A method for monitoring bending and torsion deformation of a high-aspect-ratio wing that can be used in actual engineering

Abstract

The application provides a large-aspect-ratio wing bending and torsion deformation dynamic monitoring method which can be used in actual engineering. The method comprises the following steps: installing fiber Bragg grating (FBG) sensors and torsion strain gauges on a large-aspect-ratio wing girder; measuring bending and torsion strains by using the FBG sensors and the torsion strain gauges; establishing a strain-displacement relationship model, and determining the geometric parameters required by the strain-displacement relationship model through experiments; and calculating the deformation of the large-aspect-ratio wing in actual flight by using the strain-displacement relationship model and the real-time measured strain data. The application can avoid the influence of external environmental factors on the measurement. In addition, by combining the use of the torsion strain gauges, the flexibility of arranging the measuring points is improved, so that the measurement system can adapt to beams with different geometrical shapes, and is particularly suitable for unmanned aerial vehicles with large-aspect-ratio wings in actual engineering, and can realize the measurement of the dynamic response of the large-aspect-ratio wing in actual flight state in a complex flight environment.

Description

Technical Field

[0001] This invention relates to the field of dynamic monitoring technology for wing bending and torsional deformation, and in particular to a method for dynamic monitoring of bending and torsional deformation of high aspect ratio wings that can be used in practical engineering. Background Technology

[0002] Near-space solar-powered unmanned aerial vehicles (UAVs) have broad application prospects, capable of performing tasks such as atmospheric monitoring, communication relay, and high-altitude reconnaissance. To achieve a high lift-to-drag ratio and improve aerodynamic efficiency, the wings of these UAVs are designed with a high aspect ratio. This wing structure exhibits high flexibility, resulting in large deformations and significant vibrations under fluid-structure interaction. Therefore, real-time monitoring of wing deformation is necessary to adjust the UAV's attitude promptly and prevent structural damage. However, these UAVs have stringent weight requirements, limiting the amount of measuring equipment they can carry. Furthermore, the high flexibility and nonlinearity resulting from their ultra-long wingspan make deformation measurement extremely difficult. Currently, there are three main methods:

[0003] The first type is strain measurement method, which mainly measures strain by arranging sensors and reconstructs the bending and torsional deformation of the wing based on this. Ko, William L et al. [1] arranged multiple strain measurement points on one side of the beam, along the two edges of the beam. The deformation slope of the beam edge was calculated by the strain of adjacent measurement points, and then the bending displacement of the two edges of the beam was obtained respectively; based on the displacement difference of the two edges, combined with the beam width and trigonometric function theory, the torsional angle of the beam can be calculated. Meng et al. [2] described the deformation of the beam segment in the form of reference line + section, established the relationship between beam displacement and strain based on Kirchhoff beam and Green strain tensor theory, and proposed a method to reconstruct the three-dimensional deformation of slender beams by strain. The effectiveness of the method was verified by finite element numerical simulation and experiment.

[0004] The second category is laser measurement technology. Li Xiaolu et al. [3] proposed a method for measuring the elastic deformation of an wing based on two lasers: a laser is installed at the top and bottom of the fuselage, and a reflector is installed at the wingtip. The distance between the two lasers and the reflector is measured, and the bending displacement of the wingtip can be calculated based on the geometric relationship. If the wing deformation curve is determined in advance, the deformation at any point of the wing can be deduced from the bending displacement of the wingtip.

[0005] The third category is non-contact image measurement technology, such as digital image correlation (DIC) measurement method [4]. Liu et al. [5] used the DIC method to measure the deformation and displacement of a large aspect ratio wing in gusts and analyzed the nonlinear characteristics of the gust response of a large aspect ratio wing.

[0006] For the first type of strain measurement method, most existing studies are limited to numerical simulation and static or quasi-static measurement, and there is no in-depth study on dynamic deformation, especially torsional deformation. On the other hand, the surface strain of beams is usually measured using fiber Bragg grating sensors (FBG), such as in references [2] and [6]. FBG has the advantages of small size and resistance to electromagnetic interference. However, while FBG is convenient for measuring tensile strain in the fiber direction, it is difficult to measure shear strain. To measure shear strain, the FBG needs to be arranged at a certain angle to the beam axis, such as 45°. This installation method is difficult to implement on narrow wing structure beams. If the beam adopts a non-rectangular cross section (such as circular or H-shaped) or is equipped with a rib structure, the installation will become more difficult. FBG is also easy to break during installation. These factors are not conducive to the measurement of torsional deformation.

[0007] The second type of laser measurement technology is easily affected by the accuracy of the optical components themselves and the climate environment (clouds, icing), and cannot perform multi-point measurements at the same time, so it is difficult to apply in practice.

[0008] The third category is image measurement technology. This method is intuitive, WYSIWYG, and highly accurate, but it has significant limitations: the surface of the model being measured needs to be coated with a speckle pattern, which cannot be contaminated or subject to strong reflections, otherwise the image quality will be affected, thus impacting the measurement results. Therefore, it cannot handle complex real-world environments. This technology requires multiple cameras to track wing deformation, but in practice, drones are unlikely to carry cameras and capture complete deformed wings. Furthermore, in fluid-structure interaction experiments, its requirement for specific lighting conditions prevents simultaneous measurement with other optical research methods such as PIV, thus limiting research capabilities.

[0009] The specific documents are as follows:

[0010] [1] KO WL, FLEISCHER V T. Displacement theories for in-flight deformedshape predictions of aerospace structures, NASA / TP-2007-214612[R].NASA DrydenFlight Research Center, 2007.

[0011] [2]MENG Y, XIE C, WAN Z. Strain-based Shape Prediction for FlexibleBeam-like Structures[C] / / .AIAA SciTech Forum, San Diego, California, 2019.

