A fast prediction method for dimensionless maximum dynamic load of a controllable parachute wing

Abstract

The present invention proposes a method for rapidly predicting the dimensionless maximum dynamic load of a controllable parachute wing. Based on the parachute dynamics model, the Buckingham π theorem is used to extract the dimensionless criteria numbers that affect the dynamic load of the controllable parachute wing, including mass ratio, Froude number, and Strouhal number, for the parachute structural parameters and the parachute operation conditions. The results of two numerical calculation methods, the unsteady dynamics model and the momentum conservation theorem, are averaged to establish a database of dimensionless maximum dynamic loads and other dimensionless criteria numbers. The Levenberg-Marquardt algorithm is used to perform fitting regression analysis on each dimensionless quantity, and the dimensionless maximum dynamic load criterion relationship is obtained. The maximum dynamic load of the controllable parachute wing, which is currently widely used, is then rapidly predicted based on the definition. The method of the present invention has the advantages of high speed, high accuracy, and a wide range of applicability, and can improve design efficiency and reduce design costs.

Description

Technical Field

[0001] The invention relates to a method for quickly predicting the dimensionless maximum dynamic load of a controllable parachute opening wing, and belongs to the technical field of aerodynamic deceleration. Background Art

[0002] Compared to traditional parachutes, wing parachutes have a better aerodynamic shape, a high lift-to-drag ratio, good gliding and maneuverability, and are the only wing parachutes that are currently in practical use. In order to obtain a higher glide ratio and an ideal aerodynamic shape, ram canopies are usually made of fabric with ultra-low air permeability, and the configuration of the parachute ropes is also different from that of traditional parachutes, resulting in a much faster inflation time for the wing parachute than traditional parachutes. During the parachute opening process, the above measures all cause the wing parachute opening dynamic load to be greater than that of ordinary parachutes, making it more likely to cause damage to the canopy, leading to failure to open the parachute and causing the wing parachute system to fail. Therefore, the maximum parachute opening dynamic load is the parameter that designers pay most attention to. In order to reduce the parachute opening dynamic load, almost all wing parachutes use a controllable parachute opening method, that is, the parachute opening dynamic load is reduced by extending the inflation time to ensure the safety of the parachute opening.

[0003] At present, the acquisition of the dynamic load of parafoil opening is mainly based on two types of methods: dynamic numerical calculation or airdrop test. The research on the dynamics of parafoil opening is mostly based on Newtonian mechanics. It is possible to obtain data such as load, motion, and posture of the parafoil opening process. The solution process requires programming calculation, which is relatively cumbersome and cannot quickly obtain results. Moreover, the accuracy of the calculation depends on whether the aerodynamic parameter input is accurate (refer to Potvin J, Peek G. Three-Stage Model for Slider-Reefed Parafoil Inflation. 19th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar, 2007. AIAA 2007-2501). The experimental research method of the dynamic load of parafoil opening is mainly carried out by drop test, which is divided into parachute tower drop test, hot air balloon drop test and aircraft drop test. Experimental research has a long cycle, high cost, great risk, and is greatly affected by external factors. Especially for large parafoils, the test implementation is more difficult (see Stein J, Madsen C, Strahan A. An Overview of the Guided Parafoil System Derived from X-38 Experience. 18th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar. AIAA 2005-1652).

[0004] During the parafoil design phase, a universal, dimensionless method is urgently needed to quickly and accurately predict the maximum dynamic loads during parafoil deployment. This method can avoid the risks of underdesign and the high costs of overdesign. However, no research exists on the predictive relationship between dimensionless dynamic loads during the controlled deployment of a parafoil. Therefore, the rapid prediction of the dimensionless maximum dynamic loads during the controlled deployment of a parafoil is crucial. Summary of the Invention

[0005] Based on the above problems, the present invention provides a method for quickly predicting the dimensionless maximum dynamic load of a controllable parachute. For the unsteady controllable parachute opening process of the parachute, the maximum dynamic load during the parachute opening process can be quickly calculated, thereby providing guidance for further parachute design.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solution: the present invention designs a method for quickly predicting the dimensionless maximum dynamic load of a controllable parafoil opening, which is used to obtain the dimensionless maximum dynamic load of a target parafoil opening during the controllable parafoil opening process, comprising the following steps:

[0007] Step A. According to the structural dimensions of the parafoil, the span is b, the chord length is c, and the nominal area of ​​the parafoil is A0=bc, the nominal diameter is Then proceed to step B;

[0008] Step B. For the unsteady, controllable parafoil deployment process, Buckingham's π theorem was used to perform a dimensional analysis of the key variables influencing the deployment dynamic loads, such as structural parameters and deployment conditions, to obtain dimensionless numbers. For the controllable deployment process of the target parafoil, the mass ratio was introduced to account for the added mass during flight, the Froude number was used to account for the effects of inertia, and the Strouhal number was used to account for the unsteady characteristics of the controllable parafoil deployment, making the research process more consistent with real-world deployment conditions.

