Engineering calculation method of bending moment and axial force of aircraft landing gear buffer column cross section based on optical fiber sensing technology

Abstract

The application discloses an engineering calculation method for a section bending moment and axial force of an aircraft landing gear buffer column based on an optical fiber sensing technology, and belongs to the technical field of aerospace. The method comprises the following steps: collecting a cylindrical buffer column section fiber grating strain data; performing strain discretization processing on the cylindrical buffer column section; performing high-precision interpolation augmentation on the strain of each discrete unit in the discretization processing; converting the strain into axial stress; calculating the axial force and the section bending moment through the axial stress; and determining the bending moment action plane through the section bending moment. The application adopts the above-mentioned engineering calculation method for the section bending moment and axial force of the aircraft landing gear buffer column based on the optical fiber sensing technology. Through the development of a cosine function fitting algorithm based on sparse optical fiber sensor sampling point data and relying on physical constraints, the entire section strain data augmentation is realized. Meanwhile, based on the augmented data, the section bending moment-load real-time calculation is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aerospace technology, in particular to an engineering calculation method for the bending moment and axial force of the landing gear buffer column section based on optical fiber sensing technology. BACKGROUND

[0002] The landing gear of an airplane, as one of the key load-bearing structures, plays an irreplaceable role in the process of taxiing, taking off and landing. It effectively reduces the vibration of the fuselage by buffering and dispersing the impact force during landing, ensuring the safety of passengers and the integrity of the airplane structure. However, the complex mechanical environment during takeoff and landing puts the landing gear at risk, and once it fails due to damage, it may cause catastrophic accidents. Therefore, ensuring the stability and reliability of the landing gear is the core foundation of building a flight safety system. According to statistical data, more than 66% of airplane accidents are related to landing gear system failures, the main causes of which include structural fractures caused by over-limit impact or long-term load accumulation. Therefore, it is imperative to conduct real-time load monitoring research on the landing gear, which can accurately assess the structural health status and provide data support for developing scientific maintenance strategies and extending the service life, thereby building a strong barrier for flight safety.

[0003] As a key support component of an airplane during different flight stages, the landing gear needs to cope with complex and variable load conditions. According to the difference in stress characteristics, its key components can be divided into two types: two-force bar type and non-two-force bar type. Two-force bar type components only bear axial force, typical structures such as front strut, front lock rod, rear strut and rear lock rod, etc. The axial force calculation is relatively intuitive: by arranging strain gauges or grating optical fibers along the axial direction to collect strain data, combined with parameters such as cross-sectional area and elastic modulus, the axial force value can be easily and accurately obtained. In contrast, the stress analysis of non-two-force bar type components is significantly more complex. For example, cylindrical structures such as buffer columns bear axial force and bending moment, and the circumferential strain of the cross section shows a nonlinear distribution characteristic, making it difficult to directly calculate the axial force and bending moment values through simple calculation. Compared with two-force bar type structures, the mechanical analysis of non-two-force bar type components requires more precise theoretical models and algorithms, significantly increasing the analysis difficulty. Currently, there is still a lack of mature methods for directly measuring the cross-sectional load of landing gear non-two-force bar components that need to bear bending moment and axial force simultaneously, which is a technical bottleneck that needs to be broken through. Figure 1

[0004] ​The real-time detection of the mechanical parameters of the key parts of the traditional aircraft mainly relies on the strain method and the parameter method. The strain method measures the local stress through strain gauges, and the data directly come from physical quantity collection, which is intuitive. However, this method is limited by the complexity of the strain gauge line and the limited density of the point distribution, and it is difficult to obtain continuous strain information. At the same time, the pasting, calibration and lead operation of the strain gauge have many challenges, and are easily affected by drift, damage and short service life, etc., which limits the engineering application. The parameter method is based on flight parameters, and the local stress is predicted by constructing a load equation through machine learning, but the detection accuracy is insufficient, the model training cost is high, and it is difficult to meet the actual demand. SUMMARY

[0005] The purpose of the present application is to provide an engineering calculation method for the bending moment and axial force of the aircraft landing gear buffer column section based on optical fiber sensing technology, which realizes the augmentation of the entire section strain data by developing a cosine function fitting algorithm based on the sparse optical fiber sensor sampling point data with physical constraints, and realizes the real-time calculation of the section bending moment-load based on the augmented data.

