LU102010A1 - Measurement method of dynamic position ofwing baseline based on ifem and rzt - Google Patents
Measurement method of dynamic position ofwing baseline based on ifem and rzt Download PDFInfo
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- G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
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Abstract
A measurement method of a dynamic position of a wing baseline based on the Inverse Finite Element Method (iFEM) and the Refined Zigzag Theory (RZT) is disclosed, which comprises four steps: determining a three-dimensional model of a selected wing; designing arrangement of a fiber Bragg grating (FBG) sensor array and a strain rosette on the surface of the wing; establishing an RZT-based inverse finite element simulation model; and finally reading and converting measured data, to obtain a dynamic position of a wing baseline. The present invention realizes an RZT-based measurement method of a dynamic position of a wing baseline, having good robustness and high applicability.
Description
MEASUREMENT METHOD OF DYNAMIC POSITION OF WING HUT02010
BACKGROUND OF THE INVENTION Field of the Invention The present invention relates to a measurement method of a dynamic position of a wing baseline, and in particular, to an application of the Inverse Finite Element Method (1FEM) and the Refined Zigzag Theory (RZT) in measurement of a dynamic position of a wing baseline. Description of Related Art Early warning for unmanned aerial vehicles flying at high altitude and for long endurance gains more and more attention. Such an aircraft generally uses a lightweight flexible wing with a large aspect ratio, which is characterized by a large lift-resistance ratio, light structure, and high flexibility. Under aerodynamic load, the wing is bent and twisted to produce a large deformation, seriously affecting the safety of the aircraft. However, because the wing is formed by a long-baseline antenna, its deformation may directly affect the performance of an array antenna. To offset the reduction in the electrical performance of the antenna caused by the deformation, it is necessary to accurately acquire the magnitude of the deformation of the wing. Obviously superior in terms of measurement of dynamic changes in any boundary-constrained topological structure, an iFEM does not require a priori knowledge while sensing the shape of the wing and measuring positions of special points, and further has good robustness, thus being applicable to online real-time monitoring.
SUMMARY OF THE INVENTION Technical Problem The objective of the present invention is to provide a measurement method of a dynamic position of a wing baseline based on the iIFEM and the RZT, which includesfive steps: determining a three-dimensional model of a selected wing; then designing LU102010 arrangement of a fiber Bragg grating (FBG) sensor array and a strain rosette on the surface of the wing; afterwards, establishing an RZT-based inverse finite element simulation model; and finally reading and converting measured data, to obtain a dynamic position of a wing baseline. Technical Solution In the technical solutions of the present invention, the dynamic position of the wing baseline can be measured and indirectly acquired by combining the iFEM with the arrangement of the FBG sensor array and the strain rosette. The measurement method includes the following steps: step 1: determination of a wing model: generating a three-dimensional model of a selected wing according to spatial dimension data of the wing, and then importing the model into finite element analysis (FEA) software; step 2: arrangement design of an FBG sensor array and a strain rosette on the surface of the wing: arranging the strain rosette and the FBG sensor array at different positions on the wing according to the size of the wing; step 3: establishment of an RZT-based inverse finite element simulation model: using a three-node unit in mesh generation; step 4: reading and conversion of measured data: based on data synchronization in a computer, simulating application of uniformly distributed forces of bending, torsion, and membrane deformation on the wing; reading data from FBG sensors and strain rosette sensors separately; and calculating spatial position coordinates of each point on the wing by operation; and step 5: acquisition of a dynamic position of a wing baseline: finally obtaining a dynamic measurement result of the baseline by using the data acquired from the FBG sensors and the strain rosette sensors and by means of FEA.
The wing model is usually a wing with a large aspect ratio, thus facilitating the arrangement design of the strain rosette and the FBG sensor array.
