CN110069833B - Interface rigidity optimization design method considering uncertain factors - Google Patents

Interface rigidity optimization design method considering uncertain factors Download PDF

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CN110069833B
CN110069833B CN201910256161.XA CN201910256161A CN110069833B CN 110069833 B CN110069833 B CN 110069833B CN 201910256161 A CN201910256161 A CN 201910256161A CN 110069833 B CN110069833 B CN 110069833B
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张健
吴梦翔
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Shantou University
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Abstract

The invention discloses a structural parameter optimization design method for improving interface rigidity by considering uncertain factors, which comprises the following steps of: step 1, selecting and determining a design parameter, an uncertainty parameter and an uncertainty model, and determining a value range of the design parameter and a change boundary of the uncertainty parameter and the model; step 2, finite element simulation based on design parameters, uncertainty parameters and model sampling; step 3, optimizing design scheme and interface rigidity; step 4, experimental verification and result analysis of the design scheme; step 5 is the correction of the optimization result and the feedback of the design scheme, aiming at the condition that the influence of uncertainty factors on the interface rigidity is considered, the invention adopts a design idea of combining finite element simulation, optimization prediction and experiment, and the mode can ensure that the precision of the optimization model meets the requirement only through a small amount of experimental data, thereby effectively reducing the experiment times under the condition of ensuring the result.

Description

Interface rigidity optimization design method considering uncertain factors
Technical Field
The invention relates to the technical field of optimization design of mechanical structure parameters, in particular to an interface rigidity optimization design method considering uncertain factors.
Background
The mechanical structure parameter optimization design method is an important mechanical structure optimization method and has been a research focus in related fields all the time. The method takes the structural design parameters as optimization objects, and solves the optimization objects according to a given load condition, constraint conditions and performance indexes and a certain target (such as lightest weight, maximum rigidity and the like) to obtain the optimal structural design parameters.
In the prior process of optimally designing structural parameters, an individual mechanical structural part (namely, an individual part) is often optimally designed without considering the influence of actual uncertainty factors, particularly interface rigidity uncertainty, the influence of uncertainty, particularly the influence of interface rigidity uncertainty, is ignored, the rigidity performance of the mechanical structural part under actual working conditions (assembly constraint) cannot be judged, and the performance is further used as an evaluation index to optimally design the structural parameters.
Disclosure of Invention
The technical problem to be solved by the embodiment of the invention is to provide an interface rigidity optimization design method considering uncertain factors. The mechanical structure can be optimally designed according to structural parameters under the influence of uncertainty factors.
In order to solve the above technical problem, an embodiment of the present invention provides an interface stiffness optimization design method considering uncertainty factors, including the following steps:
the method comprises the following steps: establishing an integral assembly finite element model of the optimized mechanical structural part under the actual working condition, wherein the integral assembly finite element model comprises the optimized mechanical structural part and other mechanical structural parts having an assembly constraint relation with the optimized mechanical structural part;
step two: selecting design parameters, uncertainty parameters and uncertainty models of the optimized mechanical structural part, and determining the value range of the design parameters and the change boundary of the uncertainty parameters and the models;
step three: finite element simulation based on design parameters, uncertainty parameters, and model sampling. In order to reasonably obtain a design point for optimizing the rigidity of the mechanical interface, accurately and completely reflect the performance of the rigidity of the mechanical interface as much as possible and reduce the number of the design points, different sampling methods can be selected according to specific conditions, such as a sampling mode of an orthogonal test and a sampling mode of a Latin hypercube;
step four: and optimizing the interface design scheme and rigidity. The part comprises the establishment of a relation model between various factors and interface rigidity based on the existing results (simulation results and experimental results), the optimization of the interface rigidity and the design of a corresponding interface design scheme;
step five: and (4) experimental verification and result analysis of the design scheme. Modeling is carried out again according to the optimal design parameters in the fourth step, and the test piece is processed and manufactured according to the requirements of the simulation test to carry out a verification test;
step six: and correcting an optimization result and feeding back a design scheme. When the experimental result has a large error with the prediction result, correcting the optimization result by adopting modes such as Kalman filtering and the like, and feeding the result back to the third part for establishing the model; if the requirement is met, the result is the optimal solution.