[0009] The dimensionless numbers are: mass ratio Rm, Froude number Fr, and Strouhal number Sr, specifically:

[0010]

[0011]

[0012]

[0013] Where m is the parachute system mass, ρ is the air density, v is the parachute opening speed, g is the acceleration of gravity, t is the parachute opening time, C D is the drag characteristic of the parafoil at the end of initial inflation, then proceed to step C;

[0014] Step C. For the unsteady controllable parachute opening process of the parafoil, the dimensionless maximum parachute opening dynamic load coefficient database is established by taking the average of the results of the dynamic method and the momentum theorem. The dimensionless maximum parachute opening dynamic load C is realized based on the Levenberg-Marquardt algorithm using MATLAB language. k The regression fitting of the criterion relationship is as follows:

[0015]

[0016] Specifically, for the controllable parafoil deployment process of the target parafoil, the mean data calculated using two numerical methods, a dynamic model and the momentum theorem, were used to establish a database of maximum deployment dynamic load coefficients. This approach avoids the methodological errors and cumulative deviations associated with a specific numerical simulation technique, achieving higher accuracy. Based on this database of maximum deployment dynamic load coefficients, a dimensionless maximum deployment dynamic load criterion relation was proposed using the Levenberg-Marquardt fitting regression algorithm. This method, a combination of the steepest descent method and the Gauss-Newton method, can quickly find the optimal value in nonlinear regression. Furthermore, the dimensionless representation method can be widely applied in parafoil design calculations.

[0017] Step D: The dimensionless maximum parachute opening dynamic load C obtained in step C is k Substitute the following formula:

[0018]

[0019] Get the maximum dynamic load F of the controllable parachute opening kmax .

[0020] The execution of steps A to D is used to obtain a dimensionless maximum parachute opening dynamic load for the controllable parachute opening process of the target parafoil, and then obtain the maximum parachute opening dynamic load according to the definition.

[0021] The method for rapidly predicting the dimensionless maximum dynamic load of a controllable parachute opening wing described in the present invention has the following beneficial effects compared with the prior art by using the above technical solution:

[0022] The present invention proposes a method for rapidly predicting the dimensionless maximum dynamic load of a controllable parachute. Based on the parachute dynamics model, the Buckingham π theorem is used to extract the dimensionless criteria numbers that affect the dynamic load of the controllable parachute, which are the mass ratio, the Froude number, and the Strouhal number, for the parachute structural parameters and the parachute operation conditions. The results of two numerical calculation methods, the unsteady dynamics model and the momentum conservation theorem, are used to average the results to establish a database of dimensionless maximum dynamic loads and other dimensionless criteria numbers. The Levenberg-Marquardt algorithm is used to perform fitting regression analysis on each dimensionless quantity, and the dimensionless maximum dynamic load criterion relationship is obtained. The maximum dynamic load of the controllable parachute, which is currently widely used, is then rapidly predicted based on the definition. The method of the present invention has the advantages of high speed, high accuracy, and a wide range of applicability, and can improve design efficiency and reduce design costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is a flow chart of a method for rapidly predicting the maximum dynamic load of a dimensionless parachute with controllable opening designed by the present invention;

[0024] Figure 2 It is a schematic diagram of the changes in aerodynamic characteristics during the parafoil inflation process;

[0025] Figure 3 This is a schematic diagram of the parafoil opening process trajectory;

[0026] Figure 4 It is the comparison between the dimensionless maximum parachute opening dynamic load prediction value and the original data. DETAILED DESCRIPTION

[0027] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0028] like Figures 1 to 4As shown, the present invention provides a method for rapidly predicting the dimensionless maximum dynamic load of a controllable parachute wing. For the unsteady controllable parachute opening process of the parachute, based on the idea of ​​dimensional analysis, the Buckingham π theorem is used on the basis of the parachute opening dynamics model to obtain dimensionless numbers corresponding to the parachute structural parameters and the parachute opening conditions. A dimensionless maximum dynamic load database is established using multiple sources, which is more accurate. For the controllable parachute opening situation, a dimensionless maximum dynamic load correlation criterion formula is proposed using the Levenberg-Marquardt algorithm and the fitting regression algorithm. The formula has strong versatility and can quickly calculate the maximum dynamic load during the parachute opening process, thereby providing guidance for further parachute design.