[0006] To achieve the above purpose, the present application provides an engineering calculation method for the bending moment and axial force of the aircraft landing gear buffer column section based on optical fiber sensing technology, comprising the following steps:

[0007] S1, collecting the fiber Bragg grating strain data of the cylindrical buffer column section;

[0008] S2, performing strain discretization processing on the cylindrical buffer column section;

[0009] S3, performing high-precision interpolation augmentation on the strain of each discrete unit in the discretization processing in S2;

[0010] S4, converting the strain obtained through S3 into axial stress;

[0011] S5, calculating the axial force and section bending moment from the axial stress obtained through S4;

[0012] S6, determining the bending moment action plane through the section bending moment obtained through S5, completing the fitting of the axial stress cosine function through the main action plane of the bending moment and the bending moment based on the main action plane, and obtaining the bending moment expression.

[0013] Preferably, the specific operation of S1 is:

[0014] S11, establishing a column coordinate system: the to-be-solved section of the buffer column is denoted as A section, the distance between the A section and the section Z0 at the bottom of the buffer column is L, a column coordinate system is established, the origin of the coordinate system is located at the center of the section Z0, and the Z axis of the coordinate system passes through the circle and is perpendicular to the Z0 section;

[0015] S12, layout sampling points: through ABAQUS finite element simulation analog buffer column model, N evenly distributed strain data sampling points in A section, and each sampling point is arranged with two optical fiber sensors, respectively measuring the axial strain ε z and the sampling point ring strain ε θ .

[0016] Preferably, in S12, the azimuth angles of the N sampling points are θ1, θ2, θ3, …, θ N , and the corresponding coordinates are A-a1(R, θ1, L), A-a2(R, θ2, L), A-a3(R, θ3, L), …, A-a N (R, θ N , L).

[0017] Preferably, the specific operation of S2 is to approximately divide the A section into n discrete units of the same shape and equal area, which are evenly distributed along the circumference. The discrete units are rectangular units, and there are n / N rectangular units between adjacent sampling points.

[0018] Preferably, the specific operation of S3 is to use the Lagrange interpolation method to accurately interpolate the axial strain and ring strain of the discrete units based on the fiber Bragg grating strain signal.

[0019] Preferably, in S4, the axial stress is obtained through the axial strain and the ring strain, and the calculation formula of the axial stress is:

[0020]

[0021] where σ z is the axial stress, E is the elastic modulus, and v is the Poisson's ratio.

[0022] Preferably, in S5, the calculation formulas of the axial force and the section moment are shown in formulas (2) and (3) respectively:

[0023]

[0024] where N z is the axial force, M is the moment, R is the outer diameter of the buffer column, t is the wall thickness of the cylindrical buffer column, i is the sigma summation index variable, and A i is obtained by formula (4):

[0025] A i = 2πRt / n (4).

[0026] Preferably, in S6, when the moment and the axial force act together, the axial stress shows a cosine function distribution characteristic along the circumference. The axial stress component is defined as the cosine function of the azimuth angle θ:

[0027] σ Z (θ) = B1 + B2cos(θ - θ0) (5);

[0028] Where B1, B2, θ0 are fitting parameters;

[0029] The bending moment expression of the relative bending moment equivalent action surface is further obtained by defining the axial stress component as the cosine function of the azimuth angle θ:

[0030]

[0031] Therefore, the aircraft landing gear buffer column cross-section bending moment and axial force engineering calculation method based on the optical fiber sensing technology is adopted, the strain data of the to-be-solved cross-section is augmented by using the cosine function fitting method with physical constraints based on the data provided by the sparse optical fiber sensor sampling points, and the bending moment-load is calculated based on the augmented data, so that the bending moment and axial force of the to-be-solved cross-section are monitored.

[0032] The technical solutions of the present application are further described in detail below through the drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 It is the landing gear structure, buffer column and bending moment and axial force action surface of the present application;

[0034] Figure 2 It is the typical thin-walled cylindrical structure and A cross-section of the landing gear buffer column of the present application;

[0035] Figure 3 It is the sampling point (sampling point number N) distribution diagram and sampling point marking of the A cross-section of the buffer column of the present application;

[0036] Figure 4 It is the strain direction schematic diagram of the axial and ring directions of the present application;

[0037] Figure 5 It is the A cross-section of the present application;

[0038] Figure 6 It is the cosine function fitting and fitting curve of the present application;

[0039] Figure 7 It is the axial force and bending loading model of the buffer column of the present application;

[0040] Figure 8 It is the buffer column finite element model (ring direction has 96 units) of example one of the present application;

[0041] Figure 9 It is the sampling point (sampling point number 4) distribution diagram and sampling point marking of the A cross-section of the buffer column of example one of the present application;

[0042] Figure 10 is the comparison of the axial strain and the hoop strain of the fitted embodiment one of the application with the results of the finite element extraction. DETAILED DESCRIPTION

[0043] The technical solutions of the application are further described below by means of the drawings and examples.

