A method of aerodynamic load distribution based on modal fitting

Abstract

The invention discloses a method for distributing aerodynamic loads based on modal fitting, including: constructing a fluid mesh model and a finite element mesh model of the same wing surface according to the computational fluid dynamics mesh and the finite element model mesh of the wing surface structure; calculating the rigid body modes and elastic modes of the two models respectively; combining the first n-order elastic modal vibration modes with the first six-order rigid body modal vibration modes of each model to obtain the respective total n+6-order modal vibration modes, and performing normalization processing; fitting the aerodynamic loads of each node of the fluid mesh model based on the first N-order calculated modes of the fluid mesh model; using the participation coefficient of the first N-order modes of the fluid mesh model as the weight coefficient to superimpose the first N-order modes of the finite element mesh model, calculating the fitting load of the finite element mesh model, iteratively calculating the appropriate N value based on the given error limit, and obtaining the fitting load that meets the accuracy requirements. The invention is convenient to calculate and is not subject to human interference, and effectively improves work efficiency and result accuracy.

Description

Technical Field

[0001] The invention belongs to the technical field of aviation structure dynamics modeling and relates to an aerodynamic load distribution method based on modal fitting. Background Art

[0002] In the structural strength design of aircraft, aerodynamic loads are very important design inputs. Structural strength professionals need to apply loads to finite element models as inputs for the next step of design. At present, the strength calculation software widely used in the aerospace industry, such as MSC.Patran / Nastran, Abaqus, etc., cannot automatically distribute loads to uneven surfaces. If the nodes are loaded manually, the actual finite element model will not meet the actual requirements of the project because it has a large number of nodes and different working conditions.

[0003] To solve this problem, the "multi-point row" method is commonly used in China's domestic aviation field. This method uses the minimum strain energy and static equivalence as constraints to distribute each aerodynamic load to several finite element nodes. However, this process is very cumbersome, especially on large wing surfaces, when the number of fluid grids is large, the computational workload is very huge. Not only that, the starting point of this type of load distribution is the concentrated force of the aerodynamic load after integration. The wing structure of modern large aircraft is complex, and the aerodynamic partition and structural partition are often inconsistent. Directly integrating the concentrated load on the fluid grid may transfer the load across regions, resulting in unrealistic force transmission routes; secondly, these methods artificially specify some nodes to distribute the corresponding aerodynamic loads when distributing loads, which increases the error. Therefore, when the structure and aerodynamic load distribution are very complex, the "multi-point row" method has problems such as low computational efficiency and difficulty in controlling the accuracy of the fitting function. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the prior art and provide an aerodynamic load distribution method based on modal fitting. This method uses the known airfoil modal vibration type as the basis function to fit the aerodynamic load distribution, which is convenient to calculate and free from human interference, thereby improving work efficiency and result accuracy; at the same time, the modal truncation theory is adopted to approximate the aerodynamic load obtained by CFD calculation, thereby ensuring the accuracy of the result.

[0005] To achieve the above objectives, the present invention adopts the following technical solutions.

[0006] A method for distributing aerodynamic loads based on modal fitting comprises the following steps:

[0007] Step 1: construct two virtual structural models of the same airfoil surface, namely, a fluid mesh airfoil model and a finite element mesh airfoil model, based on the computational fluid dynamics shape mesh of the airfoil structure and the surface mesh of the finite element model; unify the coordinates so that the Cartesian coordinates of the coincident nodes on the two models are the same;

[0008] The process of constructing a fluid mesh airfoil model and a finite element mesh airfoil model of the same airfoil surface includes: firstly, based on the computational fluid dynamics shape mesh of the airfoil structure, using fluent software to construct the fluid mesh airfoil model of the airfoil, then dividing the mesh on the model and adding pressure, which is given by CFD calculation; then, based on the finite element model surface mesh of the airfoil structure, using MSC.Patran software to construct the finite element mesh airfoil model of the airfoil; there is no load on the finite element mesh airfoil model, and load distribution is required.

