CN114818126A - Pneumatic load distribution method based on modal fitting - Google Patents

Pneumatic load distribution method based on modal fitting Download PDF

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CN114818126A
CN114818126A CN202210404939.9A CN202210404939A CN114818126A CN 114818126 A CN114818126 A CN 114818126A CN 202210404939 A CN202210404939 A CN 202210404939A CN 114818126 A CN114818126 A CN 114818126A
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王轲
杨翔宇
邱智勇
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a pneumatic load distribution method based on modal fitting, which comprises the following steps: constructing a fluid mesh model and a finite element mesh model of the same airfoil according to the computational fluid dynamics mesh and the finite element model mesh of the airfoil structure; respectively calculating rigid body modes and elastic modes of the two models; combining the former n-order elastic modal shape with the respective former six-order rigid body modal shape to obtain respective total n + 6-order modal shape, and performing normalization processing; fitting the pneumatic load of each node of the fluid grid model based on the previous N-order calculation mode of the fluid grid model; and (3) superposing the front N-order mode of the finite element grid model by using the participation coefficient of the front N-order mode of the fluid grid model as a weight coefficient, calculating the fitting load of the finite element grid model, iteratively calculating a proper N value based on a given error limit, and obtaining the fitting load meeting the precision requirement. The invention has convenient calculation and no artificial interference, and effectively improves the working efficiency and the result precision.

Description

Pneumatic load distribution method based on modal fitting
Technical Field
The invention belongs to the technical field of aeronautical structure dynamics modeling, and relates to a pneumatic load distribution method based on modal fitting.
Background
In the design of the structural strength of an aircraft, aerodynamic loads are very important design inputs, and the structural strength profession needs to apply the loads on a finite element model as inputs for the next design. At present, strength calculation software widely used in the aerospace industry, such as MSC, Patran/Nastran, Abaqus and the like, cannot automatically realize load distribution on uneven surfaces. If the nodes are loaded manually, the actual requirements of engineering cannot be met because the actual finite element model has a large number of nodes and different working conditions.
In order to solve the problem, a multi-point arranging method is commonly used in the domestic aviation field of China. The method takes minimum strain energy and static force equivalent as constraint conditions, and each pneumatic load is distributed to a plurality of finite element nodes. However, the process is very complicated, and especially on a large airfoil surface, when the number of the fluid grids is large, the calculation workload is very large. Moreover, the starting point of the load distribution is the concentrated force of the integrated aerodynamic load, the wing surface structure of the modern large-scale airplane is complex, the aerodynamic partition and the structural partition are often inconsistent, the concentrated load directly integrated on the fluid grid can possibly transfer the load across the region, and the force transfer route is not real; secondly, when the methods distribute the load, some nodes are artificially appointed to distribute the corresponding pneumatic load, and the error is enlarged. Therefore, when the structure and the aerodynamic load distribution are very complicated, the 'multi-point row' method has the problems of low calculation efficiency, difficulty in controlling the accuracy of the fitting function and the like.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a pneumatic load distribution method based on mode fitting. The method takes the known airfoil modal shape as a basis function to fit the aerodynamic load distribution, is convenient and fast to calculate and free from human interference, and improves the working efficiency and the result accuracy; meanwhile, the pneumatic load obtained by CFD calculation is approximately fitted by adopting a modal truncation theory, so that the result precision is ensured.
In order to achieve the purpose, the invention adopts the following technical scheme.
A pneumatic load distribution method based on mode fitting comprises the following steps:
step 1, constructing two virtual structure models of the same airfoil surface, namely a fluid grid airfoil model and a finite element grid airfoil model, according to a computational fluid dynamics shape grid of an airfoil structure and a finite element model surface grid; unifying coordinates to ensure that the Cartesian coordinates of coincident nodes on the two models are the same;
the fluid grid airfoil model and the finite element grid airfoil model for constructing the same airfoil surface comprise the following steps: firstly, according to a computational fluid dynamics shape grid of an airfoil structure, a fluid grid airfoil model of the airfoil is constructed by using fluent software, then grids are divided on the model, and pressure intensity is added, wherein the pressure intensity is given by CFD calculation; then, constructing a finite element grid airfoil model of the airfoil by using MSC.Patran software according to the finite element model surface grid of the airfoil structure; the finite element mesh airfoil model has no load temporarily, and load distribution is needed.
