Theoretical analysis method for steady damping load of aircraft arresting system

Abstract

The invention discloses a steady damping load theoretical analysis method for an aircraft arresting system, and belongs to the technical field of aircraft arresting net equipment characteristic research. According to the method, on the basis that the time scale of pulling the arresting belt out of each circle is very small, it can be approximately considered that the water turbine energy absorber is subjected to the steady damping load effect within the time scale of each circle, the parameter that the arresting belt of the first circle is pulled out can be obtained according to the initial net collision speed of an airplane, and the state of the previous circle serves as input of the next circle; parameters of each circle can be iteratively calculated until the speed of the aircraft becomes zero, and final arresting data can be obtained. According to the method, various factors in the aircraft ground arresting process are comprehensively considered, arresting process parameter prediction close to a real environment is provided, and the change rule of aircraft overload, aircraft speed and arresting belt tension in the aircraft arresting process is obtained, so that the theoretical research system of an aircraft arresting system is enriched.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft arresting net equipment characteristics research, and relates to a steady damping load theoretical analysis method for an aircraft arresting system. Background Art

[0002] The aircraft arresting system has nonlinear properties and many uncertain factors, such as the roughness of the ground under different environments, the deformation of the arresting belt, the viscous resistance law of the fluid working medium inside the water turbine brake, etc., which usually require nonlinear theoretical analysis and research when mathematically modeling. In addition, in terms of usage requirements, the aircraft arresting system should ensure that key parameters such as the arresting distance, motion overload, arresting belt tension, and water turbine speed meet the technical index requirements. This greatly increases the difficulty of mathematical modeling and theoretical analysis of the aircraft arresting process. The existing technical means is to use the Simulink module in MATLAB to numerically solve the control equations of the aircraft arresting process. The main problems are as follows: (1) In order to simplify the mathematical model, factors such as headwind resistance and ground friction are usually ignored, which deviates from the actual problem and leads to insufficient accuracy of the prediction results; (2) Moreover, this solution method has high requirements on computing resources and performance configuration; (3) In order to improve accuracy, a high-order numerical solution method is usually used, and the calculation efficiency is low. Summary of the invention

[0003] In order to expand the theoretical research on the system characteristics of the existing aircraft arresting process, the present invention proposes a theoretical analysis method for the steady damping load of the aircraft arresting system based on the motion characteristics of the water turbine energy absorber, and compares the method with the experimental data of a certain type of aircraft collision with the net, thereby enriching the theoretical research system of the aircraft arresting system; the steady damping load theoretical analysis method provided by the present invention believes that within the time scale of each circle when the arresting belt is pulled out, the rotor of the water turbine energy absorber is subjected to a steady damping load and rotates at a uniform speed.

[0004] In order to achieve the above object, the technical solution of the present invention is:

[0005] A steady damping load theoretical analysis method for an aircraft arresting system. The analysis method first obtains initial parameters of an aircraft and an aircraft arresting system, and calculates the total number of turns n of a water turbine energy absorber. Since the time scale of each turn of the arresting tape is very small, it is considered that within the time scale of each turn of the arresting tape, the rotor of the water turbine energy absorber rotates at a uniform speed and is subjected to a steady damping load. Secondly, the aircraft collision speed v in the initial parameters of the aircraft is used as the reference value. 1 As input, the parameters of the aircraft hitting the net and the aircraft speed increment △v during the time period when the first arresting belt is pulled out are calculated. 1, and then obtain the final speed of the aircraft after the first arresting tape is completely pulled out, and use this as input to calculate the input value of the aircraft collision net parameter during the time period when the second arresting tape is pulled out; finally, perform progressive calculations along the time dimension to obtain the aircraft collision net parameters during the time period when each arresting tape is pulled out until the aircraft speed decreases to zero, and obtain the aircraft collision net parameter value during the entire process of the aircraft collision net. It includes the following steps:

[0006] Step 1: Derivation of theoretical calculation process

[0007] Step 1.1: Obtain the initial parameters of the aircraft and the aircraft arresting system, including the aircraft collision speed, the aircraft frontal area, the aircraft weight, the radius of the belt reel shaft, the arresting belt thickness, the arresting belt length, the energy absorber diameter, the arresting net length, etc. According to the initial parameters of the aircraft arresting system, calculate the total number of turns n of the water turbine energy absorber belt reel;

[0008]

[0009] In the formula, r 0 is the radius of the reel axis, in m; δ is the thickness of the arresting belt, in m; ε l It is the total length of the brake belt, in m.