Further, the uncertainty model in the second step refers to an uncertainty model of the contact stiffness of the mechanical interface joint surface, which may be obtained through existing data or experiments.
The essence of obtaining an uncertainty model is to divide the actual model containing the rough surface into: an ideal model with the same length and an equivalent contact system with a thickness-free and rigid interface. Normal stiffness K of ideal model1Can be obtained by experiment and finite element analysis, the normal rigidity of the practical model containing the rough surface is K, and the rigidity of the non-thickness combination surface is K2。
K、K1And K2Satisfies the following relation, and the normal stiffness of the actual model of the rough surface can be obtained by using the following formulaK：
Figure 142686DEST_PATH_IMAGE001
。
Further, in the third step, finite element simulation based on design parameters, uncertainty parameters and model sampling is performed. A multi-layer test design is included for the design parameters as well as the uncertainty parameters and models.
Since different parameter types are involved: design parameters and uncertainty parameters and models. For this purpose, a multi-layer experimental design mode is adopted, firstly aiming atiA design parameter is sampled and divided intomGroup testing, then considering design parameters for each groupjAn uncertainty parameter and model are sampled and divided intonAnd (4) carrying out group test. And finally, carrying out finite element simulation according to the designed test scheme and the test requirements, and obtaining a finite element simulation result.
Further, the fourth step includes the following steps:
in the part, a multi-stage optimization model considering design parameters, uncertainty parameters and the relation between the uncertainty model and the mechanical interface rigidity is established through analyzing the existing data. On the basis, the design of the mechanical interface design scheme and the optimization of the rigidity are carried out.
Constructing uncertainty parameter U for each set of design parametersPAnd uncertainty model UMAnd step two, solving a relation model between the finite element result d and the finite element result d to obtain the maximum value d of the rigidity corresponding to each group of design parametersM。
And f, Find: each set of design parameters corresponds to a maximum value of stiffness
Maximize：dM=g(UP,UM,d)
Subject to：
Figure 477852DEST_PATH_IMAGE002
Wherein
Figure 269091DEST_PATH_IMAGE003
、
Figure 347905DEST_PATH_IMAGE004
Is an uncertainty parameter UPThe upper and lower boundaries of (a) are,
Figure 845883DEST_PATH_IMAGE005
、
Figure 742164DEST_PATH_IMAGE006
is an uncertainty model UMUpper and lower boundaries of (1).
Constructed to design parameters DPA maximum value d of rigidity corresponding to each set of design parametersMThe relation model between the two, and the optimization and rigidity prediction of the interface design scheme, finally the optimal design method D of the interface under the minimum rigidity S is obtainedPCase;
find: design parameter with minimum mechanical interface rigidity
Minimize：S=f(DP,dM)
Subject to：
Figure 758049DEST_PATH_IMAGE007
Wherein
Figure 702871DEST_PATH_IMAGE008
、
Figure 55355DEST_PATH_IMAGE009
Is a design parameter DPThe upper and lower bounds of (c).
Further, the fifth step includes the following steps:
aiming at the optimization result in the step five, the interface design scheme is verified in an experimental verification mode. And taking the interface design scheme optimized in the step five as a design parameter, establishing a three-dimensional model, processing and manufacturing, carrying out an experiment according to the test requirements in the finite element simulation process, and finally comparing the experiment result with the optimization result. If the error value of the experimental result and the optimization result is within the allowable range, the optimization result is considered to be convergent, namely the interface design scheme is the optimal design scheme; if the error value of the two is larger than the allowable range, the optimization result needs to be corrected and fed back.
Further, the correction and feedback of the optimization result as described in step six are characterized in that the optimization result is corrected by using a kalman filter or other manners, the optimization result is continuously corrected through the experimental data in step five, and the design of the mechanical interface design scheme and the optimization of the stiffness are performed again by feeding the corrected design scheme back to step 4. The Kalman filtering feedback regulation comprises the following steps:
kalman filtering seeks to reduce the effects of noise using dynamic information about the target, resulting in a good estimate of the target's position. This estimate may be an estimate of the current target position (filtered), an estimate of the future position (predicted), or an estimate of the past position (interpolated or smoothed). The optimal estimation can also be seen as a filtering process, since the observed data includes the effects of noise and interference in the system.