[0044] Unless otherwise defined, the technical terms or scientific terms used in the present application shall have the usual meaning understood by a person with ordinary skill in the art to which the present application belongs.

[0045] The application provides an engineering calculation method for the bending moment and axial force of the aircraft landing gear buffer column cross section based on optical fiber sensing technology. The method is suitable for landing gear buffer column structures, but is not limited to landing gears, including various cylindrical, constant cross-section, variable cross-section barrel structures, such as wind turbine support columns, offshore platform support seats, etc. The method realizes the augmentation of the strain data of the to-be-solved cross section by means of sparse optical fiber sensor sampling points, fits the strain data of the N sampling points through the cosine function, further obtains the strain distribution of the entire cross section, and finally calculates the bending moment and axial force of the cross section based on the same. The method specifically includes the following steps:

[0046] S1, collecting the fiber Bragg grating strain data of the cylindrical buffer column cross section, and the specific operation is as follows:

[0047] S11, establishing a column coordinate system: the to-be-solved cross section of the buffer column is denoted as A cross section, which is a circular ring as shown in the drawing, the distance between the A cross section and the cross section Z0 at the bottom of the buffer column is L, a column coordinate system is established, and the origin of the coordinate system is located at the center of the cross section Z0, and the Z axis of the coordinate system passes through the circle and is perpendicular to the cross section Z0; Figure 2

[0048] S12, arranging sampling points: N strain data sampling points are uniformly arranged on the A cross section, the more the sampling points, the more accurate the augmented strain (N is recommended to be not less than 4), and the N data collection points are uniformly distributed on the circular ring of the A cross section, and details are shown in the drawing. Figure 3 Each sampling point is arranged with two optical fiber sensors to measure the axial strain ε z and the hoop strain ε θ at the sampling point, as shown in the drawing. Figure 4

[0049] Among them, the azimuth angles of the N sampling points are θ1, θ2, θ3, …, θ N , and the corresponding coordinates are A-a1(R, θ1, L), A-a2(R, θ2, L), A-a3(R, θ3, L), …, A-a N (R, θ N , L).

[0050] ​​S2, the cylindrical buffer column section is subjected to strain discretization processing, and the specific operation is as follows: the A section is approximately divided into n discrete units with the same shape and equal area, the discrete units are uniformly distributed along the circumferential direction, the discrete units are rectangular units, and n / N rectangular units are contained between adjacent sampling points. The discretization accuracy increases with N, and when N→∞, the discrete model tends to be a continuous section, Figure 5 The discretization schematic diagram is shown in FIG. 2.

[0051] S3, the strain of each discrete unit in the discretization processing in S2 is subjected to high-precision interpolation augmentation, and the specific operation is as follows: based on the fiber grating strain signal, the Lagrange interpolation method is used to accurately interpolate the axial strain and the circumferential strain of the discrete unit.

[0052] S4, the strain obtained through S3 is converted into axial stress; the axial stress is obtained through the axial strain and the circumferential strain, and the calculation formula of the axial stress is as follows:

[0053]

[0054] Wherein, σ z is the axial stress, E is the elastic modulus, and v is the Poisson's ratio.

[0055] S5, the axial force and the section bending moment are calculated based on the axial stress obtained through S4, and the calculation formulas of the axial force and the section bending moment are shown in formulas (2) and (3) respectively:

[0056]

[0057] Wherein, N z is the axial force, M is the bending moment, R is the outer diameter of the buffer column, t is the wall thickness of the cylindrical buffer column, i is the sigma summation index variable, and A i is obtained through formula (4):

[0058] A i = 2πRt / n (4).

[0059] S6, the bending moment plane is determined based on the section bending moment obtained through S5, and in the working conditions such as sliding, taking off and landing, the bending moment plane of the landing gear buffer column changes dynamically due to the influence of factors such as tire steering, so the main bending moment action direction needs to be determined in real time. When the bending moment and the axial force act together, the axial stress is distributed along the circumferential direction in the form of a cosine function, and the axial stress component is defined as the cosine function of the azimuth angle θ:

[0060] σ Z (θ) = B1 + B2cos(θ-θ0) (5);

[0061] Wherein, B1, B2 and θ0 are fitting parameters, and the cosine function fitting and the fitting curve are shown in FIG. 3. Figure 6(a) and Figure 6 As shown in (b) of the diagram.