[0009] Step 2, respectively calculating the rigid body modes and elastic modes of the fluid mesh airfoil model and the finite element mesh airfoil model; combining the first n-order elastic modal vibration modes with the first six-order rigid body modes of each, and obtaining the total n+6-order modal vibration modes of each of the two mesh models; and then performing normalization processing;

[0010] The process of calculating the rigid body mode of the fluid mesh airfoil model includes:

[0011] Step 2.1. The total number of nodes of the fluid grid airfoil model is D1. First, consider the three translational degrees of freedom of each node. After determining the overall Cartesian coordinate system, perform unit translation on the fluid grid airfoil model along the three coordinate axes to obtain the rigid body modal vibration shapes of the first three translations. The modal vibration shape of the i-th node on the fluid grid airfoil model is expressed as:

[0012]

[0013] in, They represent the first, second and third order rigid body mode vibration shapes of the i-th node of the fluid mesh airfoil model respectively;

[0014] Then, the fluid grid wing model is rotated around the x-axis, y-axis, and z-axis by a certain angle, and the coordinate displacement of the node is used to represent the vibration vector of the third-order rotational rigid body mode. Assume that the coordinate of the i-th node of the model is (x i ,y i ,z i ), the rotation angle is θ1, then the subsequent rigid body mode vibration shape of the i-th node of the fluid grid airfoil model is expressed as:

[0015]

[0016]

[0017]

[0018] in, They respectively represent the fourth, fifth, and sixth order rigid body mode vibration shapes of the i-th node of the fluid mesh airfoil model.

[0019] The process of calculating the rigid body mode of the finite element mesh wing model includes: counting the total number of nodes of the finite element mesh wing model as D2; after determining the overall Cartesian coordinate system, the finite element mesh wing model is unit translated along the three coordinate axes to obtain the rigid body modal vibration modes of the first three order translations; the modal vibration mode of the jth node on the finite element mesh wing model can be expressed as:

[0020]

[0021] in, They represent the first, second and third order rigid body mode shapes of the jth node of the finite element mesh airfoil model respectively;

[0022] Then, the finite element mesh wing model is rotated around the x-axis, y-axis, and z-axis by a certain angle, and the coordinate displacement of the node is used to represent the vibration vector of the third-order rotational rigid body mode. Assume that the coordinate of the jth node of the model is (x j ,y j ,z j ), the rotation angle is θ2, then the subsequent rigid body mode vibration shape of the jth node is expressed as:

[0023]

[0024]

[0025]

[0026] in, They respectively represent the fourth, fifth and sixth order rigid body mode vibration shapes of the jth node of the finite element mesh airfoil model.

[0027] Furthermore, in the step 2, MSC.Patran / Nastran software is used to calculate the first n elastic modal vibration modes of the airfoil under the fluid mesh airfoil model and the finite element mesh airfoil model respectively, and the first n elastic modal vibration modes obtained are combined with the first six rigid body modal vibration modes of each to obtain the total n+6 modal vibration modes of each under the two mesh models.

[0028] The normalization processing refers to: normalizing the n+6th order modal vibration modes of the fluid grid airfoil model and the finite element grid airfoil model according to the maximum amplitude of all their degrees of freedom, respectively, to obtain the modal vector; the selection and construction of the basis function are completed, that is, the N (N=n+6)th order modal vectors corresponding to the fluid grid airfoil model and the finite element grid airfoil model respectively; the first N-order modal vector matrix of the fluid grid airfoil model is Φ1, Φ1 is a 3D1×N matrix; the first N-order modal vector matrix of the finite element grid airfoil model is Φ2, Φ2 is a 3D2×N matrix.

[0029] Step 3: Based on the first N-order calculation modes of the fluid mesh airfoil model, fit the aerodynamic loads of each node of the fluid mesh airfoil model calculated by fluid dynamics, that is, calculate the participation coefficients of the first N-order modes by the least square method or other optimization methods; use the participation coefficients of the first N-order modes as weight coefficients to superimpose the first N-order modes, calculate the fitting loads on the finite element mesh airfoil model, compare the resultant force, resultant moment amplitude and pressure center position errors of the fitting loads and aerodynamic loads, and calculate the appropriate N value through iteration based on the given error limit. The process specifically includes:

[0030] Step 3.1. Calculate the fitting coefficients:

[0031] The pressure at each node position on the fluid mesh airfoil model is taken as the node pressure on the node; each node pressure is decomposed, expressed as components in Cartesian coordinates, and arranged according to the node number; the decomposed node pressure array of the fluid mesh airfoil model is recorded as P1, which is a 3D1×1 column vector; the modal vector of the fluid mesh airfoil model is used to fit the distribution of aerodynamic loads: the relationship between P1 and Φ1 is as follows:

[0032] Φ1·Q=P1 (9)

[0033] Where P1 is generally a known condition, Φ1 is the first N-order modal vector matrix of the fluid grid airfoil model, and the fitting coefficient is obtained after matrix operation:

[0034] Q=Φ1 -1 ·P1 (10)

