CN114880792A - Deformation prediction-based omnibearing multi-angle optimization method - Google Patents

Deformation prediction-based omnibearing multi-angle optimization method Download PDF

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CN114880792A
CN114880792A CN202210414615.3A CN202210414615A CN114880792A CN 114880792 A CN114880792 A CN 114880792A CN 202210414615 A CN202210414615 A CN 202210414615A CN 114880792 A CN114880792 A CN 114880792A
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deformation
auxiliary support
elastic deformation
blade
optimization
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戴佳伟
王海军
毛东立
张超凡
孙振鸣
王金玉
王舒祥
王月丽
吴汉钦
范颖
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Hubei University of Education
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
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Abstract

The invention provides an omnibearing multi-angle optimization method based on deformation prediction, which is characterized in that when a curved surface thin-wall working condition is oriented, a blade milling finite element simulation model is established to predict the deformation of a curved surface, in order to reduce the deformation of the curved surface, the GA-SVR (GAs-assisted support surface shear) based thin-wall blade takes auxiliary support layout and milling cutting parameters as design variables, and the maximum processing elastic deformation and the integral elastic deformation mean square error as the quality evaluation indexes of the auxiliary support layout; calculating the quality evaluation index of the auxiliary support layout and generating a sample set, training the sample set to obtain a proxy model of the evaluation index, predicting the maximum processing elastic deformation and the integral elastic deformation mean square error of the actual thin-wall blade under the auxiliary support layout through the proxy model, optimizing the process parameters, and reducing the elastic deformation in an iterative compensation mode. The invention has the beneficial effects that: the method optimizes the algorithm, shortens the processing time, and improves the processing efficiency and the processing precision of the blade.

Description

Deformation prediction-based omnibearing multi-angle optimization method
Technical Field
The invention relates to the field of blade deformation optimization under the curved surface thin-wall working condition, in particular to an all-dimensional multi-angle optimization method based on deformation prediction.
Background
The blade is used as an important part in impellers of various mechanical equipment, the processing quality and the processing precision of the blade directly influence the overall working performance and the service life of the equipment, and the electronic digital signal control milling is used as a high-precision and high-efficiency processing mode and is widely applied to the precision forming of various blades. However, as a typical complex curved surface thin-wall device, the blade is easily affected by cutting force during the milling process, so that the blade is subjected to cutter back, namely elastic deformation. Therefore, the actual cutting position of the cutter deviates from the theoretical cutting position in the milling process, the machining precision of the blade does not reach the standard, and the service performance of equipment is affected. Therefore, the research on how to enable the processing in the process to be more stable and inhibit the occurrence of elastic deformation has important significance for ensuring the processing precision and improving the overall performance of the equipment.
The premise of controlling the elastic deformation of thin-wall parts in machining is to realize the prediction of deformation, which is always a research hotspot of a plurality of scholars. The Caoyijie establishes a five-axis milling machining deformation prediction method of a complex curved surface thin-wall part based on a machining deformation flexible iterative algorithm. The method is characterized in that the influence of material removal on the machining rigidity of the blade in the milling process is ignored on the basis of considering the coupling effect of milling force and elastic deformation, and the like, so that an iterative calculation format of the elastic deformation of the point milling machining of the thin-wall blade is established. However, these methods are computationally lengthy, complicated and do not take into account the effect of the material on the manufacturing process. And aiming at the milling auxiliary support of the blade body profile of the thin-wall blade, corresponding research is lacked at present.
Disclosure of Invention
In order to solve the problems, the invention provides an omnibearing multi-angle optimization method based on deformation prediction, which is oriented to the curved surface thin-wall working condition and mainly comprises the following steps:
s1: considering material removal and a coupling effect of milling force and elastic deformation, establishing a blade milling finite element simulation model to predict curved surface deformation;
s2: in order to reduce the curved surface deformation predicted in the step S1, the thin-wall blade based on the linear regression algorithm model (GA-SVR) takes the auxiliary support layout and the milling cutting parameters as design variables, and the maximum processing elastic deformation and the overall elastic deformation mean square error as the quality evaluation indexes of the auxiliary support layout; and calculating the quality evaluation indexes of the auxiliary support layout by adopting a 'unit life and death' technology, Latin hypercube test design and a blade milling finite element simulation model, generating a sample set, training the sample set by regression of a support vector machine, and obtaining a proxy model of the evaluation indexes.