[0010] Step 1.2: Let the number of turns of the arresting belt be i (1≤i≤n). According to step 1.1, the outer diameter R of the belt reel before the arresting belt is pulled out for the i-th turn is obtained. i The calculation formula is:

[0011] R i =(n-i+1)δ+r 0 (2)

[0012] Step 1.3: According to step 1.2, the sum of the length of the arresting belt that has been released after the arresting belt is pulled out of the i-th circle and half of the length of the arresting net is obtained;

[0013] l i = l 0 +2(n-i+1)πR i –(n-i+1)(ni)δπ (3)

[0014] In the formula, l 0 It is half of the length of the barrier net, unit: m.

[0015] Step 1.4: Based on step 1.3, use the Pythagorean theorem to calculate the braking distance S generated during the time period of the i-th barrier strip being pulled out. i and braking distance increment △S i :

[0016]

[0017] ΔSi =S i -S i-1 (5)

[0018] Where a is half of the distance between the two water vortex energy absorbers, unit: m.

[0019] Step 1.5: According to steps 1.3 to 1.4, the angle α between the arresting belt and the aircraft's moving direction during the i-th arresting belt pull-out period is obtained. i Cosine value cos(α i )for:

[0020] cos(α i )=S i / l i (6)

[0021] Step 1.6: Since the time scale of each arresting belt being pulled out is very small, it is assumed that within the time scale of each arresting belt being pulled out, the rotor of the water turbine absorber rotates at a uniform speed and is subjected to a steady damping load. The time △t for the arresting belt of the ith circle to be pulled out is i The calculation formula is:

[0022] Δt i =ΔS i / v i (7)

[0023] In the formula, v i It is the initial speed of the aircraft during the time period when the i-th arresting tape is pulled out, that is, the terminal speed of the aircraft during the time period when the i-1-th arresting tape is pulled out.

[0024] Then the speed of the energy absorber during the time when the i-th arresting belt is pulled out is N i for:

[0025] N i =60 / Δt i (8)

[0026] Step 1.7: According to step 1.6, the absorbed power P of the energy absorber during the time when the i-th barrier strip is pulled out is obtained. i for:

[0027] P i =K 1 D x N i y (9)

[0028] In the formula, K 1 represents the correction coefficient, D represents the rotor diameter of the water vortex energy absorber, and x and y are both exponential coefficients.

[0029] Step 1.8: According to step 1.7, the braking torque M of the energy absorber during the time period when the i-th arresting belt is pulled out is obtained. i for:

[0030] M i =9550P i / N i (10)

[0031] Step 1.9: According to equations (2), (6) and (10), the resistance F that the aircraft encounters during the time period when the i-th arresting strip is pulled out is obtained: i for:

[0032] F i =2cos(α i )M i / R i +F a +F b (11)

[0033] In the formula, F a represents the headwind resistance, which is calculated from the aircraft headwind area obtained in step 1.1, F b Represents the friction resistance of the airport runway.

[0034] Step 1.10: According to step 1.7, the aircraft acceleration a during the time when the arresting strip of the i-th circle is pulled out is obtained. i and the aircraft velocity increment △v i for:

[0035] a i =F i / m(12)

[0036] Δv i =a i Δt i (13)

[0037] Where m represents the mass of the aircraft.

[0038] Step 1.11, using the aircraft collision speed v obtained in step 1.1 1 As input, through steps 1.2 to 1.10, the parameters of the aircraft hitting the net during the time period when the first arresting belt is pulled out, as well as the aircraft speed increment △v during the time period when the first arresting belt is pulled out are calculated. 1 According to formula (14), calculate the final speed v of the aircraft after the first arresting strip is completely pulled out. 2 :

[0039] v i+1 =v i -Δv i (14)

[0040] v 2 As the input value for calculating the parameters of the aircraft hitting the net during the time period when the second arresting tape is pulled out, repeat this step, perform progressive calculation along the time dimension, obtain the parameters of the aircraft hitting the net during the time period when each arresting tape is pulled out until the speed of the aircraft decreases to zero, and obtain the parameters of the aircraft hitting the net during the entire process of the aircraft hitting the net; wherein the aircraft hitting the net parameters include braking distance, acceleration, and resistance encountered by the aircraft during the process of hitting the net.