[0035] Step 3.2. Calculate the fitted loads:

[0036] The fitting coefficient Q is used as the weighting coefficient, and the modal vectors of the finite element mesh airfoil model are superimposed to obtain the array P2 of the fitting node load of the finite element mesh airfoil model after decomposition in the Cartesian coordinate system:

[0037]

[0038] Among them, P jx , P jy , P jz They represent the D2×1 column vectors of the projection of the fitting node load in the x-axis, y-axis, and z-axis directions in the Cartesian coordinate system, and P2 is a 3D2×1 column vector;

[0039] Step 3.3. Determine the value of N:

[0040] The resultant force F of the aerodynamic load is calculated based on the node pressure array and node and unit information of the fluid grid wing model. c and pressure heart (X c ,Yc ), and then calculate the resultant force F′ of the fitting load according to the fitting node load array and node and unit information of the finite element mesh wing model c and pressure center (X′ c ,Y′ c ); find their respective errors:

[0041]

[0042]

[0043]

[0044] Among them, W F is the error between the fitting load and the resultant aerodynamic load, W X , W Y To fit the errors of the load pressure center and the aerodynamic load pressure center in the chord direction and span direction of the wing, X c , Y c are the positions of the pressure center of the aerodynamic load in the chord direction and span direction of the airfoil, X′ c , Y′ c are the calculated positions of the fitting load pressure center in the chord direction and span direction of the airfoil respectively;

[0045] According to the requirements, the errors of the resultant force and the pressure center are weighted, and the weights are a, b, c (0≤a, b, c≤1 and a+b+c=1). If the resultant force needs to be more accurate, a can be greater than b+c; if the weights of the three are the same, the values ​​of a, b, and c are all 1 / 3; it is also possible not to take the weight coefficient, and take the three errors being less than the corresponding threshold at the same time as the judgment condition; if weighted judgment is adopted, the following formula is used to judge whether the error meets the requirements:

[0046] aW F +bW X +cW Y ≤γ (15)

[0047] If the initially selected N value makes formula (15) or other judgment conditions not hold, increase the N value until it is satisfied;

[0048] When (15) or other judgment conditions are met, the N value can be determined. At this time, P2 is the load array after the fitting node load of the finite element mesh airfoil model that meets the accuracy requirements is decomposed in the Cartesian coordinate system;

[0049]

[0050] P is the node load array of the finite element mesh airfoil model, which is a D2×1 column vector.

[0051] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0052] 1. The present invention uses the modal vibration shape of the structure as the basis function, has local linear independence, can better handle the load distribution problem of special points (such as nodes on the boundary), and improves the accuracy of the load distribution process.

[0053] 2. The load distribution calculation method of the present invention adopts the modal vibration type of the structure as the basis function to fit the aerodynamic load distribution. It is not only naturally convenient, but also the principle of load distribution is simple, not subject to human interference, and can achieve a more accurate load distribution effect without a large amount of calculation. At the same time, the modal truncation theory is adopted to approximately fit the aerodynamic load obtained by CFD calculation, which reduces the amount of calculation while fully ensuring the accuracy of the results.

[0054] 3. The method of the present invention not only highly guarantees the authenticity of the load, but is also more convenient and efficient, so that when faced with a large number of nodes and grids in wing design, it can significantly reduce the workload, save costs, and complete the rapid application of surface distributed loads on the structural calculation finite element model with high quality.

[0055] 4. The present invention converts the load from a dense grid to a sparse grid. Further development can be carried out on the basis of the present invention to verify the feasibility of converting the load from a sparse grid to a dense grid and improve the technology of converting the load from a sparse grid to a dense grid. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flow chart of an embodiment method of the present invention.

[0057] Figure 2 It is a schematic diagram of the fluid grid of the wing surface of an embodiment of the present invention, which contains 609 aerodynamic load nodes and 560 grids.

[0058] Figure 3 It is a schematic diagram of the structural finite element mesh of the airfoil of an embodiment of the present invention.

[0059] Figure 4 1 is an aerodynamic load distribution diagram of an embodiment of the present invention.