S3: the maximum processing elastic deformation and the integral elastic deformation mean square error of the actual thin-wall blade under the auxiliary support layout are predicted through the proxy model by taking the minimum two characteristics of the maximum processing elastic deformation and the integral deformation mean square error of the thin-wall blade as optimization targets;
s4: and (4) optimizing the auxiliary support layout of the thin-wall blade by adopting an elite strategy genetic algorithm in combination with the optimization target obtained in the step S3, and optimizing the process parameters by taking the residual stress deformation as constraint and the maximum processing efficiency as a target, wherein the elastic deformation in the step S1 is reduced in an iterative compensation mode on the basis.
Further, the method for predicting surface deformation comprises the following steps:
s11: establishing a blade milling finite element simulation model, and solving the initial normal cutting force of each node according to the cutting sequence;
s12: according to the initial normal cutting force, using MATLAB to call ANSYS, and solving an initial value of the elastic deformation of the initial thin-wall blade;
s13: updating the normal cutting force;
s14: correcting the rigidity matrix of the unit to be removed by utilizing a blade milling finite element simulation model;
s15: and (5) coupling the milling force and the elastic deformation cycle for iteration by adopting a method like the steps S12-S14, and outputting the elastic deformation quantity of all nodes when the preset precision or the preset maximum iteration times is reached.
Further, the auxiliary support layout comprises: the method comprises the steps of auxiliary support layout design based on an Euler identity (OLHD), a proxy model construction method based on support vector machine regression (SVR), support vector machine regression (SVR) hyper-parameter optimization based on grid search (GS-CV), auxiliary support layout optimization modeling and auxiliary support layout optimization based on a genetic algorithm (E-GA).
Further, the auxiliary support layout design based on the euler identity (OLHD) is based on an optimal latin hypercube design, different auxiliary support layout schemes are generated for the blade basin profile to serve as initial sample input, a blade milling finite element simulation model is adopted, and target deformation characteristics of the blades under the corresponding layout schemes, namely the maximum processing elastic deformation and the integral deformation mean square error, are calculated to serve as sample output.
Further, the design variables are mapped to a high-dimensional space, the problem of low-dimensional nonlinearity is converted into linear regression in the high-dimensional space, and an SVR-based proxy model is established.
Further, the agent model construction method comprises the following steps: obtaining a sample set, constructing a regression model, analyzing model parameters and obtaining a kernel function.
Further, GS-CV optimization is carried out to respectively obtain a training model of mean square deviation of maximum processing elastic deformation and integral deformation of the blade, and the optimization process comprises the following steps: determining an over-parameter range, performing over-parameter gridding processing, K-fold cross validation and over-parameter grid combination.
Furthermore, the auxiliary support layout optimization modeling takes the minimum two characteristics of the maximum processing elastic deformation and the integral deformation mean square error of the thin-wall blade as optimization targets, and establishes a two-point auxiliary support layout optimization model.
Further, the E-GA-based auxiliary support layout optimization is to optimize the two-point auxiliary support layout of the leaf pot by adopting the E-GA, set the population size to be 40, the evolution algebra to be 100, the cross probability to be 0.9, the mutation probability to be 0.1, the elite selection operator to be 0.02, and continuously iterate and screen to finally determine the optimal support layout.
The technical scheme provided by the invention has the beneficial effects that: the blades are arranged on the impeller, and numerical analysis is carried out on the impeller with contour errors on different parts of the surface of the blades and the impellers with different surface contour error sizes. The result shows that the machining error influences the performance of the impeller, and changes the internal flow of the impeller, so that the efficiency and the pressure ratio of the impeller are reduced. The influence of the machining error in the middle of the blade on the performance of the impeller is the largest for the front, middle and rear of the blade, and the regular error S is the largest in consideration of the front, middle and rear errors. With the addition of different sized regular S-shaped surface profile errors, the efficiency and pressure ratio losses occur at the maximum at a surface profile of 0.15mm, rather than at the maximum of 0.2 mm. The quality of the blade shape is closely related to the efficiency of the impeller. The method optimizes the algorithm, shortens the processing time, improves the processing efficiency and the processing precision of the blade, ensures the good surface of the blade, and has important practical significance.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of deformation prediction in an embodiment of the present invention.
FIG. 2 is a schematic illustration of the calculation of an initial normal cutting force in an embodiment of the present invention.
Fig. 3 is a schematic diagram of the thin-walled blade of the embodiment of the invention elastically deformed by the cutting force so that the actual cutting depth is less than the nominal cutting depth.
FIG. 4 is a schematic diagram of an embodiment of the present invention simulating insufficient removal of material (i.e., a cell death technique) by "incompletely" killing the cell to be removed.