[0012] [3] Li Xiaolu, Jiang Yuesong, He Yuntao. Principle of real-time measurement of wing deformation using dual lasers [J]. Optical Technology, 2006, 32(3):333-336.

[0013] [4]WANG L,BI S,LU X,et al.Deformation measurement of high-speedrotating drone blades based on digital image correlation combined with ringprojection transform and orientation codes[J].Measurement,2019,148:106899.

[0014] [5]LIU Y,

[0015] [6] Si Yawen, Zeng Jie, Xia Yubin, et al. Distributed fiber optic monitoring and reconstruction method for strain field of airfoil model [J]. Vibration. Testing and Diagnosis, 2020, 40(04):800-806. Summary of the Invention

[0016] One objective of this invention is to provide a dynamic monitoring method for bending and torsional deformation of high-aspect-ratio airfoils that can be applied to practical engineering projects, avoiding the influence of external environmental factors on the measurement. Furthermore, the combination with torsional strain gauges enhances the flexibility of measuring point placement, enabling the measurement system to adapt to beams of different geometries. It is particularly suitable for unmanned aerial vehicles (UAVs) with high-aspect-ratio airfoils in practical engineering, measuring the dynamic response of high-aspect-ratio airfoils during actual flight and adapting to complex flight environments.

[0017] This invention provides a method for dynamic monitoring of bending and torsional deformation of high aspect ratio airfoils that can be used in practical engineering, comprising:

[0018] FBG sensors and torsional strain gauges were installed on the main beam of the high aspect ratio airfoil model.

[0019] Establish a strain-displacement relationship model and determine the required geometric parameters for the strain-displacement relationship model through experiments;

[0020] The deformation of a high aspect ratio airfoil during actual flight was calculated using a strain-displacement relationship model and real-time strain measurement data.

[0021] The rules for constructing the strain-displacement relationship model include:

[0022] Let z F,k and z S,j These represent the distances between the wing root and the k-th FBG sensor and the j-th torsional strain gauge, respectively.

[0023] The bending strain ε at point k caused by bending k From the formula ε k =(ε u,k -ε d,k The result is obtained by calculating ) / 2, where ε u,k and ε d,k It is the strain on the upper and lower surfaces of the beam measured by FBG sensors;

[0024] Shear strain γ j It is obtained by connecting four strain gauges using a full-bridge connection method;

[0025] The high aspect ratio airfoil model is discretized into multiple beam elements, where the dividing boundary S is set. i If z is the span section where the centers of two adjacent FBG sensors are located, then in the i-th beam element, z = z e,i Bending strain (ε) at the point e,i ) and shear strain (γ) e,i (Given by the measurement point or obtained through interpolation)

[0026] ε e,i =ε i (1)

[0027]

[0028] Section S of the beam element i Composed of key nodes, the cross section is represented by a set of position vectors of the key nodes, i.e., S. i =(r 0,i ,r 1,i ,…), where r 0,i =[x 0,i ,y 0,i ,z 0,i ] T The vector representing the chord center position of the cross section, r 1,i r 2,i Equal to represent section S i The position vectors of other points on it;

[0029] Let S0 be the original standard cross section, located on the z=0 plane, with the chord of the original standard cross section in the positive x-axis direction and the center point of the chord at r. 0,0 =[0,0,0] T All cross sections S of the wing i All of them will be obtained from the transformation of S0;

[0030] Based on S i Establish a local coordinate system (xoyz) i The upper right corner mark 'i' indicates that in S i The local coordinate system is set at point A, with the origin at point A; x i The axis runs along the chord, with its positive direction pointing from the center of the chord to the leading edge; z i The axis is S i The normal direction is from node A to node B; y i The axis is determined by x i axis and z i The axis is determined by the right-hand rule; the cross section S i and S i+1 In the local coordinate system (xoyz) i The middle is recorded as and

[0031] Local coordinate system (xoyz) i In the beam element, the displacement of each point is referenced to S. i (or Therefore, S i (or ) is a standard cross section, that is, there is always

[0032] It can be regarded as being caused by S i i The following transformation process is required:

[0033] First, consider the bending effect. Rotation Δθ around the string ρ,i Then, due to torsion, the cross-section Rotation Δθ relative to its own normal at this moment γ,i After that, Translate a vector Δr i get This process can be represented as:

[0034]

[0035] When i = 0, that is This indicates that the local coordinate system is established at S0, and the first section S1 of the wing is obtained by transforming S0, denoted as in the local coordinate system. When i = 1, This indicates that the local coordinate system is established at S1, the second section of the wing. Depend on Obtained by transformation;

[0036] In formula (3) Φ i It is a transformation matrix containing the rotation T around the chord. x (Δθ ρ,i and rotation T around its own normal z (Δθ γ,i ):

[0037] Φ i =T x (Δθ ρ,i )T z (Δθ γ,i (4)

[0038] in:

[0039]

[0040]

[0041] In equation (5), the twist angle Δθ γ,i It is the shear strain γ e，i The function can be represented as:

[0042]

[0043] C twst These are geometric parameters, measured in advance experimentally; L h L is the thickness of the beam web. e,i Let be the length of the i-th beam element AB; when i = 0, it means that S0 is transformed into S1; because the root section of the wing is a fixed boundary and there is no torsional deformation, therefore Δθ γ,0 =0°.

[0044] Δθ in equation (6) ρ,i Caused by bending The angle of rotation relative to the chord, that is, the arc angle of A'B, is determined by the bending strain ε. e,i Decision; when ε e,i When ≠0, Δθ ρ,i It can be given by the following formula:

[0045] Δθ ρ,i =sign(ε e,i )L e,i / R ρ,i (8)

[0046] R ρ,iIt is the radius of the arc A'B. According to mechanics of materials, we have:

[0047] R ρ,i =|C bend L h / (2ε e,i )|,(9)

[0048] Considering the irregular cross-sectional shape and the errors generated during the manufacturing process, a geometric parameter C is added to equation (9). bend This parameter was determined experimentally.