It is assumed that both the measured and predicted noise is white noise that follows a gaussian distribution. And multiplying the probability densities of the two noises to obtain a new approximate expression true value of the probability density. The kalman filter model is as follows:
Figure 997903DEST_PATH_IMAGE010
in the formula: x (n) is a system state vector; u (n) is the drive input vector; w (n) is estimated noise; A. b is a constant coefficient matrix which is a state equation in a state space; z (n) is an observation (measurement) result; h (n) is an observation vector; v (n) is observation noise.
The entire process of kalman filtering can be described as the following 5 formulas:
1) state estimation
Figure 498154DEST_PATH_IMAGE011
2) Minimum mean square error matrix
Figure 918772DEST_PATH_IMAGE012
3) Kalman gain factor (weight)
Figure 391341DEST_PATH_IMAGE013
4) Modified estimated value (the first
Figure 567108DEST_PATH_IMAGE014
Time of day optimum estimate
Figure 492338DEST_PATH_IMAGE015
5) Minimum mean square error matrix
Figure 716646DEST_PATH_IMAGE016
The embodiment of the invention has the following beneficial effects: in the optimization design process of the structural parameters of the mechanical structural part, the influence of uncertain parameters, particularly the uncertainty of the rigidity of the joint surface of the interface, on the performance of the mechanical structure is considered, so that the whole optimization simulation is set to be more consistent with the actual situation; the performance (namely the structural mechanical performance of the whole assembly model) of the mechanical structural part under the actual working condition (assembly constraint and uncertainty factors) can be judged, and the performance is used as an optimization target performance evaluation index to carry out optimization design on the structural part parameters. The structural mechanical property of the integral assembly model is selected as an optimized target performance evaluation index, so that the actual working condition of the mechanical structural part is better met, and the parameter optimization design result of the mechanical structural part is more accurate and reliable.
Drawings
FIG. 1 is a schematic diagram of the design variables for structural parameter optimization of the present invention;
FIG. 2 is a final mechanical interface faying surface stiffness contact model;
FIG. 3 is a detailed flange plate optimization process;
FIG. 4a is the result of the optimization of design parameters A, B;
FIG. 4b is the result of the optimization of design parameters C, D;
FIG. 4c is the result of the optimization of design parameters A, E;
fig. 5 shows the variation trend of the experimental and optimized results.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings.
The invention is further explained by taking the optimized design of the structural parameters of the flange as an example and combining the attached drawings and the example.
The method comprises the following steps: establishing an integral assembly finite element model of the optimized mechanical structural part under the actual working condition, wherein the integral assembly finite element model comprises the mechanical structural part and other mechanical structural parts which have assembly constraint relation with the optimized mechanical structural part;
taking the optimization design of the structural parameters of the flange plate as an example, establishing an integral assembly finite element model of the optimized mechanical structural part under the actual working condition, wherein the integral assembly finite element model comprises the optimized mechanical structural part and other mechanical structural parts which have assembly constraint relation with the optimized mechanical structural part: an integral assembly finite element model which has an assembly constraint relation with the flange structural member is constructed based on commercial finite element software, the flange 1, the bolt 2 and the nut 3 are modeled by adopting a three-dimensional solid unit, and are made of 45 steel materials, the elastic modulus is 200GPa, the Poisson ratio is 0.3, and the density is 7850kg/m3Wherein the bolt and the nut are 8.8 grades.
And (3) boundary constraint: and fixing and restricting the end surface of one flange in the flange assembly.
The load is: in the invention, only the condition that the flange plate is loaded vertically downwards is considered, and the loading condition in other directions is not considered, the invention selects the load F =10KN in the vertical direction and the bolt pretightening force F0=10KN。
And finally, obtaining the integral assembly finite element model of the optimized mechanical structural part under the actual working condition.