Fig. 5 is a schematic diagram of a coupling iterative operation process performed on the processing elastic deformation of a certain node on the blade basin surface in the embodiment of the present invention.
Fig. 6 is a schematic view of the distribution of elastic deformation of the entire blade in the embodiment of the present invention.
FIG. 7 is a schematic diagram of an auxiliary support layout according to an embodiment of the present invention.
FIG. 8 is a block diagram of a method for constructing an SVR-based proxy model according to an embodiment of the present invention.
FIG. 9 is a parameter diagram of an analytical model in an embodiment of the present invention.
FIG. 10 is a diagram of an optimization result after searching the hyperparametric combined grid in the embodiment of the present invention.
FIG. 11 is a flow chart of an embodiment of the present invention for obtaining an optimal secondary support layout.
FIG. 12 is a schematic diagram of an evolutionary algebra for obtaining an optimal auxiliary support layout scheme according to an embodiment of the present invention.
FIG. 13 is a diagram illustrating the optimization of the elastic deformation of the lower blade basin profile for optimal auxiliary support placement in accordance with an embodiment of the present invention.
FIG. 14 is a graph of the relationship between the machining elastic deformation value and the chord direction of the lower blade basin in the best auxiliary support layout in the embodiment of the present invention.
Detailed Description
For a more clear understanding of the technical features, objects and effects of the present invention, embodiments of the present invention will now be described in detail with reference to the accompanying drawings.
The invention provides an omnibearing multi-angle optimization method based on deformation prediction, which is oriented to a curved surface thin-wall working condition and mainly comprises the following steps of:
s1: considering material removal and a coupling effect of milling force and elastic deformation, establishing a blade milling finite element simulation model to predict curved surface deformation;
s2: in order to reduce the curved surface deformation predicted in the step S1, the GA-SVR-based thin-wall blade takes the auxiliary support layout and the milling cutting parameters as design variables, and the maximum processing elastic deformation and the integral elastic deformation mean square error as the quality evaluation indexes of the auxiliary support layout; and calculating the quality evaluation indexes of the auxiliary support layout by adopting a 'unit life and death' technology, Latin hypercube test design and a blade milling finite element simulation model, generating a sample set, training the sample set by regression of a support vector machine, and obtaining a proxy model of the evaluation indexes.
S3: the maximum processing elastic deformation and the integral elastic deformation mean square error of the actual thin-wall blade under the auxiliary support layout are predicted through the proxy model by taking the minimum two characteristics of the maximum processing elastic deformation and the integral deformation mean square error of the thin-wall blade as optimization targets;
s4: and (4) optimizing the auxiliary support layout of the thin-wall blade by adopting an elite strategy genetic algorithm in combination with the optimization target obtained in the step S3, and optimizing the process parameters by taking the residual stress deformation as constraint and the maximum processing efficiency as a target, wherein the elastic deformation in the step S1 is reduced in an iterative compensation mode on the basis.
Referring to fig. 1, fig. 1 is a flowchart of deformation prediction in an embodiment of the present invention, which specifically includes the following steps:
s11: establishing a blade milling finite element simulation model, and solving the initial normal cutting force of each node according to the cutting sequence;
s12: according to the initial normal cutting force, using MATLAB to call ANSYS, and solving an initial value of the elastic deformation of the initial thin-wall blade;
s13: updating the normal cutting force;
s14: correcting the rigidity matrix of the unit to be removed by utilizing a blade milling finite element simulation model;
s15: and (5) coupling the milling force and the elastic deformation cycle for iteration by adopting a method like the steps S12-S14, and outputting the elastic deformation quantity of all nodes when the preset precision or the preset maximum iteration times is reached.
In this embodiment, the cutting force is the cutting load in the drawing, and the specific steps are as follows:
(1) calculating the initial normal cutting force
Solving the initial normal cutting force of each node according to the cutting sequence, and then adding auxiliary support position constraint under the corresponding layout in an APDL script program of ANSYS software.
1) Direction of cutting force
In order to facilitate the application of cutting load during the solving process and the acquisition of the normal elastic deformation of the node in the post-processing stage, as shown in fig. 2.
In the pre-processing stage, the z-axes of all the blade profile node coordinate systems are sequentially rotated to respective normal vector directions through command streams, and the rotation angles of the node coordinate systems obtained by utilizing the rotation matrix transformation are respectively as follows:
Figure BDA0003605080890000051
in the formula: n is s ＝(i s ,j s ,k s ) Is the normal vector of the surface at the s-th node, theta s Angle of rotation, beta, about the x-axis s Is the angle of rotation about the y' axis.