[0049] Local coordinate system (xoyz) i The translation vector from node A' to node B' is:

[0050]

[0051] If ε e,i =0 (i.e., the beam element is not bent), which can be specified

[0052] Δθ ρ,i =0, (11)

[0053] Δr i =[0,0,L e,i ] T (12)

[0054] When i = 0, Δθ ρ,0 =0°, Δr 0 =[0,0,0] T .

[0055] We obtain the following from formulas (3)-(12) Then, transform it from the local coordinate system to the global coordinate system:

[0056]

[0057] In formula (13) r 0,i It is S i The position of the chord center in the global coordinate system, and Γ(i) is determined by the following equation:

[0058]

[0059] In the above formula, I one It is an identity matrix, and Γ(1)=Φ0=T x (Δθ ρ,0 =0)T z (Δθ γ,0 =α0); Formula (3)-(13) represent this process: for S i -S i+1The cut beam segment, S i+1 It is by S i The transformation process is as follows: S i -S i+1 The beam segment is placed in a local coordinate system, such that S i Located at S0, denoted as Considering bending and torsion, let The cross section is obtained by rotating the cross section around its own chord and normal, and then translating it by a vector. Then Restore to the global coordinate system;

[0060] Substituting equation (3) into equation (13), we get:

[0061]

[0062] Equation (15) represents the section S in the global coordinate system. i+1 This can be viewed as performing a series of rotational transformations (Γ(i+1)) and a translational transformation on S0. The result;

[0063] Formula (15) simplifies to:

[0064] S0=Γ -1 (i+1)(S i+1 -(Γ(i)Δr i +r 0,i ),i=0,1,2…,(16)

[0065] Δr i It is in the local coordinate system from S i To S i+1 The translation vector, Γ(i)Δr i It is Δr i Convert to the form in the global coordinate system, r 0,i It is S i The heart of the string, therefore S represents i+1 The string of r 0,i+1 ;

[0066] Formula (16) simplifies to:

[0067] S0=Γ -1 (i+1)(S i+1 -r 0,i+1 )=Γ -1 (i)(S i -r 0,i ), i = 0, 1, 2…,(17)

[0068] Substituting formula (17) into formula (15), we can obtain the result from S. i To Si+1 The recurrence relation:

[0069] S i+1 =Γ(i)Φ i Γ -1 (i)(S i -r 0,i )+Γ(i)Δr i +r 0,i ,i=0,1,2…,(18)

[0070] Using equation (15) or (18), the cross sections of the wing along the wingspan can be generated one by one, and the deformed wing can be reconstructed. For example, the first cross section (root section) of the wing is:

[0071] S1=Γ(1)S0+Γ(0)Δr 0 +r 0,0 =Φ0S0;

[0072] This means that S1 is only a rigid body rotation relative to S0 caused by the installation angle of attack α0, and there is no change caused by deformation.

[0073] The second section S2 of the wing is:

[0074] S2=Γ(2)S0+Γ(1)Δr 1 +r 0,1 =Φ0Φ1S0+Φ0Δr 1 +r 0,1 ;

[0075] r 0,1 It is the global coordinate system position vector of the chord center S1; the formula means that the beam segment S1-S2 is first placed in the local coordinate system, so that S1 coincides with S0 (denoted as ). ),Then After a series of rotational transformations Φ1 and then translation Δr 1 Obtain a new plane And after transformation Φ0 and translation r 0,1 Reverting to the global coordinate system, we get S2 and Δr. 1 Φ1 is determined by the bending and torsional strains of the first beam element according to equations (10) and (4).

[0076] For geometric parameter C bend and C twst Calibration includes:

[0077] Assume C bend and C twst The initial value of each is 1;

[0078] A pre-set large-amplitude bending-torsional composite displacement is applied to a cantilevered, high-aspect-ratio wing, allowing the wing to undergo free damping vibration. The bending and torsional strains of the wing are measured, and the displacement is calculated. At the same time, the displacement of the wing is measured using the DIC method as a reference value.

[0079] Adjust C bend and C twst This ensures that the calculated displacement and the reference displacement value meet the error range.

[0080] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings.

[0081] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0082] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0083] Figure 1 (a) is a schematic diagram of the high aspect ratio wing model and the installation of FBG sensor and torsional strain gauge in an embodiment of the present invention;

[0084] Figure 1 (b) is a schematic diagram of the process of reconstructing wing deformation by strain in an embodiment of the present invention;

[0085] Figure 1 (c) is a schematic diagram of the reconstructed and deformed high aspect ratio wing model in an embodiment of the present invention;

[0086] Figure 2 This is a schematic diagram showing the arrangement of the FBG sensor and torsional strain gauge and the division of beam elements in the wing model in an embodiment of the present invention.

[0087] Figure 3 (a) is a 3D deformation reconstruction diagram of the wing in an embodiment of the present invention;

[0088] Figure 3 (b) is a detailed view of the deformable beam unit AB in the embodiment of the present invention. Detailed Implementation

[0089] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0090] First, let's explain the relevant terms:

[0091] FBG (Fiber Bragg Grating Sensor) and DIC (Digital Image Correlation Non-Contact Full-Field Strain Measurement System).

[0092] This invention provides a method for dynamic monitoring of bending and torsional deformation of high aspect ratio airfoils that can be used in practical engineering, comprising:

[0093] FBG sensors and torsional strain gauges are installed on the main beam of the high aspect ratio airfoil model. The measurement points of the FBG sensors and torsional strain gauges do not overlap. Each measurement point has an FBG sensor symmetrically distributed on the upper and lower surfaces of the main beam, or a torsional strain gauge symmetrically distributed on the upper and lower surfaces of the main beam.