[0029] First, for a general parafoil, according to the structural dimensions of the parafoil, the span is b, the chord length is c, and the nominal area of ​​the parafoil A0 = bc, the nominal diameter

[0030] In view of the unsteady controllable parachute opening process of the parafoil, the Buckingham π theorem is used to conduct a dimensional analysis of the main variables affecting the parachute opening dynamic load, such as structural parameters and parachute opening conditions. The dimensionless numbers obtained are: the mass ratio Rm considering the influence of the additional mass during the flight process, the Froude number Fr considering the influence of the inertial force, and the Strouhal number Sr considering the unsteady characteristics of the controllable parachute opening. The three are specifically:

[0031]

[0032] Where m is the parachute system mass, ρ is the air density, v is the parachute opening speed, g is the acceleration of gravity, t is the parachute opening time, C D is the drag characteristic of the parafoil at the end of initial inflation.

[0033] Afterwards, for the controllable parachute opening process, the dimensionless parachute opening dynamic load was obtained based on two numerical calculation methods: the dynamic method and the momentum-impulse theorem.

[0034] Method 1: Kinetic method:

[0035] Without considering the additional mass of the parafoil and the relative position changes between the parafoil-borne systems during the inflation process, the parafoil opening dynamics model of the parafoil system in the track coordinate system is established:

[0036]

[0037] Where m s 、m w 、C D,w A w ,θ gj 、F k 、C D,s 、C L,sThey represent the mass of the parafoil, the mass of the payload, the drag area of ​​the payload, the trajectory angle, the dynamic load of the parafoil opening, the parafoil drag coefficient and the lift coefficient respectively. The controllable parafoil opening and inflation process of the parafoil can be assumed to be two stages: the controllable expansion stage of the wing surface and the inflation stage of the air chamber, and the time elapsed is t f1 and t f2 In the first stage, the parafoil does not generate lift, and the drag coefficient increases until it reaches the wing surface resistance; the second stage is the air chamber inflation stage, in which the drag coefficient decreases and the lift coefficient increases until the lift and drag coefficients of the parafoil are reached when it is in stable gliding. This example takes the controllable parafoil with closed-end fabric widely used in engineering as an example, and the inflation time of the two stages is t f1 =18×D0 / v,t f2 =2.5×D0 / v. Assume that the lift and resistance coefficients in the above two stages change linearly, such as Figure 2 As shown, according to the parachute model and the parachute opening condition, the above dynamic equation (2) can be programmed and calculated to obtain the maximum parachute opening dynamic load F kmax , then according to the definition The dimensionless maximum parachute opening dynamic load is obtained.

[0038] Method 2: Momentum-Impulse Theory:

[0039] Assume that during the controlled parachute opening process, the parafoil resistance is always tangent to the flight trajectory, such as Figure 3 As shown in the figure, the subscripts c and z represent the initial and final moments of the parachute opening, respectively. The following equation is established for the parafoil inflation process along the flight trajectory:

[0040]

[0041] Transform the above formula to get:

[0042]

[0043] definition According to the analysis of a large number of experimental data at home and abroad, it is found that F is about 0.5, and further deformation results in:

[0044]

[0045] A dimensionless maximum parachute deployment dynamic load database was established based on the average values ​​obtained from the dynamics method and the momentum theorem. This avoids the methodological errors and cumulative deviations caused by a specific numerical simulation technique, achieving higher accuracy. Table 1 shows selected data from the database.

[0046] Table 1 Dimensionless maximum parachute opening dynamic load database (excerpt)

[0047] Serial number Rm Fr Sr <![CDATA[C k ]]> Serial number Rm Fr Sr <![CDATA[C k ]]> 1 2.053 51.713 0.050 0.310 11 0.421 5.872 0.050 0.264 2 1.465 36.673 0.040 0.245 12 0.445 5.501 0.040 0.284 3 1.465 36.673 0.033 0.227 13 2.053 116.355 0.040 0.227 4 1.054 26.080 0.040 0.218 14 1.054 58.681 0.033 0.144 5 0.875 21.415 0.050 0.223 15 0.875 48.185 0.050 0.164 6 0.771 18.650 0.050 0.214 16 0.771 41.963 0.050 0.154 7 0.650 15.397 0.040 0.191 17 0.537 27.412 0.033 0.109 8 0.612 14.332 0.040 0.189 18 0.593 19.049 0.033 0.146 9 0.582 13.478 0.033 0.178 19 0.602 18.969 0.033 0.149 10 0.557 12.775 0.050 0.199 20 0.610 18.893 0.050 0.174

