CN114154371A - Multi-objective optimization method for reinforced gearbox based on response surface method - Google Patents
Multi-objective optimization method for reinforced gearbox based on response surface method Download PDFInfo
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Abstract
The invention provides a multi-objective optimization method for a reinforced gearbox based on a response surface method. The method comprises the following steps: drawing a reducer model, wherein the reducer model comprises an upper box cover and a lower box body, and different numbers of rib shells are distributed on the box body; initializing design variables and parameters of the rib shell; inputting the whole size parameter of the gearbox as a target function, and setting a constraint condition; generating a design point through experimental design, and optimizing the model by using the constructed response surface to generate a response surface model; establishing a mathematical model of a multi-objective optimization problem to obtain a Pareto optimal solution of multi-objective optimization; after constraint conditions and a plurality of objective functions are set, setting an intelligent optimization algorithm and optimizing parameters of the algorithm; and judging the optimization result and the constraint condition. The method provides the optimal solution of multi-objective optimization, namely the final size parameter according to different optimal solution comparison results. The optimization method has higher practicability and economy.
Description
Technical Field
The invention relates to the technical field of design of a reinforced gearbox, in particular to a multi-objective optimization method for the reinforced gearbox based on a response surface method.
Background
In the practical use of the gear box, in order to reduce the adverse effects such as abnormal sound and uneven local stress generated by vibration, the inherent characteristics and working conditions of mechanical products are changed by adopting a stiffened plate structure mode, and the method gradually becomes a low-cost and high-benefit method. The strengthening method by reasonably adding the rib plates is widely applied to the following steps: the fields of large-scale ship machinery, aerospace, automobiles and the like. It generally has the advantages of light weight, strong bearing capacity, high supporting capacity and the like. The use of webs, although accumulating a great deal of experience in the mechanical field, has been followed by a number of new problems, such as: in order to change the rib plates increased by local ultimate stress, if the thin rib plates are used as stress-bearing parts to relieve load, the phenomenon of deformation and even fracture often occurs, so that the effect of relieving stress is lost.
Disclosure of Invention
According to the technical problems provided by the method, a multi-objective optimization method for the reinforced gearbox based on the response surface method is provided. The invention adopts the proxy model to replace the real finite element calculation, not only can save the design time, but also does not need complete calculation because the approximate value is only calculated through the response surface in the analysis design space, and the invention has shorter time and higher modification simplicity degree for subsequent redesign modules such as model modification, target function change and the like. The technical means adopted by the invention are as follows:
a multi-objective optimization method for a reinforced gearbox based on a response surface method comprises the following steps:
step 4, generating a design point through experimental design, and optimizing the model by using the constructed response surface to generate a response surface model;
step 5, establishing a mathematical model of the multi-objective optimization problem to obtain a Pareto optimal solution of the multi-objective optimization;
step 6, setting constraint conditions and a plurality of objective functions, and then setting an intelligent optimization algorithm and optimizing parameters of the algorithm;
and 7, judging the optimization result and the constraint condition, if so, outputting the optimization result, and if not, returning to the step 2.
Further, in the step 1, drawing a model entity based on Solidworks software, and carrying out parameterization setting on all design variables in advance; and importing the drawn model into Ansys workbench to perform finite element calculation and response surface optimization.
Further, the optimal design model meets the requirement of light weight, and the function expression of the optimal design problem is as follows:
in the formula: f is an objective function; m is the total mass of the model; vDiIs a design variable; vDLAnd VDUUpper and lower limits for each design variableAnd a1 is the mass of the model.
Furthermore, in the optimization design, the model has the primary function of bearing dynamic and static loads, and the maximum stress of the model can be ensured not to exceed the product of the allowable stress and the safety factor when the peak load is ensured; secondly, in order to ensure that the deformation amount under the working condition does not exceed a certain limit and avoid the interference phenomenon of workpieces, the equivalent stress and the total deformation are selected as target functions, and on the basis, in order to avoid the resonance of parts, the first-order natural frequency is improved to the maximum level within the allowable range so as to ensure the overall dynamic performance.