[0060] Figure 5 It is a load conversion error display diagram under different modal orders of an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The present invention relates to the load distribution between different grids of the wing surface of the structural dynamics modeling technology. Generally, the load on the fluid grid wing surface model is equivalently distributed to the finite element grid wing surface model. Since the number of units and nodes of the two grids is large, and most of the nodes do not overlap, the classical load distribution method has the problems of complex calculation and insufficient precision. The present invention uses the modal vector obtained after the modal vibration mode of the wing surface under the fluid grid is normalized as the basis function to approximate the aerodynamic load calculated by CFD, and obtains the modal coordinates of the aerodynamic load, that is, the weight coefficient of the fitting function. Since the continuum structure has an infinite number of modes, the modal truncation method is used to determine the modal order to be used, so as to reduce the amount of calculation and ensure the calculation accuracy. Finally, the fitting load on the finite element grid is obtained by using the weight coefficient and according to the modal vibration mode of the wing surface model constructed by the finite element grid.

[0062] The present invention is further described in detail below with reference to the accompanying drawings.

[0063] like Figure 1 As shown, the present invention starts from the fluid mesh airfoil model and the finite element mesh airfoil model to be allocated, has two branches, corresponding to steps 1 to 3, and the last two branches are combined to obtain the load of each node on the finite element mesh airfoil model, including the following steps:

[0064] Step 1: construct two virtual structural models of the same airfoil surface based on the computational fluid dynamics shape mesh and the finite element model surface mesh of the airfoil structure, namely, the fluid mesh airfoil model and the finite element mesh airfoil model; unify the coordinates so that the Cartesian coordinates of the overlapping nodes on the two models are the same.

[0065] For the same airfoil, first construct the fluid mesh airfoil model of this airfoil based on the computational fluid dynamics shape mesh of the airfoil structure, that is, use the fluent software to build the airfoil model, and then divide the mesh on the model and add pressure. After that, construct the finite element mesh airfoil model of this airfoil based on the finite element model surface mesh of the airfoil structure, that is, use the MSC.Patran software to build the airfoil surface model, and then divide the nodes on the model. Although most of the nodes of the two models do not overlap, some nodes (such as vertices) overlap, and the coordinates are unified so that the Cartesian coordinates of these overlapping nodes of the two models are the same. Usually, the pressure on the fluid mesh airfoil model is given by CFD calculation, and there is no load on the finite element mesh airfoil model, so load distribution is required.

[0066] Step 2: Calculate the modes of the fluid mesh airfoil model and the finite element mesh airfoil model, including rigid body modes and elastic modes: Since the rigid body modes calculated by the two models based on commercial software will be different, it is necessary to give a unified rigid body modal vector expression. Combine the first n-order elastic mode vibration shapes with the first six-order rigid body modes of each to obtain the total n+6-order mode vibration shapes of each of the two mesh models; then perform normalization.

[0067] The value of n is obtained by modal truncation. Since in theory, the modal has infinite order, but the effective mass of the low-order modal accounts for a large proportion of the total mass of the structure, the present invention only intercepts the first n-order elastic modal vibration modes and the first six-order rigid body modes when using the modal for calculation, and combines the first n-order elastic modal vibration modes of the two grids with the first six-order rigid body modes of each to obtain the total n+6-order modal vibration modes of each under the two grid models; and then performs normalization processing.

[0068] Specifically, step 2 includes:

[0069] Step 2.1. Calculate the first six rigid body modes of the fluid mesh airfoil model:

[0070] The total number of nodes in the fluid mesh airfoil model is D1. First, consider the three translational degrees of freedom of each node. After determining the overall Cartesian coordinate system, the fluid mesh airfoil model is translated along the three coordinate axes to obtain the rigid body modal vibration shapes of the first three translations. The modal vibration shape of the i-th node on the fluid mesh airfoil model is expressed as:

[0071]

[0072] in, They represent the first, second and third order rigid body mode vibration shapes of the i-th node of the fluid mesh airfoil model respectively.

[0073] Then rotate the fluid grid wing model around the x-axis, y-axis, and z-axis by a certain angle, and use the node coordinate displacement to represent the third-order rotational rigid body mode vibration vector. Assume that the coordinates of the i-th node of the model are (x i ,y i ,z i ), the rotation angle is θ1, then the subsequent rigid body mode vibration shape of the i-th node of the fluid grid airfoil model is expressed as:

[0074]

[0075]

[0076]

[0077] in, They respectively represent the fourth, fifth, and sixth order rigid body mode vibration shapes of the i-th node of the fluid mesh airfoil model.

[0078] Thus, the first six rigid body modes of the fluid mesh airfoil model are obtained.