The normal vector (i, j, k) of the node is obtained through UG secondary development, so that the subsequent analysis of the deformation rule of the blade body is facilitated, and the equal-parameterization coordinates (u, v) of the node on the profile of the blade body are extracted. The node information of the first discrete cutting tool path is shown in the following table.
Figure BDA0003605080890000052
Figure BDA0003605080890000061
2) Magnitude of cutting force
The blade is usually machined by five-axis point milling, and the time-varying cutter shaft inclination angle in the milling process tends to cause the cutting condition between the cutter and the workpiece to vary. Therefore, on the basis of a traditional empirical formula model, aiming at the point milling machining cutter position characteristics of the thin-wall blade, the influence factor of the cutter shaft inclination angle is introduced, a five-factor empirical formula is established, and through orthogonal experimental design and multiple linear regression, the five-axis cutting force empirical formula of the ball nose cutter is calibrated to be
Figure BDA0003605080890000062
In the formula: fx, Fy, Fz are cutting force components of the cutting force in the x, y, z directions respectively; a is p Is the cutting depth; a is e Is the cutting width; v. of c Is the cutting speed; f. of z Feeding for each tooth; psi is the cutter shaft inclination angle.
As shown in fig. 2, the cutter shaft inclination angle of each cutting position can be determined through the obtained node normal vector information, and the theoretical cutting force of each node position can be calculated by substituting the cutting parameter and the cutter shaft inclination angle into formula (2). Further, the theoretical cutting force of each node is projected along the normal vector direction of the curved surface at the node, so that the normal cutting force of the current position can be obtained and used as the cutting load of the finite element simulation. The normal cutting force is calculated by the formula
F nor,s ＝F s ·n s ＝(F x,s ,F y,s ,F z，s )·(i s ，j s ，k s ) (3)
(2) Solving initial value of elastic deformation of blade
And reading the normal cutting force of the node obtained by the last iteration by the APDL program, calling an ANSYS background by MATLAB to execute the APDL script program, solving the elastic deformation values of all the discrete tool path nodes and outputting the elastic deformation values.
(3) Renewing normal cutting force
And (3) substituting the obtained elastic deformation values of all the nodes into the formula (5), updating the cutting depth of each node, and updating and calculating the normal cutting force of each node through the formula (6).
1) The principle is as follows:
the thin-walled blade elastically deforms under the cutting force such that the actual cutting depth is less than the nominal cutting depth, as shown in fig. 3.
This results in an actual cutting force that is less than the initial theoretical cutting force calculated for the nominal depth of cut. This also means that the milling force and the elastic deformation are in a coupled relationship with each other. The traditional method for predicting the milling elastic deformation of the thin-wall part directly uses the nominal cutting depth to calculate the theoretical milling force, and calculates the processing elastic deformation of the blade only through one-time finite element simulation, so that the coupling effect between the cutting force and the elastic deformation is completely ignored, and the prediction precision is not high.
In order to predict the machining elastic deformation of the blade more accurately, a coupling iteration format of the milling force and the elastic deformation is established, as shown in formula (5), the theoretical cutting depth is corrected according to the machining elastic deformation obtained through simulation calculation each time, the calculation of the cutting force is carried out again, and the coupling iteration is repeated for multiple times until convergence, so that the final machining elastic deformation predicted value is obtained.
Figure BDA0003605080890000071
In the formula:
Figure BDA0003605080890000072
and
Figure BDA0003605080890000073
respectively representing the theoretical cutting depth of the S-th node and the cutting depth after h iterations;
Figure BDA0003605080890000074
performing finite element calculation on the S-th node after h-1 iteration to obtain normal elastic deformation;
Figure BDA0003605080890000075
cutting force of the S-th node at h-1 iteration:
Figure BDA0003605080890000076
(4) modifying a stiffness matrix of a unit to be removed
And (4) calculating a rigidity correction factor according to the formula (7) and the deformation value of the current node, and then correcting the rigidity matrix of the unit to be removed of the blade body through an APDL program.
The insufficient material removal caused by the elastic deformation allows only a partial volume of the pre-divided allowance cell to be removed during the actual cutting process. Therefore, in order to avoid the tedious grid redrawing work and improve the calculation efficiency, as shown in fig. 4, the insufficient removal of the material is simulated by killing the unit to be removed incompletely, i.e. the insufficient removal of the material is performed by adopting a 'unit life and death' technology.