Further, the optimization result comprises the height of the rib plate of the upper box body, the thickness of the large bearing seat of the lower box body and the thickness of the small bearing seat of the lower box body.
Further, in the step 4, a kriging interpolation method is adopted to construct the response surface.
Further, in the step 4, when the response surface method is used for performing the optimized approximate calculation, the fitting degree of the response surface is also checked, and the check index includes a certainty coefficient R2Maximum relative residual, root mean square error
The three are respectively:
wherein n is the number of sample points, yi、
The actual measured value, the actual measured average value and the predicted value of the response surface are respectively, and corresponding inspection parameters are obtained through a fitting degree optimal selection table.
Further, the mathematical model of the established multi-objective optimization problem is as follows:
min y＝f(x)＝[f1(x)，f2(x)，...，fn(x)]
n＝1，2，...，N
s.t.gi(x)≤0 i＝1，2，...，m
hj(x)＝0 j＝1，2，...，k
X＝[x1，x2，...，xd，...，xD]
xd_min≤xd≤xd_max d＝1，2，...，D
in the formula: x is a vector of a D-dimensional design variable; y is the vector of the multi-dimensional objective function, fi(x) The number of the ith objective function is N, and the total number of the objective functions is N; gi(x) The ith inequality constraint is less than or equal to 0; h isj(x) 0 is the jth equality constraint; x is a design variable design set domain; x is the number ofd_min、xd_maxIs a feasible domain boundary.
Further, in the step 6, based on the NSGA-II variant algorithm MOGA, the local optimal solution trap is avoided from being trapped, and a global optimal solution is searched. The algorithm obtains a generation filial generation population by an initial population and using three basic processes of selection, hybridization and mutation of a genetic algorithm, continuously selects new individuals to form a parent population by combining a parent and the filial generation, and finally outputs the optimal individuals to finally obtain an ideal solution meeting the optimization target.
Further, the iterative calculation criterion is: and when 70% of samples are distributed on the front edge of the Pareto solution set optimization, ending the iteration.
According to the invention, the whole structure parameters of the gear box are input, a plurality of optimal correlation degree parameters are obtained through correlation analysis, and the numerical values of the optimal correlation degree parameters are optimized through a subsequent algorithm program, so that the strength characteristic and the light weight design in the gear box design process are enhanced. The method provides the optimal solution of multi-objective optimization, namely the final size parameter according to different optimal solution comparison results. Finite element analysis verifies that the optimized result shows that the structural strength under the size meets the design requirement, the maximum stress value is reduced by 2.16 percent compared with the initial value, the structural mass is reduced by 0.21Kg, and the optimization method has higher practicability and economy.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a finite element structural model;
FIG. 3 is a cross section of a unit cell;
FIG. 4 is a simulation result before and after single-target optimization; wherein (a) the equivalent stress of the workpiece before optimization for a single target; (b) the workpiece equivalent stress after the single-target optimization; (c) optimizing the total deformation of the front workpiece for a single target; (d) the total deformation of the workpiece after optimization for a single target.
FIG. 5 is a simulation result after multi-objective optimization; wherein (a) is the equivalent stress of the workpiece after multi-objective optimization; (b) the total deformation of the workpiece after multi-objective optimization.
FIG. 6 is a solid model after the optimization method.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to carry out multi-objective optimization on a gear box, the overall structure parameters of the gear box are input through the algorithm program, a plurality of optimal correlation degree parameters are obtained through correlation analysis, and the numerical values of the optimal correlation degree parameters are optimized through a subsequent algorithm program, so that the strength characteristic and the light weight design in the gear box design process are enhanced.
As shown in fig. 1, the present invention comprises the steps of:
step 4, generating a design point through experimental design, and optimizing the model by using the constructed response surface to generate a response surface model;
step 5, establishing a mathematical model of the multi-objective optimization problem to obtain a Pareto optimal solution of the multi-objective optimization;
step 6, setting constraint conditions and a plurality of objective functions, and then setting an intelligent optimization algorithm and optimizing parameters of the algorithm;
and 7, judging the optimization result and the constraint condition, if so, outputting the optimization result, and if not, returning to the step 2.
