Fiber Bragg Grating Sensor Determination Method for the Flapping and Lagging Decoupling Position of Helicopter Rotor Blades

Abstract

A method for determining the decoupling positions of the flapping and lagging of helicopter blades based on fiber Bragg grating sensors, comprising the following steps: evenly and parallelly paste a plurality of fiber Bragg grating sensors on the upper and lower surfaces of the helicopter blade to be measured from the leading edge to the trailing edge; apply flapping and lagging bending moments to the blade respectively, and measure the corresponding strain values; according to the sensor positions and their strain measurement data, use the Kriging interpolation method to interpolate at points with the same spacing to obtain the estimated values of the corresponding spatial positions; establish a decoupling coefficient evaluation function for lagging / flapping and flapping / lagging; perform a global traversal on the interpolation results, calculate the evaluation function values and sort them, and finally determine the decoupling positions.

Description

Technical Field

[0001] The present invention belongs to the technical field of helicopter rotor load identification, and specifically provides a method for determining the flapping and pitching decoupling positions of helicopter blades based on fiber Bragg grating sensors. Background Art

[0002] During the research and development process of helicopters, the measurement of rotor loads is a crucial step. Due to the differences in blade airfoils and the special nature of the rotor's own movement, the following challenges are faced when studying loads and deformations: Flapping loads will cause strain responses in the pitching direction, while pitching loads will also generate strain in the flapping direction, resulting in coupling problems. In order to reveal the specific relationship between loads and strains, it is necessary to separate the coupling relationship.

[0003] For the decoupling and calibration tests of helicopter blade loads, traditional methods mainly rely on strain gauges for measurement. However, the limited size of strain gauges makes the measured strain values only reflect the average state of local areas, and it is difficult to obtain the complex strain distribution on the blade surface, especially in high stress gradient regions. In addition, strain gauges adopt a single-point measurement mode, and each strain gauge needs to be connected to a strain gauge through two wires, which not only increases the complexity of the test system but also causes an additional weight burden on the structure, especially in scenarios where multi-point measurement needs to be arranged, the impact is more significant. More importantly, as an electrical signal-based measurement device, strain gauges are easily affected by external interference in a complex electromagnetic environment, resulting in signal distortion. Currently, fiber Bragg grating sensors have been gradually applied to the decoupling and calibration tests of helicopter blade loads. Compared with traditional electrical measurement technologies, fiber Bragg grating sensors rely on optical signals for strain measurement and are completely unaffected by electromagnetic interference, possessing excellent anti-interference performance. In addition, fiber Bragg grating sensors can be deployed in series, and dozens of sensors can be connected in series on one optical fiber, greatly simplifying the wiring difficulty and significantly reducing the weight of the measurement system. It is particularly worth emphasizing that the size of fiber Bragg grating sensors is extremely small, with a diameter of about 250 micrometers and a minimum length that can be controlled within 3 millimeters, enabling high-precision strain measurement, especially suitable for monitoring strain changes in high stress gradient regions and achieving multi-point distributed monitoring.

[0004] The key to helicopter blade load decoupling lies in accurately positioning the positions on the blade surface that are only affected by a single load. Since modern helicopter blades usually use anisotropic composite materials and are supplemented with honeycomb structures, traditional material mechanics theories and finite element simulations are difficult to accurately predict the decoupling positions. In actual engineering, it often relies on empirical trial-and-error methods to determine the decoupling positions, but this method is inefficient and costly. Especially for blades with a short chord length, the accurate positioning of the decoupling positions is more challenging and it is difficult to achieve effective judgment. Summary of the Invention

[0005] Objective of the Invention: Aiming at the problems of high difficulty, low efficiency and high cost in determining the decoupling position of helicopter blade loads, the present invention proposes a method for determining the flapping and pitching loads decoupling position of helicopter blades based on fiber Bragg grating sensors. This method first uniformly arranges fiber Bragg grating sensors on the upper and lower surfaces of a specific section of the blade, then applies specific flapping and pitching loads to the blade, and records the strain values measured by the sensors. Next, the Kriging method is used to interpolate and estimate the strain values at equally spaced points on the upper and lower surfaces of the blade. Finally, by traversing the interpolation results and performing a global search, the position combination with the smallest coupling coefficient is found, thereby accurately positioning the decoupling position.

