CN117235902A - Section optimization method based on full-parameterized vehicle body mathematical model - Google Patents
Section optimization method based on full-parameterized vehicle body mathematical model Download PDFInfo
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Abstract
The application belongs to the technical field of automobile body design, and particularly relates to a section optimization method based on a full-parameterized automobile body mathematical model, which comprises the following steps: s1: constructing a truss type vehicle body structure geometric simplified model; s2: decomposing a truss type vehicle body structure geometric simplified model into a plurality of chain beam structures, establishing a full-parameterized chain beam structure mathematical model by adopting a transfer matrix method, and constructing a calculation expression of deformation of a loading point in a loading direction and vehicle body bending rigidity; s3: taking the minimum mass of the vehicle body as an objective function and the bending rigidity of the vehicle body as a constraint condition, and establishing an optimization model related to geometric dimension parameters of the chain beam structure; s4: and obtaining the optimal geometric dimension parameter of the cross section of the vehicle body under the action of the current loading point based on a random gradient genetic algorithm, solving the optimal vehicle body performance under the whole vehicle frame beam, reducing the vehicle body mass, improving the vehicle body rigidity and realizing the light-weight design of the vehicle body.
Description
Technical Field
The application belongs to the technical field of automobile body design, and particularly relates to a section optimization method based on a full-parameterized automobile body mathematical model.
Background
Both the basic structure and the main performance of a vehicle body depend on the results of conceptual design, and it is important to study the design model and design method of the vehicle body concept, which are easy to modify and calculate. In the traditional method, the optimization of the cross section of the vehicle body in the conceptual design process of the vehicle body is often realized by comparing the cross section of the vehicle body with the cross section of the same type, and the optimization direction and the optimization basis are not clear, so that the optimization efficiency of the cross section design of the vehicle body is low, and the time consumption is long.
At present, finite element analysis is widely applied to the design of vehicle body institutions, is based on the finite element principle, combines with a vehicle body concept design analysis tool CAE, and performs CAE network analysis and verification on a vehicle body and a cross-section structure, so that an unreasonable structure needs to be improved and re-verified for analysis, and the operation is repeated until the whole analysis process meets the standard.
However, the concept design of the vehicle body has the problems of large data input amount, long design development period and slow scheme optimization process, the constructed CAE model has no reusability, and meanwhile, the design is changed by involving a large amount of parameter changes, so that the calculated amount is increased, and a large amount of manpower and material resources are required to be input for verifying the structure and the performance of the vehicle body, so that the cost is increased.
Disclosure of Invention
The application provides a section optimization method based on a full-parameterized vehicle body mathematical model, which constructs a truss type vehicle body structure geometric simplified model into a chain beam structure mathematical model which is easy to modify and calculate quickly, has no grid, is simplified and is full-parameterized by utilizing a transmission matrix, constructs a functional relation of deformation of a loading point in a loading direction relative to a vehicle body section geometric dimension parameter and a vehicle body bending stiffness calculation expression, constructs an optimization model relative to the vehicle body section geometric dimension parameter by taking the minimum vehicle body mass as an objective function and the vehicle body bending stiffness as a constraint condition, and further adopts a random gradient genetic algorithm to solve and obtain optimal vehicle body performance so as to reduce the vehicle body mass, improve the vehicle body stiffness and realize the light-weight design of the vehicle body.
A section optimization method based on a full-parameterized vehicle body mathematical model comprises the following steps:
s1: constructing a truss type vehicle body structure geometric simplified model;
s2: decomposing a truss type vehicle body structure geometric simplified model into a plurality of chain beam structures, establishing a full-parameterized chain beam structure mathematical model by adopting a transfer matrix method, and constructing a calculation expression of deformation of a loading point in a loading direction and vehicle body bending rigidity;
s3: taking the minimum mass of the vehicle body as an objective function and the bending rigidity of the vehicle body as a constraint condition, and establishing an optimization model related to geometric dimension parameters of the chain beam structure;
s4: and obtaining optimal geometric dimension parameters of the cross section of the vehicle body under the action of the current loading point based on a random gradient genetic algorithm, and solving the optimal vehicle body performance under the whole vehicle frame beam.
The truss type vehicle body structure geometric simplified model is constructed into a grid-free, simplified and fully parameterized chain beam structure mathematical model which is easy to modify and calculate quickly by utilizing a transmission matrix, a functional relation of deformation of a loading point in a loading direction relative to geometric dimension parameters of a vehicle body section and a vehicle body bending stiffness calculation expression are constructed, an optimization model is constructed relative to the geometric dimension parameters of the vehicle body section by taking the vehicle body mass as a minimum objective function and the vehicle body bending stiffness as a constraint condition, and then a random gradient genetic algorithm is adopted to solve and obtain optimal vehicle body performance so as to lighten the vehicle body mass, improve the vehicle body stiffness and realize the light-weight design of the vehicle body.