The multi-objective optimization algorithm program researched by the invention is realized by numerical simulation of sample points. The model entity is drawn based on Solidworks software, parameterization setting is carried out on all design variables in advance, finite element calculation and response surface optimization are carried out for the next step of importing an Ansys workbench, and a bedding is made. The bearing seat structure is divided into two parts, namely a front bearing seat structure and a rear bearing seat structure, and the bearing seats mainly bear circumferential force and radial force due to the fact that the inner parts of the bearing seats are straight toothed spur gears. Because the size of the whole model is not large, the size of the global seed is 3cm, and the medium grid quality is obtained. The whole body adopts a tetrahedral grid. The bottom of the structure is designed to be fixed by bolts, and in order to optimize the simulation design computing environment, the boundary condition of the structure adopts a fixing mode that the bottom surface is completely fixedly connected and has no degree of freedom. The stress directions of the model are respectively pointing to the center of a circle of the bearing seat and tangent to the circle, the magnitude of the stress directions is 20000N and 50000N, and the local maximum stress of the model can be guaranteed not to exceed the yield limit of the model.
The optimized input parameters of the invention are the overall dimension parameters of the gearbox, including the characteristic parameters of the upper box body and the lower box body, and the essence of the group is a group of variables which can be expressed by a column vector:
x＝(x1，x2，...，xn)T
the order of the components in the vector may be arbitrary, and the design variables may be altered according to specific operational requirements. Once a certain arrangement of vectors is specified, any one of the vectors can be regarded as a "design", a space composed of n design variables as coordinates is called a design space, and each "design" can be represented by a vector end point of one design variable in the design space, and becomes a design point. The structural parameters of the model can be divided into overall dimension parameters, upper and lower box body rib plate parameters, the size of the borne load and the like. One possible design requires that certain design constraints, called constraints, be met. Considering the practical engineering problem, the problem can be roughly divided into two types according to the different kinds of constraint conditions: performance constraints and side constraints. Due to the consideration of installation difficulty and manufacturability technology, the size of the original model is limited within a certain range, and the phenomena of incapability of assembling, interference with other accessories and the like are avoided. If only the allowed size range is constrained, it is also referred to as a side constraint.
In all the optimization feasible designs, some designs with obvious advantages are found in the method, and usually have some better characteristics than other designs, if the characteristics can be expressed in the form of a set of design variables, a calculation function can be generated, and conversely, the calculation function can be optimized to obtain the needed design. This function that can be used to optimize the design is an objective function, and can be used to evaluate the merits of the design as f (x) to emphasize its correlation with the design parameters. For a single-variable optimization problem, in order to optimize a certain performance, generally, optimization is performed on an objective function composed of variables, so that a satisfactory result is obtained, but in some design problems, two or more objective functions are often encountered, and jointly determine a certain property of a product, which is a multi-objective optimization problem. The objective function of the method can be mass, length, stress, strain, volume and the like or other actual performance indexes such as power, yield and the like, if the objective function is a function consisting of n variables, a function image of the objective function can be described only in an n + 1-dimensional space, so that in order to reflect the change condition of the objective function, a representation method of an isosurface of the objective function is often adopted, and the mathematical expression of the representation method is as follows:
f(x)＝c
after design parameters, constraint conditions and an objective function are defined, the optimal design scheme can be expressed in a mathematical form, and as for the optimal design model in the invention, the weight reduction requirement is met, the optimal design model is optimized on the basis that the mass of the model is not increased, the mass of the model is estimated to be 391.21kg, and the functional expression of the optimal design problem is as follows:
in the formula: f is the objective function (deformation, stress); m is the total mass of the model; vDiIs a design variable; vDLAnd VDURespectively, the upper and lower limits of each design variable. For the model in the patent, the first effect is to bear the dynamic and static loads, ensure that the maximum stress does not exceed the product of the allowable stress and the safety factor when the peak load is ensured, and secondly, in order to ensure that the deformation amount does not exceed a certain limit under the working condition and avoid the interference phenomenon of the workpiece, the equivalent stress and the total deformation are selected as target functions, on the basis, in order to avoid the resonance of the part, the first-order natural frequency is increased to the maximum level within the allowable range so as to ensure the integral dynamic and static loadThe state property.