[0041] Step 2: Perform simulation calculations

[0042] According to the equivalent relationship between the parameters of each aircraft collision in step 1, a calculation program is written in Matlab to perform progressive calculations along the time dimension. The calculation end condition is that the aircraft speed decreases to zero. The initial parameters of the aircraft and the aircraft arresting system obtained in step 1.1 are used as input, and the aircraft collision parameter values ​​in the entire process of the aircraft collision are calculated through the written calculation program.

[0043] The principle of the present invention is that the time scale of each arresting belt being pulled out is very small, so it can be approximately considered that within the time scale of each arresting belt being pulled out, the rotor of the water turbine energy absorber rotates at a uniform speed and is subjected to a steady damping load. Then, according to the initial collision speed of the aircraft, the time when the first arresting belt is pulled out, the aircraft speed change, the belt pulling distance and other parameters can be obtained. The state of the previous circle is used as the input of the next circle, and the calculation process of the first circle is repeated. The parameters of each circle can be iteratively calculated until the aircraft speed becomes zero cutoff, and the final arresting data such as the arresting distance, the maximum overload value, and the maximum belt pulling force can be obtained.

[0044] Beneficial effects of the present invention:

[0045] (1) A theoretical analysis method for aircraft arresting system under steady damping load is proposed;

[0046] (2) It has realized the rapid prediction of key characteristics of current aircraft ground arresting equipment, providing theoretical support for its optimization and improvement;

[0047] (3) Comprehensively consider various factors of the aircraft ground arrest process and provide a prediction of arrest process parameters in a near-real environment;

[0048] (4) The theoretical research system of aircraft arresting system characteristics has been expanded, and the analysis capability of aircraft arresting system has been improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Calculation process for theoretical method.

[0050] Figure 2The following are comparison diagrams of theoretical results and experimental results, where (a) is the speed-time diagram, (b) is the overload-time diagram, and (c) is the arresting belt tension-time diagram. DETAILED DESCRIPTION

[0051] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the specific implementation methods of the present invention will be described in detail below with reference to the technical solution.

[0052] For the arresting process of a certain type of aircraft arresting net equipment, the theoretical analysis method of the steady damping load of the arresting system is as follows:

[0053] Step 1: Derivation of theoretical calculation process

[0054] Obtain the initial parameters of the aircraft and the aircraft arresting system, and combine the actual aircraft collision situation of a certain type of aircraft arresting net equipment to give the aircraft collision speed v 1 =182km / h, aircraft frontal area A = 60.8m 2 , aircraft weight m = 15000kg, reel shaft radius r 0 =0.192m, barrier thickness δ =0.0085m, barrier length ε l =220m, energy absorber diameter D = 0.87m, half of the length of the barrier net l 0 =31.611m.

[0055] According to formulas (1) and (2), the number of winding turns of the arresting belt and the total outer diameter of the belt reel are 71 and 0.7955 m respectively.

[0056] According to Formula 2, the sum of the length of the arresting belt released at the i-th circle and half of the length of the arresting net can be obtained as shown in Formula (3); the braking distance S generated by pulling out the i-th circle of arresting belt can be obtained by using the Pythagorean theorem i and braking distance increment △S i As shown in equations (4) and (5), the angle α between the arresting belt and the aircraft's moving direction during the i-th arresting belt pull-out period is obtained. i Cosine value cos(α i ) as formula (6); Based on the aircraft collision speed v 1 According to equations (1) to (5), calculate the time △t when the arresting belt of the i-th circle is pulled out i , the energy absorber speed N during the time when the arresting belt of the i-th circle is pulled out i As shown in equations (7) and (8), the absorbed power P of the energy absorber during the period when the i-th barrier strip is pulled out is obtained. i As shown in formula (9), the braking torque M of the energy absorber during the time period when the arresting belt of the i-th circle is pulled out is obtained: iAs shown in formula (10); According to formula (2), formula (6) and formula (10), the resistance F that the aircraft encounters during the time period when the i-th arresting belt is pulled out is obtained i As shown in formula (11); according to formulas (12) and (13), the aircraft acceleration a during the time period when the arresting strip of the i-th circle is pulled out is obtained: i and the aircraft velocity increment △v i .