Step 2, respectively calculating rigid body modes and elastic modes of the fluid grid airfoil model and the finite element grid airfoil model; combining the front n-order elastic modal shape with the respective front six-order rigid body mode to obtain the respective total n + 6-order modal shape under the two grid models; then carrying out normalization processing;
the rigid body mode of the fluid grid airfoil model is calculated, and the process comprises the following steps:
step 2.1, the total number of nodes of the fluid grid airfoil model is D 1 Firstly, considering three translational freedom degrees of each node; after an integral Cartesian coordinate system is determined, the fluid grid airfoil model is subjected to unit translation along three coordinate axes respectively to obtain rigid body mode vibration patterns of the first three-order translation; the modal shape of the ith node on the fluid grid airfoil model is represented as:
Figure BDA0003601423350000021
wherein,
Figure BDA0003601423350000022
respectively representing a first, a second and a third-order rigid body mode vibration modes of an ith node of the fluid grid airfoil model;
then the fluid grid airfoil model respectively rotates for a certain angle around an x axis, a y axis and a z axis, and the coordinate displacement of the node is respectively used for representing the three-order rotation rigid body mode shape vector; let the ith node coordinate of the model be (x) i ,y i ,z i ) The angle of rotation being theta 1 Then, the rigid body mode shape subsequent to the ith node of the fluid grid airfoil model is represented as:
Figure BDA0003601423350000023
Figure BDA0003601423350000024
Figure BDA0003601423350000025
wherein,
Figure BDA0003601423350000026
respectively representing the fourth, fifth and sixth order rigid body mode vibration modes of the ith node of the fluid grid airfoil model.
The rigid body mode of the finite element grid airfoil model is calculated, and the process comprises the following steps: counting the total number of the finite element grid airfoil model nodes as D 2 (ii) a After an integral Cartesian coordinate system is determined, the finite element grid airfoil model is subjected to unit translation along three coordinate axes respectively to obtain rigid body mode shapes of the first three-order translation; the modal shape of the jth node on the finite element mesh airfoil model can be expressed as:
Figure BDA0003601423350000027
wherein,
Figure BDA0003601423350000028
respectively representing the first, second and third-order rigid body mode vibration modes of the jth node of the finite element grid airfoil model;
then, respectively rotating the finite element grid airfoil model by certain angles around an x axis, a y axis and a z axis, and respectively representing three-order rotation rigid body mode shape vectors by using coordinate displacement of nodes; let the jth node coordinate of the model be (x) j ,y j ,z j ) The angle of rotation being theta 2 Then, the rigid body mode shape subsequent to the jth node is expressed as:
Figure BDA0003601423350000031
Figure BDA0003601423350000032
Figure BDA0003601423350000033
wherein,
Figure BDA0003601423350000034
respectively representing the fourth, fifth and sixth order rigid body mode vibration modes of the jth node of the finite element grid airfoil model.
Further, in the step 2, msc.patran/Nastran software is used to calculate respective front n-order elastic modal modes of the airfoil under the fluid grid airfoil model and the finite element grid airfoil model, and the obtained front n-order elastic modal modes are combined with respective front six-order rigid body modal modes to obtain respective total n + 6-order modal modes under the two grid models.
The normalization processing refers to: respectively carrying out n +6 order modal vibration modes of the fluid grid airfoil model and the finite element grid airfoil model according to the maximum amplitude values in all the degrees of freedom of the fluid grid airfoil model and the finite element grid airfoil modelNormalization processing is carried out to obtain a modal vector; selecting and constructing basis functions, namely N (N +6) -order modal vectors corresponding to the fluid grid airfoil model and the finite element grid airfoil model respectively; recording the front N-order modal vector matrix of the fluid grid airfoil model as phi 1 ，Φ 1 Is one 3D 1 A xN matrix; the front N-order modal vector matrix of the finite element grid airfoil model is phi 2 ，Φ 2 Is one 3D 2 X N matrix.