[0048] Based on the extracted database, the general objective function of the regression fitting of the dimensionless maximum parachute opening dynamic load criterion is:

[0049] C k =f(Rm,Fr,Sr)=f(R,β) (6)

[0050] Among them, R = (Rm, Fr, Sr) is the independent variable of the objective function, β = (a1, a2, ..., a m ) is the unknown coefficient. The next goal is to find the regression parameter β so that the sum of squares of the residuals χ(β) between the regression values ​​and the experimental values ​​of each group of data is minimized, that is:

[0051]

[0052] The Levenberg-Marquardt algorithm is used to deal with the nonlinear least squares fitting problem in this method. The LM algorithm is a combination of the steepest descent method and the Gauss-Newton method. It can quickly find the optimal value in nonlinear regression. First, an initial parameter β is given. Then, in each iteration step, the parameter vector β is replaced by a new estimate β+h, and the parameter increment is h=(h1,h2,…,h m ), for f(R i ,β+h) to perform Taylor expansion, we have:

[0053] f(R i ,β+h)=f(R i ,β)+J i h+O(h T h) (8)

[0054] Among them, the Jacobian matrix Further, the vector form of χ(β+h) is:

[0055] χ(β+h)≈||C k -f(β)-Jh|| 2 (9)

[0056] Among them C k =(C k,1 ,C k,2 ,…,C kn, ), f(β)=[f(R1,β),f(R2,β)…,f(R n ,β)],the above formula is h The derivative is 0. At the same time, in order to avoid irreversibility in the actual solution, the damping term is introduced and the above formula is transformed into:

[0057] [J T J+λE]h=J T [Ck -f(β)] (10)

[0058] E is the identity matrix, and λ is the non-negative damping factor, which is adjusted continuously with the iterative calculation. In addition, the LM algorithm replaces E with the diagonal matrix diag(J T J), specifically:

[0059] [J T J+λ·diag(J T J)]h=J T [C k -f(β)] (11)

[0060] For the controllable parachute opening process, based on the database, the MATLAB language is used to implement the regression fitting of the dimensionless maximum parachute opening dynamic load criterion relationship, and the specific results are:

[0061]

[0062] The coefficient of determination R of the dimensionless maximum parachute opening dynamic load criterion relationship obtained by this method is 2 =0.9922, the fitting relationship is relatively ideal and the correlation is high. The comparison distribution between the prediction results and the original data in the database is as follows Figure 4 As shown in the figure, it can be seen that the prediction results using the standard relationship in this paper are consistent with the original data. Overall, the average absolute percentage error between the fitting results and the original data is 4.93%, and only a very small number of points are not within the error range (20%).

[0063] Substitute the predicted dimensionless maximum parachute opening dynamic load, parachute opening conditions and structural parameters into the following formula:

[0064]

[0065] The maximum dynamic load of the parafoil opening can be obtained, providing a reference for design.

[0066] Taking the Stiletto parafoil as an example, this type of parafoil uses a sliding cloth to close the opening for controllable parachute. The specific structural parameters are as follows: the parachute load system mass m = 90.72 kg, the load body resistance area C D,w A w = 0.1, span b = 6.10m, chord c = 2.29m, and the nominal area of ​​the parafoil is A0 = bc = 13.94m 2 , nominal diameter The controllable parachute opening conditions are: parachute opening speed v = 54.25m / s, air density during parachute opening ρ = 1.12kg / m 3 , gravitational acceleration g = 9.8 m / s 2 , the drag coefficient C of the parafoil at the end of initial inflationD Take 1.0, and the parachute opening time t = 1.59s. Substituting the structural parameters and parachute opening conditions into formula (1) yields the mass ratio Rm = 1.5570, Strouhal number Sr = 0.0488, and Froude number Fr = 71.3063. Substituting Rm, Fr, and Sr into formula (12), we obtain the dimensionless maximum parachute opening dynamic load C k =0.2140. Using the airdrop test method, the dimensionless maximum parachute opening dynamic load C of the Stiletto parafoil obtained under this working condition is k =0.2253, the error between the two is 5.00%, which meets the calculation requirements of the flexible parafoil.

[0067] According to the dimensionless maximum parachute opening dynamic load, combined with the parachute opening conditions and structural parameters, based on formula (13), the maximum parachute opening dynamic load of the Stiletto parafoil can be obtained to be 4916.6N.

[0068] The embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by ordinary technicians in this field without departing from the spirit of the present invention.