[0094] Establish a strain-displacement relationship model and determine the required geometric parameters for the strain-displacement relationship model through experiments;

[0095] The deformation of a high aspect ratio wing during actual flight is calculated using a strain-displacement relationship model and real-time strain measurement data.

[0096] The rules for constructing the strain-displacement relationship model include:

[0097] Let z F,k and z S,j These represent the distances between the wing root and the k-th FBG sensor and the j-th torsional strain gauge, respectively.

[0098] The bending strain ε at point k caused by bending k From the formula ε k =(ε u,k -ε d,k The result is obtained by calculating ) / 2, where ε u,k and ε d,k It is the strain on the upper and lower surfaces of the beam measured by FBG sensors;

[0099] Shear strain γ j It is obtained by connecting four strain gauges using a full-bridge connection method;

[0100] The high aspect ratio airfoil model is discretized into multiple beam elements, where the dividing boundary S is set. i If z is the span section where the centers of two adjacent FBG sensors are located, then in the i-th beam element, z = z e,i Bending strain (ε) at the point e,i ) and shear strain (γ) e,i (Given by the measurement point or obtained through interpolation)

[0101] ε e,i =ε i (1)

[0102]

[0103] Section S of the beam element i Composed of key nodes, the cross section is represented by a set of position vectors of the key nodes, i.e., S. i =(r 0,i ,r 1,i ,…), where r 0,i =[x 0,i ,y 0,i ,z 0,i ] T The vector representing the chord center position of the cross section, r 1,i r 2,i Equal to represent section S i The position vectors of other points on it;

[0104] Let S0 be the original standard cross section, located on the z=0 plane, with the chord of the original standard cross section in the positive x-axis direction and the center point of the chord at r. 0,0 =[0,0,0] T All cross sections S of the wing i All of them will be obtained from the transformation of S0;

[0105] Based on S i Establish a local coordinate system (xoyz) i The upper right corner mark 'i' indicates that in S i The local coordinate system is set at point A, with the origin at point A; x i The axis runs along the chord, with its positive direction pointing from the center of the chord to the leading edge; z i The axis is S i The normal direction is from node A to node B; y i The axis is determined by x i axis and z i The axis is determined by the right-hand rule; the cross section S i and S i+1 In the local coordinate system (xoyz) i The middle is recorded as and

[0106] Local coordinate system (xoyz) i In the beam element, the displacement of each point is referenced to S. i (or Therefore, S i (or ) is a standard cross section, that is, there is always

[0107] It can be regarded as being caused by The following transformation process is required:

[0108] First, consider the bending effect. Rotation Δθ around the string ρ,i Then, due to torsion, the cross-section Rotation Δθ relative to its own normal at this moment γ,i After that, Translate a vector Δr i get This process can be represented as:

[0109]

[0110] When i = 0, that is This indicates that the local coordinate system is established at S0, and the first section S1 of the wing is obtained by transforming S0, denoted as in the local coordinate system. When i = 1, This indicates that the local coordinate system is established at S1, the second section of the wing. Depend on Obtained by transformation;

[0111] In formula (3) Φ i It is a transformation matrix containing the rotation T around the chord. x (Δθ ρ,i and rotation T around its own normal z (Δθ γ,i ):

[0112] Φ i =T x (Δθ ρ,i )T z (Δθ γ,i (4)

[0113] in:

[0114]

[0115]

[0116] In equation (5), the twist angle Δθ γ,i It is the shear strain γ e，i The function can be represented as:

[0117]

[0118] C twst These are geometric parameters, measured in advance experimentally; L h L is the thickness of the beam web. e,i Let be the length of the i-th beam element AB; when i = 0, it means that S0 is transformed into S1; because the root section of the wing is a fixed boundary and there is no torsional deformation, therefore Δθ γ,0=0°.

[0119] Δθ in equation (6) ρ,i Caused by bending The angle of rotation relative to the chord, that is, the arc angle of A'B, is determined by the bending strain ε. e,i Decision; when ε e,i When ≠0, Δθ ρ,i It can be given by the following formula:

[0120] Δθ ρ,i =sign(ε e,i )L e,i / R ρ,i (8)

[0121] R ρ,i It is the radius of the arc A'B. According to mechanics of materials, we have:

[0122] R ρ,i =|C bend L h / (2ε e,i )|,(9)

[0123] Considering the irregular cross-sectional shape and the errors generated during the manufacturing process, a geometric parameter C is added to equation (9). bend This parameter was determined experimentally.

[0124] Local coordinate system (xoyz) i The translation vector from node A' to node B' is:

[0125]

[0126] If ε e,i =0 (i.e., the beam element is not bent), which can be specified

[0127] Δθ ρ,i =0, (11)

[0128] Δr i =[0,0,L e,i ] T (12)

[0129] When i = 0, Δθ ρ,0 =0°, Δr 0 =[0,0,0] T .

[0130] S is obtained from formulas (3)-(12) i i +1 Then, transform it from the local coordinate system to the global coordinate system:

[0131]

[0132] In formula (13) r 0,i It is S i The position of the chord center in the global coordinate system, and Γ(i) is determined by the following equation:

[0133]

[0134] In the above formula, I one It is an identity matrix, and Γ(1)=Φ0=T x (Δθ ρ,0 =0)T z (Δθ γ,0 =α0); Formula (3)-(13) represent this process: for S i -S i+1 The cut beam segment, S i+1 It is by S i The transformation process is as follows: S i -S i+1 The beam segment is placed in a local coordinate system, such that S i Located at S0, denoted as Considering bending and torsion, let The cross section is obtained by rotating the cross section around its own chord and normal, and then translating it by a vector. Then Restore to the global coordinate system;

[0135] Substituting equation (3) into equation (13), we get:

[0136]

[0137] Equation (15) represents the section S in the global coordinate system. i+1 This can be viewed as performing a series of rotational transformations (Γ(i+1)) and a translational transformation on S0. The result;