Step 3, fitting aerodynamic loads of all nodes of the fluid grid airfoil model calculated by fluid dynamics on the basis of the first N-order calculation mode of the fluid grid airfoil model, namely calculating participation coefficients of the first N-order mode by a least square method or other optimization methods; and (3) superposing the former N-order mode by using the participation coefficient of the former N-order mode as a weight coefficient, calculating the fitting load on the finite element grid airfoil model, comparing the resultant force of the fitting load and the aerodynamic load, the resultant moment amplitude and the error of the pressure center position, and calculating a proper N value through iteration on the basis of a given error limit. The process specifically comprises the following steps:
step 3.1, calculating a fitting coefficient:
taking the pressure at each node position on the fluid grid airfoil model as the node pressure on the node; decomposing the pressure intensity of each node, expressing the pressure intensity by components under Cartesian coordinates, and arranging the pressure intensity according to the node number; the node pressure intensity array of the decomposed fluid grid airfoil model is marked as P 1 Is 3D 1 A column vector of x 1; fitting the distribution of aerodynamic loads with the modal vectors of the fluid grid airfoil model: p 1 And phi 1 The relationship of (a) to (b) is as follows:
Φ 1 ·Q＝P 1 (9)
wherein P is 1 Generally of known condition,. phi., 1 obtaining a fitting coefficient for a front N-order modal vector matrix of the fluid grid airfoil model after matrix operation:
Q＝Φ 1 -1 ·P 1 (10)
and 3.2, calculating the fitting load:
using the fitting coefficient Q as a weighting coefficient, and superposing a model of the finite element grid airfoil surface modelState vector, obtaining array P after decomposing fitting node load of finite element grid airfoil model in Cartesian coordinate system 2 ：
Figure BDA0003601423350000041
Wherein, P jx 、P jy 、P jz Respectively representing the projection D of the fitting node load to the directions of the x axis, the y axis and the z axis under a Cartesian coordinate system 2 X 1 column vector, P 2 Is a 3D 2 A column vector of x 1;
step 3.3, determining the value of N:
calculating the resultant force F of the pneumatic load according to the node pressure intensity array, the node and unit information of the fluid grid airfoil model c And heart pressure (X) c ,Y c ) Calculating the resultant force F 'of the fitting load according to the fitting node load array, the node and the unit information of the finite element grid airfoil model' c And pith (X' c ,Y′ c ) (ii) a Calculating respective errors:
Figure BDA0003601423350000042
Figure BDA0003601423350000043
Figure BDA0003601423350000044
wherein, W F To fit the error of the resultant force of the load and the pneumatic load, W X 、W Y For fitting the errors, X, of the load pressure centers and of the aerodynamic load pressure centers in the chord-wise and span-wise positions, respectively, of the wing c 、Y c Core of aerodynamic load in chord-wise and span-wise position of airfoil, X' c 、Y′ c Respectively calculating the chord direction and the span direction positions of the fitted load pressure center on the airfoil surface;
according to the requirement, the errors of resultant force and pressure center are weighted, the weights are respectively a, b and c (a is more than or equal to 0, b, c is less than or equal to 1, and a + b + c is 1), if the resultant force is more accurate, a is more than b + c; if the weights of the three are the same, the values of a, b and c are 1/3; or taking three errors smaller than the corresponding threshold value at the same time as a judgment condition without taking a weight coefficient; if the weighted judgment is adopted, whether the error meets the requirement is judged by the following formula:
aW F +bW X +cW Y ≤γ (15)
if the initially selected N value causes the equation (15) or other judgment conditions to be not satisfied, increasing the N value until the N value is satisfied;
when the formula (15) or other judgment conditions are satisfied, the value of N is determined, and P is determined at this time 2 The load array is obtained after the load of the fitting node of the finite element grid airfoil model meeting the precision requirement is decomposed in a Cartesian coordinate system;
Figure BDA0003601423350000045
p is a node load array of the finite element grid airfoil model, and is D 2 A column vector of x 1.
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the invention takes the modal shape of the structure as a basis function, has local linear independence, can better process the load distribution problem of special points (such as nodes on the boundary) and improves the precision in the load distribution process.
2. The load distribution calculation method for fitting the pneumatic load distribution by adopting the structural modal shape as the basis function has the characteristics of natural and convenient performance, has a simple load distribution principle, is not interfered by man-made factors, and can achieve a more accurate load distribution effect without a large amount of calculation; meanwhile, the pneumatic load obtained by CFD calculation is approximately fitted by adopting a modal truncation theory, so that the calculation amount is reduced, and the result precision is fully ensured.
3. The method not only highly ensures the authenticity of the load, but also is more convenient and efficient, so that when a large number of nodes and grids are faced in the wing design, the workload can be obviously reduced, the cost is saved, and the rapid application of the surface distribution load on the structure calculation finite element model can be finished with high quality.
4. The invention converts the load from the dense grid to the sparse grid, can be further developed on the basis of the invention, verifies the feasibility of converting the sparse grid to the dense grid load, and perfects the load conversion technology of the dense grid.
Drawings
FIG. 1 is a flow diagram of a method of an embodiment of the present invention.
FIG. 2 is a schematic representation of a fluid grid for an airfoil according to an embodiment of the present invention, wherein 609 aerodynamic load nodes are included, 560 grids.
FIG. 3 is a schematic view of a structural finite element mesh of an airfoil according to an embodiment of the present invention.
FIG. 4 is a pneumatic load profile for an embodiment of the present invention.
Fig. 5 is a load transfer error display diagram for different modal orders according to an embodiment of the present invention.
