CN114970247A - Automatic modeling method of high-fidelity finite element model for leaf disc structure - Google Patents

Automatic modeling method of high-fidelity finite element model for leaf disc structure Download PDF

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CN114970247A
CN114970247A CN202210496292.7A CN202210496292A CN114970247A CN 114970247 A CN114970247 A CN 114970247A CN 202210496292 A CN202210496292 A CN 202210496292A CN 114970247 A CN114970247 A CN 114970247A
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姚建尧
梁道森
曹芝腑
贾子初
张睿
吴昱霖
张旭
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Chongqing University
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Abstract

The invention relates to the field of modeling of an aero-engine blade disc, and particularly discloses an automatic modeling method of a high-fidelity finite element model facing a blade disc structure, which comprises the steps of obtaining point cloud data of a whole blade disc measured by an optical scanner; extracting point cloud data of the blades, and distinguishing a point cloud data set of each blade by using a blade identification algorithm; step 3, performing feature classification on the point cloud data of each blade by adopting a multi-feature clustering analysis algorithm to respectively obtain subdivision data sets of the top of each blade, the pressure surface and the suction surface; and 4, adopting a grid deformation algorithm to move corresponding nodes in the standard finite element model to fit the classified subdivided data set, and simultaneously using a radial basis kernel function to keep the shape and mapping of the unit to obtain a geometric detuning finite element model matched with the measured blisk. The method can quickly convert the subdivided scanning data into a high-fidelity finite element model, and simultaneously ensures higher robustness and precision.

Description

High-fidelity finite element model automatic modeling method for leaf disc structure
Technical Field
The invention relates to the field of modeling of aero-engine blade discs, in particular to an automatic modeling method of a high-fidelity finite element model facing to a blade disc structure.
Background
Due to manufacturing tolerances, material dispersion, and wear during use, the physical and geometric parameters of the individual blades in a blisk may not be perfectly identical, but may differ slightly, such slight differences in the blisk structure being referred to as "detuning". Detuning can result in the concentration of vibrational energy in a few sectors, a so-called "vibration localization" phenomenon. The geometric detuning actually present in the blisk changes both the stiffness and the mass distribution of the actual model, which in some cases has a significant influence on the vibration behavior. Therefore, the standard finite element model directly established according to the physical and geometric parameters is not beneficial to researching the dynamic characteristics of the leaf disc, and a high-fidelity model of the leaf disc structure needs to be established.
In the prior art, the non-contact optical measurement can measure the geometric coordinates of the blisk with high precision, and a geometric detuned blisk subdivision model (TSD) is reconstructed by using the measurement Data. These subdivision models may be reverse engineered into Computer Aided Design (CAD) models and input into mesh generation software to divide Finite element meshes (Finite elements) for Finite element analysis.
However, the process of generating a CAD model from machine scan data and subdividing a mesh cannot guarantee the accuracy of the mesh model, and the mesh divided by human each time is difficult to maintain consistent parameters, and lacks robustness. Moreover, the operation is very tedious and time-consuming, a long time is required for the user to operate the single blade model from TSD → CAD → FEM, and the operation is difficult to realize if finite element modeling is performed on the detuned blade scanning data in batch. Therefore, the subdivided scanning data are quickly and accurately converted into a high-fidelity finite element model, and meanwhile, higher robustness and accuracy are guaranteed, and the method is of great importance for geometric detuning analysis of the blade.
Disclosure of Invention
The invention aims to provide a set of automatic modeling method for a finite element model of a detuned leaf disc, which can automatically generate a high-fidelity finite element model through point cloud data of the leaf disc, so as to solve the technical problems that in the prior art, the precision of a grid model cannot be ensured in the process of generating a CAD model from machine scanning data and then dividing the grid, the operation is very complicated, the time is consumed, and the robustness is lacked.
The invention discloses an automatic modeling method of a high-fidelity finite element model facing a leaf disk structure, which comprises the following steps of
Step 1, acquiring blisk point cloud data measured by an optical scanner;
step 2, extracting point cloud data of the blades in the point cloud data of the blisk, and distinguishing a point cloud data set of each blade by using a blade identification algorithm;
step 3, performing feature classification on the point cloud data of each blade by adopting a multi-feature clustering analysis algorithm to respectively obtain subdivision data sets of the top of each blade, the pressure surface and the suction surface;
and 4, adopting a grid deformation algorithm to move corresponding nodes in the standard finite element model to fit the classified subdivided data set, and simultaneously using a radial basis kernel function to keep the shape and mapping of the unit to obtain a geometric detuning finite element model matched with the measured blisk.