Step two: selecting design parameters, uncertainty parameters and uncertainty models of the optimized mechanical structural part, and determining the value range of the design parameters and the change boundary of the uncertainty parameters and the models;
selecting structural parameter optimization design variables as shown in figure 1 according to the structural characteristics: the flange plate has the outer diameter D1, the nominal diameter D2 of the flange, the diameter D3 of the neck of the flange, the thickness H1 of the flange, the radius R of bolt hole distance and the diameter D of a bolt hole. The following parameters are selected as uncertainty parameters: the material density F, the elastic modulus G, the bolt pretightening force H and the equivalent elastic modulus I of the joint surface (obtained by experiments).
The optimization constraints defined according to the structural design parameters and the variation range of the uncertainty parameters are shown in tables 1 and 2,
table 1 design parameter value range table
Figure 840460DEST_PATH_IMAGE017
TABLE 2 uncertainty parameter value range Table
Figure 124811DEST_PATH_IMAGE018
And acquiring a mechanical interface joint surface rigidity contact model in an experimental mode.
Processing the test piece by using the material described in the step one, and processing two groups of cylindrical test pieces in total, wherein the first group of test pieces comprises the following steps: a cylindrical test piece with the diameter of phi 115 mm and the height of 100 mm; second group of test pieces: and two cylindrical test pieces with the diameter of phi 115 mm and the height of 50 mm are formed. And processing the contact end face of the test piece by using the same machine tool, the same cutter and the same processing parameters so as to ensure the consistency of the surface roughness of the processed end face.
Experimental equipment: the SHT4305 microcomputer is adopted to control the electro-hydraulic servo universal tester to apply load, and the measurement precision is 1N; the device for measuring the deformation of the test piece is a Y50/10-N electronic extensometer, and the measurement precision is 0.1 mu m; the detection system is a DCS-300 full-digital closed-loop measurement and control system.
The experimental process comprises the following steps: for each group of test pieces, firstly, an electronic extensometer is used for calibrating the test distance of the test pieces to be 50 mm, then, a load is applied to 10KN for a compression test, and the change rule of the interface joint surface rigidity along with the load is found.
The final mechanical interface joint surface stiffness contact model is shown in fig. 2.
Step three: finite element simulation based on design parameters, uncertainty parameters, and model sampling.
In order to reasonably obtain the design point of mechanical interface rigidity optimization, reflect the performance of flange interface rigidity as accurately and completely as possible and reduce the number of design points. With respect to the design parameters, uncertainty parameters, and model of the flange, finite element simulations are performed herein in the following manner.
Dividing the 5 design parameters into 32 groups of tests by using orthogonal tests, and then designing 30 groups of tests by using a sampling method of Latin hypercube by considering 6 uncertainty parameters and an uncertainty model for each group of design parameters;
l calculating the above by using ANSYS workbench finite element software. Thus for each set of design parameters, 30 sets of data on the uncertainty parameters and the effect of the model are obtained, which results in 960 sets of finite element simulation data.
Step four: and aiming at the optimization of interface design scheme and rigidity. The part comprises the establishment of a relation model between various factors and interface rigidity based on the existing results (simulation results and experimental results), the optimization of the interface rigidity and the design of a corresponding interface design scheme;
for the above design parameters, uncertainty parameters, and uncertainty models, the present study uses interval numbers to describe their parameter ranges. Through the analysis of the existing data, a multi-stage optimization model considering the design parameters, the uncertainty parameters and the relationship between the uncertainty model and the mechanical interface rigidity is established. On the basis, the rigidity of the mechanical interface is optimized.