Detailed Description
The invention relates to load distribution among different grids of an airfoil in a structural dynamics modeling technology, which generally distributes load on a fluid grid airfoil model to a finite element grid airfoil model in an equivalent way. According to the method, a modal vector obtained after normalization of the modal shape of the airfoil under the fluid grid is used as a basis function to approximately fit the aerodynamic load obtained by CFD calculation, and the modal coordinate of the aerodynamic load, namely the weight coefficient of the fitting function, is obtained. And because the continuum structure has infinite multi-order modes, the modal order to be used is determined by adopting a modal truncation method, so that the calculation amount is reduced and the calculation precision is ensured. And finally, obtaining the fitting load on the finite element mesh by using the weight coefficient and according to the modal shape of the airfoil model constructed by the finite element mesh.
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1, the method starts from a fluid grid airfoil model and a finite element grid airfoil model to be distributed, has two branches corresponding to steps 1 to 3, and finally combines the two branches to obtain the load of each node on the finite element grid airfoil model, and comprises the following steps:
step 1, constructing two virtual structure models of the same airfoil surface, namely a fluid grid airfoil model and a finite element grid airfoil model, according to a computational fluid dynamics shape grid of an airfoil structure and a finite element model surface grid; and (4) unifying coordinates to enable the Cartesian coordinates of the coincident nodes on the two models to be the same.
For the same airfoil, a fluid grid airfoil model of the airfoil is constructed according to a computational fluid dynamics shape grid of an airfoil structure, namely the airfoil model is established by using fluent software, and then the grid is divided on the model and pressure is added. And then, constructing a finite element grid airfoil model of the airfoil according to the finite element model surface grid of the airfoil structure, namely establishing an airfoil surface model by using MSC. Although most nodes of the two models are not overlapped, partial nodes (such as vertexes) are overlapped and have unified coordinates, so that the Cartesian coordinates of the partial overlapped nodes of the two models are the same. Typically, the pressure on the fluid mesh airfoil model is given by CFD calculations, and the finite element mesh airfoil model is temporarily unloaded and requires load sharing.
Step 2, respectively calculating the modes of the fluid grid airfoil model and the finite element grid airfoil model, wherein the modes comprise a rigid body mode and an elastic mode: because the rigid body modes of the two models calculated based on commercial software are different, the rigid body mode vector expression mode needs to be given uniformly. Combining the front n-order elastic modal shape with the respective front six-order rigid body mode to obtain the respective total n + 6-order modal shape under the two grid models; then normalization processing is carried out.
The n value is obtained by modal truncation. Because the mode has infinite order in theory, but the effective mass of the low-order mode occupies a large part of the total mass of the structure, when the mode is adopted for calculation, only the front n-order elastic mode shape and the front six-order rigid body mode are intercepted, and the front n-order elastic mode shapes of the two grids are combined with the respective front six-order rigid body modes to obtain the respective total n + 6-order mode shapes under the two grid models; then normalization processing is carried out.
Specifically, the step 2 process comprises:
step 2.1, calculating the front six-order rigid body mode of the fluid grid airfoil surface model:
total number of nodes of fluid grid airfoil model is D 1 First, consider three translational degrees of freedom for each node. After the integral Cartesian coordinate system is determined, the fluid grid airfoil model is subjected to unit translation along three coordinate axes respectively, and the rigid body mode vibration mode of the first three-order translation can be obtained. The modal shape of the ith node on the fluid grid airfoil model is represented as:
Figure BDA0003601423350000061
wherein,
Figure BDA0003601423350000062
and respectively representing the first, second and third-order rigid body mode vibration modes of the ith node of the fluid grid airfoil model.
And rotating the fluid grid airfoil model by certain angles around an x axis, a y axis and a z axis respectively, and representing three-order rotation rigid body mode shape vectors by using coordinate displacement of nodes respectively. Let the ith node coordinate of the model be (x) i ,y i ,z i ) The angle of rotation being theta 1 Then, the rigid body mode shape subsequent to the ith node of the fluid grid airfoil model is represented as:
Figure BDA0003601423350000063
Figure BDA0003601423350000071
Figure BDA0003601423350000072
wherein,
Figure BDA0003601423350000073
respectively representing the fourth, fifth and sixth order rigid body mode vibration modes of the ith node of the fluid grid airfoil model.
Thereby, the first six-order rigid body modes of the fluid grid airfoil model are obtained.
Step 2.2, calculating the first six-order rigid body mode of the finite element grid airfoil model:
counting the total number of the finite element grid airfoil model nodes as D 2 . After the integral Cartesian coordinate system is determined, the finite element grid airfoil model is subjected to unit translation along three coordinate axes respectively, and the rigid body mode vibration mode of the first three-order translation can be obtained. The modal shape of the jth node on the finite element mesh airfoil model can be expressed as:
Figure BDA0003601423350000074
wherein,
Figure BDA0003601423350000075
respectively representing the first, second and third-order rigid body mode shapes of the jth node of the finite element grid airfoil model.