The wing model is a tri-layered structure; a coordinate system is an orthogonal coordinate system (x1, x2, Z), where (x1, Xz) indicates coordinates in a plane, and z indicates a coordinate of the wing in a thickness direction, namely, in a deflection direction; and the used three-node unit has an anisotropic property, and each node hasnine degrees of freedom. LU102010 Derivation formulas of membrane displacements respectively in x; and x» directions and a transverse deflection along the z axis are respectively as follows: u(x) = > (Nu +16) (I tel vn) =Y (Ny, +M6,) ©) ist 3 xX) == > [Vo LO Au) M, (0. T 9,)] (3) i=] where u(x) and v(x) denote membrane displacements in x1 and x; directions respectively; w(x) denotes the transverse deflection along the z axis; 1 denotes the ith layer, where i=1, 2, 3; u;, vi, and w; denote degrees of freedom of the three-node unit along positive directions of the xi, x2 and z axes respectively; 0x and 0,; denote degrees of freedom for typical counterclockwise rotation along the x; and x axes respectively; Pay and ¢, denote degrees of freedom for zigzag counterclockwise rotation along the x; and x» axes respectively; 8, denotes a degree of freedom for rotation about a corner point on the z axis; p-; denotes a degree of freedom for manual zigzag rotation along the z axis; N; denotes coordinates of linear area parameters of a triangle; and L; and M; denote equal interpolation functions.
Derivation formulas of the transverse deflection w(x) along the z axis, the bending amplitude P1(x) in the positive direction of the x; axis, and the zigzag rotation amplitude P(x) in a negative direction of the x; axis may be shown by the degrees of freedom of the nodes: w;, Ou, and Pai (a= x, y), as follows respectively: 3 = [No -L(0,-0,9-M(0,-0,] © i=l 3 P(x)=H NP, (P=6,p (5) i] Px)=-2 NP, (P=0,p) (6) i=t Configuration of each sensor employs a smoothing analysis method, namely, dividing the wing into several triangular units according to the size of the wing. During the simulation of application of uniformly distributed forces of bending,
torsion, and membrane deformation on the wing, derivation formulas for membrane LU102010 strain measurement e(u“), bending curvature Æ(u°), and zigzag torsional strain measurement u(u“) of the three-node unit based on the RZT are respectively as follows: elu) =u, Vo Ug EV, |'=B°n° (7) K(u”)= la, 0, 0, +0, ï =B" u (8) Hu) = Py Pn BP +0] = H Bu’ (9) where #0 0 0 H,=i0 ¢, 0 0 (10) 004% u = [uf HS u] (1) uy = [er v, a; 0, 9, a, Dei Ps Or J (i = 1,2,3) (12) N, 0 600 L, 000 B:=10 N,000 M, 000 (13) N, N, 000M, +L,000 000 0 N, 0000 B'= 000 -N, 0 0000 (18) 000 -N, N, 0000 6000000 0 NW, 0000000 —N, 0 BY = Vad (15) 0000000 O0 0 6000000 -N, 0 where #“ denotes a node displacement matrix; ¢; and #2 denote RZT-based zigzag functions in x; and x» directions respectively that are obtained after thickness segmentation of the wing; Bf denotes a derivative matrix of a membrane strain shape; BY denotes a derivative matrix of a bending deformation shape; BF denotes a derivative matrix of a zigzag torsion deformation shape; and i=1, 2, 3.
In step 2, during layout design of the strain rosette and the FBG sensor array on LU102010 the wing according to the size of the wing, the strain rosette and the FBG sensor array are arranged at four different densities: very dense, dense, sparse, and very sparse; very dense, dense, and sparse arrangement manners are used in tri-axial strain 5 measurement, and very sparse FBG sensors are used in uniaxial strain measurement; and the use of the very sparse arrangement manner in the uniaxial measurement makes it important to calibrate the sensors. According to the data obtained from the FBG sensors and the strain rosette sensors in step 4, discrete surface strain data of the wing is derived and measured by using a first-order continuous derivative (C1) function, and a weighted least squares function is used to perform derivation and calculation for each individual RZT-based unit, where the derivation formula is as follows: (uy = w eu) ~ Ew Je) -K + uw) M 02 +w, pro) - rf + w, J(u) — Hl | where De(u°) denotes the weighted least squares function; (k) denotes the kth layer after the three-node unit is divided into three layers; and j denotes the jth layer in cross-sectional strain measurement; / denotes a membrane strain function, X denotes a bending strain function, and M denotes a zigzag section strain; and lee) — El? , Ik) = KI, |) + M], ly) -Tl?, and ln(u®) — H||? are square norms corresponding to e(u°), k(u®), u(u°), y(u°), and n(u°) respectively; y(u°) and n(u“) denote measured values of transverse shear strains of the first layer and the second layer respectively; /' and H denote shear strain functions corresponding to y(w°) and n(u“) respectively; and wa (à = e, k, u, y, n) denotes a weighting constant vector of each individual strain. Advantageous Effect The measurement method of a dynamic position of a wing baseline in the present invention is easy and convenient to operate, and has low requirements for staff skills and environment. Thus, a device to be targeted can be rapidly and accurately targeted, and a target release method is simple and universally applicable.
BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 shows a three-node unit model; and FIG. 2 shows zigzag (Z-shaped) mesh generation.
DETAILED DESCRIPTION OF THE INVENTION HUT02010 FIGs. 1 and 2 show preferred embodiments of the present invention. A measurement method of a dynamic position of a wing baseline based on the iFEM and the RZT in the present invention includes the following five steps: Step 1: Determination of a wing model: A three-dimensional model of a selected wing is generated according to spatial dimension data of the wing, and then the model is imported into FEA software.
Step 2: Arrangement design of an FBG sensor array and a strain rosette on the surface of the wing: The strain rosette and the FBG sensor array are arranged at different positions on the wing according to the size of the wing. Step 3: Establishment of an RZT-based inverse finite element simulation model: A three-node unit is used in mesh generation. Step 4: Reading and conversion of measured data: Based on data synchronization in a computer, application of uniformly distributed forces of bending, torsion, and membrane deformation on the wing is simulated; data from FBG sensors and strain rosette sensors are separately read; and spatial position coordinates of each point on the wing are calculated by operation. Step 5: Acquisition of a dynamic position of a wing baseline: A dynamic measurement result of the baseline is finally obtained by using the data acquired from the FBG sensors and the strain rosette sensors and by means of FEA. The wing model is usually a wing with a large aspect ratio, thus facilitating the arrangement design of the strain rosette and the FBG sensor array. The wing model is a tri-layered structure. A coordinate system is an orthogonal coordinate system (x1, x2, Z), where (x1, Xz) indicates coordinates in a plane, and z indicates a coordinate of the wing in a thickness direction (deflection direction). The used three-node unit has an anisotropic property, and each node has nine degrees of freedom. Derivation formulas of membrane displacements respectively in x; and x» directions and a transverse deflection along the z axis are respectively as follows: 3 w(x)=> (Nu, +L6,) (1) a
; LU102010 vx) =X (Nv, + MO.) (2) i=l 3 o(x)=0= 5 [N.@, LCD) MAO, - 0.) (3) i=l where u(x) and v(x) denote membrane displacements in x1 and x; directions respectively; w(x) denotes the transverse deflection along the z axis; 1 denotes the ith layer, where i=1, 2, 3; u;, vi, and w; denote degrees of freedom of the three-node unit along positive directions of the xi, x» and z axes respectively; 8. and 6,; denote degrees of freedom for typical counterclockwise rotation along the x; and x axes respectively; @x and ¢,; denote degrees of freedom for zigzag counterclockwise rotation along the x; and x» axes respectively; 8, denotes a degree of freedom for rotation about a corner point on the z axis; ¢. denotes a degree of freedom for manual zigzag rotation along the z axis; N; denotes coordinates of linear area parameters of a triangle; and L; and M; denote equal interpolation functions.
Derivation formulas of the transverse deflection w(x) along the z axis, the bending amplitude P1(x) in the positive direction of the x; axis, and the zigzag rotation amplitude P(x) in a negative direction of the x; axis may be shown by the degrees of freedom of the nodes: wi, Ou, and Mai (a= x, y), as follows respectively: wo) =Y [Na -L(0,-0,)-M(0,-0,)] 4) i) P(x)= y NP, (P=6,p) (5) Fl Px) =-Y NP, (P=0.p) (6) Is} Configuration of each sensor employs a smoothing analysis method, namely, dividing the wing into several triangular units according to the size of the wing.