[0006] Technical Solution: To achieve the above objective, the present invention adopts the following technical solutions:

[0007] A method for determining the decoupling position of helicopter blade flapping and pitching by fiber Bragg grating sensors, comprising the following steps:

[0008] Step 1: Select a section on the helicopter blade to be measured, and paste n fiber Bragg grating sensors parallel at equal intervals on the upper and lower surfaces of the blade respectively. The coordinates of the fiber Bragg grating sensors on the upper surface are:

[0009]

[0010] The coordinates of the fiber Bragg grating sensors on the lower surface are:

[0011]

[0012] Step 2: Apply a flapping load perpendicular to the chord line to the blade, with the direction pointing from the upper surface to the lower surface, and the acting point at the 1 / 4 chord line of the blade. Record the strains measured by the n fiber Bragg grating sensors on the upper surface as:

[0013]

[0014] Record the strains measured by the fiber Bragg grating sensors on the lower surface as:

[0015]

[0016] Step 3: According to equations (1)(3) and equations (2)(4), use the Kriging method to interpolate the strains at points 1 mm apart on the upper and lower surfaces of the blade; obtain the strain interpolation set on the upper surface under the flapping load The strain interpolation set on the lower surface

[0017] Step 4: Apply a pitching load coinciding with the chord line to the helicopter blade, with the direction pointing from the leading edge to the trailing edge; repeat Step 2 and Step 3, and use the Kriging interpolation algorithm to obtain the strain interpolation set under the pitching load, which is The lower surface is

[0018] Step 5: Construct decoupling coefficient evaluation functions, namely the flapping - lag decoupling coefficient k L,F , as shown in Equation (8), and the lag - flapping decoupling coefficient k F,L , as shown in Equation (9):

[0019]

[0020] K = k L,F + k F,L (10)

[0021] Among them, the flapping - lag decoupling coefficient k L,F is used to evaluate the decoupling position of the lag sensor under the action of the flapping load; the lag - flapping decoupling coefficient k F,L is used to evaluate the decoupling position of the flapping sensor under the action of the lag load; summing the flapping - lag decoupling coefficient k L,F and the lag - flapping decoupling coefficient k F,L yields the decoupling coefficient evaluation function K of Equation (10). The smaller the value of this function, the closer it is to the ideal decoupling position;

[0022] Step 6: Under the action of the flapping load and the lag load, traverse the set of strain data on the upper and lower surfaces of the blade interpolated by the Kriging method, substitute it into Formulas (8) and (9), and calculate the decoupling coefficient evaluation function values corresponding to each decoupling position combination; sort the calculation results of all combinations in ascending order; after removing unreasonable combinations, the combination ranked first is the finally determined flapping and lag decoupling positions.

[0023] The present invention first uniformly arranges fiber Bragg grating sensors on the upper and lower surfaces of a specific section of the blade, then applies specific flapping and lag loads to the blade, and records the strain values measured by the sensors. Then, the Kriging method is used to interpolate and estimate the strain values at equally spaced points on the upper and lower surfaces of the blade. Finally, by traversing the interpolation results and performing a global search, the position combination with the smallest coupling coefficient is found, thereby accurately positioning the decoupling position. Brief Description of the Drawings

[0024] Figure 1 It is a schematic diagram of the adherent body of the fiber Bragg grating sensor.

[0025] Figure 2 It is a schematic diagram of the flapping load application.

[0026] Figure 3 It is a schematic diagram of the lag load application. Detailed Embodiment

[0027] Fiber Bragg grating sensor measurement method for the decoupling position of helicopter blade flapping and lagging. On the upper and lower surfaces of the helicopter blade to be measured, several fiber Bragg grating sensors are evenly and parallelly pasted from the leading edge to the trailing edge of the blade; the blade is respectively loaded with flapping and lagging bending moments, and the corresponding strain values are measured; according to the sensor positions and their strain measurement data, Kriging interpolation method is used to interpolate at points with the same spacing, and the estimated values of the corresponding spatial positions are obtained; establish the evaluation functions for lagging / flapping and flapping / lagging decoupling coefficients; perform a global traversal on the interpolation results, calculate the evaluation function values and sort them, and finally determine the decoupling position.