And rotating the finite element grid airfoil model by certain angles around an x axis, a y axis and a z axis respectively, and representing the three-order rotation rigid body mode shape vector by using the coordinate displacement of the node respectively. Let the jth node coordinate of the model be (x) j ,y j ,z j ) The angle of rotation being theta 2 Then, the rigid body mode shape subsequent to the jth node is expressed as:
Figure BDA0003601423350000076
Figure BDA0003601423350000077
Figure BDA0003601423350000078
wherein,
Figure BDA0003601423350000079
respectively representing the fourth, fifth and sixth order rigid body mode vibration modes of the jth node of the finite element grid airfoil model.
Therefore, the first six-order rigid body mode shape of the finite element grid airfoil model is obtained.
Step 2.3, calculating the elastic mode: respectively calculating the respective front n-order elastic modal shape of the airfoil under the fluid grid airfoil model and the finite element grid airfoil model by using software such as MSC, Patran/Nastran and the like, and combining the obtained front n-order elastic modal shape with the respective front six-order rigid body modal shape to obtain the respective total n + 6-order modal shape under the two grid models.
Step 2.4, normalization treatment: the respective n +6 order modal shapes of the fluid grid airfoil model and the finite element grid airfoil model are obtained through the steps 2.1, 2.2 and 2.3, but the modal shapes can only be determined to the extent that the proportion of each component is unchanged, and cannot be used for subsequent calculation, so that the n +6 order modal shapes of the fluid grid airfoil model and the finite element grid airfoil model need to be normalized according to the maximum amplitude values in all the degrees of freedom respectively, and modal vectors are obtained. And (4) completing selection and construction of the basis functions, namely obtaining N (N +6) -order modal vectors corresponding to the fluid grid airfoil model and the finite element grid airfoil model respectively.
Recording the front N-order modal vector matrix of the fluid grid airfoil model as phi 1 ，Φ 1 Is one 3D 1 X N matrix. The front N-order modal vector matrix of the finite element grid airfoil model is phi 2 ，Φ 2 Is one 3D 2 X N matrix.
Step 3, fitting aerodynamic loads of all nodes of the fluid grid airfoil model calculated by fluid dynamics on the basis of the first N-order calculation mode of the fluid grid airfoil model, namely calculating participation coefficients of the first N-order mode by a least square method or other optimization methods; and calculating the fitting load on the finite element grid airfoil model by superposing the front N-order mode of the finite element grid airfoil model by using the participation coefficient of the front N-order mode of the fluid grid airfoil model as a weight coefficient, comparing the resultant force of the fitting load and the aerodynamic load and the error of the pressure center position, and calculating a proper N value through iteration on the basis of a given error limit.
The specific process of the step 3 comprises the following steps:
step 3.1. calculating fitting coefficient
The pressure at each node location on the fluid grid airfoil model is taken as the node pressure at that node. For convenience of operation, the pressure intensity of each node is decomposed, is expressed by components under Cartesian coordinates, and is well arranged according to the node number. The node pressure intensity array of the decomposed fluid grid airfoil model is marked as P 1 Is 3D 1 A column vector of x 1. Fitting the distribution of aerodynamic loads with the modal vectors of the fluid grid airfoil model:
P 1 and phi 1 The relationship of (a) to (b) is as follows:
Φ 1 ·Q＝P 1 (9)
wherein P is 1 Generally of known condition,. phi., 1 and (3) solving a fitting coefficient by the front N-order modal vector matrix of the fluid grid airfoil model obtained in the step (2) through matrix operation:
Q＝Φ 1 -1 ·P 1 (10)
step 3.2. calculating the fitting load
The fitting coefficient Q is an N x 1 column vector, which in this case represents the modal coordinates of the aerodynamic loads on the fluid grid airfoil model. Theoretically, the larger the value of the modal order N is, the larger the calculation amount is, but the more the fitting load calculated according to the fitting coefficient Q converges to the real load.
Using the fitting coefficient Q as a weighting coefficient, and overlapping finite element grid airfoil surfacesObtaining model modal vector, and obtaining array P after decomposing fitting node load of finite element grid airfoil model in Cartesian coordinate system 2 ：
Figure BDA0003601423350000081
Wherein, P jx 、P jy 、P jz Respectively representing the projection D of the fitting node load to the directions of the x axis, the y axis and the z axis under a Cartesian coordinate system 2 X 1 column vector, P 2 Is a 3D 2 A column vector of x 1.