During the simulation of application of uniformly distributed forces of bending, torsion, and membrane deformation on the wing, derivation formulas for membrane strain measurement e(u“), bending curvature k(w“), and zigzag torsional strain measurement u(u“) of the three-node unit based on the RZT are respectively as follows:
; LU102010 e(u“) Ju, Va ly FY J =B‘u° (7) kw )=[6, 6. 6,+6, T =Bw (8) uu’) =|, Pa PP, À P2+P NE HB“ u (9) where g 0 0 0 H,=0 ¢ 0 0 (10) 0 0808 u = [ui us ut | (11) ui =f, 00,0,0,0,0,0] (2123) (12) N, 0 600 L, 000 B:=10 N,000 M, 000 (13) N, N, 000M, +L,000 000 0 N, 0000 B'= 000 -N, 0 0000 (18) 000 -N, N, 0000 0000000 0 WN, 00000600 -N, 0 BY = os (15) 0000000 O0 0 0000000 —N, 0 ; where #“ denotes a node displacement matrix; ¢; and #2 denote RZT-based zigzag functions in x; and x, directions respectively that are obtained after thickness segmentation of the wing; Bf denotes a derivative matrix of a membrane strain shape; BY denotes a derivative matrix of a bending deformation shape; BF denotes a derivative matrix of a zigzag torsion deformation shape; and i=1, 2, 3. In step 2, during layout design of the strain rosette and the FBG sensor array on the wing according to the size of the wing, the strain rosette and the FBG sensor array may be arranged at four different densities: very dense, dense, sparse, and very sparse.
Very dense, dense, and sparse arrangement manners are used in tri-axial strain LU102010 measurement, and very sparse FBG sensors are used in uniaxial strain measurement. The use of the very sparse arrangement manner in the uniaxial measurement makes it important to calibrate the sensors.
According to the measured data obtained in step 4, discrete surface strain data of the wing is derived and measured by using a C1 function (C1 represents a first-order continuous derivative), and a weighted least squares function is used to perform derivation and calculation for each individual RZT-based unit, where the derivation formula is as follows: D (#)=w, leu’) = El + w, rl) — K| + we (a) M , , (22) 0 + w. ly (Y= I +, pu) = H| where De(u°) denotes the weighted least squares function; (k) denotes the kth layer after the three-node unit is divided into three layers; and j denotes the jth layer in cross-sectional strain measurement; / denotes a membrane strain function, X denotes a bending strain function, and M denotes a zigzag section strain; and lee) — El? , IkCu®)- KI, |) + M], ly) — |? , and ln(u®) — H||? are square norms corresponding to e(u°), k(u®), u(u°), y(u°), and n(u°) respectively; y(u°) and n(u“) denote measured values of transverse shear strains of the first layer and the second layer respectively; /' and H denote shear strain functions corresponding to y(w°) and n(u“) respectively; and wa (à = e, k, u, y, n) denotes a weighting constant vector of each individual strain.
Claims (6)
1. A measurement method of a dynamic position of a wing baseline based on the Inverse Finite Element Method (iFEM) and the Refined Zigzag Theory (RZT), comprising the following steps: step 1: determination of a wing model: generating a three-dimensional model of a selected wing according to spatial dimension data of the selected wing, and then importing the model into finite element analysis (FEA) software; step 2: arrangement design of a fiber Bragg grating (FBG) sensor array and a strain rosette on the surface of the wing: arranging the strain rosette and the FBG sensor array at different positions on the wing according to the size of the wing; step 3: establishment of an RZT-based inverse finite element simulation model: using a three-node unit in mesh generation; step 4: reading and conversion of measured data: based on data synchronization in a computer, simulating application of uniformly distributed forces of bending, torsion, and membrane deformation on the wing; reading data from the FBG sensors and the strain rosette sensors separately; and calculating spatial position coordinates of each point on the wing by operation; and step 5: acquisition of a dynamic position of a wing baseline: finally obtaining a dynamic measurement result of the baseline by using the data acquired from the FBG sensors and the strain rosette sensors and by means of FEA.