[0079] Step 2.2. Calculate the first six rigid body modes of the finite element mesh airfoil model:

[0080] The total number of nodes in the finite element mesh airfoil model is counted as D2. After determining the overall Cartesian coordinate system, the finite element mesh airfoil model is unit translated along the three coordinate axes to obtain the rigid body modal vibration shapes of the first three order translations. The modal vibration shape of the jth node on the finite element mesh airfoil model can be expressed as:

[0081]

[0082] in, They represent the first, second and third order rigid body mode vibration shapes of the jth node of the finite element mesh airfoil model respectively.

[0083] Then rotate the finite element mesh wing model around the x-axis, y-axis, and z-axis by a certain angle, and use the node coordinate displacement to represent the third-order rotational rigid body mode vibration vector. Assume that the coordinates of the jth node of the model are (x j ,y j ,z j ), the rotation angle is θ2, then the subsequent rigid body mode vibration shape of the jth node is expressed as:

[0084]

[0085]

[0086]

[0087] in, They respectively represent the fourth, fifth and sixth order rigid body mode vibration shapes of the jth node of the finite element mesh airfoil model.

[0088] Thus, the first six rigid body mode vibration shapes of the finite element mesh airfoil model are obtained.

[0089] Step 2.3. Calculate elastic modes: Use MSC.Patran / Nastran and other software to calculate the first n elastic modal vibration modes of the airfoil under the fluid mesh airfoil model and the finite element mesh airfoil model respectively, combine the first n elastic modal vibration modes obtained with the first six rigid body modal vibration modes of each, and obtain the total n+6 modal vibration modes of each under the two mesh models.

[0090] Step 2.4. Normalization: The n+6th order modal vibration modes of the fluid mesh airfoil model and the finite element mesh airfoil model are obtained from steps 2.1, 2.2, and 2.3, but the modal vibration modes can only be determined to the extent that the proportions between the components remain unchanged, and cannot be used for subsequent calculations. Therefore, it is necessary to normalize the n+6th order modal vibration modes of the fluid mesh airfoil model and the finite element mesh airfoil model according to the maximum amplitude of all their degrees of freedom to obtain the modal vector. The selection and construction of the basis function are completed, which is the N (N=n+6)th order modal vector corresponding to the fluid mesh airfoil model and the finite element mesh airfoil model.

[0091] The first N-order modal vector matrix of the fluid mesh airfoil model is Φ1, which is a 3D1×N matrix. The first N-order modal vector matrix of the finite element mesh airfoil model is Φ2, which is a 3D2×N matrix.

[0092] Step 3, based on the first N order calculation modes of the fluid mesh airfoil model, fit the aerodynamic loads of each node of the fluid mesh airfoil model calculated by fluid dynamics, that is, calculate the participation coefficients of the first N order modes by the least square method or other optimization methods; use the participation coefficients of the first N order modes of the fluid mesh airfoil model as weight coefficients to superimpose the first N order modes of the finite element mesh airfoil model to calculate the fitting loads on the finite element mesh airfoil model, compare the resultant force of the fitting loads with the aerodynamic loads and the error of the pressure center position, and calculate the appropriate N value through iteration based on the given error limit.

[0093] The specific process of step 3 includes:

[0094] Step 3.1. Calculate the fitting coefficients

[0095] Take the pressure at each node position on the fluid mesh airfoil model as the node pressure on the node. For the convenience of calculation, decompose each node pressure, express it with components in Cartesian coordinates, and arrange them according to the node number. The decomposed node pressure array of the fluid mesh airfoil model is recorded as P1, which is a 3D1×1 column vector. Use the modal vector of the fluid mesh airfoil model to fit the distribution of aerodynamic loads:

[0096] The relationship between P1 and Φ1 is as follows:

[0097] Φ1·Q=P1 (9)

[0098] Where P1 is generally a known condition, Φ1 is the first N-order modal vector matrix of the fluid grid airfoil model obtained in step 2, and the fitting coefficient is obtained after matrix operation:

[0099] Q=Φ1 -1 ·P1 (10)

[0100] Step 3.2. Calculate the fitted loads

[0101] The fitting coefficient Q is an N×1 column vector, which represents the modal coordinates of the aerodynamic load on the fluid grid airfoil model. Theoretically, the larger the modal order N, the greater the amount of calculation, but the fitting load calculated based on the fitting coefficient Q is more convergent to the real load.

[0102] The fitting coefficient Q is used as the weighting coefficient, and the modal vectors of the finite element mesh airfoil model are superimposed to obtain the array P2 of the fitting node load of the finite element mesh airfoil model after decomposition in the Cartesian coordinate system:

[0103]

[0104] Among them, P jx , P jy , P jz They represent the D2×1 column vectors of the projections of the fitting node loads in the Cartesian coordinate system toward the x-axis, y-axis, and z-axis directions, respectively. P2 is a 3D2×1 column vector.