Further, in step 2, a blade disk shape function f is utilized disc (x) Performing Boolean operation on the point cloud data of the blisk, and dividing the point cloud data of the blisk into a blisk P D And the blade P B Two part data sets.
Further, for the shape function f of the blade disk disc (x) Setting the redundancy E 0
Further, the process of distinguishing each blade by using the blade identification algorithm in step 2 includes, at P B In randomly selecting a point P Bij Finding out the connection point, and then finding out the connection point by taking the found connection point as a starting point; this operation is iterated until there are no more connection points, all connection points found in the above process and the point P Bij I.e. a point cloud data set P of individual blades Bi
Then from P B Removing the point cloud dataset P of the blade Bi And repeating the operation in the rest point cloud data until all the blades are distinguished.
Further, step 2 includes sorting the blades.
Further, the sorting process comprises the steps of collecting the point cloud data sets P according to each blade Bi And calculating the included angle between the gravity center vector of each blade and the central shaft of the blade disc, and sequencing the blades according to the size of the included angle.
Further, in step 3, the process of classifying the features of each blade point cloud data includes,
clustering for the first time: using a blade point cloud dataset P Bi Point coordinate P in Bi-XYZ Performing clustering analysis on the P as features Bi Divided into blade upper segment point cloud data set P Bi-UP And a blade upper point cloud data set P Bi-Bottom
And (5) clustering for the second time: using a blade point cloud dataset P Bi Normal vector P in (1) Bi-UVW Is a feature pair P Bi-UP Performing cluster analysis to extract a leaf top surface point cloud data set P Bi-TS
And (3) clustering for the third time: using a blade point cloud dataset P Bi Normal vector P in (1) Bi-UVW Is characterized by removing P Bi-TS Blade point cloud data set P Bi Performing cluster analysis on the rest part to extract a point cloud data set P of the pressure surface of the blade Bi-PS Point cloud data set P of suction surface of blade Bi-SS
Further, in step 4, the moving process of the edge nodes in the standard finite element model includes:
point cloud dataset P at surface Bi-TS 、P Bi-SS And P Bi-PS Finding out edge points, extracting the edge points and fitting a smooth edge curve;
calculating the position parameter of each node on the edge curve of the node according to the edge nodes in the standard finite element model, wherein the distance between each section of the node is used as the arc length;
performing equal reference points in an edge curve according to the position parameters of the edge nodes, and performing difference between the obtained equal reference points and the corresponding edge nodes to obtain displacement vectors of the edge nodes in the standard finite element model;
assigning the displacement vectors to neighboring nodes of the edge node using radial basis functions;
and moving the corresponding nodes in the standard finite element model according to the displacement vectors and the allocated displacement vectors.
Further, the edge curves were fitted by the NURBS method.
Further, in step 4, the moving process of the surface and internal nodes in the standard finite element model includes:
obtaining a normal vector of a surface node in a standard finite element model, projecting the node along the direction of the normal vector, finding a subdivision surface triangle intersected with the normal vector in a surface point cloud data set, and calculating the distance from the node to the subdivision surface triangle;
moving each corresponding surface node in the normal vector direction according to the distance;
assigning the distances to internal nodes of the standard finite element model using radial basis functions;
each respective internal node is moved in the normal vector direction according to the distance.
According to the invention, a standard leaf disk finite element grid model is corrected by using the integral leaf disk point cloud data obtained by measurement of an optical scanner, so that a high-fidelity finite element grid is directly generated, a CAD model does not need to be generated for each measured scanning surface data, and the generated grid model has consistent parameters to ensure the model precision. The point cloud classification algorithm improves the precision and stability of the deformation algorithm, and the grid deformation algorithm directly converts the standard finite element model into the finite element model of the actual geometric shape. The method has the advantages of converting detuned blade scanning data into a high-fidelity finite element model quickly and accurately, having higher robustness and precision, realizing batch conversion and greatly improving the efficiency.