[0138] Formula (15) simplifies to:

[0139] S0=Γ -1 (i+1)(S i+1 -(Γ(i)Δr i +r 0,i ),i=0,1,2…,(16)

[0140] Δr i It is in the local coordinate system from S i To S i+1 The translation vector, Γ(i)Δr i It is Δr i Convert to the form in the global coordinate system, r 0,iIt is S i The heart of the string, therefore S represents i+1 The string of r 0,i+1 ;

[0141] Formula (16) simplifies to:

[0142] S0=Γ -1 (i+1)(S i+1 -r 0,i+1 )=Γ -1 (i)(S i -r 0,i ), i = 0, 1, 2…,(17)

[0143] Substituting formula (17) into formula (15), we can obtain the result from S. i To S i+1 The recurrence relation:

[0144] S i+1 =Γ(i)Φ i Γ -1 (i)(S i -r 0,i )+Γ(i)Δr i +r 0,i ,i=0,1,2…,(18)

[0145] Using equation (15) or (18), the cross sections of the wing along the wingspan can be generated one by one, and the deformed wing can be reconstructed. For example, the first cross section (root section) of the wing is:

[0146] S1=Γ(1)S0+Γ(0)Δr 0 +r 0,0 =Φ0S0;

[0147] This means that S1 is only a rigid body rotation relative to S0 caused by the installation angle of attack α0, and there is no change caused by deformation.

[0148] The second section S2 of the wing is:

[0149] S2=Γ(2)S0+Γ(1)Δr 1 +r 0,1 =Φ0Φ1S0+Φ0Δr 1 +r 0,1 ;

[0150] r 0,1 It is the global coordinate system position vector of the chord center S1; the formula means that the beam segment S1-S2 is first placed in the local coordinate system, so that S1 coincides with S0 (denoted as ). ),Then After a series of rotational transformations Φ1 and then translation Δr 1Obtain a new plane And after transformation Φ0 and translation r 0,1 Reverting to the global coordinate system, we get S2 and Δr. 1 Φ1 is determined by the bending and torsional strains of the first beam element according to equations (10) and (4).

[0151] The C bend and C twst Calibration includes:

[0152] Assume C bend and C twst The initial value of each is 1;

[0153] A pre-set large-amplitude bending-torsional composite displacement is applied to a cantilevered, high-aspect-ratio wing, allowing the wing to undergo free damping vibration. The bending and torsional strains of the wing are measured, and the displacement is calculated. At the same time, the displacement of the wing is measured using the DIC method as a reference value.

[0154] Adjust C bend and C twst This ensures that the calculated displacement and the reference displacement value meet the error range.

[0155] The specific working principle and beneficial effects of the above technical solution are as follows:

[0156] I. Overall Approach

[0157] This method achieves the following: Figure 1 As shown: (1) FBG sensors and torsional strain gauges are installed on the main beam of the high aspect ratio wing model. Figure 1 (a) ;(2) FBG sensor and torsional strain gauge respectively measure the bending and torsional strain of the large aspect ratio wing structure beam due to deformation; (3) according to the strain-displacement relationship model construction method proposed in this invention, the bending and torsional deformation of the wing is calculated. Figure 1 b); (4) Reconstructing the three-dimensional deformation of the wing ( Figure 1 c).

[0158] II. Specific Working Principle

[0159] like Figure 2 The diagram shows the positions of the FBG sensor and torsional strain gauge along the axial direction of the wing main sparsity. F,k and z S,j These represent the distances between the wing root and the k-th FBG sensor and the j-th torsional strain gauge, respectively. The measurement points of the FBG sensor and the torsional strain gauge do not overlap; each measurement point has one FBG sensor symmetrically distributed on the upper and lower surfaces of the beam, or one torsional strain gauge symmetrically distributed on the upper and lower surfaces of the beam. The bending strain ε at point k caused by bending is... k From the formula ε k =(εu,k -ε d,k The result is obtained by calculating ) / 2, where ε u,k and ε d,k These are the strains measured by FBG sensors on the upper and lower surfaces of the beam. Shear strain γ j It is obtained by connecting four strain gauges using the "full-bridge connection" method. Figure 2 The image shows the measurement of ε at 7 selected points. k Gamma was measured at 4 points. j The wing model is discretized into beam elements, where the boundary S is segmented. i This is the spanwise section where the centers of two adjacent FBG sensors are located. At this point, in the i-th beam element, z = zi. e,i Bending strain (ε) at the point e,i ) and shear strain (γ) e,i The values ​​are given by the measuring points or obtained through interpolation:

[0160] ε e,i =ε i (1)

[0161]

[0162] Section S of the beam element i Composed of key nodes, the cross section is represented by a set of node position vectors, i.e., S. i =(r 0,i ,r 1,i ,…)(See Figure 3 (a)), where r 0,i =[x 0,i ,y 0,i ,z 0,i ] T The vector representing the chord center position of the cross section, r 1,i r 2,i Equal to represent section S i The position vectors of other points on the wing are typically selected from special points such as the leading and trailing edges. This is done when determining the position vectors of various wing sections S. i After that position, we get the deformed wings.

[0163] Let S0 be the original standard cross section (without a preset angle of attack), located on the z=0 plane, with its chord in the positive x-axis direction and the center point of the chord at r. 0,0 =[0,0,0] T All cross sections S of the wing iAll sections are derived from S0. For example, the first section of the wing is the root section S1. Because it is a fixed end, there is no bending or torsional deformation, only the angle of attack α0 set during installation. Therefore, S0 is rotated by α0 degrees relative to the z-axis to obtain S1 (when α0 = 0°, S1 = S0). The generation of subsequent wing sections needs to consider bending and torsional deformation. Using section S... i and S i+1 Taking the i-th beam element AB between them as an example (see...) Figure 3 (a)). Nodes A and B are S... i and S i+1 The center point of the chord in the beam. Since beam element AB is both bending and tortuous, it can be determined by adjusting S. i A series of transformations are performed to obtain the cross section S. i+1 .