[0028] Specifically, it includes the following steps:

[0029] Step 1: As Figure 1 shown, select a section on the helicopter blade to be measured, and evenly and parallelly paste n fiber Bragg grating sensors on the upper and lower surfaces of the blade at equal distances. The coordinates of the fiber Bragg grating sensors on the upper surface are:

[0030]

[0031] The coordinates of the fiber Bragg grating sensors on the lower surface are:

[0032]

[0033] Step 2: Apply a flapping load perpendicular to the chord line to the blade, with the direction from the upper surface to the lower surface, and the acting point at the 1 / 4 chord line of the blade. Record the strains measured by the n fiber Bragg grating sensors on the upper surface as:

[0034]

[0035] Record the strains measured by the fiber Bragg grating sensors on the lower surface as:

[0036]

[0037] As Figure 2 shown, the flapping load loading schematic diagram of the present invention. The blade is placed horizontally, the chord line is parallel to the horizontal plane, and the blade root is fixed. The flapping load is vertically downward, and the acting point is at the 1 / 4 chord line position.

[0038] Step 3: According to equations (1)(3) and equations (2)(4), use the Kriging method to interpolate the strains at points 1 mm apart on the upper and lower surfaces of the blade. The strain distribution of the helicopter blade is closely related to the spatial position. The Kriging interpolation method provides the optimal unbiased estimation result by comprehensively considering the spatial autocorrelation of the strain data, and effectively obtains the spatial variation law of the strain distribution. Usually, it is difficult to achieve a positioning accuracy higher than 0.5 mm by manually scribing and pasting fiber Bragg grating sensors on the blade surface. Therefore, a 1 mm spacing is selected for interpolation.

[0039] Taking the interpolation process of the upper surface of the blade as an example, first, a semivariogram is constructed to describe the correlation of spatial data, that is, the relationship between the distance between data points and the difference in strain values measured at the i-th and j-th measurement points. The upper and lower surfaces of the profile are interpolated separately. Assuming that n fiber Bragg grating sensors are attached parallel to the upper surface, then i, j = 1, 2, …, n.

[0040]

[0041] As shown in Equation (5), a spherical model can be used to construct the semivariogram, where h is the distance between two points, N(h) is the number of point pairs with a distance of h, and are the strain values of two points.

[0042] Then, different weights are assigned to the known data points. The weights are determined according to the spatial distance and spatial correlation between points. The weight λ is calculated through the following matrix equation i :

[0043]

[0044] where μ is the Lagrange multiplier to ensure the unbiasedness constraint condition. γ is the semivariogram represented by Equation (5), generally including spherical model, exponential model, Gaussian model, and linear model, etc. x in Equation (6) represents the coordinates of the interpolation point. Substituting this x into Equation (6) can obtain the system of equations about λ i . Here, x is replaced by x new to make it more eye-catching.

[0045]

[0046] Solving this system of equations can obtain the weight vector λ i , and then substituting the weight vector λ i into Equation (7), the value at the x position can be calculated. m in the following formula represents that the interpolation of m points has been completed. n in Equation (7) represents that there are n known points, that is, the n fiber Bragg grating sensors attached parallel to the upper surface.

[0047] Finally, the strain interpolation set under the flapping load is calculated through Equation (7)

[0048]

[0049] Using the same method, the strain interpolation set of the lower surface can also be calculated

[0050] Step 4: Apply the flapping load that coincides with the chord line to the helicopter blade, with the direction pointing from the leading edge to the trailing edge. Repeat Steps 2 and 3, and use the Kriging interpolation algorithm to obtain the strain interpolation set under the flapping load. The upper surface is The lower surface is

[0051] As Figure 3 shown, it is the flapping load application schematic diagram of the present invention. The blade is placed vertically, the chord line is perpendicular to the horizontal plane, and the blade root is fixed. The flapping load is vertically downward, and the acting point is at the 1 / 4 chord line position.