[0105] This method of load distribution using modal fitting is simple in principle and easy to operate, especially when faced with a large number of nodes and grids, it can significantly reduce the workload.

[0106] Theoretically, a structure has an infinite number of modes, but in actual test measurements or finite element analysis, only limited modes can be obtained, and they may all be low-order modes. Therefore, the modes obtained in measurement and analysis are only part of all the modes of the structure, which is modal truncation. In the present invention, if the modal order is too small, the fitting accuracy will be insufficient and the error will be large; if the modal order is too large, the amount of calculation will increase, and the improvement of the result accuracy will not be obvious, which will reduce the calculation efficiency. Therefore, the modal truncation is first used to take the first N modes for calculation. If the accuracy requirement is not met, the N value is increased until the accuracy requirement is met.

[0107] Step 3.3. Determine the value of N

[0108] The accuracy of load distribution is evaluated by the resultant force and the pressure center. By setting the error threshold γ, it is judged whether the error meets the requirements, and then further judge whether the value of N is reasonable. The resultant force F of the aerodynamic load is calculated based on the node pressure array and node and unit information of the fluid grid airfoil model. c and pressure heart (X c ,Y c ), and then calculate the resultant force F′ of the fitting load according to the fitting node load array and node and unit information of the finite element mesh wing model c and pressure center (X′ c ,Y′ c ). Find their respective errors:

[0109]

[0110]

[0111]

[0112] Among them, W F is the error between the fitting load and the resultant aerodynamic load, W X , W Y To fit the errors of the load pressure center and the aerodynamic load pressure center in the chord direction and span direction of the wing, X c , Y c are the positions of the pressure center of the aerodynamic load in the chord direction and span direction of the airfoil, X′ c , Y′ c are the calculated positions of the fitting load pressure center in the chord direction and span direction of the airfoil respectively.

[0113] According to the requirements, the errors of the resultant force and the pressure center are weighted, and the weights are a, b, c (0≤a, b, c≤1 and a+b+c=1). If the resultant force needs to be more accurate, a can be greater than b+c; if the weights of the three are the same, the values ​​of a, b, and c are all 1 / 3. It is also possible not to take the weight coefficient, and take the three errors as being less than the corresponding threshold at the same time as the judgment condition. If weighted judgment is used, the following formula can be used to judge whether the error meets the requirements:

[0114] aW F +bW X +cW Y ≤γ (15)

[0115] If the initially selected N value makes formula (15) or other judgment conditions invalid, then increase the N value until it is satisfied.

[0116] When formula (15) or other judgment conditions are met, the value of N can be determined. At this time, P2 is the load array after the fitting node load of the finite element mesh airfoil model that meets the accuracy requirements is decomposed in the Cartesian coordinate system.

[0117]

[0118] P is the node load array of the finite element mesh airfoil model, which is a D2×1 column vector.

[0119] The modal truncation method is used to ensure the accuracy of the calculation results without wasting too much calculation time.

[0120] Compared with the classical load method, the method of the present invention has higher calculation accuracy and speed.

[0121] The following is a specific embodiment of the method of the present invention:

[0122] A simple wing (0.5 m long in the x-axis (chord-wise) direction, 0.1 m long in the y-axis direction, and 0.7 m long in the z-axis (span-wise) direction) was selected to verify this method. Figure 2 It is a schematic diagram of the fluid grid of an airfoil of this embodiment, which contains 609 aerodynamic load nodes and 560 grids. Figure 3 for Figure 2 The schematic diagram of the structural finite element mesh of the wing shown in Figure 1 contains 99 finite element nodes and 80 units. Assume that the aerodynamic load distribution is as follows: Figure 2 The lower left vertex of the wing surface shown is the coordinate origin, (x i ,y i ,z i ) is the coordinate value of the jth discrete point of the fluid grid airfoil model:

[0123]

[0124] P i The direction is perpendicular to the plane where the node is located and downward. Figure 4 4 is the aerodynamic load distribution diagram of this embodiment, and the load increases from the lower left to the upper right. The four-point method and the load distribution method based on modal fitting are used for calculation respectively. When N=12, the results are shown in Table 1. Figure 5 The load conversion error for different modal orders is shown.