(5) Cyclically coupling milling force and elastic deformation for iteration
And starting the coupled iterative loop operation of the milling force and the elastic deformation, introducing the updated normal cutting force into an APDL program, and calculating the elastic deformation of each node of the next generation.
As shown in equation (7), the 'incomplete' killing of the unit is realized by correcting the rigidity matrix of the current cut grid unit in the simulation process, and the correction coefficient is the ratio of the deformation value obtained by the unit in the last calculation in the iteration process to the initial thickness of the unit.
Figure BDA0003605080890000081
In the formula:
Figure BDA0003605080890000082
and
Figure BDA0003605080890000083
the initial stiffness matrix of the t unit and the stiffness after h iterations respectivelyA matrix;
Figure BDA0003605080890000084
a stiffness correction factor for the t unit at the h iteration;
Figure BDA0003605080890000085
taking the elastic deformation value of the unit which is the t-th unit after h iterations, and taking the deformation value of the nearest node of the unit;
Figure BDA0003605080890000086
the theoretical depth of cut for the t-th element.
Taking a certain node on the molded surface of the leaf basin as an example, coupling iterative operation is carried out on the elastic deformation of the blade basin until the change rate of the deformation obtained by two iterations is smaller than the set convergence precision, the node converges after seven iterations, and the iteration process is shown in fig. 5.
(6) Output elastic deformation quantity
And comparing whether the change rate of the elastic deformation amount of each node in two times before and after is smaller than the set precision e, and outputting the elastic deformation amount of all the current nodes if the change rate is converged to obtain the elastic deformation distribution of the whole blade as shown in fig. 6.
Deformation suppression of auxiliary support layout of thin-walled blade based on GA-SVR
The processing elastic deformation amount of the blade is changed with different auxiliary support layouts, and the number and the positions of the auxiliary supports are two key parameters of the layout scheme. The existing research results show that the auxiliary support applied to the same blade section exceeds two points, the effect of inhibiting the elastic deformation in machining is improved very slightly, and the multi-section support can obviously reduce the machining efficiency.
The layout method of the auxiliary support is divided into five steps as shown in fig. 7: the method comprises the steps of OLHD-based auxiliary support layout design, an SVR-based agent model construction method, GS-CV-based SVR hyper-parameter optimization, auxiliary support layout optimization modeling and E-GA-based auxiliary support layout optimization.
(1) OLHD-based auxiliary support layout optimization design
Based on the optimal Latin hypercube design, different auxiliary support layout schemes are generated for the leaf basin molded surface to serve as initial sample input. And calculating the target deformation characteristics of the blades under the corresponding layout scheme by adopting finite element simulation, namely, outputting the maximum processing elastic deformation and the integral deformation mean square error as a sample.
1) Principle of
The processing elastic deformation amount of the blade is changed with different auxiliary support layouts, and the number and the positions of the auxiliary supports are two key parameters of the layout scheme. In order to ensure that the support positions generated by sampling can be positioned on the blade profile, the positions of the auxiliary supports on the blade curved surface are determined by isoparametric coordinates. The design variables for secondary support layout optimization can be expressed as:
Figure BDA0003605080890000091
in the formula: x is the number of i The layout scheme is the ith auxiliary support layout scheme; m is the number of support points; x is the number of ij ＝(u ij ，v ij ) Isoparametric coordinates for the jth support point of the ith layout scheme, where u ij 、v ij ∈[0，1]。
In order to improve the processing efficiency and avoid excessive interference of the multi-point rod-shaped auxiliary support to the processing process, only the single-section two-point auxiliary support is arranged on the thin-wall blade in the processing process, and the layout design variable can be written as
x i ＝[x i1 ，x i2 ]＝[(u i1 ，v i1 )，(u i2 ，v i2 )]＝(u i1 ，u i2 ，v i ) (9)
In the formula: since the two support points are located on the same blade section, there is v i ＝v i1 ＝v i2 。
In order to increase the uniformity of the distribution of the sample points in the design space, different auxiliary support layout schemes are generated for the leaf basin profile as initial sample input based on the optimal Latin hypercube design. And calculating the target deformation characteristics of the blades under the corresponding layout scheme by adopting finite element simulation, namely, outputting the maximum processing elastic deformation and the integral deformation mean square error as a sample.