[0057] The speed of the aircraft hitting the net v 1 As input, through equations (2) to (13), the parameters of the aircraft hitting the net during the time period when the first arresting belt is pulled out are calculated, including the resistance F during the aircraft hitting the net 1 、Aircraft acceleration a 1 and braking distance S 1 , and the aircraft speed increment △v during the first arresting belt pullout period 1 According to formula (14), calculate the final speed v of the aircraft after the first arresting strip is completely pulled out. 2 ; v 2 The parameters of the aircraft hitting the net during the time period when the second arresting tape is pulled out are used as the input values ​​for calculating the parameters of the aircraft hitting the net during the time period when the second arresting tape is pulled out. Progressive calculation is performed along the time dimension to obtain the parameters of the aircraft hitting the net during the time period when each arresting tape is pulled out until the speed of the aircraft decreases to zero, and the parameters of the aircraft hitting the net during the entire process of the aircraft hitting the net are obtained.

[0058] Step 2: Perform simulation calculations

[0059] According to the equivalent relationship between the parameters of each aircraft hitting the net in step 1, a calculation program is written in Matlab to perform progressive calculations along the time dimension. The calculation ends when the speed of the aircraft decreases to zero. The calculation process is as follows: Figure 1 As shown; using the initial parameters of the aircraft and aircraft arresting system obtained in step 1.1 as input, the aircraft collision parameter values ​​during the entire process of the aircraft collision are calculated through the written calculation program.

[0060] Step 3: Compare the calculation results with the net collision test data to verify the accuracy of the theoretical calculation.

[0061] Figure 2A comparison between the theoretical results and the test results is given. The maximum overload value obtained by theoretical calculation is 1.78g, and the aircraft overload value shows a development trend of first increasing and then decreasing. The aircraft's arresting distance is 176m, which meets the aircraft's arresting requirements. Combining the results of step one and step two, it can be seen that the overall trend of the aircraft speed predicted by the steady damping load theory is basically consistent with the test results, and both show a "sine function" development trend. The results of the theoretical prediction of the aircraft overload value are consistent with the development trend of the test data, but the theoretical prediction results develop faster than the test results, and the peak of the aircraft overload is at the end of the 1st second. The theoretical prediction results of the arresting belt tension are basically consistent with the development trend of the test results, but after comparison, it is found that the peak value of the theoretically predicted arresting belt tension appears earlier than the test results and has a larger value.

Claims

1. A theoretical analysis method for steady damping load of an aircraft arresting system, characterized in that: Firstly, the initial parameters of the aircraft and the aircraft arresting system are obtained, and the total number of turns n of the water turbine energy absorber's reel is calculated. In the time scale of each arresting tape being pulled out, the rotor of the water turbine energy absorber rotates at a uniform speed and is subjected to a steady damping load. Secondly, the aircraft collision net speed v1 in the aircraft initial parameters is used as input to calculate the aircraft collision net parameters and the aircraft speed increment △v1 in the time period when the first arresting tape is pulled out, and then the aircraft terminal speed after the first arresting tape is completely pulled out is obtained, and this is used as input to calculate the input value of the aircraft collision net parameters in the time period when the second arresting tape is pulled out. Finally, a progressive calculation is performed along the time dimension to obtain the aircraft collision net parameters in the time period when each arresting tape is pulled out until the aircraft speed decreases to zero, and the aircraft collision net parameter values ​​in the whole process of the aircraft collision net are obtained.