[0125] Table 1. Comparison of the results of two load distribution calculation methods

[0126]

[0127] The "four-point method" takes 15.238 seconds to calculate the given working condition, and the resultant force still has an error of more than 8%. The error of the pressure center in the chord direction of the wing is -3.28%, and the error in the span direction is -3.02%. However, using the method of the present invention, the MATLAB program takes 6.53 seconds to calculate, and the errors of the resultant force and the pressure center are both within -1%. The method of the present invention saves 57.15% of time compared to the "four-point method" and completes the load distribution more accurately. This can effectively solve the problem that the load distribution takes a lot of time when the number of model nodes is too large.

Claims

1. A method for distributing aerodynamic loads based on modal fitting, characterized in that: The following steps are involved: Step 1: construct two virtual structural models of the same airfoil surface, namely, a fluid mesh airfoil model and a finite element mesh airfoil model, based on the computational fluid dynamics shape mesh of the airfoil structure and the surface mesh of the finite element model; unify the coordinates so that the Cartesian coordinates of the coincident nodes on the two models are the same; Step 2, respectively calculating the rigid body modes and elastic modes of the fluid mesh airfoil model and the finite element mesh airfoil model; combining the first n-order elastic modal vibration modes with the first six-order rigid body modes of each, and obtaining the total n+6-order modal vibration modes of each of the two mesh models; and then performing normalization processing; Step 3, based on the first N-order calculation modes of the fluid mesh airfoil model, the aerodynamic loads of each node of the fluid mesh airfoil model calculated by fluid dynamics are fitted, that is, the participation coefficients of the first N-order modes are calculated by the least square method or other optimization methods; the first N-order modes of the finite element mesh airfoil model are superimposed with the participation coefficients of the first N-order modes of the fluid mesh airfoil model as weight coefficients, the fitting loads on the finite element mesh airfoil model are calculated, the resultant force of the fitting loads and the errors of the pressure center position are compared with the aerodynamic loads, and based on the given error limit, the appropriate N value is calculated by iteration; The process of step 3 includes: Step 3.

1. Calculate the fitting coefficients: The pressure at each node position on the fluid mesh airfoil model is taken as the node pressure on the node; each node pressure is decomposed, expressed as components in Cartesian coordinates, and arranged according to the node number; the decomposed node pressure array of the fluid mesh airfoil model is recorded as P1, which is a 3D1×1 column vector; the modal vector of the fluid mesh airfoil model is used to fit the distribution of aerodynamic loads: the relationship between P1 and Φ1 is as follows: Φ1·Q=P1 (9) Where P1 is generally a known condition, Φ1 is the first N-order modal vector matrix of the fluid grid airfoil model, and the fitting coefficient is obtained through matrix operation: Q=Φ1 -1 ·P1 (10) Step 3.

2. Calculate the fitted loads: The fitting coefficient Q is used as the weighting coefficient, and the modal vectors of the finite element mesh airfoil model are superimposed to obtain the array P2 of the fitting node load of the finite element mesh airfoil model after decomposition in the Cartesian coordinate system: Among them, P jx , P jy , P jz They represent the D2×1 column vectors of the projection of the fitting node load in the x-axis, y-axis, and z-axis directions in the Cartesian coordinate system, and P2 is a 3D2×1 column vector; Step 3.

3. Determine the value of N: The resultant force F of the aerodynamic load is calculated based on the node pressure array and node and unit information of the fluid grid wing model. c and pressure heart (X c ,Y c ), and then calculate the resultant force F of the fitting load according to the fitting node load array and node and unit information of the finite element mesh wing model c ' and pressure heart (X c ',Y c '); Find their respective errors: Among them, W F is the error between the fitting load and the resultant aerodynamic load, W X , W Y To fit the errors of the load pressure center and the aerodynamic load pressure center in the chord direction and span direction of the wing, X c , Y c are the positions of the pressure center of the aerodynamic load in the chord direction and span direction of the airfoil, respectively, c ', Y c ' are the calculated positions of the fitting load pressure center in the chord direction and span direction of the airfoil; According to the requirements, the errors of the resultant force and the pressure center are weighted, and the weights are a, b, c, 0≤a, b, c≤1 and a+b+c=1. If the resultant force needs to be more accurate, a can be greater than b+c; if the weights of the three are the same, the values ​​of a, b, and c are all 1 / 3; it is also possible not to take the weight coefficient, and take the three errors being less than the corresponding threshold at the same time as the judgment condition; if weighted judgment is adopted, the following formula is used to judge whether the error meets the requirements: aW F +bW X + cW Y ≤γ (15) If the initially selected N value makes formula (15) or other judgment conditions not hold, increase the N value until it is satisfied; When (15) or other judgment conditions are met, the N value can be determined. At this time, P2 is the load array after the fitting node load of the finite element mesh airfoil model that meets the accuracy requirements is decomposed in the Cartesian coordinate system; P is the node load array of the finite element mesh airfoil model, which is a D2×1 column vector.