Through the relevance analysis of the algorithm program, a group of optimal design parameters in the embodiment obtained for optimizing the gearbox are respectively as follows: the height of the rib plate of the upper box body, the thickness of the large bearing seat of the lower box body and the thickness of the small bearing seat of the lower box body are taken as output parameters. The following is a multi-objective optimization design flow designed to calculate the optimal solution for the set of output parameters.
For the design point sampling method of the multi-objective optimization, the DOE method is selected. Design Of Experiment (DOE for short) is a method for researching and processing the relation between multiple factors and response variables. The method reasonably selects test conditions, arranges tests, and analyzes test data to establish a functional relation between response and factors or find an overall optimal improvement scheme. The most basic test algorithm program is a full factor test method, the required test times are the most, and other test algorithm programs aim at reducing the test times, such as a partial factor test, an orthogonal test, a uniform test and the like. Because the calculation amount of the direct optimization analysis process is too large and good suggestions cannot be provided for design, the model is often optimized by using a response surface method, and the main current method for constructing the response surface is through DOE experimental design. When the model is optimized in terms of structural performance indexes, the relevance and the corresponding relation between the size design parameters and the mechanical performance parameters of the model are realized by constructing a response surface mathematical model, and the fitting of the mathematical model replaces a real experimental result so as to reduce the design time and the number of design schemes. Aiming at the model, an optimized Space-Filling Design (optimized Space-Filling Design) is adopted, and an optimized Space-Filling algorithm program can allow the adoption of fewer experimental times to provide necessary effective information, reduce the error of a response surface and have better Space Filling capacity, so that the sampling method is more suitable for generating complex response surfaces, such as response surfaces generated based on Kriging, Non-Parametric Regression or Neural Networks. The principle of optimizing the space filling design is to fit each dimension of the coordinate space in the n-dimensional design space
k∈[1,n]Evenly divided into m intervals, and each interval is denoted as
i∈[1,m]. And randomly selecting m test points to ensure that only one factor exists in each horizontal direction, so as to form a design space with n-dimensional space and m sample numbers, and increasing the sample density to ensure that the filling optimization space degree is higher. The basic idea of using the response surface method in the invention is to express an implicit function by approximately constructing a polynomial with an explicit expression form. Essentially, the response surface method is a set of statistical methods that are used to find the best response value that takes into account variations or uncertainties in the input variable values.
According to the method, a response surface is constructed by adopting a Kriging interpolation method, and the method is based on a statistical mode, and performs optimal design and unbiased estimation on a variable in a design space from the relevance and variability of an optimized quantity. The response surface is a multi-dimensional interpolation function, the output is also a polynomial, and the common influence factors of local and global can be considered at the same time, so Kriging can carry out interpolation between DOE points. The mathematical expression of the correspondence between the input variables and the system response can be written as:
Output＝f(inputs)+z(inputs)
where f is a full quadratic polynomial, i.e., the global design space; z is a special term, i.e. the model local bias; the deviation also needs to satisfy the following characteristics:
E[δ(x)]＝0
Var[δ(x)]＝σ2
Cov[δ(xi),δ(xj)]＝σ2RT[R(xi,xj)]
in the formula: delta (x) is an objective function expression; e is periodInspection; sigma2Is the variance; cov is covariance; RT is a symmetric correlation matrix; r (x)i，xj) Is a functional relationship between the sampling points xi and xj.
When the response surface method is adopted for carrying out optimized approximate calculation, the fitting degree of the response surface is necessary to be checked, the situation that the error is too large and the practical significance is lost is avoided, and common check indexes are as follows: a certainty Coefficient R2 (best value of 1); maximum Relative Residual (best 0%); root Mean Square Error (Root Mean Square Error, optimum 0), which is expressed as:
in the formula: n is the number of sample points, yi、
The actual measured value, the actual measured average value and the predicted value of the response surface are respectively. The corresponding test parameters are obtained from a Goodness of fit preference table (Goodness OfFit).