Constructing uncertainty parameters for each set of design parameters
Figure 599654DEST_PATH_IMAGE019
And uncertainty model
Figure 627653DEST_PATH_IMAGE020
With the above finite element results
Figure 809236DEST_PATH_IMAGE022
The model is solved to obtain the maximum value of the rigidity corresponding to each group of design parameters
Figure 61226DEST_PATH_IMAGE023
Find: each set of design parameters corresponds to a maximum value of stiffness
Maximize：dM=g(UP,UM,d)
Subject to：UP=(F,G,H)；UM=I
Since the flange structure has 4 bolts in total, H = (H1, H2, H3, H4);
Figure 961049DEST_PATH_IMAGE024
，
Figure 589476DEST_PATH_IMAGE025
，
Figure 950532DEST_PATH_IMAGE026
constructed to design parameters DPA maximum value d of rigidity corresponding to each set of design parametersMOptimizing the design scheme of the interface to finally obtain the optimal design scheme of the interface with the minimum rigidity S;
find: design parameter with minimum mechanical interface rigidity
Minimize：S=f(DP,dM)（4）
Subject to：DP=(A,B,C,D,E)
16mm≤A≤28mm，36mm≤B≤42mm，12mm≤C≤18mm
38.5mm≤D≤42.5mm，E∈(8,10,12,14)
Wherein: dP= (a, B, C, D, E) 5-dimensional design vector, UP= (F, G, H) 6-dimensional uncertainty vector, A, B, C, D, E design parameter; F. g, H, I are uncertainty parameters, where H = (I1, I2, I3, I4); s = f (D)P,dM) Is an objective function.
The specific optimization process of the flange plate is shown in FIG. 3
Step five: and (4) experimental verification and result analysis of the design scheme. Modeling is carried out again according to the optimal design parameters in the fourth step, and the test piece is processed and manufactured according to the requirements of the simulation test to carry out a verification test;
in order to verify the accuracy of the method, modeling analysis is carried out again according to the optimal result obtained by the optimization. Also, using 45 # steel, the test piece was machined under certain machining conditions, and then subjected to a compression test with a load of 10KN to examine the deformation of the test piece. And comparing the experimental result with the optimized result. If the error value of the experimental result and the optimization result is within the allowable range, the optimization result is considered to be convergent, namely the interface design scheme is the optimal design scheme; if the error value of the two is larger than the allowable range, the optimization result needs to be corrected and fed back through Kalman filtering.
The following takes the first kalman filter as an example to specifically describe how to correct the optimization result through the experimental result. The result interval of the first optimization obtained by the optimization analysis and experiment is <5.3,0.65>, and the result interval of the first experiment is <5.65,0.75 >. The first kalman filtering process is as follows.
(1) The state value is shown by the formula (6)
Figure 311106DEST_PATH_IMAGE027
(2) The minimum mean square error of the equation (7)
Figure 698225DEST_PATH_IMAGE028
(3) From equation (8), the Kalman gain factor is
Figure 130343DEST_PATH_IMAGE029
(4) From equation (9), the modified estimated value
Figure 20939DEST_PATH_IMAGE030
(5) The minimum mean square error of the equation (10)
Figure 880310DEST_PATH_IMAGE031
The kalman filtering results are shown in table 3.
Figure 489146DEST_PATH_IMAGE032
Step six: and correcting an optimization result and feeding back a design scheme. When the experimental result and the prediction result have large errors, correcting the optimization result by adopting modes such as Kalman filtering and the like, and feeding the result back to the step for three purposes for establishing the model; if the requirement is met, the result is an optimal solution;
after the flange plate is optimized and corrected four times, the final optimization result is shown in fig. 4a, 4b and 4 c. Specific values of the final optimization results are shown in table 4.
TABLE 4 Final optimization results of the flanges
Figure 662639DEST_PATH_IMAGE033
The experimental and optimized results are compared as shown in table 4. By comparing the experimental result with the optimized result, the maximum deformation error between the finally obtained optimized result and the experimental result is within 5 percent; and compared with the deformation before the optimization, the deformation amount of the final experimental deformation is reduced by 12.7 percent compared with the maximum value of the deformation before the optimization. As shown in fig. 5, after observing the variation trend of the experimental result and the optimization result, the experimental result shows that the deformation of the flange plate has an obvious downward trend along with the optimization, the experimental result continuously approaches the optimization result, and the contact ratio between the experimental result and the result interval of the optimization result is higher and higher. This shows that the accuracy of the method is continuously improved with the continuous correction of the experimental results to the optimization results.