[0062] By defining the axial stress components as the cosine function of the azimuth angle θ, the expression for the bending moment of the equivalent action surface of the relative bending moment is further obtained as follows:

[0063]

[0064] Example 1

[0065] In Example 1, the buffer column model has an outer diameter of 300mm and a length of 1500mm. The distance from section A to the bottom surface of the buffer column is L = 700mm. A reference point is coupled at the bottom center, and the degree of freedom of the reference point is coupled to the bottom node. Two shear forces are applied to the reference point at the bottom center of the model: one 10N in the positive X-axis direction and the other 10N in the positive Y-axis direction. Simultaneously, an axial load of 10N in the positive Z-axis direction is applied. See details... Figure 7 For details of the finite element mesh of the buffer column, please refer to [link / reference]. Figure 8 In (a), there are 96 discrete elements in the circumferential direction. Figure 8 (b) in the figure is a magnified view of a local finite element mesh.

[0066] This invention provides an engineering calculation method for the bending moment and axial force of the aircraft landing gear buffer column section based on fiber optic sensing technology, including the following steps:

[0067] S1. Acquire strain data of the fiber optic grating cross-section of the cylindrical buffer column; the specific operation of S1 is as follows:

[0068] S11. Establish a cylindrical coordinate system: Denote the section to be determined on the buffer column as section A. The distance between section A and section Z0 at the bottom of the buffer column is L. Establish a cylindrical coordinate system with the origin located at the center of section Z0. The Z-axis of the coordinate system passes through the circle and is perpendicular to section Z0.

[0069] S12. Sampling Point Layout: Using ABAQUS finite element simulation, simulate the buffer column model and uniformly arrange four virtual fiber optic sensor sampling points (A-a1 to A-a4) along the circumferential direction at section A, with azimuth angles of 0°, 90°, 180°, and 270° respectively (e.g., ...). Figure 9 As shown in the figure, all strain data are directly extracted from ABAQUS simulation results.

[0070] The azimuth angles of the N sampling points are θ1, θ2, θ3, ..., θ N The corresponding coordinates are A-a1(R, θ1, L), A-a2(R, θ2, L), A-a3(R, θ3, L), ..., Aa N (R, θ) N L).

[0071] S2. The cross section of the cylindrical buffer column is subjected to strain discretization. The specific operation is as follows: the cross section A is approximately divided into 96 discrete units with the same shape and area. The discrete units are evenly distributed along the circumference. The discrete units are rectangular units, and there are 24 rectangular units between adjacent sampling points.

[0072] S3. Based on the strain data (derived from finite element results) of four sampling points (A-a1~A-a4, azimuth angles 0° / 90° / 180° / 270°) of section A, the strain augmentation of the circumferential elements of the section is performed using the cosine function fitting method. The specific process is as follows:

[0073] 1) Coordinate system establishment: Establish a cylindrical coordinate system with the line connecting A-a1 and the center of the circle as the polar axis. The sampling points are evenly distributed along the circumference, and the angle between adjacent points is 90°.

[0074] 2) Axial strain augmentation: A cosine function fitting model was constructed using axial strain data from four sampling points.

[0075] 3) Circumferential Strain Augmentation: Similarly, a fitting model is established for the circumferential strain data, ultimately obtaining the axial and circumferential strain distributions of all circumferential nodes in the cross-section, achieving high-precision reconstruction of the strain field. The fitted axial and circumferential strains are almost identical to the results extracted by the finite element method, such as... Figure 10 As shown, where Figure 10 In the figure, (a) shows the fitted axial strain and circumferential strain results. Figure 10 (b) in the figure represents the result of finite element extraction.

[0076] S4. The strain obtained through S3 is converted into axial stress; the axial stress is obtained from the axial strain and the circumferential strain, and the formula for calculating the axial stress is:

[0077]

[0078] Where, σ z ν is the axial stress, E is the elastic modulus with a value of 210 GPa, and v is Poisson's ratio with a value of 0.3.

[0079] S5. The axial force and section bending moment are calculated from the axial stress obtained in S4. The calculation formulas for the axial force and section bending moment are shown below:

[0080]

[0081] S6, S6, the bending moment obtained from section S5 determines the plane of action of the bending moment. Using the principal plane of action of the bending moment and the bending moment based on the principal plane, the axial stress cosine function is fitted to obtain the bending moment expression. The fitted cosine function is:

[0082] σZ (θ)=B1+B2cos(θ-θ0) (5);

[0083] Where B1 = 660 Pa, B2 = 660 Pa,

[0084] That is, the principal plane of bending moment is at 135° to the polar axis at θ = 0°.

[0085] The bending moment expression for the relative bending moment equivalent action surface can be further obtained:

[0086]

[0087] According to the load setting of the finite element method, the principal action plane of the bending moment at section A can be directly obtained. The principal action plane is 135° to the polar axis at θ = 0°. This is consistent with the 135° obtained by the engineering algorithm.