Finally, 100 sets of sample data are obtained as shown in the table. In order to improve the identification precision of the subsequent blade processing elastic deformation prediction model training, the sample output data in the table is normalized before training:
Figure BDA0003605080890000093
in the formula: delta max And Δ min Respectively a maximum value and a minimum value in the sample output data; delta i For auxiliary support layout x i Maximum working elastic deformation delta of lower blade profile max (x i ) Or the mean square error of the global deformation Δ sd (x i )，y i Representing normalized secondary support layout x i Sample response values of.
Figure BDA0003605080890000094
(2) Agent model construction method based on SVR
The design variables are mapped to a high-dimensional space, the problem of low-dimensional nonlinearity is converted into linear regression in the high-dimensional space, modeling is carried out, a solution is obtained, and the model construction method comprises the following four steps as shown in figure 8: obtaining a training set sample, constructing a regression model, analyzing model parameters and obtaining a kernel function.
a. Obtaining a set of training samples
X＝{(x 1 ,y 1 ),…,(x i ，y i ),…，(x n ,y n ) In the formula: x is the number of i And y i Respectively, the ith support layout and the deformation response thereof, and n is the number of training samples.
b. Constructing a regression model
Figure BDA0003605080890000101
In the formula: (x) is a regression estimation function of the support vector;
Figure BDA0003605080890000102
is a non-linear function that maps samples to a high-dimensional feature space; omega and b are undetermined parameters and are also the key for training the SVR model.
c. Analyzing model parameters
As shown in FIG. 9, a spacer band with a width of 2 ε is constructed centering on f (X), and an ε -insensitive loss function l is introduced ε :
Figure BDA0003605080890000103
When the training sample point falls within this interval band, i.e., the return value f (x) of the regression function i ) And the sample output value y i When the difference is less than or equal to (b), the loss is considered to be 0, i.e. the training samples can be correctly predicted, and the sample points falling outside the interval band are called support vectors. The SVR problem can then be formalized as:
Figure BDA0003605080890000104
introducing a relaxation variable xi i And xi i Formula (14) can be rewritten as
Figure BDA0003605080890000105
In the formula: l is an objective function; c is a regularization constant and is also called a penalty coefficient, and the larger C is, the larger the penalty is on the sample with the error exceeding xi; ξ specifies the error limit of the SVR function.
Solving equation (15) according to the structural risk minimization criterion can obtain w and b, and in order to further make the modeling accurate, introducing a Lagrangian function and converting L into a dual form:
Figure BDA0003605080890000106
in the formula: k (x) i ,x j )＝Ψ(x i ) T Ψ(x j ) Is a kernel function; a is i ，α i Is a lagrange multiplier.
Solving equation (16) yields the optimal solution of
Figure BDA0003605080890000111
Thus, it can be further derived that parameters ω and b are
Figure BDA0003605080890000112
In the formula: n is sv Is the number of support vectors. Substituting equation (18) for equation (12) may yield a regression function for the support vector machine as:
Figure BDA0003605080890000113
d. obtaining kernel functions
Selecting an RBF to construct a kernel function of the SVR:
Figure BDA0003605080890000114
in the formula: 1/2 sigma 2 I.e., the width of the RBF.
(3) GS-CV-based SVR hyper-parameter optimization
And respectively obtaining a maximum processing elastic deformation and integral deformation mean square error training model of the blade through GS-CV optimization. The optimization process is divided into four steps: determining an over-parameter range, performing over-parameter gridding processing, K-fold cross validation and over-parameter grid combination.
1) Principle of
a. Determining the value range of the hyper-parameter (C, gamma)
The value range is [2-10, 210 ].
b. Hyper-parametric meshing process
Taking logarithm from base 2 of the value range of the super-parameter to obtain (log2C, log2 gamma) epsilon-10, 10), carrying out cross value taking with 0.25 as an interval, and obtaining 81 multiplied by 81 to 6561 super-parameter combinations in total.
c.K fold cross validation
From 100 sets of sample data, 80 were taken as training data set and 20 were taken as test data set. And (5) dividing the training data set into 5 parts, taking each part of data as a verification set in turn, evaluating the quality of the model obtained by training the rest 4 parts of data, and finally taking the super parameter with the minimum mean square prediction error as the optimal super parameter in the cross verification.
d. Hyper-parametric combinatorial lattice search
And c, selecting the next group of super-parameter combinations, and repeating the step c until the super-parameter combination with the minimum mean square error is found and used as the optimal SVR model super-parameter in the current sample set. When different parameter y combinations (C, gamma) correspond to the same cross validation precision in the model training process, a set of parameters with smaller C is selected so as to improve the generalization capability of the model. The optimization results are shown in fig. 10.