Different from single-target optimization in the previous research method, although both the single-target optimization and the multi-target optimization are composed of three elements of design variables, constraint conditions and target functions, the multi-target optimization aims to find the optimal solution capable of meeting a plurality of target functions, and the optimization result often conflicts among the target functions and is sometimes difficult to get away, and a mathematical model for generally establishing the multi-target optimization problem is as follows:
min y＝f(x)＝[f1(x)，f2(x)，...，fn(x)]
n＝1，2，...，N
s.t.gi(x)≤0 i＝1，2，...，m
hj(x)＝0 j＝1，2，...，k
X＝[x1，x2，...，xd，...，xD]
xd_min≤xd≤xd_max d＝1，2，...，D
in the formula: x is a vector of a D-dimensional design variable; y is the vector of the multi-dimensional objective function, fi(x) The number of the ith objective function is N, and the total number of the objective functions is N; gi(x) The ith inequality constraint is less than or equal to 0; h isj(x) 0 is the jth equality constraint; x is a design variable design set domain; x is the number ofd_min、xd_maxIs a feasible domain boundary.
From the above mathematical model, the multi-objective optimization problem is different from the single-objective optimization problem in essence, that is: when single-target optimization is carried out, the obtained different solutions can be conveniently compared with each other, and are completely ordered; the multi-objective optimization is vector optimization, so that the magnitude of values cannot be compared between solution sets, and the comparison between any two solutions is very complex and semi-ordered, which is a difficult point of the multi-objective optimization problem. However, in the multi-objective optimization scheme, the optimization result of some design variables is expected by the actual engineering, and even if the optimization result is not the optimal solution of all objective functions, the design has guiding significance in the actual design, so that the Pareto optimal solution (or non-inferior solution) of the multi-objective optimization can be obtained. The solution method of multi-objective optimization is many and can be mainly classified as: (1) directly solving to select better results; (2) solving and processing methods, namely, properly adjusting the solving process of the multi-objective optimization; (3) a coordination curve method for solving a design problem that a plurality of design objectives contradict each other; (4) and the target planning method is used for optimizing based on the expected value of each target function. By utilizing a Pareto optimal solution set concept, a mutation operator is changed, the overall parameters of the helicopter are optimized by adopting an MOGA algorithm with an elite strategy, and the following points are pointed out: the algorithm can search a Pareto solution set with higher fitness; the multi-objective genetic algorithm is suitable for solving the multi-objective optimization problem and can improve the quality and the distribution uniformity of the solution.
After constraint conditions and a plurality of objective functions are set, the method avoids trapping in a local optimal solution trap and searches for a global optimal solution based on an NSGA-II variant algorithm MOGA. The algorithm obtains a generation filial generation population by an initial population and using three basic processes of selection, hybridization and mutation of a genetic algorithm, continuously selects new individuals to form a parent population by combining a parent and the filial generation, and finally outputs the optimal individuals to finally obtain an ideal solution meeting the optimization target.
The method comprises the following steps: in an ANSYS Workbench optimization module, the initial population number is set to be 1000, the maximum iteration number is 20, the cross probability is set to be 0.7, the convergence stability is 0.02, the maximum candidate point number is 3, and a simulation program is established. The iterative calculation criteria are: and when 70% of samples are distributed on the front edge of the Pareto solution set optimization, ending the iteration. Finally, after 20 iterations, a group of Pareto optimal solution sets are obtained, and finally, the optimization results in table 4 are obtained.
Compared with the prior art, the method obtains the optimization result after the agent model is adopted through multi-objective optimization. The results of the multi-objective versus single-objective comparison confirm the effectiveness and utility of the proposed optimization method. And the mechanism of optimizing the model is discussed. In addition, numerical design shows that the fitting degree after multi-objective optimization is enhanced through correlation analysis.