[0052] Step 5: Construct the decoupling coefficient evaluation functions, namely the flapping - lag decoupling coefficient k L,F , as shown in Equation (8), and the lag - flapping decoupling coefficient k F,L , as shown in Equation (9): Assume that under the flapping load and the lag load, m values are interpolated respectively at the same coordinate position. Among them, ε l represents the strain value under the lag load, and ε f represents the strain value under the flap load. Then, substitute them in pairs into Equation (8) to solve for the decoupling coefficient. Therefore, ε l1 and ε f1 represent the strain under the lag load and the strain under the flap load interpolated at the coordinate position x1; ε l2 and ε f2 represent the strain under the lag load and the strain under the flap load interpolated at the coordinate position x2.

[0053]

[0054] K = k L,F + k F,L (10)

[0055] Among them, the flapping - lag decoupling coefficient k L,F is used to evaluate the decoupling position of the lag sensor under the flap load. Ideally, k L,F →0. The two fiber Bragg gratings sensors located at the lag decoupling position should measure almost the same strain value, that is, the strain difference approaches zero. This means that the lag sensor is not affected by the flap load, achieving effective decoupling of the load. Similarly, the lag - flapping decoupling coefficient k F,L is used to evaluate the decoupling position of the flap sensor under the lag load. Ideally, k F,L →0, that is, the sensors pasted at the flap decoupling position are not affected by the lag load at all. For the flapping - lag decoupling coefficient k L,F and the lag - flapping decoupling coefficient k F,LThe decoupling coefficient evaluation function K is obtained by summation as shown in Equation (10). The smaller the function value, the closer it is to the ideal decoupling position.

[0056] Step 6: Under the action of the flapping load and the lag load, traverse the set of strain data on the upper and lower surfaces of the blade obtained by Kriging interpolation, and substitute it into Equation (8) and Equation (9) to calculate the decoupling coefficient evaluation function values corresponding to each decoupling position combination. Then, sort the calculation results of all combinations in ascending order. After excluding unreasonable combinations, the combination ranked first is the finally determined flapping and lag decoupling position.

Claims

1. A method for measuring the fiber Bragg grating sensor at the decoupling position of the helicopter blade flapping and lagging, characterized in that Including the following steps: Step 1: Select a section on the helicopter blade to be measured, and paste fiber Bragg grating sensors parallelly and equidistantly on the upper and lower surfaces of the blade respectively. The coordinates of the fiber Bragg grating sensors on the upper surface are: and the coordinates of the fiber Bragg grating sensors on the lower surface are: （1） The coordinates of the fiber Bragg grating sensors on the lower surface are: （2） Step 2: Apply a flapping load perpendicular to the chord line of the blade, with the direction pointing from the upper surface to the lower surface, and the acting point at the 1 / 4 chord line of the blade, and record the strain measured by fiber Bragg grating sensors on the upper surface as follows: （3） Record the strain measured by the fiber Bragg grating sensors on the lower surface as: （4） Step 3: According to Equations (1) (3) and (2) (4), use Kriging method to interpolate the strain of points 1 mm apart on the upper and lower surfaces of the blade; obtain the strain interpolation set on the upper surface under the flapping load , and the strain interpolation set on the lower surface ; Step 4: Apply a flapping load that coincides with the chord line to the helicopter blade, with the direction pointing from the leading edge to the trailing edge; repeat Step 2 and Step 3, and use the Kriging interpolation algorithm to obtain the strain interpolation set under the flapping load. The upper surface is , and the lower surface is ; Step 5: Construct decoupling coefficient evaluation functions, namely the flapping - lag decoupling coefficient , as shown in Equation (8), and the lag - flapping decoupling coefficient , as shown in Equation (9): （8） （9） （10） Among them, the flapping - lag decoupling coefficient is used to evaluate the decoupling position of the lag sensor under the action of the flapping load; the flapping - lag decoupling coefficient is used to evaluate the decoupling position of the flapping sensor under the action of the lag load; for the flapping - lag decoupling coefficient and the flapping - lag decoupling coefficient summation gives the decoupling coefficient evaluation function of Equation (10) , the smaller the function value, the closer it is to the ideal decoupling position; Step 6: Under the action of the flapping load and the lag load, traverse the strain data sets of the upper and lower surfaces of the blade interpolated by the Kriging method, substitute them into Formula (8) and Formula (9), and calculate the decoupling coefficient evaluation function values corresponding to each decoupling position combination; arrange the calculation results of all combinations in ascending order; after removing the unreasonable combinations, the combination ranked first is the finally determined flapping and lag decoupling position.

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