The mode fitting mode is used for load distribution, the principle is simple, the operation is not complicated, and especially when a large number of nodes and grid numbers are faced, the workload can be obviously reduced.
Theoretically, the structure has infinite multi-order modes, but in actual experimental measurement or finite element analysis, only limited-order modes, and possibly low-order modes, can be obtained. Therefore, the modes obtained in the measurement and analysis are only a part of the overall modes of the structure, which is the mode truncation. In the invention, if the modal order is too small, the fitting precision is insufficient, and the error is large; if the modal order is too large, the calculation amount is increased, the improvement on the result precision is not obvious, and the calculation efficiency is reduced. Therefore, the former N-order mode is firstly cut off by the modes to be calculated, and if the precision requirement is not met, the N value is increased until the precision requirement is met.
Step 3.3. determining the value of N
The accuracy of the load distribution is evaluated with the total force and the pressure center. And judging whether the error meets the requirement or not by setting an error threshold gamma, and further judging whether the value of N is reasonable or not. Calculating the resultant force F of the pneumatic load according to the node pressure intensity array, the node and unit information of the fluid grid airfoil model c And heart pressure (X) c ,Y c ) Calculating the resultant force F 'of the fitting load according to the fitting node load array, the node and the unit information of the finite element grid airfoil model' c And pith (X' c ,Y′ c )。Calculating respective errors:
Figure BDA0003601423350000091
Figure BDA0003601423350000092
Figure BDA0003601423350000093
wherein, W F To fit the error of the resultant force of the load and the pneumatic load, W X 、W Y For fitting the errors, X, of the load and aerodynamic load centroids in the chordwise and spanwise positions of the wing, respectively c 、Y c Core of aerodynamic load in chord-wise and span-wise position of airfoil, X' c 、Y′ c Respectively the calculated positions of the fitting load pressure center in the chord direction and the span direction of the airfoil.
According to the requirement, the errors of resultant force and pressure center are weighted, the weights are respectively a, b and c (a is more than or equal to 0, b, c is less than or equal to 1, and a + b + c is 1), if the resultant force is more accurate, a is more than b + c; if the weights of the three are the same, the values of a, b and c are 1/3. Or, without taking the weighting coefficient, taking the three errors smaller than the corresponding threshold values at the same time as the judgment condition. If the weighted judgment is adopted, whether the error meets the requirement can be judged by the following formula:
aW F +bW X +cW Y ≤γ (15)
if the initially selected value of N makes equation (15) or other judgment conditions false, the value of N is increased until the value of N is satisfied.
When the formula (15) or other judgment conditions are satisfied, the value of N is determined, and P is determined at the same time 2 The load array is obtained after the fitted node loads of the finite element grid airfoil model meeting the precision requirement are decomposed in a Cartesian coordinate system.
Figure BDA0003601423350000094
P is a node load array of the finite element grid airfoil model, and is D 2 A column vector of x 1.
And the mode truncation is adopted, so that the accuracy of a calculation result is ensured, and excessive calculation time cannot be wasted.
Compared with the classical load method, the method has higher calculation precision and speed.
The following is a specific embodiment of the method of the invention:
a simple airfoil (with a length of 0.5m in the x-axis (chordwise) direction, a length of 0.1m in the y-axis direction, and a length of 0.7m in the z-axis (spanwise) direction) is selected to verify the method. FIG. 2 is a schematic representation of a fluid grid for an airfoil of this embodiment, including 609 aerodynamic load nodes and 560 grids. FIG. 3 is a schematic view of a structural finite element mesh of the airfoil of FIG. 2. Contains 99 finite element nodes and 80 units. Assuming the aerodynamic load distribution as follows, with the apex at the lower left of the airfoil shown in FIG. 2 as the origin of coordinates, (x) i ,y i ,z i ) Coordinate values for the jth discrete point of the fluid grid airfoil model:
Figure BDA0003601423350000101
P i the direction is vertical to the plane of the node, and the pneumatic load distribution diagram of the embodiment is shown in FIG. 4, and the load is increased from the lower left to the upper right. The calculation was performed by the four-point method and the mode-fitting-based load distribution method, and the results are shown in table 1 when N is 12. Fig. 5 shows the load conversion error at different modal orders.
TABLE 1 comparison of results of two load distribution calculation methods
Figure BDA0003601423350000102
For the given working condition, the four-point method still has the error of more than 8 percent when the MATLAB program is used for operation for 15.238s, the pressure center is-3.28 percent in the wing chord direction, and the error in the unfolding direction is-3.02 percent. When the method is used, the MATLAB program is operated for 6.53s, and the errors of the resultant force and the pressure center are all within-1%. Compared with a four-point method, the method saves time by 57.15 percent, and more accurately completes load distribution. Therefore, the problem that load distribution needs to be time-consuming and huge due to the fact that the number of model nodes is too large can be effectively solved.