2. The measurement method of a dynamic position of a wing baseline based on the iFFM and RZT according to claim 1, wherein the wing model is usually a high-aspect-ratio wing, thus facilitating the arrangement design of the strain rosette and the FBG sensor array.
3. The measurement method of a dynamic position of a wing baseline based on the iFEM and RZT according to claim 1, wherein the wing model is a tri-layered structure; a coordinate system is an orthogonal coordinate system (x1, x2, z), wherein (x1, x2) indicates coordinates in a plane, and z indicates a coordinate of the wing in a thickness direction, namely, in a deflection direction; and the used three-node unit has an anisotropic property, and each node has nine degrees of freedom;
derivation formulas of membrane displacements respectively in x; and x» directions HU102010 and a transverse deflection along the z axis are respectively as follows: 3 u(x)=Y (Nu, +L0,) (1) f=] 3 v(x) = > (Ny, + MO.) {2) Gest 3 ox)=eo=S|Ne -L(0,-0,)-M(6,-0,)1 © i=l wherein u(x) and v(x) denote membrane displacements in x; and x; directions respectively; w(x) denotes the transverse deflection along the z axis; 1 denotes the ithlayer, where i=1, 2, 3; u;, vi, and w; denote degrees of freedom of the three-node unitalong positive directions of the xi, x2 and z axes respectively; 0x and 0,; denotedegrees of freedom for typical counterclockwise rotation along the x; and x axesrespectively; @x and ¢, denote degrees of freedom for zigzag counterclockwise rotation along the x; and x» axes respectively; 6, denotes a degree of freedom forrotation about a corner point on the z axis; ¢, denotes a degree of freedom for manualzigzag rotation along the z axis; N; denotes coordinates of linear area parameters of atriangle; and L; and M; denote equal interpolation functions;
derivation formulas of the transverse deflection w(x) along the z axis, the bending amplitude P1(x) in the positive direction of the x; axis, and the zigzag rotationamplitude P2(x) in a negative direction of the x; axis are shown by the degrees offreedom of the nodes: wi, 84, and Mai (a= x, y), as follows respectively:
00) =Y [No ~ L100, ~0)- M0, ~0p,)] © Fl P(x)=X NP, (P=6,0) (5) i=l P(x) = X NP, (P=8,œ) (6) a ; andconfiguration of each sensor employs a smoothing unit analysıs method, namely,
dividing the wing into several triangular units according to the size of the wing.
4. The measurement method of a dynamic position of a wing baseline based on the iFEM and RZT according to claim 1, wherein during the simulation of application of uniformly distributed forces of bending, torsion, and membrane deformation on the wing, derivation formulas for membrane strain measurement e(#°), bending curvature k(u®), and zigzag torsional strain measurement u(u“) of the three-node unit based on the RZT are respectively as follows: eu’) =u, Vy U,V, J =B‘u° (7) K(u°)= la. 8. At Ohr Ÿ =B u (8) p(u”) =|4 Ds GPs DOLD, I= H Bu“ (9) wherein gp 0 000 H,=0 ¢ 0 0 (10) 0 04 # H = lu? uu; Ï (11) u = fr, v, @ 0, 0; 0, 9, Dei Pr I (i=123) (12) N, 0 000 L, 000 B/=0 N.000 M, 000 (13) N, N, OOO M,+L,000 000 0 N, 0000 B°=000 -N, 0 0000 (14) 1000 -N, N, 0000 ’ 7 0000000 0 M , 0000000 -N.
Ô BY = I (15) 0000000 O0 0 0000000 -N, 0 wherein u“ denotes a node displacement matrix; ¢; and ÿ2 denote RZT-based zigzag functions in x; and x, directions respectively that are obtained after thicknesssegmentation of the wing; Bf denotes a derivative matrix of a membrane strain HU102010 shape; BY denotes a derivative matrix of a bending deformation shape; BF denotes a derivative matrix of a zigzag torsion deformation shape; and i=1, 2, 3.
5. The measurement method of a dynamic position of a wing baseline based on the 1FEM and RZT according to claim 1, wherein in step 2, during layout design of the strain rosette and the FBG sensor array on the wing according to the size of the wing, the strain rosette and the FBG sensor array are arranged at four different densities: very dense, dense, sparse, and very sparse; very dense, dense, and sparse arrangement manners are used in tri-axial strain measurement, and very sparse FBG sensors are used in uniaxial strain measurement; and the use of the very sparse arrangement manner in the uniaxial measurement makes it important to calibrate the sensors.