The optimized parameters are shown in the figure:
hyper-parameter Maximum processing elastic deformation training model Integral deformation mean square error training model
Penalty coefficient C 5.6569 22.6274
Kernel function width gamma 2.8284 1.6817
(4) Auxiliary support layout optimization
Establishing a two-point auxiliary support layout optimization model by taking the minimum two characteristics of the maximum processing elastic deformation and the integral deformation mean square error of the thin-wall blade as optimization targets:
Figure BDA0003605080890000121
in the formula: Δ j (xi) is the deformation value of the jth node on the blade profile; delta (xi) is the average value of all node deformations on the blade profile;
Figure BDA0003605080890000122
respectively the tangential and normal contact forces between the support rod and the molded surface; x is a feasible clamping design domain; μ is the coefficient of friction.
According to the two-point auxiliary support layout optimization model, calculating an objective function when optimizing 2 target deformation characteristics of maximum elastic deformation and integral deformation mean square error by adopting an SVR (support vector regression) agent model instead of a finite element method:
Figure BDA0003605080890000123
in the formula: fmax (xi) and fsd (xi) are the mean square deviations of the maximum processing elastic deformation and the overall elastic deformation of the blade under the auxiliary support layout xi predicted by the SVR proxy model, respectively.
Figure BDA0003605080890000131
(4) E-GA auxiliary support layout optimization
And E-GA is adopted to optimize the two-point auxiliary support layout of the leaf pot, the population size is set to be 40, the evolution algebra is set to be 100, the cross probability is 0.9, the mutation probability is 0.1, the elite selection operator is 0.02, and the optimal support layout is finally determined by continuous screening. As shown in fig. 11-12, the elite in the parent is retained and substituted for the individual with the lowest fitness in the offspring population, so that the optimal individual appearing in the evolution process is effectively prevented from being lost and damaged by selection, crossover and mutation operations, and the global convergence capability of the standard genetic algorithm is improved.
As shown in fig. 13-14, the optimized layout of the optimum processing auxiliary support for the leaf basin is xopimal ═ [ (0.32,0.42), (0.90,0.42) ], and the corresponding overall deformation distribution is as shown in fig. 14, and compared with the state without auxiliary support, the maximum processing elastic deformation is reduced from 178.2 μm to 64.4 μm and is reduced by 63.9%; the mean square deviation of the whole deformation is reduced from 42.4 mu m to 12.9 mu m, the mean square deviation is reduced by 69.6 percent, and the effect of inhibiting the elastic deformation in processing is obvious. Meanwhile, compared with a random two-point auxiliary support layout Xrandom ═ [ (0.26,0.59), (0.84,0.59) ], the maximum processing elastic deformation of the lower blade basin-shaped surface of the optimal auxiliary support layout is found to be smaller, and the overall deformation trend is more uniform.
The invention has the beneficial effects that: the numerical analysis is carried out on the impeller with contour errors at different parts of the surface of the blade and the impellers with different surface contour error sizes. The results show that machining errors affect the performance of the impeller and change the internal flow of the impeller, resulting in reduced impeller efficiency and pressure ratio. The influence of the machining error in the middle of the blade on the performance of the impeller is the largest for the front, middle and rear of the blade, and the regular error S is the largest in consideration of the front, middle and rear errors. With the addition of different sized regular S-shaped surface profile errors, the efficiency and pressure ratio losses occur at the maximum at a surface profile of 0.15mm, rather than at the maximum of 0.2 mm. The quality of the blade shape is closely related to the efficiency of the impeller. The method optimizes the algorithm, shortens the processing time, improves the processing efficiency and the processing precision of the blade, ensures good blade surface and has important practical significance.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (9)

1. An omnibearing multi-angle optimization method based on deformation prediction is characterized in that: the method comprises the following steps:
s1: when the curved surface thin-wall working condition is oriented, a blade milling finite element simulation model is established by considering material removal and the coupling effect of milling force and elastic deformation so as to predict curved surface deformation;
s2: in order to reduce the curved surface deformation predicted in the step S1, the GA-SVR-based thin-wall blade takes the auxiliary support layout and the milling cutting parameters as design variables, and the maximum processing elastic deformation and the integral elastic deformation mean square error as the quality evaluation indexes of the auxiliary support layout; and calculating the quality evaluation indexes of the auxiliary support layout by adopting a 'unit life and death' technology and a blade milling finite element simulation model, generating a sample set, training the sample set by regression of a support vector machine, and obtaining a proxy model of the evaluation indexes.