Claims (7)

1. A pneumatic load distribution method based on mode fitting is characterized by comprising the following steps:
step 1, constructing two virtual structure models of the same airfoil surface, namely a fluid grid airfoil model and a finite element grid airfoil model, according to a computational fluid dynamics shape grid of an airfoil structure and a finite element model surface grid; unifying coordinates to ensure that the Cartesian coordinates of coincident nodes on the two models are the same;
step 2, respectively calculating rigid body modes and elastic modes of the fluid grid airfoil model and the finite element grid airfoil model; combining the front n-order elastic modal shape with the respective front six-order rigid body mode to obtain the respective total n + 6-order modal shape under the two grid models; then carrying out normalization processing;
step 3, fitting aerodynamic loads of all nodes of the fluid grid airfoil model calculated by fluid dynamics on the basis of the first N-order calculation mode of the fluid grid airfoil model, namely calculating participation coefficients of the first N-order mode by a least square method or other optimization methods; and superposing the front N-order mode of the finite element grid airfoil model by using the participation coefficient of the front N-order mode of the fluid grid airfoil model as a weight coefficient, calculating the fitting load on the finite element grid airfoil model, comparing the resultant force of the fitting load and the aerodynamic load and the error of the pressure center position, and calculating a proper N value through iteration on the basis of a given error limit.
2. The method of claim 1, wherein in step 1, the fluid grid airfoil model and the finite element grid airfoil model of the same airfoil surface are constructed by a process comprising:
firstly, according to a computational fluid dynamics shape grid of an airfoil structure, a fluid grid airfoil model of the airfoil is constructed by using fluent software, then grids are divided on the model, and pressure intensity is added, wherein the pressure intensity is given by CFD calculation; then, constructing a finite element grid airfoil model of the airfoil by using MSC.Patran software according to the finite element model surface grid of the airfoil structure; the finite element mesh airfoil model has no load temporarily, and load distribution is needed.
3. The method of claim 1, wherein the step 2 of calculating the rigid body mode of the fluid grid airfoil model comprises the steps of:
step 2.1, the total number of nodes of the fluid grid airfoil model is D 1 Firstly, considering three translational freedom degrees of each node; after an integral Cartesian coordinate system is determined, the fluid grid airfoil model is subjected to unit translation along three coordinate axes respectively to obtain rigid body mode vibration patterns of the first three-order translation; the modal shape of the ith node on the fluid grid airfoil model is represented as:
Figure FDA0003601423340000011
wherein,
Figure FDA0003601423340000012
respectively representing a first, a second and a third-order rigid body mode vibration modes of an ith node of the fluid grid airfoil model;
then the fluid grid airfoil model respectively rotates for a certain angle around an x axis, a y axis and a z axis, and the coordinate displacement of the node is respectively used for representing the three-order rotation rigid body mode shape vector; let the ith node coordinate of the model be (x) i ,y i ,z i ) The angle of rotation being theta 1 Then, the rigid body mode shape subsequent to the ith node of the fluid grid airfoil model is represented as:
Figure FDA0003601423340000013
Figure FDA0003601423340000021
Figure FDA0003601423340000022
wherein,
Figure FDA0003601423340000023
respectively representing the fourth, fifth and sixth order rigid body mode vibration modes of the ith node of the fluid grid airfoil model.
4. A method according to claim 1, wherein in step 2, the rigid body mode of the finite element mesh airfoil model is calculated by the process comprising:
step 2.2, counting the total number of the finite element grid airfoil model nodes as D 2 (ii) a After an integral Cartesian coordinate system is determined, the finite element grid airfoil model is subjected to unit translation along three coordinate axes respectively to obtain rigid body mode shapes of the first three-order translation; the mode shape of the jth node on the finite element mesh airfoil model can be expressed as:
Figure FDA0003601423340000024
wherein,
Figure FDA0003601423340000025
respectively representing the first, second and third-order rigid body mode vibration modes of the jth node of the finite element mesh airfoil model;
then the finite element grid airfoil model is respectively rotated for a certain angle around the x axis, the y axis and the z axisRespectively representing three-order rotation rigid body mode shape vectors by using coordinate displacement of the nodes; let the jth node coordinate of the model be (x) j ,y j ,z j ) The angle of rotation being theta 2 Then, the rigid body mode shape subsequent to the jth node is expressed as:
Figure FDA0003601423340000026
Figure FDA0003601423340000027
Figure FDA0003601423340000028
wherein,
Figure FDA0003601423340000029
respectively representing the fourth, fifth and sixth order rigid body mode vibration modes of the jth node of the finite element grid airfoil model.
