node of the blade root and the No. 481 node of the blade body to obtain a displacement-displacement conversion coefficient vector Tss(ii) a Table 4 lists the scaling factor and relative error for the first third harmonic response analysis and the modal analysis. From Table 4, it can be seen thatThe strain-strain conversion coefficient obtained by the calculation method is very close to that obtained by the harmonic response analysis method, and the relative error of the first three orders does not exceed 1%.
TABLE 4 conversion factor of strain to strain for single mode vibration
| Order of the order | First order | Second order | Third order |
| Modal method | -0.399054 | -0.055659 | 0.543791 |
| Harmonic response | -0.399066 | -0.055259 | 0.543218 |
| Relative error% | 0.003145 | 0.721521 | 0.105428 |
Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments and application fields, and the above-described embodiments are illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto without departing from the scope of the invention as defined by the appended claims.
Claims (10)
1. A blade displacement strain measurement method based on a mode shape comprises the following steps:
in the first step (S1), a three-dimensional finite element model of the blade to be measured is established, a displacement mode shape and a strain mode shape are generated based on the three-dimensional finite element model, and the front n of the three-dimensional finite element model is extracted through modal analysismOrder mode shape including size ndof× 1 displacement mode shape phiiAnd a size of 2ndof× 1 strain mode psiiConstructing a blade full-field displacement modal shape matrix
Size ndof×nm(ii) a Constructing blade full-field strain mode vibration matrix
Size of 2ndof×nm(ii) a Wherein n ismRepresenting the number of modes, i representing the order of the modes, ndofRepresenting the number of degrees of freedom of the finite element model of the blade, the strain of each finite element model node of the blade comprises 3 positive strainsx、y、zAnd 3 shear strains gammaxy、γyz、γxzA total of 6 strain components;
in the second step (S2), arranging a measuring unit at a preset measuring point of the blade, measuring the blade displacement u (t) and/or the strain S (t), and determining the vibration mode order of the blade;
in the third step (S3), a mapping relation between the displacement u (t) of the measuring point and the full-field strain and displacement and/or a mapping relation between the strain S (t) of the measuring point and the full-field strain and displacement are/is established to obtain a strain-displacement conversion coefficient matrix for measuring the full-field strain or displacement of the blade.
2. The method according to claim 1, wherein in the second step (S2), the measuring unit comprises a tip timing sensor, a strain gauge, a laser vibrometer, a high-speed camera, a laser displacement sensor or an eddy current sensor, and the number n of measuring unitsdNumber n of modes or moremWherein, the positions and the directions of the measuring points of the sensor are in one-to-one correspondence with the degrees of freedom of the nodes in the finite element model, and the measuring point displacement modal shape phi is obtained by extracting from the full-field displacement modal shape matrix phi or the full-field strain modal shape matrix psidOr gauge point strain mode psidAll sizes are nd×nm。
3. The method according to claim 2, wherein in the third step (S3), a mapping S (T) ═ T of finite point displacement u (T) under multi-modal excitation to full-field all-node strain S (T) is establisheddsu (t); wherein, the calculation formula of the displacement-strain conversion coefficient matrix is
Size of 2ndof×nd；
Modal shape matrix phi for representing displacement of measuring pointdThe inverse of (c).
4. The method according to claim 3, wherein in the third step (S3), a mapping relation U (T) ═ T between the finite point displacement u (T) and the displacement U (T) of all nodes in the full field under multi-modal excitation is establishedddu (t); wherein, the matrix calculation formula of the displacement-displacement conversion coefficient is as follows
Size ndof×nd。
5. The method according to claim 3, wherein in a third step (S3), multimode is establishedMapping relation U (T) of finite point strain s (T) under state excitation and displacement U (T) of all nodes in full fieldsds (t); wherein the strain-displacement conversion coefficient matrix is calculated by the following formula
Size ndof×nd；
Modal shape matrix for representing displacement of measuring point
The inverse of (c).
6. The method according to claim 3, wherein in the third step (S3), a mapping S (T) ═ T of finite point strain u (T) and all node strain U (T) in the full field under multi-modal excitation is establishedsss (t); wherein the strain-strain conversion coefficient matrix calculation formula is
Size of 2ndof×nd。
7. The method of claim 3, wherein in a third step (S3), a displacement u of the j lower point of the ith order modal excitation is establishedj(T) mapping relation S (T) with all-field node strain S (T)dsuj(t); wherein the vector calculation formula of the displacement-strain conversion coefficient is as follows
Size of 2ndof× 1, wherein phij，iThe i-th order displacement mode shape of the measuring point j is shown.
8. The method of claim 3, wherein in a third step (S3), a displacement u of the j lower point of the ith order modal excitation is establishedjMapping of (t) to the full-field all-node displacement U (t)The relationship of U (T) ═ TddUj(t); wherein the vector calculation formula of the displacement-displacement conversion coefficient is as follows
Size ndof×1。
9. The method of claim 3, wherein in a third step (S3), establishing an i-th order modal excitation down-point j strain Sj(T) mapping relation U (T) to total node displacement U (T)sdsj(t); wherein the vector calculation formula of the strain-displacement conversion coefficient is as follows
Size ndof× 1, wherein psij，iAnd the ith order strain mode shape of the measuring point j is shown.
10. The method of claim 3, wherein in a third step (S3), establishing an i-th order modal excitation down-point j strain Sj(T) mapping relation S (T) with all-field node strain S (T)sssj(t); wherein the vector calculation formula of the strain-strain conversion coefficient is as follows
Size of 2ndof×1。
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