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FIG. 1 is a schematic diagram of the measurement results of geometric deviation and damage types of engineering blisks used in the embodiment of the present invention;
FIG. 2 is a flow chart of an automatic modeling method of a high-fidelity finite element model facing a leaf disc structure in the embodiment of the invention;
FIG. 3 is a flowchart of a leaf disk point cloud data processing and classification algorithm in the present embodiment;
FIG. 4 is a flow chart of a finite element mesh deformation algorithm in an embodiment of the present invention;
FIG. 5 is a comparison graph of finite element calculation results and experimental data of the high fidelity model of the engineering blisk established in the embodiment of the present invention.
Detailed Description
The present embodiment exemplifies the method of the present invention by using a compressor blisk as an example. Firstly, point cloud data of a blisk is required to be obtained, the specific form of the measured geometric deviation of each blade of the engineering blisk is shown in fig. 1, wherein the top of No. 3 blade has large deformation, 11, 12, 14 and 15 blades are damaged blades, and the front edge of the blade tip is unfilled corner. Wherein the mean value of the deviation of the damaged leaves is below 0.05mm, and the mean value of the damaged leaves is 0.1mm-0.25 mm.
The automatic modeling method for the high-fidelity finite element model facing the blade disc structure is basically as shown in fig. 1, and comprises the steps of firstly processing point cloud data (TSD model) of a measured whole blade disc, carrying out Boolean operation to delete the point cloud data of the wheel disc, distinguishing and sequencing each blade by using a blade identification algorithm, then classifying point cloud data sets of each blade, and obtaining point cloud data of the top of each blade, a pressure surface and a suction surface.
As shown in fig. 2, the leaf disk point cloud processing and classifying algorithm specifically operates as follows:
(1.1) first, extracting point cloud data of a single blade from the point cloud data of the leaf disk, as shown in the left side of FIG. 2, according to a leaf disk shape function f disc (x) And performing Boolean operation on the point cloud data of the blisk, and dividing the point cloud data into a disk and a blade. To avoid the occurrence of blades and inventories due to manufacturing errorsAt the connecting portion, in this embodiment f disc (x) And also is provided with a redundancy E 0
And then, extracting a single blade from all the blade point cloud data by utilizing the rule that no triangular mesh connection exists between different blades. Specifically, in P B In randomly selecting a point P Bij Finding out the connection point, and then finding out the connection point by taking the found connection point as a starting point; this operation is iterated until there are no more connection points, all connection points and points P found in the above process Bij I.e. a point cloud dataset P of individual blades Bi (ii) a Then from P B Removing the point cloud dataset P of the blade Bi And repeating the operation in the rest point cloud data until all the blades are distinguished.
In addition, due to P Bi Is randomly selected and cannot determine P Bi Position of, extracted P Bi A correct ordering is required.
Specifically, a point cloud data set P is obtained according to each blade Bi Calculating the included angle between the gravity center vector of each blade and the central axis of the blade disc, and finally calculating P Bi And (4) sequencing the blades according to the included angle between the gravity center vector and the central axis and the included angle between the gravity center vector and each blade at each position by 0-360 degrees.
And (1.2) detecting the surface characteristics of the blade point cloud data through cluster analysis of multi-geometric characteristics to adapt to the large deformation condition of the finite element grid, wherein characteristic points of the front edge, the rear edge, the pressure surface, the suction surface and the top surface of the blade need to be identified from the blade point cloud data. As the top of the blade is an uncertain curve and the pressure surface and the suction surface are both complex curved surfaces, only P is used Bi-XYZ The point coordinates are used as features to hardly extract all surfaces, so that the normal vector feature P of the point cloud is adopted Bi-UVW As a second identified geometric attribute.