Claims

1. A method for rapidly predicting the dimensionless maximum dynamic load of a controllable parafoil, which enables the target parafoil to obtain the maximum dynamic load during the controllable parafoil opening process, characterized in that: The steps include: Step A. According to the structural dimensions of the parafoil, the span is b, the chord length is c, and the nominal area of ​​the parafoil is A0=bc, the nominal diameter is Then proceed to step B; Step B. For the unsteady controllable parachute deployment process, Buckingham π theorem is used to perform dimensional analysis on the variables that affect the parachute deployment dynamic load, namely the parachute structural parameters and the unsteady controllable parachute deployment conditions, to obtain dimensionless numbers; Step C. Based on the dimensionless number, for the unsteady controllable parachute opening process of the parafoil, the dimensionless maximum parachute opening dynamic load coefficient database is established by taking the average of the results of the two numerical calculation methods, the dynamic method and the momentum theorem; based on the database, the dimensionless maximum parachute opening dynamic load criterion relational expression is implemented by regression fitting using the Levenberg-Marquardt algorithm in MATLAB language to obtain the dimensionless maximum parachute opening dynamic load C. k ; Step D. Based on the dimensionless parachute opening dynamic load and the maximum parachute opening dynamic load F kmax The relationship The dimensionless maximum parachute opening dynamic load C obtained in step C is k Substituting into the equation, we can get the maximum dynamic load F of the controllable parachute opening. kmax : Where ρ is the air density, v is the parachute opening speed, and C D is the drag characteristic of the parafoil at the end of initial inflation.

2. The method for rapidly predicting the dimensionless maximum dynamic load of a controllable parachute opening according to claim 1, characterized in that: In step B, for the controllable parachute opening process of the target parafoil, the mass ratio is introduced to consider the additional mass during the flight process, the Froude number is introduced to consider the influence of inertial force, and the Strouhal number is introduced to consider the unsteady characteristics of the controllable parachute opening, making the research process more consistent with the actual parachute opening situation.

3. The method for rapidly predicting the dimensionless maximum dynamic load of a controllable parachute opening according to claim 2, characterized in that: In step B, dimensional analysis is performed using Buckingham's π theorem, and the dimensionless numbers obtained are: mass ratio Rm, Froude number Fr, and Strouhal number Sr, specifically: Where m is the parachute system mass, ρ is the air density, v is the parachute opening speed, g is the acceleration of gravity, t is the parachute opening time, C D is the drag characteristic of the parafoil at the end of initial inflation.

4. The method for rapidly predicting the dimensionless maximum dynamic load of a controllable parafoil opening according to claim 3 is characterized in that: The calculation steps based on the dynamic method in step C are as follows: step C1, establishing the parachute opening dynamics model of the parafoil system in the track coordinate system; step C2, dividing the controllable parachute opening and inflation process of the parafoil into two stages: the controllable wing surface expansion stage and the air chamber inflation stage, and obtaining the inflation time of the two stages based on engineering experience; step C3, programming and calculating the parachute opening dynamics model according to the parafoil model and the parachute opening working condition, and obtaining the maximum parachute opening dynamic load F kmax According to the definition, the dimensionless maximum parachute opening dynamic load C is obtained k .

5. The method for rapidly predicting the dimensionless maximum dynamic load of a controllable parafoil opening according to claim 4, characterized in that: In step C, the dimensionless maximum parachute opening dynamic load C is obtained based on the momentum theorem method. k for Where v is the parachute opening speed, subscripts c and z represent the initial and final moments of parachute opening, respectively. F is the aerodynamic drag integration factor, θ gj is the trajectory angle.

6. A method for rapidly predicting the dimensionless maximum dynamic load of a controllable parafoil opening according to claim 1 or 5, characterized in that: In step C, based on the database, the regression fitting of the dimensionless maximum parachute opening dynamic load criterion is specifically as follows: establish the objective function C k =f(Rm,Fr,Sr)=f(R,β), where R=(Rm,Fr,Sr) is the independent variable of the objective function, β=(a1,a2,…,a m ) is the unknown coefficient; the Levenberg-Marquardt algorithm is used to find the optimal value of the nonlinear regression, that is, the regression parameter β, so that the sum of squares of the residuals χ(β) between the regression values ​​of each group of data in the database and the experimental values ​​is minimized; finally, the dimensionless maximum parachute opening dynamic load C is obtained. k for:

7. A method for rapidly predicting the dimensionless maximum dynamic load of a controllable parafoil opening according to claim 6, characterized in that: The execution of steps A to D is used to obtain a dimensionless maximum parachute opening dynamic load for the controllable parachute opening process of the target parafoil, and then obtain the maximum parachute opening dynamic load according to the definition.

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