5. A method for aerodynamic load distribution based on mode fitting according to claim 1, wherein in step 2, msc.
6. The method according to claim 1, wherein the normalization in step 2 is performed by:
respectively enabling the n +6 order modal modes of the fluid grid airfoil model and the finite element grid airfoil model to be in all degrees of freedomNormalizing the maximum amplitude to obtain a modal vector; selecting and constructing basis functions, namely N (N +6) -order modal vectors corresponding to the fluid grid airfoil model and the finite element grid airfoil model respectively; recording the front N-order modal vector matrix of the fluid grid airfoil model as phi 1 ，Φ 1 Is one 3D 1 A xN matrix; the front N-order modal vector matrix of the finite element grid airfoil model is phi 2 ，Φ 2 Is one 3D 2 Xn matrix.
7. The modal-fitting-based pneumatic load distribution method according to claim 1, wherein the process of step 3 comprises:
step 3.1, calculating a fitting coefficient:
taking the pressure at each node position on the fluid grid airfoil model as the node pressure on the node; decomposing the pressure intensity of each node, expressing the pressure intensity by components under Cartesian coordinates, and arranging the pressure intensity according to the node number; the node pressure intensity array of the decomposed fluid grid airfoil model is marked as P 1 Is 3D 1 A column vector of x 1; fitting the distribution of aerodynamic loads with the modal vectors of the fluid grid airfoil model: p 1 And phi 1 The relationship of (a) to (b) is as follows:
Φ 1 ·Q＝P 1 (9)
wherein P is 1 Generally of known condition,. phi., 1 obtaining a fitting coefficient for a front N-order modal vector matrix of the fluid grid airfoil model after matrix operation:
Q＝Φ 1 -1 ·P 1 (10)
and 3.2, calculating the fitting load:
taking the fitting coefficient Q as a weighting coefficient, superposing the modal vector of the finite element grid airfoil model, and obtaining an array P after the fitted node load of the finite element grid airfoil model is decomposed in a Cartesian coordinate system 2 ：
Figure FDA0003601423340000031
Wherein, P jx 、P jy 、P jz Respectively representing the projection D of the fitting node load to the directions of the x axis, the y axis and the z axis under a Cartesian coordinate system 2 X 1 column vector, P 2 Is a 3D 2 A column vector of x 1;
step 3.3, determining the value of N:
calculating the resultant force F of the pneumatic load according to the node pressure intensity array, the node and unit information of the fluid grid airfoil model c And heart pressure (X) c ,Y c ) Then, the resultant force F of the fitting load is calculated according to the fitting node load array, the node and the unit information of the finite element grid airfoil model c ' and Xin (X) c ',Y c ') to a host; calculating respective errors:
Figure FDA0003601423340000032
Figure FDA0003601423340000041
Figure FDA0003601423340000042
wherein, W F To fit the error of the resultant force of the load and the pneumatic load, W X 、W Y For fitting the errors, X, of the load and aerodynamic load centroids in the chordwise and spanwise positions of the wing, respectively c 、Y c The location of the pressure centers of the aerodynamic loads in the chord and span direction, X, of the airfoil c '、Y c ' the calculated positions of the fitted load pressure center in the chord direction and the span direction of the airfoil are respectively obtained;
according to the requirement, the errors of resultant force and pressure center are weighted, the weights are respectively a, b and c (a is more than or equal to 0, b, c is less than or equal to 1, and a + b + c is 1), if the resultant force is more accurate, a is more than b + c; if the weights of the three are the same, the values of a, b and c are 1/3; or taking three errors smaller than the corresponding threshold value at the same time as a judgment condition without taking a weight coefficient; if the weighted judgment is adopted, whether the error meets the requirement is judged by the following formula:
aW F +bW X +cW Y ≤γ (15)
if the initially selected N value causes the equation (15) or other judgment conditions to be not satisfied, increasing the N value until the N value is satisfied;
when the formula (15) or other judgment conditions are satisfied, the value of N is determined, and P is determined at this time 2 The load array is obtained after the load of the fitting node of the finite element grid airfoil model meeting the precision requirement is decomposed in a Cartesian coordinate system;
Figure FDA0003601423340000043
p is a node load array of the finite element grid airfoil model, and is D 2 A column vector of x 1.
CN202210404939.9A 2022-04-18 2022-04-18 Pneumatic load distribution method based on modal fitting Pending CN114818126A (en)

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