As shown on the right side of fig. 2, a total of cubic cluster analyses were performed:
the first clustering analysis considers the excessive bending of the blade root of the blisk, the normal vector of the blade root can also influence the identification of the top surface, and then a blade point cloud data set P is used Bi Point coordinate P in Bi-XYZ Performing clustering analysis on the P as features Bi Divided into blade upper segment point cloud data set P Bi-UP And a blade upper point cloud data set P Bi-Bottom
And (5) clustering for the second time: using a blade point cloud dataset P Bi Normal vector P in (1) Bi-UVW Is a feature pair P Bi-UP Performing cluster analysis to extract a leaf top surface point cloud data set P Bi-TS
And (3) clustering for the third time: using a blade point cloud dataset P Bi Normal vector P in (1) Bi-UVW Is characterized by removing P Bi-TS Blade point cloud data set P Bi Performing cluster analysis on the rest part to extract a point cloud data set P of the pressure surface of the blade Bi-PS Point cloud data set P of suction surface of blade Bi-SS . And (1.3) after the characteristic surface in the blade point cloud data is identified, searching the edge point in the surface point cloud data.
As shown in fig. 2, the cubic cluster analysis in the present embodiment employs a gradient descent-K nearest neighbor algorithm (GD-KNN).
Since the points between the pressure surface and the suction surface belong to the leading edge line and the trailing edge line, these points are extracted and fitted to obtain a smooth edge curve. After fitting the edge points, the curve can be used to infer function values without point cloud data and generate more edge parameter points, which is helpful for aligning the edge nodes of the standard finite element model. The fitted curve is obtained by a NURBS method, which is defined as a function of the vector values of one or more parameters, which transforms a multi-dimensional space into at least one single dimension. The basic function of NURBS is evaluated by using a Cox-de Boor recursive method, and the specific form of NURBS is as follows:
Figure BDA0003633335210000051
Figure BDA0003633335210000052
Figure BDA0003633335210000053
where ξ is the parameter value, N i,p Is the ith order basis function and p is the control point. Since C (0) and C (1) are extreme points of the NURBS curve of the edge, it is sufficient to search for the vertices of the blade edge (including the leading edge vertex and the trailing edge vertex) that are farthest from the central axis.
After the classification is finished, the nodes of the standard finite element model are moved by adopting a grid deformation algorithm to be fitted to the classified subdivision data set, and meanwhile, the shape and the mapping of the unit are kept by using the radial basis kernel function, so that the geometric detuning finite element model matched with the measurement model can be obtained. The specific process of the part is shown in fig. 3, and includes two parts, namely blade edge node movement and blade internal point cloud data movement, as follows:
and (2.1) obtaining a displacement vector of the finite element edge node, wherein equal reference points are required to be carried out on the NURBS edge curve for this purpose, and the equal reference points correspond to the finite element nodes one by one. And calculating the position parameters (the starting point is 0, and the end point is 1) of each edge node on the NURBS edge curve aiming at the edge nodes in the standard finite element model, wherein the distance between each section of nodes is used as the arc length. Then, according to the position parameters of the edge nodes, carrying out equal reference points in the edge curve, and carrying out difference on the obtained equal reference points and the corresponding edge nodes to obtain displacement vectors of the edge nodes in the standard finite element model;
and (2.2) when the edge curve is moved, when the displacement of the blade tip node is too large, the conditions of unit deformity, unsmooth surface depression and the like can be caused. To solve the above problem, after obtaining the edge node displacement vectors, the displacements are assigned to neighboring nodes using Radial Basis Functions (RBFs), which can reduce the probability of cell malformation. The influence between node displacements depends on the Euclidean distance between FEM nodes, so that the Gaussian kernel is in the specific form:
Figure BDA0003633335210000054
Figure BDA0003633335210000055
where s is the hyperparameter of the Gaussian kernel, R is the Euclidean distance of two vectors (u, V in the formula), V is the vector of variance, V [ x ] i ]Is the variance calculated over the ith component of all points.
Each edge node has its own displacement vector and will interact with each other. And solving the local displacement vector through the local Gaussian kernel matrix to enable the final displacement to be in accordance with the node displacement vector. The movement of all nodes in the standard finite element model is shown as follows:
Figure BDA0003633335210000061
wherein N is i-1 As the coordinates of the node before movement, N i For the node coordinates after movement, K is the gaussian kernel radial basis matrix.