S3: the maximum processing elastic deformation and the integral elastic deformation mean square error of the actual thin-wall blade under the auxiliary support layout are predicted through the proxy model by taking the minimum two characteristics of the maximum processing elastic deformation and the integral deformation mean square error of the thin-wall blade as optimization targets;
s4: and (4) optimizing the auxiliary support layout of the thin-wall blade by adopting an elite strategy genetic algorithm in combination with the optimization target obtained in the step S3, and optimizing the process parameters by taking the residual stress deformation as constraint and the maximum processing efficiency as a target, wherein the elastic deformation in the step S1 is reduced in an iterative compensation mode on the basis.
2. The deformation prediction-based all-dimensional multi-angle optimization method of claim 1, wherein: in step S1, the method for predicting the deformation of the curved surface includes:
s11: establishing a blade milling finite element simulation model, and solving the initial normal cutting force of each node according to the cutting sequence;
s12: according to the initial normal cutting force, using MATLAB to call ANSYS, and solving an initial value of the elastic deformation of the initial thin-wall blade;
s13: updating the normal cutting force;
s14: correcting the rigidity matrix of the unit to be removed by utilizing a blade milling finite element simulation model;
s15: and (5) coupling the milling force and the elastic deformation cycle for iteration by adopting a method like the steps S12-S14, and outputting the elastic deformation quantity of all nodes when the preset precision or the preset maximum iteration times is reached.
3. The deformation prediction-based all-dimensional multi-angle optimization method of claim 1, wherein: in step S2, the auxiliary support layout includes: OLHD-based auxiliary support layout design, an SVR-based agent model construction method, GS-CV-based SVR hyper-parameter optimization, auxiliary support layout optimization modeling and E-GA-based auxiliary support layout optimization.
4. The deformation prediction-based all-dimensional multi-angle optimization method of claim 3, wherein: the OLHD-based auxiliary support layout design is based on an optimal Latin hypercube design, different auxiliary support layout schemes are generated aiming at the blade basin profile and used as initial sample input, a blade milling finite element simulation model is adopted, and the target deformation characteristics of the blades under the corresponding layout schemes, namely the maximum processing elastic deformation and the integral deformation mean square error, are calculated and used as sample output.
5. The deformation prediction-based all-dimensional multi-angle optimization method of claim 3, wherein: and mapping the design variables to a high-dimensional space, converting the problem of low-dimensional nonlinearity into linear regression in the high-dimensional space, and establishing an SVR-based proxy model.
6. The deformation prediction-based all-dimensional multi-angle optimization method of claim 5, wherein: the agent model construction method comprises the following steps: obtaining a sample set, constructing a regression model, analyzing model parameters and obtaining a kernel function.
7. The deformation prediction-based all-dimensional multi-angle optimization method of claim 1, wherein: through GS-CV optimization, a training model of the maximum processing elastic deformation and the integral deformation mean square error of the blade is respectively obtained, and the optimization process comprises the following steps: determining an over-parameter range, performing over-parameter gridding processing, K-fold cross validation and over-parameter grid combination.
8. The deformation prediction-based all-dimensional multi-angle optimization method of claim 3, wherein: the auxiliary support layout optimization modeling takes the minimum two characteristics of the maximum processing elastic deformation and the integral deformation mean square error of the thin-wall blade as optimization targets, and establishes a two-point auxiliary support layout optimization model.
9. The deformation prediction-based all-dimensional multi-angle optimization method of claim 3, wherein: the E-GA-based auxiliary support layout optimization is to optimize two-point auxiliary support layout of a leaf pot by adopting the E-GA, set the population size to be 40, the evolution algebra to be 100, the cross probability to be 0.9, the mutation probability to be 0.1, the elite selection operator to be 0.02, and continuously iterate and screen to finally determine the optimal support layout.
CN202210414615.3A 2022-04-20 2022-04-20 Deformation prediction-based omnibearing multi-angle optimization method Pending CN114880792A (en)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117420761A (en) * 2023-12-19 2024-01-19 合肥工业大学 Point location layout optimization method of follow-up supporting head in mirror image milling and follow-up supporting head

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117420761A (en) * 2023-12-19 2024-01-19 合肥工业大学 Point location layout optimization method of follow-up supporting head in mirror image milling and follow-up supporting head
CN117420761B (en) * 2023-12-19 2024-02-13 合肥工业大学 Point location layout optimization method of follow-up supporting head in mirror image milling and follow-up supporting head

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