TABLE 5 comparison of experimental and optimization results
Figure 735637DEST_PATH_IMAGE034
The experimental result shows that after 4 times of feedback adjustment, the flange plate obtains a satisfactory result based on the interface rigidity optimization problem of interval uncertainty. The error between the final test result and the result of design optimization is less than 5%, and compared with the result before optimization, the rigidity of the result after optimization is improved by 12.7%, which shows that the rigidity performance of the flange plate can be effectively improved by the method provided by the invention.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims (4)

1. An interface rigidity optimization design method considering uncertain factors is characterized by comprising the following steps:
the method comprises the following steps: establishing an integral assembly finite element model of an optimized mechanical structural part under an actual working condition, wherein the integral assembly finite element model comprises the optimized mechanical structural part and the mechanical structural part which has an assembly constraint relation with the optimized mechanical structural part;
step two: selecting design parameters, uncertainty parameters and uncertainty models of the optimized mechanical structural part, and determining the value range of the design parameters, the uncertainty parameters and the change boundary of the models; the uncertainty model is an uncertainty model of the contact stiffness of the joint surface of the mechanical interface, and is obtained through existing data or experiments;
obtaining an actual model of the uncertainty model containing the rough surface is divided into: an equivalent contact system with an ideal model of the same length and an interface of no thickness and with stiffness, the normal stiffness K of said ideal model1From experiments and finite element analysis, the normal stiffness of the actual model containing the rough surface wasKThe rigidity of the non-thickness combination surface is K2；
K、K1And K2Satisfies the following relation, and obtains the normal stiffness of the actual model of the rough surface by using the following formulaK：
Figure 93637DEST_PATH_IMAGE001
；
Step three: finite element simulation sampled according to the design parameters, the uncertainty parameters and the uncertainty model;
step four: aiming at the optimization of an interface design scheme and rigidity, the method comprises the steps of establishing a relation model between various factors and the interface rigidity according to the existing results, optimizing the interface rigidity and designing the corresponding interface design scheme;
step five: carrying out experimental verification and result analysis on the design scheme, modeling again according to the optimal design parameters in the step four, processing and manufacturing the test piece according to the requirements of the simulation test, and carrying out a verification test;
step six: correcting an optimization result and feeding back a design scheme, when an experimental result has a large error with a prediction result, correcting the optimization result by adopting Kalman filtering, and feeding back the corrected result to the establishment of the uncertainty model; if the requirement is met, the result is the optimal solution.
2. The method for optimally designing interface rigidity considering uncertain factors according to claim 1, wherein the step three comprises adopting a multilayer experimental design mode aiming at design parameters and multilayer experimental design of uncertain parameters and models, and firstly aiming at design parameters and uncertain parameters and modelsiA design parameter is sampled and divided intomGroup testing, then considering design parameters for each groupjAn uncertainty parameter and model are sampled and divided intonAnd (4) performing a group test, and finally performing finite element simulation according to the designed test scheme and the test requirements to obtain a finite element simulation result.
3. The method for optimally designing interface rigidity according to the uncertain factors of claim 1, wherein the fourth step comprises the following steps:
establishing a multi-stage optimization model considering design parameters, uncertainty parameters and the relation between the uncertainty model and the mechanical interface rigidity by analyzing the existing data, and designing a mechanical interface design scheme and optimizing the rigidity;
for each set of design parametersNumber, construct with uncertainty parameter UPAnd uncertainty model UMAnd step two, solving a relation model between the finite element result d and the finite element result d to obtain the maximum value d of the rigidity corresponding to each group of design parametersM；
Constructed to design the parameters DPA maximum value d of rigidity corresponding to each set of design parametersMAnd optimizing and predicting the rigidity of the interface design scheme by using a relation model between the two, and finally obtaining the optimal design scheme of the interface under the minimum rigidity S.
4. The method for optimally designing the rigidity of the interface in consideration of the uncertain factors as claimed in claim 3, further comprising the steps of establishing a three-dimensional model by taking the optimal design scheme of the interface as design parameters, processing and manufacturing the three-dimensional model, carrying out experiments according to test requirements in a finite element simulation process, finally comparing experimental results with optimized results, and if error values of the experimental results and the optimized results are within an allowable range, considering that the optimized results are convergent, namely the design scheme of the interface is the optimal design scheme; if the error value of the two is larger than the allowable range, the optimization result needs to be corrected and fed back.
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