[0164] To better describe the transformation process, based on S i ( Figure 3 (b) A local coordinate system (xoyz) was established. i The upper right corner mark "i" indicates that in S i The local coordinate system is set at point A, with the origin at point A. i The axis runs along the chord, with its positive direction pointing from the center of the chord to the leading edge. i The axis is S i The normal direction of y is from node A to node B. i The axis is determined by x i axis and z i The axis is determined by the right-hand rule. Section S i and S i+1 In the local coordinate system (xoyz) i The middle is recorded as and Note that this local coordinate system means that the displacements of points in the beam element are all referenced to S. i (or Therefore, S i (or ) is a standard cross section, that is, there is always

[0165] It can be regarded as being caused by The following transformation process is used to obtain the result: First, considering the bending effect... Rotation Δθ around the string ρ,i Then, due to torsion, the cross-section Rotation Δθ relative to its own normal at this moment γ,i After that, then... Translate a vector Δr i get This process can be written as:

[0166]

[0167] For example, when i = 0, that is The local coordinate system is established at S0, and the first section (root section) S1 of the wing is obtained by transforming S0, denoted as S1 in the local coordinate system. When i = 1, This indicates that the local coordinate system is established at S1 (equivalent to placing S1 at the same position as S0, denoted as S0). ), the second section of the wing Depend on Obtained by transformation.

[0168] In formula (3) Φ i It is a transformation matrix containing the rotation T around the chord. x (Δθ ρ,i and rotation T around its own normal z (Δθ γ,i ):

[0169] Φ i =T x (Δθ ρ, i )T z (Δθ γ, i (4)

[0170] in:

[0171]

[0172]

[0173] In equation (5), the twist angle Δθ γ,i It is the shear strain γ e，i The function can be represented as:

[0174]

[0175] C twst These are geometric parameters, measured beforehand experimentally. L h L is the thickness of the beam web. e,i Let AB be the length of the i-th beam element (which is also equal to the length of arc A'B'). Specifically, when i = 0, it means S0 is transformed into S1. Because the root section of the wing is a fixed boundary with no torsional deformation, Δθ... γ,0 =0°.

[0176] Δθ in equation (6) ρ,i Caused by bending The angle of rotation relative to the chord, that is, the arc angle of A'B, is determined by the bending strain ε. e,i Decision. When ε e,i When ≠0, Δθ ρ,i It can be given by the following formula:

[0177] Δθ ρ, i =sign(ε e, i )L e, i / R ρ, i (8)

[0178] R ρ,i It is the radius of the arc A'B. According to mechanics of materials, we have:

[0179] R ρ, i =|C bend L h / (2ε e, i )|, (9)

[0180] Considering the irregular cross-sectional shape and the errors generated during the manufacturing process, a geometric parameter C is added to equation (9). bend This parameter was determined experimentally.

[0181] Local coordinate system (xoyz) i The translation vector from node A' to node B' is:

[0182]

[0183] If ε e,i =0 (i.e., the beam element is not bent), which can be specified

[0184] Δθ ρ,i =0, (11)

[0185] Δr i =[0,0,L e,i ] T (12)

[0186] When i = 0, Δθ ρ,0 =0°, Δr 0 =[0,0,0] T .

[0187] We obtain the following from formulas (3)-(12) Then, transform it from the local coordinate system to the global coordinate system:

[0188]

[0189] In formula (13) r 0,i It is S i The position of the chord center in the global coordinate system, and Γ(i) is determined by the following equation:

[0190]

[0191] In the above formula, I one It is an identity matrix, and Γ(1)=Φ0=T x (Δθ ρ,0 =0)T z (Δθ γ,0 =α0). Formula (3)-(13) represent this process: for S i -S i+1 The cut beam segment, S i+1 It is by S i The transformation process is as follows: S i -S i+1 The beam segment is placed in a local coordinate system, such that S i Located at S0, denoted as Considering bending and torsion, let The cross section is obtained by rotating the cross section around its own chord and normal, and then translating it by a vector. (Formula (3)), then Restore to the global coordinate system (Formula (13)).

[0192] Substituting equation (3) into equation (13), we get:

[0193]

[0194] Equation (15) represents the section S in the global coordinate system. i+1 This can be viewed as performing a series of rotational transformations (Γ(i+1)) and a translational transformation on S0. The result is as follows. Formula (15) is further simplified below. Formula (15) is rewritten as:

[0195] S0=Γ -1 (i+1)(S i+1 -(Γ(i)Δr i +r 0,i ),i=0,1,2…,(16)

[0196] Δr i It is in the local coordinate system from S i To S i+1 The translation vector, Γ(i)Δr i It is Δr i Convert to the form in the global coordinate system, r 0,i It is Si The heart of the string, therefore S represents i+1 The string of r 0,i+1 ( Figure 3 (a)).

[0197] Formula (16) can be written as:

[0198] S0=Γ -1 (i+1)(S i+1 -r 0,i+1 )=Γ -1 (i)(S i -r 0,i ), i = 0, 1, 2…,(17)

[0199] Substituting formula (17) into formula (15), we can obtain the result from S. i To S i+1 The recurrence relation:

[0200] S i+1 =Γ(i)Φ i Γ -1 (i)(S i -r 0,i )+Γ(i)Δr i +r 0,i ,i=0,1,2…,(18)

[0201] Using equation (15) or (18), the cross sections of the wing along the wingspan can be generated one by one, and the deformed wing can be reconstructed. For example, the first cross section (root section) of the wing is:

[0202] S1=Γ(1)S0+Γ(0)Δr 0 +r 0,0 =Φ0S0,

[0203] This means that S1 is only a rigid body rotation caused by the installation angle of attack α0 relative to S0, without any transformation caused by deformation.