[0088] The bending moment based on the principal action surface is 9899.49 N·mm, which has an error of 3.4% compared to the 10236.23 N·mm obtained by the engineering algorithm. The method is clearer after demonstration in Example 1, and the reliability and practicality of this patent can be further verified by comparing the simulation results with those calculated by this patent method.

[0089] Therefore, this invention adopts the above-mentioned engineering calculation method for bending moment and axial force of aircraft landing gear buffer column section based on fiber optic sensing technology. By developing a cosine function fitting algorithm with physical constraints based on sparse fiber optic sensor sampling point data, the strain data of the entire section is augmented. At the same time, based on the augmented data, the bending moment-load of the section is calculated in real time.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An engineering calculation method for bending moment and axial force of aircraft landing gear buffer column sections based on fiber optic sensing technology, characterized in that: Includes the following steps: S1. Collect strain data of fiber optic gratings on the cross-section of the cylindrical buffer column; S2. Perform strain discretization on the cross-section of the cylindrical buffer column; S3. Perform high-precision interpolation augmentation on the strain of each discrete unit in the discretization process of S2; S4 converts the strain passed through S3 into axial stress; S5. The axial force and section bending moment are calculated from the axial stress obtained in S4. In S5, the calculation formulas for axial force and section bending moment are shown in equation (2) and equation (3), respectively: (2)； (3)； in, N z For axial force, M For bending moment, R The outer diameter of the buffer column. t The cylindrical buffer column has a thick wall. i Index variable for sigma summation. A i We obtain the following from equation (4): (4)； Where n is the number of discrete units with the same shape and area; S6. Determine the plane of action of the bending moment by the cross section bending moment obtained from S5. Fit the axial stress cosine function by the main plane of action of the bending moment and the bending moment based on the main plane of action to obtain the bending moment expression. In S6, when bending moment and axial force act together, the axial stress exhibits a cosine function distribution along the circumferential direction. The axial stress components are defined as azimuth angles. θ The cosine function form: (5)； in, B 1 , B 2 , θ 0 These are the fitting parameters; The azimuth angle is defined by the axial stress component. θ The cosine function is further used to obtain the bending moment expression for the equivalent action surface of the relative bending moment: (6)。 2. The method for calculating the bending moment and axial force of the aircraft landing gear buffer column section based on fiber optic sensing technology according to claim 1, characterized in that: The specific operation of S1 is as follows: S11. Establish a cylindrical coordinate system: Denote the section to be determined on the buffer column as section A. The distance between section A and section Z0 at the bottom of the buffer column is L. Establish a cylindrical coordinate system with the origin located at the center of section Z0. The Z-axis of the coordinate system passes through the circle and is perpendicular to section Z0. S12. Setting up sampling points: Using ABAQUS finite element simulation, N strain data sampling points are uniformly set up on section A, with two fiber optic sensors at each sampling point to measure the axial strain ε at the sampling point. z and the circumferential strain ε at the sampling point θ .

3. The method for calculating the bending moment and axial force of the aircraft landing gear buffer column section based on fiber optic sensing technology according to claim 2, characterized in that: In S12, the azimuth angles of the N sampling points are respectively θ 1 , θ 2 , θ 3 , ..., θ N The corresponding coordinates are A-a1( R, θ 1 ，L ), A-a2( R, θ 2 ，L ), A-a3 ( R, θ 3 ，L ), ..., Aa N ( R, θ N ，L ).

4. The method for calculating the bending moment and axial force of the aircraft landing gear buffer column section based on fiber optic sensing technology according to claim 3, characterized in that: The specific operation of S2 is as follows: the cross section A is approximately divided into n discrete units with the same shape and area. The discrete units are uniformly distributed along the circumference. The discrete units are rectangular units, and there are n / N rectangular units between adjacent sampling points.

5. The method for calculating the bending moment and axial force of the aircraft landing gear buffer column section based on fiber optic sensing technology according to claim 1, characterized in that: The specific operation of S3 is as follows: based on the fiber optic grating strain signal, the Lagrange interpolation method is used to accurately interpolate the axial strain and circumferential strain of the discrete element.

6. The method for calculating the bending moment and axial force of the aircraft landing gear buffer column section based on fiber optic sensing technology according to claim 2, characterized in that: In S4, the axial stress is obtained through axial strain and circumferential strain. The formula for calculating the axial stress is: (1)； in, σ z Let E be the axial stress, E be the elastic modulus, and v be Poisson's ratio.

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