And (2.3) after the first movement, acquiring normal vectors of all surface nodes, projecting the surface nodes along the normal vector direction, and finding a subdivision surface triangle intersected with the normal vectors. The general idea of the algorithm for judging the intersection of the ray and the triangle is to calculate the intersection point of the ray and the plane of the triangle, and then judge whether the intersection point is inside the triangle, and the method specifically comprises the following steps:
for a ray in space, the starting point is O (finite element node), the ray direction is D (finite element node normal vector), and according to the parameter formula of the ray, any point (namely the intersection point of the requirement and the triangular plane) is N (t):
N(t)=O+tD (5)
when the intersection point of the ray and the triangular plane is calculated, the parameter equation of the ray and the parameter equation of the plane are evaluated in a simultaneous manner. If the parameter equation of the space triangle is known, the intersection point can be directly obtained by combining the parameter equation of the space triangle and the parameter equation of the ray. For the point V 0 ,V 1 ,V 2 The formed space triangle, assuming any point N (t) in the triangle, has the following parameter equation:
N(t)=(1-u-v)V 1 +uV 2 +uV 3 (6)
where u, V are V 2 And V 3 1-u-V is V 1 And satisfies u>=0,v>=0,u+v<1. By combining the ray equation (5) with the triangle parameter equation (6), the following equation can be obtained.
(1-u-v) V 1 +u V 2 +v V 3 =O+tD (7)
It is clear that u, v, t are all unknowns and that after the work-up the following system of linear equations is obtained:
Figure BDA0003633335210000062
let E 1 =V 2 -V 1 ,E 2 =V 3 -V 1 ,T=O-V 1 From the claime rule, the following formula is derived:
Figure BDA0003633335210000063
the above algorithm needs to traverse all surface nodes and corresponding normal vectors for calculation, and find out the triangle intersected with it. However, the number of triangle subdivision surfaces is huge, and in order to reduce the calculation time of intersection of the ray and the triangle in each step, it is necessary to find out a plurality of triangles which are closest to the finite element nodes to test whether the triangles intersect, and in the embodiment, the close triangles are selected by using a nearest neighbor algorithm based on the euclidean distance.
Finally, calculating the distance between the surface node and the subdivision surface triangle intersected with the surface node, and moving each corresponding surface node along the normal vector direction according to the distance; and assigning the distances to the interior nodes of the standard finite element model using radial basis functions, and moving each respective interior node in accordance with the distances in the normal vector direction.
And finally obtaining the updated finite element model through the two steps of movement.
In table 1, the natural frequencies of the blisks of each order are obtained by finite element calculation and compared with the test data. The comparison result of the first bending and one twisting natural frequency of the engineering blade disc is shown in fig. 5, and it can be seen from the graph that the relative error range of the frequency calculated by using the finite element model obtained in the present embodiment to the test data is 0.0133% -0.289%, and the relative error of the frequency of 10 blades is below 0.1%. The mean relative error of the one-bending natural frequency of all the blades is 0.087632%. The relative error range of the nondestructive blade frequency in the torsional natural frequency of the engineering blade disc is 0.01415-0.328%, and the relative error of the frequency of 8 blades is below 0.1%. The damage-free blade torsional natural frequency relative error mean value is 0.09791%. Therefore, for the structural high-fidelity modeling, the error between the numerical result and the actual measurement result of the first bending and twisting of the blades of the engineering blade disc is less than 0.1 percent.
TABLE 1 Experimental data of natural frequency of each blade of engineering blade disc and statistical data of detuning model
Figure BDA0003633335210000071
The principles and embodiments of the present invention are explained in this application using specific examples, which are provided to help understand the core concepts of the present invention. It is noted that it will be readily apparent to those skilled in the art that various modifications may be made to the embodiments, or equivalents may be substituted for some or all of the features thereof, and that the generic principles defined herein may be applied to other embodiments without the use of inventive faculty. Therefore, the present invention is not limited to the above embodiments, and those skilled in the art should make improvements and modifications within the scope of the present invention based on the disclosure of the present invention.

Claims (10)

1. A high-fidelity finite element model automatic modeling method facing a leaf disc structure is characterized by comprising the following steps
Step 1, acquiring blisk point cloud data measured by an optical scanner;
step 2, extracting point cloud data of the blades in the point cloud data of the blisk, and distinguishing a point cloud data set of each blade by using a blade identification algorithm;
step 3, performing feature classification on the point cloud data of each blade by adopting a multi-feature clustering analysis algorithm to respectively obtain subdivision data sets of the top of each blade, the pressure surface and the suction surface;
and 4, adopting a grid deformation algorithm to move corresponding nodes in the standard finite element model to fit the classified subdivided data set, and simultaneously using a radial basis kernel function to keep the shape and mapping of the unit to obtain a geometric detuning finite element model matched with the measured blisk.