[0204] The second section S2 of the wing is:

[0205] S2=Γ(2)S0+Γ(1)Δr 1 +r 0,1 =Φ0Φ1S0+Φ0Δr 1 +r 0,1 ,

[0206] r 0,1 It is the global coordinate system position vector of the chord center S1. The formula means that beam segment S1-S2 is first placed in the local coordinate system, so that S1 coincides with S0 (denoted as S0). ),Then After a series of rotational transformations Φ1 and then translation Δr1 Obtain a new plane And after transformation Φ0 and translation r 0,1 Restoring to the global coordinate system, this is S2.Δr 1 Φ1 is determined by the bending and torsional strains of the first beam element according to equations (10) and (4).

[0207] By analogy, we can obtain the various cross-sections of the deformed wing.

[0208] Regarding C bend and C twst Experimental determination

[0209] In the laboratory, we can study C bend and C twst Perform calibration. First, assume C... bend and C twst The initial values ​​for all parameters are 1. Then, a large combined bending-torsional displacement is applied to the cantilevered, high-aspect-ratio wing, allowing it to undergo free damping vibration. The bending and torsional strains of the wing are measured, and the displacement is calculated. Simultaneously, other measurement methods, such as the DIC method, are used to measure the wing displacement as a reference value. Adjust C... bend and C twst This ensures that the calculated displacement and the reference displacement value meet the error range. C was calibrated. bend and C twst They can then be used to measure the dynamic displacement of high aspect ratio wings under wind loads.

[0210] III. Beneficial Effects

[0211] This invention can be applied to unmanned aerial vehicles (UAVs) with high aspect ratio wings in practical engineering. By embedding sensors within the wing's internal structure, this invention avoids the influence of external environmental factors (such as wind and rain) on the measurement. Furthermore, the combination with torsional strain gauges enhances the flexibility of measuring point placement, allowing the measurement system to adapt to beams of different geometries (such as circular, rectangular, and H-shaped), making it particularly suitable for measuring the dynamic response of high aspect ratio wings during actual flight in complex flight environments. Existing non-contact measurement methods, such as DIC and laser measurement, are easily affected by the actual environment or are difficult to implement with key measuring instruments like cameras, making them impractical for real-world applications.

[0212] This invention can measure large-scale dynamic bending and torsional deformation of high-aspect-ratio wings, providing a more comprehensive monitoring of the structural dynamic response of actual unmanned aerial vehicles. Existing strain-based measurement techniques mainly focus on large-scale bending measurements, and are mostly static or quasi-static, without in-depth research on dynamic large-scale torsional deformation. This technical solution achieves accurate measurement of both large-scale dynamic bending and torsional deformation simultaneously.

[0213] This invention can work synchronously with other optical measurement methods (such as PIV), facilitating multi-angle studies of fluid-structure interaction phenomena. This synchronous measurement capability enriches experimental research methods and improves the accuracy and comprehensiveness of experimental data. In contrast, some existing measurement techniques, such as DIC measurement methods, cannot work together due to conflicts between the light source and PIV.

[0214] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for dynamic monitoring of bending and torsional deformation of high aspect ratio airfoils applicable to practical engineering, characterized by: FBG sensors and torsional strain gauges were installed on the main beam of the model to measure bending and torsional strain. Establish a strain-displacement relationship model; The required geometric parameters for the strain-displacement relationship model were determined experimentally. The deformation of a high aspect ratio wing during actual flight was calculated using a strain-displacement relationship model and real-time strain measurement data. The rules for constructing the strain-displacement relationship model are as follows: Let z F,k and z S,j These represent the distances between the wing root and the k-th FBG sensor and the j-th torsional strain gauge, respectively. The bending strain ε at point k caused by bending k From the formula ε k =(ε u,k -ε d,k The result is obtained by calculating ) / 2, where ε u,k and ε d,k It is the strain on the upper and lower surfaces of the beam measured by FBG sensors; Shear strain γ j It is obtained by connecting four strain gauges using a full-bridge connection method; The high aspect ratio airfoil model is discretized into multiple beam elements, where the dividing boundary S is set. i If z is the span section where the centers of two adjacent FBG sensors are located, then in the i-th beam element, z = z e,i Bending strain (ε) at the point e,i ) and shear strain (γ) e,i (Given by the measurement point or obtained through interpolation) e e,i =e i , (1) Section S of the beam element i Composed of key nodes, the cross section is represented by a set of position vectors of the key nodes, i.e., S. i =(r 0,i ,r 1,i ,…), where r 0,i =[x 0,i ,y 0,i ,z 0,i ] T The vector representing the chord center position of the cross section, r 1,i r 2,i Equal to represent section S i The position vectors of other points on it; Let S0 be the original standard cross section, located on the z=0 plane, with the chord of the original standard cross section in the positive x-axis direction and the center point of the chord at r. 0,0 =[0,0,0] T All cross sections S of the wing i All of them will be obtained from the transformation of S0.