2. The steady damping load theoretical analysis method of an aircraft arresting system according to claim 1 is characterized in that: The specific steps of the steady damping load theoretical analysis method are as follows: Step 1.1: Obtain the initial parameters of the aircraft and the aircraft arresting system, including the aircraft collision speed, the aircraft frontal area, the aircraft weight, the radius of the belt reel shaft, the arresting belt thickness, the arresting belt length, the energy absorber diameter, and the arresting net length; according to the initial parameters of the aircraft arresting system, calculate the total number of turns n of the water turbine energy absorber belt reel; Where r0 is the radius of the reel shaft, in m; δ is the thickness of the barrier, in m; ε l is the total length of the brake belt, in m; Step 1.2: Let the number of turns of the arresting belt be i, where 1≤i≤n. According to step 1.1, the outer diameter R of the reel before the arresting belt is pulled out for the i-th turn is obtained. i The calculation formula is: R i =(n-i+1)δ+r0(2) Step 1.3: According to step 1.2, the sum of the length of the arresting belt released after the arresting belt is pulled out of the i-th circle and half of the length of the arresting net is obtained; l i =l0+2(n-i+1)πR i –(n-i+1)(ni)δπ(3) Where, l0 is half of the length of the barrier net, unit: m; Step 1.4: According to step 1.3, calculate the braking distance S generated during the i-th arresting belt pull-out period i and braking distance increment △S i ; Step 1.5: According to steps 1.3 to 1.4, the angle α between the arresting belt and the aircraft's moving direction during the i-th arresting belt pull-out period is obtained. i Cosine value cos(α i )for: cos(a i )=S i / l i (6) Step 1.6: Assume that within the time scale of each circle of the arresting belt being pulled out, the rotor of the water turbine energy absorber rotates at a uniform speed and is subjected to a steady damping load. Then the time △t for the arresting belt of the ith circle to be pulled out is i The calculation formula is: Δt i =ΔS i / v i (7) In the formula, v i is the initial speed of the aircraft during the time period when the i-th arresting tape is pulled out, that is, the terminal speed of the aircraft during the time period when the i-1-th arresting tape is pulled out; Then the speed of the energy absorber during the time when the i-th arresting belt is pulled out is N i for: N i =60 / Δt i (8) Step 1.7: According to step 1.6, the absorbed power P of the energy absorber during the time when the i-th barrier strip is pulled out is obtained. i for: P i =K1D x N i y (9) In the formula, K1 represents the correction coefficient, D represents the rotor diameter of the water vortex energy absorber, and x and y are both exponential coefficients; Step 1.8: According to step 1.7, the braking torque M of the energy absorber during the time period when the i-th arresting belt is pulled out is obtained. i for: M i =9550P i / N i (10) Step 1.9: According to equations (2), (6) and (10), the resistance F that the aircraft encounters during the time period when the i-th arresting strip is pulled out is obtained: i for: F i =2cos(α i )M i / R i +F a +F b (11) In the formula, F a Represents the windward resistance, F b represents the friction resistance of the airport runway; Step 1.10: According to step 1.7, the aircraft acceleration a during the time when the arresting strip of the i-th circle is pulled out is obtained. i and the aircraft velocity increment △v i for: a i =F i / m(12) Δv i =a i Δt i (13) Where m represents the mass of the aircraft; Step 1.11, using the aircraft collision speed v1 obtained in step 1.1 as input, through steps 1.2 to 1.10, calculate the aircraft collision parameters during the time period when the first arresting tape is pulled out, and the aircraft speed increment △v1 during the time period when the first arresting tape is pulled out. According to formula (14), calculate the aircraft terminal speed v2 after the first arresting tape is completely pulled out: v i+1 =v i -Δv i (14) Use v2 as the input value for calculating the parameters of the aircraft hitting the net during the time period when the second arresting tape is pulled out, repeat this step, perform progressive calculation along the time dimension, obtain the parameters of the aircraft hitting the net during the time period when each arresting tape is pulled out until the speed of the aircraft decreases to zero, and obtain the parameters of the aircraft hitting the net during the entire process of the aircraft hitting the net; wherein the aircraft hitting the net parameters include braking distance, acceleration, and resistance encountered by the aircraft during the process of hitting the net.

3. The steady damping load theoretical analysis method of an aircraft arresting system according to claim 2 is characterized in that: The braking distance S generated during the time period of the i-th barrier strip being pulled out in step 1.4 is i and braking distance increment △S i Using the Pythagorean theorem we can get: ΔS i =S i -S i-1 (5) Where a is half of the distance between the two water vortex energy absorbers, unit: m.

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