2. Method according to claim 1, characterized in that in step 2 a blisk shape function f is used disc (x) Performing Boolean operation on the point cloud data of the blisk, and dividing the point cloud data of the blisk into a blisk P D And the blade P B Two part data sets.
3. Method according to claim 2, characterized in that the function f is a blisk shape disc (x) Setting the redundancy E 0
4. The method of claim 2, wherein the step 2 of distinguishing each blade using the blade identification algorithm comprises, at P B In randomly selecting a point P Bij Finding out the connection point, and then finding out the connection point by taking the found connection point as a starting point; this operation is iterated until there are no more connection points, all connection points found in the above process and the point P Bij I.e. a point cloud data set P of individual blades Bi
Then from P B Removing the point cloud dataset P of the blade Bi And repeating the operation in the rest point cloud data until all the blades are distinguished.
5. The method of claim 1, wherein step 2 further comprises ordering the individual blades.
6. The method of claim 5, wherein the ordering comprises a point cloud dataset P from each blade Bi And calculating the included angle between the gravity center vector of each blade and the central shaft of the blade disc, and sequencing the blades according to the size of the included angle.
7. The method of claim 1, wherein the step 3 of performing feature classification on each blade point cloud data comprises,
clustering for the first time: using a blade point cloud dataset P Bi Point coordinate P in Bi-XYZ Performing clustering analysis on the P as features Bi Divided into blade upper segment point cloud data set P Bi-UP And a blade upper point cloud data set P Bi-Bottom
And (5) clustering for the second time: using a blade point cloud dataset P Bi Normal vector P in (1) Bi-UVW Is a feature pair P Bi-UP Performing cluster analysis to extract a leaf top surface point cloud data set P Bi-TS
And (3) clustering for the third time: using a blade point cloud dataset P Bi Normal vector P in (1) Bi-UVW Is characterized by removing P Bi-TS Blade point cloud data set P Bi Performing cluster analysis on the rest part to extract a point cloud data set P of the pressure surface of the blade Bi-PS Point cloud data set P of suction surface of blade Bi-SS
8. The method of claim 7, wherein the step 4 comprises the following steps for the moving process of the edge nodes in the standard finite element model:
point cloud dataset P at surface Bi-TS 、P Bi-SS And P Bi-PS Finding out edge points, extracting the edge points and fitting a smooth edge curve;
calculating the position parameter of each node on the edge curve of the node according to the edge nodes in the standard finite element model, wherein the distance between each section of the node is used as the arc length;
performing equal reference points in an edge curve according to the position parameters of the edge nodes, and performing difference between the obtained equal reference points and the corresponding edge nodes to obtain displacement vectors of the edge nodes in the standard finite element model;
assigning the displacement vectors to neighboring nodes of the edge node using radial basis functions;
and moving the corresponding nodes in the standard finite element model according to the displacement vectors and the allocated displacement vectors.
9. The method of claim 8, wherein the edge curve is fitted by a NURBS method.
10. The method of claim 8, wherein the step 4 comprises the following steps for the movement process of the surface and internal nodes in the standard finite element model:
obtaining a normal vector of a surface node in a standard finite element model, projecting the node along the normal vector direction, finding a subdivision surface triangle intersecting with the normal vector in a surface point cloud data set, and calculating the distance from the node to the subdivision surface triangle;
moving each corresponding surface node in the normal vector direction according to the distance;
assigning the distances to internal nodes of the standard finite element model using radial basis functions;
each respective internal node is moved in the normal vector direction according to the distance.
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CN116415377A (en) * 2023-06-12 2023-07-11 陕西空天信息技术有限公司 She Panmo type generation method and device, electronic equipment and storage medium
CN116415377B (en) * 2023-06-12 2023-09-01 陕西空天信息技术有限公司 She Panmo type generation method and device, electronic equipment and storage medium

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