In the numerical calculation example, a reducer model is drawn based on Solidworks software, design variables are parameterized and are led into an Ansys workbench for finite element calculation and response surface optimization, and the model is shown in FIG. 2. The parameters of the retarder material are shown in table 1. The size of the global seed is 3cm, the tetrahedral mesh suitable for the body in any shape is selected for division, the tetrahedral mesh is divided into 36278 tetrahedral meshes and 66876 nodes, the optimization design requirement is met, the quality of the mesh is judged to be good after quality detection is carried out on the mesh, and the simulation calculation requirement is met. The overall size parameters of the gearbox are input as a target function, and as the number of parameters contained in the model is large, in order to reduce unnecessary calculation amount, optimization sensitivity analysis is firstly carried out, parameters which are not high in relevance with the structural strength of the model are eliminated, output parameters are obtained, and then a multi-objective optimization algorithm program is carried out, so that the final multi-objective optimization output parameter range of the gearbox is obtained as shown in table 2.
TABLE 1 physical Properties of the carbon structural steels
TABLE 2 Primary optimization design variables
And optimizing the model by constructing a response surface through DOE (design of engineering) experiments, and realizing the relevance and the corresponding relation between the size design parameters and the mechanical property parameters of the model so as to reduce the design time and the number of design schemes. And by optimizing the space filling design sampling diagram, performing the DOE experiment by adopting the sampling method, and solving and calculating parameter combinations of different design variables to form a sample matrix, 15 sample points in total as shown in the following table are obtained, as shown in table 3.
Table 3 model structure experimental design results
From the mathematical model, the multi-objective optimization problem and the single-objective optimization problem have an essential difference, namely, when the single-objective optimization is carried out, different solutions obtained can be conveniently compared with each other and are ordered; and because the multi-objective optimization is vector optimization, the solution sets cannot only compare the numerical values, and are semi-ordered. However, in the multi-objective optimization scheme, the optimization result of some design variables is expected by practical engineering, and the design variables have guiding significance in practical design even if not the optimal solution of all objective functions. The invention adopts a variant algorithm MOGA based on NSGA-II to avoid trapping in a local optimal solution trap and search a global optimal solution. The algorithm obtains a generation filial generation population by an initial population and using three basic processes of selection, hybridization and mutation of a genetic algorithm, continuously selects new individuals to form a parent population by combining a parent and the filial generation, and finally outputs the optimal individuals to obtain an ideal solution meeting the optimization target. The parameter settings are shown in fig. 3.
And finally, carrying out simulation calculation on the examples according to the existing model and algorithm, and briefly analyzing the optimization result. According to optimization requirements, optimization targets (equivalent stress maximum, total deformation maximum and quality) are respectively calculated to obtain respective optimal solutions, and finally, single-target solution results are compared with multi-target solution results of the same algorithm to analyze the superiority and inferiority of the multi-target optimization results, so that the influence degree of optimization of a plurality of target functions on a certain single-target function limit optimization result is researched. The single-target simulation results are shown in fig. 4, the multi-target optimization results are shown in fig. 5, the optimization results of the design variables are shown in table 4, the comparison results are shown in table 5, and the final optimized solid model is shown in fig. 6.
TABLE 4 model optimized dimensional parameters
TABLE 5 comparison of Single-target and Multi-target optimization results
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (10)
1. A multi-objective optimization method for a reinforced gearbox based on a response surface method is characterized by comprising the following steps:
step 1, drawing a reducer model, wherein the reducer model comprises an upper box cover and a lower box body, and different numbers of rib shells are distributed on the box body;
step 2, initializing design variables and parameters of the rib shell;
step 3, inputting the whole size parameter of the gear box as a target function, and setting a constraint condition;
step 4, generating a design point through experimental design, and optimizing the model by using the constructed response surface to generate a response surface model;
step 5, establishing a mathematical model of the multi-objective optimization problem to obtain a Pareto optimal solution of the multi-objective optimization;
step 6, setting constraint conditions and a plurality of objective functions, and then setting an intelligent optimization algorithm and optimizing parameters of the algorithm;
and 7, judging the optimization result and the constraint condition, if so, outputting the optimization result, and if not, returning to the step 2.