2. The dynamic monitoring method for bending and torsional deformation of a high aspect ratio airfoil as described in claim 1, applicable to practical engineering, is characterized in that... Also includes: Based on S i Establish a local coordinate system (xoyz) i The upper right corner mark 'i' indicates that in S i The local coordinate system is set at point A, with the origin at point A; x i The axis runs along the chord, with its positive direction pointing from the center of the chord to the leading edge; z i The axis is S i The normal direction is from node A to node B; y i The axis is determined by x i axis and z i The axis is determined by the right-hand rule; the cross section S i and S i+1 In the local coordinate system (xoyz) i The middle is recorded as and Local coordinate system (xoyz) i In the beam element, the displacement of each point is referenced to S. i or Therefore S i or It is a standard cross section, meaning it always has... It can be regarded as being caused by The following transformation process is required: First, consider the bending effect. Rotation Δθ around the string ρ,i Then, due to torsion, the cross section S i i Rotation Δθ relative to its own normal at this moment γ,i After that, Translate a vector Δr i get This process can be represented as: When i = 0, that is This indicates that the local coordinate system is established at S0, and the first section S1 of the wing is obtained by transforming S0, denoted as in the local coordinate system. When i = 1, This indicates that the local coordinate system is established at S1, the second section of the wing. Depend on Obtained by transformation; In formula (3) Φ i It is a transformation matrix containing the rotation T around the chord. x (Δθ ρ,i and rotation T around its own normal z (Δθ γ,i ): F i =T x (Dth ρ,i )T z (Dth γ,i ), (4) in: In equation (5), the twist angle Δθ γ,i It is the shear strain γ e，i The function can be represented as: C twst These are geometric parameters, measured in advance experimentally; L h L is the thickness of the beam web. e,i Let be the length of the i-th beam element AB; when i = 0, it means that S0 is transformed into S1; because the root section of the wing is a fixed boundary and there is no torsional deformation, therefore Δθ γ,0 =0°. Δθ in equation (6) ρ,i Caused by bending The angle of rotation relative to the chord, that is, the arc angle of A'B, is determined by the bending strain ε. e,i Decision; when ε e,i When ≠0, Δθ ρ,i It can be given by the following formula: Dth ρ,i =sign(e e,i )L e,i / R ρ,i , (8) R ρ,i It is the radius of the arc A'B. According to mechanics of materials, we have: R ρ,i =|C bend L h / (2ε e,i )|, (9) Considering the irregular cross-sectional shape and the errors generated during the manufacturing process, a geometric parameter C is added to equation (9). bend This parameter was determined experimentally. Local coordinate system (xoyz) i The translation vector from node A' to node B' is: If ε e,i =0, meaning the beam element is not bent, which can be specified. Dth ρ,i =0,(11) Δr i =[0,0,L e,i ] T ,(12) When i = 0, Δθ ρ,0 = 0°, Δr 0 = [0, 0, 0] T . We obtain the following from formulas (3)-(12) Then, transform it from the local coordinate system to the global coordinate system: In formula (13) r 0,i It is S i The position of the chord center in the global coordinate system, and Γ(i) is determined by the following equation: In the above formula, I one It is an identity matrix, and Γ(1)=Φ0=T x (Δθ ρ,0 =0)T z (Δθ γ,0 =α0); Formula (3)-(13) represent this process: for S i -S i+1 The cut beam segment, S i+1 It is by S i The transformation process is as follows: S i -S i+1 The beam segment is placed in a local coordinate system, such that S i Located at S0, denoted as Considering bending and torsion, let The cross section is obtained by rotating the cross section around its own chord and normal, and then translating it by a vector. Then Restore to the global coordinate system; Substituting equation (3) into equation (13), we get: Equation (15) represents the section S in the global coordinate system. i+1 This can be viewed as performing a series of rotational transformations Γ(i+1) and a translational transformation on S0. The result; Formula (15) simplifies to: S0=Γ -1 (i+1)(S i+1 -(Γ(i)Δr i +r 0,i )),i=0,1,2…, (16) Δr i It is in the local coordinate system from S i To S i+1 The translation vector, Γ(i)Δr i It is Δr i Convert to the form in the global coordinate system, r 0,i It is S i The heart of the string, therefore S represents i+1 The string of r 0,i+1 ; Formula (16) simplifies to: S0=Γ -1 (i+1)(S i+1 -r 0,i+1 )=Γ -1 (i)(S i -r 0,i ),i=0,1,2…, (17) Substituting formula (17) into formula (15), we can obtain the result from S. i To S i+1 The recurrence relation: S i+1 =Γ(i)Φ i C -1 (i)(S) i -r 0,i )+Γ(i)Δr i +r 0,i ,i=0,1,2…, (18) Using equation (15) or equation (18), the cross sections of the wing along the wingspan can be generated one by one, and the deformed wing can be reconstructed; the first cross section of the wing, i.e. the root cross section, is: S1=Γ(1)S0+Γ(0)Δr 0 +r 0,0 =Φ0S0; This means that S1 is only a rigid body rotation relative to S0 caused by the installation angle of attack α0, and there is no change caused by deformation. The second section S2 of the wing is: S2=Γ(2)S0+Γ(1)Δr 1 +r 0,1 =Φ0Φ1S0+Φ0Δr 1 +r 0,1 ; r 0,1 It is the global coordinate system position vector of the chord center S1; the formula means that the beam segment S1-S2 is first placed in the local coordinate system, so that S1 coincides with S0, denoted as Then After a series of rotational transformations Φ1 and then translation Δr 1 Obtain a new plane And after transformation Φ0 and translation r 0,1 Restored to the global coordinate system, we have S2 and Δr. 1 Φ1 is determined by the bending and torsional strains of the first beam element according to equations (10) and (4); In the laboratory, the geometric parameter C was tested. bend and C twst The calibration process includes the following steps: Assume C bend and C twst The initial value of each is 1; A pre-defined large-amplitude combined bending-torsional displacement is applied to a cantilevered, high-aspect-ratio wing, allowing the wing to undergo free-dampening vibration. The bending and torsional strains of the wing are measured, and the displacement is calculated. Simultaneously, the wing displacement is measured using at least digital image correlation methods as a reference value; C is adjusted. bend and C twst This ensures that the calculated displacement and the reference displacement value meet the error range.

3. The dynamic monitoring method for bending and torsional deformation of a high aspect ratio airfoil, as described in claim 1, which can be used in practical engineering, is characterized in that... FBG sensors and torsional strain gauges are used in combination for flexible placement.

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