2. The aerodynamic load distribution method based on modal fitting according to claim 1 is characterized in that: In step 1, the process of constructing a fluid mesh airfoil model and a finite element mesh airfoil model of the same airfoil surface includes: First, based on the computational fluid dynamics shape grid of the wing structure, the fluid grid wing model of this wing is constructed using the fluent software, and then the grid is divided on the model and the pressure is added, which is given by the CFD calculation; then, based on the finite element model surface grid of the wing structure, the finite element grid wing model of this wing is constructed using the MSC.Patran software; there is no load on the finite element grid wing model, and load distribution is required.

3. The aerodynamic load distribution method based on modal fitting according to claim 1 is characterized in that: In step 2, the rigid body mode of the computational fluid mesh airfoil model includes: Step 2.

1. The total number of nodes of the fluid grid airfoil model is D1. First, consider the three translational degrees of freedom of each node. After determining the overall Cartesian coordinate system, perform unit translation on the fluid grid airfoil model along the three coordinate axes to obtain the rigid body modal vibration shapes of the first three translations. The modal vibration shape of the i-th node on the fluid grid airfoil model is expressed as: in, They represent the first, second and third order rigid body mode vibration shapes of the i-th node of the fluid mesh airfoil model respectively; Then, the fluid grid wing model is rotated around the x-axis, y-axis, and z-axis by a certain angle, and the coordinate displacement of the node is used to represent the vibration vector of the third-order rotational rigid body mode. Assume that the coordinate of the i-th node of the model is (x i ,y i ,z i ), the rotation angle is θ1, then the subsequent rigid body mode vibration shape of the i-th node of the fluid grid airfoil model is expressed as: in, They respectively represent the fourth, fifth, and sixth order rigid body mode vibration shapes of the i-th node of the fluid mesh airfoil model.

4. The aerodynamic load distribution method based on modal fitting according to claim 1 is characterized in that: In step 2, the process of calculating the rigid body mode of the finite element mesh airfoil model includes: Step 2.

2. Count the total number of nodes of the finite element mesh airfoil model as D2; after determining the overall Cartesian coordinate system, perform unit translation on the finite element mesh airfoil model along the three coordinate axes to obtain the rigid body modal vibration shapes of the first three order translations; the vibration shape of the jth node on the finite element mesh airfoil model can be expressed as: in, They represent the first, second and third order rigid body mode shapes of the jth node of the finite element mesh airfoil model respectively; Then, the finite element mesh wing model is rotated around the x-axis, y-axis, and z-axis by a certain angle, and the coordinate displacement of the node is used to represent the vibration vector of the third-order rotational rigid body mode. Assume that the coordinate of the jth node of the model is (x j ,y j ,z j ), the rotation angle is θ2, then the subsequent rigid body mode vibration shape of the jth node is expressed as: in, They respectively represent the fourth, fifth and sixth order rigid body mode vibration shapes of the jth node of the finite element mesh airfoil model.

5. The aerodynamic load distribution method based on modal fitting according to claim 1 is characterized in that: In the step 2, MSC.Patran / Nastran software is used to calculate the first n elastic modal vibration modes of the airfoil under the fluid mesh airfoil model and the finite element mesh airfoil model respectively, and the first n elastic modal vibration modes obtained are combined with the first six rigid body modal vibration modes of each to obtain the total n+6 modal vibration modes of each under the two mesh models.

6. The aerodynamic load distribution method based on modal fitting according to claim 1 is characterized in that: The normalization process described in step 2 refers to: The n+6th order modal vibration modes of the fluid mesh airfoil model and the finite element mesh airfoil model are normalized according to the maximum amplitude of all their degrees of freedom to obtain the modal vectors; the selection and construction of the basis function are completed, and N=n+6 is recorded, which is the Nth order modal vector corresponding to the fluid mesh airfoil model and the finite element mesh airfoil model respectively; the first N-order modal vector matrix of the fluid mesh airfoil model is recorded as Φ1, and Φ1 is a 3D1×N matrix; the first N-order modal vector matrix of the finite element mesh airfoil model is recorded as Φ2, and Φ2 is a 3D2×N matrix.

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