2. The multi-objective optimization method for the stiffened gearbox based on the response surface method as recited in claim 1, wherein in the step 1, drawing of a model entity is performed based on Solidworks software, and parameterization setting is adopted for all design variables in advance; and importing the drawn model into Ansys workbench to perform finite element calculation and response surface optimization.
3. The multi-objective optimization method for the reinforced gearbox based on the response surface method as claimed in claim 1, wherein the optimization design model meets the requirement of light weight, and the function expression of the optimization design problem is as follows:
in the formula: f is an objective function; m is the total mass of the model; vDiIs a design variable; vDLAnd VDUThe upper and lower limits of each design variable are respectively, and a1 is the quality of the model.
4. The multi-objective optimization method for the stiffened gearbox based on the response surface method as claimed in claim 1, wherein in the optimization design, the model has the primary functions of bearing dynamic and static loads and ensuring that the maximum stress does not exceed the product of allowable stress and safety factor when the peak load is ensured; secondly, in order to ensure that the deformation amount under the working condition does not exceed a certain limit and avoid the interference phenomenon of workpieces, the equivalent stress and the total deformation are selected as target functions, and on the basis, in order to avoid the resonance of parts, the first-order natural frequency is improved to the maximum level within the allowable range so as to ensure the overall dynamic performance.
5. The multi-objective optimization method for the stiffened gearbox based on the response surface method according to claim 1, wherein the optimization results comprise the height of a rib plate of the upper gearbox, the thickness of a large bearing seat of the lower gearbox and the thickness of a small bearing seat of the lower gearbox.
6. The multi-objective optimization method for the stiffened gearbox based on the response surface method as recited in claim 1, wherein in the step 4, a kriging interpolation method is adopted to construct the response surface.
7. The multi-objective optimization method for the stiffened gearbox based on the response surface method as claimed in claim 1 or 6, wherein in the step 4, when the response surface method is adopted for the approximate calculation of the optimization, the fitting degree of the response surface is also checked, and the check index comprises a certainty coefficient R2Maximum relative residual, root mean square error
The three are respectively:
wherein n is the number of sample points, yi、
The actual measured value, the actual measured average value and the predicted value of the response surface are respectively, and corresponding inspection parameters are obtained through a fitting degree optimal selection table.
8. The multi-objective response surface method-based optimization method for a stiffened gearbox of claim 1, wherein the mathematical model of the established multi-objective optimization problem is as follows:
miny＝f(x)＝[f1(x),f2(x),…,fn(x)]
n＝1,2,…,N
s.t.gi(x)≤0 i＝1,2,…,m
hj(x)＝0 j＝1,2,…,k
X＝[x1,x2,…,xd,…,xD]
xd_min≤xd≤xd_max d＝1,2,…,D
in the formula: x is a vector of a D-dimensional design variable; y is the vector of the multi-dimensional objective function, fi(x) The number of the ith objective function is N, and the total number of the objective functions is N; gi(x) The ith inequality constraint is less than or equal to 0; h isj(x) 0 is the jth equality constraint; x is designA variable design set domain; x is the number ofd_min、xd_maxIs a feasible domain boundary.
9. The multi-objective optimization method for the stiffened gearbox based on the response surface method as claimed in claim 1, wherein in the step 6, the variant algorithm MOGA based on NSGA-II is used for avoiding trapping in a local optimal solution trap and searching for a global optimal solution, a generation offspring population is obtained by using three basic processes of selection, hybridization and variation of a genetic algorithm through an initial population, new individuals are continuously selected to form a parent population by combining the parent and the offspring, and finally, the optimal individuals are output, and finally, an ideal solution meeting the optimization objective is obtained.
10. The multi-objective response surface method-based optimization method for a stiffened gearbox of claim 9, wherein the iterative calculation criteria is: and when 70% of samples are distributed on the front edge of the Pareto solution set optimization, ending the iteration.
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