6. The measurement method of a dynamic position of a wing baseline based on the iFEM and RZT according to claim 1, wherein according to the data obtained from the FBG sensors and the strain rosette sensors in step 4, discrete surface strain data of the wing is derived and measured by using a first-order continuous derivative (C1) function, and a weighted least squares function is used to perform derivation and calculation for each individual RZT-based unit, wherein the derivation formula is as follows:
0.0) = eur ew ot] aw + w, (a) — rf + w, M") — | ‘ wherein De(u°) denotes the weighted least squares function; (k) denotes the kth layer after the three-node unit is divided into three layers; and j denotes the jth layer in cross-sectional strain measurement; / denotes a membrane strain function, X denotes a bending strain function, and M denotes a zigzag section strain; and led) — El, Nk) — KI2, [[u®@) — MI, lye) = TI%, and IIn(u®) — H||? are square norms corresponding to e(u®), ku), u(u°), yu‘), and n(u) respectively; y(u°) and n(u“) denote measured values of transverse shear strains of thefirst layer and the second layer respectively; I” and H denote shear strain functions HU102010 corresponding to y(w°) and n(u“) respectively; and wa (à = e, k, u, y, n) denotes a weighting constant vector of each individual strain.
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| Application Number | Priority Date | Filing Date | Title |
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| CN201910203304.0A CN109948245B (en) | 2019-03-18 | 2019-03-18 | Wing baseline dynamic position measurement method based on iFEM method and RZT theory |
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| LU102010B1 LU102010B1 (en) | 2020-12-30 |
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| CN114154220A (en) * | 2021-12-03 | 2022-03-08 | 山东大学 | Strain change rate damage identification method and system for beam structure |
| CN117892598A (en) * | 2024-03-13 | 2024-04-16 | 浙江大学海南研究院 | Enhanced inverse finite element shape sensing reconstruction system for offshore wind turbine tower |
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| CN109948245B (en) * | 2019-03-18 | 2023-06-06 | 东南大学 | Wing baseline dynamic position measurement method based on iFEM method and RZT theory |
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| CN102944183B (en) * | 2012-10-31 | 2015-10-21 | 中国航天空气动力技术研究院 | A kind of high-aspect ratio elastic wing measuring method |
| CN103852760B (en) * | 2012-12-04 | 2016-02-03 | 中国科学院电子学研究所 | A kind of many base measurements method based on rigidity and flexible baseline combination |
| EP3077281A4 (en) * | 2013-12-05 | 2017-07-26 | Tamarack Aerospace Group, Inc. | Wingtip device |
| CN108801166B (en) * | 2018-05-29 | 2020-05-26 | 北京航空航天大学 | Fiber bragg grating wing deformation measurement modeling and calibration method based on cantilever beam theory |
| CN109323659B (en) * | 2018-09-29 | 2024-03-29 | 株洲菲斯罗克光电科技股份有限公司 | Method and device for measuring baseline length of airborne synthetic aperture radar |
| CN109443224A (en) * | 2018-10-30 | 2019-03-08 | 哈尔滨工业大学 | A kind of antenna arrays of radar deformation measuring system and method |
| CN109948245B (en) * | 2019-03-18 | 2023-06-06 | 东南大学 | Wing baseline dynamic position measurement method based on iFEM method and RZT theory |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114154220A (en) * | 2021-12-03 | 2022-03-08 | 山东大学 | Strain change rate damage identification method and system for beam structure |
| CN117892598A (en) * | 2024-03-13 | 2024-04-16 | 浙江大学海南研究院 | Enhanced inverse finite element shape sensing reconstruction system for offshore wind turbine tower |
| CN117892598B (en) * | 2024-03-13 | 2024-06-07 | 浙江大学海南研究院 | Enhanced inverse finite element shape sensing reconstruction system for offshore wind turbine tower |
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| CN109948245B (en) | 2023-06-06 |
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