Further, in the step S1, the process of constructing the truss type vehicle body structure geometric simplified model specifically includes:
s11: selecting a main bearing beam of a vehicle body based on a truss-type vehicle body;
s12: based on the main bearing beam of the vehicle body, simplifying the main bearing beam to establish a truss type vehicle body structure geometric simplified model;
s13: based on a truss type vehicle body structure geometric simplified model, main feature points and main feature data of a vehicle body structure are extracted according to the shape of a vehicle body of a passenger vehicle, and coordinates of each main feature point are recorded in a global coordinate system.
Further, in the step S2, the process of decomposing the truss type vehicle body structure geometric simplified model into a plurality of chain type beam structures, establishing a full-parameterized chain type beam structure mathematical model by adopting a transmission matrix method, and constructing the deformation of the loading point in the loading direction and the calculation expression of the vehicle body bending rigidity specifically includes the following steps:
s21: decomposing the truss type vehicle body structure geometric simplified model into a plurality of parts, and decomposing each part into a chain type beam structure with a plurality of framework beams;
s22: based on a single chain beam structure, a transmission matrix equation of the single chain beam structure is obtained by adopting a transmission matrix method;
s23: obtaining unknown load vectors at coupling points in each chain beam structure, constructing corresponding boundary conditions, and obtaining a mathematical model of a single chain beam structure;
s24: based on unknown load vectors of all coupling points in each part, constructing a functional relation of the coupling points, and calculating a state vector of any node by combining a mathematical model of a corresponding chain beam structure;
s25: based on the coupling relation and the topological relation of each chained beam structure, a functional relation of the deformation of the loading point in the loading direction relative to the geometric dimension parameter of the vehicle body section and a calculation expression of the bending rigidity of the vehicle body are constructed.
Further, in S22, the calculation expression of the transfer matrix equation of the single chain beam structure is:
；
in the method, in the process of the application,is->Beam unit number in individual chain beam structure +.>,/>Is->Leftmost beam unit number in the individual chain beam structure +.>Is->The rightmost beam unit number in the individual chain beam structure +.>，/>The total number of the chain beam structures in the part; />Is->A coordinate conversion matrix of each beam unit; />Is->A field matrix of individual beam elements; />Is->Dot transfer matrix of left and right state vectors of each beam unit>、/>、/>Node->External load at the location; />Is->The rightmost state vector in the individual beam cell; />Is->The leftmost state vector in the beam element.
Further, in S23, the mathematical model for obtaining the single chain beam structure according to the boundary condition is as follows:
in the method, in the process of the application,is->Mechanical property set of individual beam unit sections, +.>；/>The deformation of the loading point in the loading direction is used;
wherein,for the cross-sectional area of the beam unit, the expression is calculated as:
；
the moment of inertia of the beam unit section in the Y-axis direction is calculated as:
；
the moment of inertia of the beam unit section in the X-axis direction is calculated as:
；
in the method, in the process of the application,、/>、/>the wall thickness, the wall height and the wall width of the beam unit section respectively form geometric dimension parameters of the beam unit section>I.e. +.>。
Further, in S25, the process of constructing a functional relation of the deformation of the loading point in the loading direction with respect to the geometric dimension parameter of the vehicle body section and a calculation expression of the bending stiffness of the vehicle body based on the coupling relation and the topological relation of the chain beam structures specifically includes the following steps:
s251: constructing a functional relation between the deformation of the loading point in the loading direction and the geometric dimension parameter set of the vehicle body section;
deformation of loading point in loading directionParameter set of geometric dimension of cross section of vehicle body +.>The functional relation of (2) is:
；
wherein,is->The set of geometrical parameters of the individual beam unit sections, i.e.>；
S252: the method comprises the steps of constructing a calculation expression of the bending rigidity of the vehicle body, and specifically:
；
in the method, in the process of the application,applying a force in a loading direction for the loading point; />Is the bending rigidity of the vehicle body under the current whole vehicle skeleton chain.
Further, in the step S3, an optimization model of geometric parameters of the chain beam structure is constructed by taking the vehicle body mass minimization as an objective function and the vehicle body bending stiffness as a constraint condition, and the mathematical expression is as follows:
；
；
in the method, in the process of the application,the weight of the vehicle body; />Is->The length of the individual beam units; />The density of the aluminum alloy material of the automobile body; wherein (1)>、/>Are all known amounts; />The maximum value of the deformation of the loading point in the loading direction; />、/>Respectively the minimum value and the maximum value of the wall height of the cross section of the beam unit; />、/>Respectively the minimum value and the maximum value of the wall width of the cross section of the beam unit; />、/>Is the minimum value and the maximum value of the wall thickness of the cross section of the beam unit.
Further, in the step S4, the process of obtaining the optimal geometric parameters of the vehicle body section under the action of the current loading point based on the random gradient genetic algorithm specifically includes the following steps:
s41: initializing a population;
s411: determining population sizeHybridization probability, mutation probability;
s412: determining parameters of local search;
s413: setting an orthogonal test and randomly generating an initialization population;
s42: constructing an intermediate population;
s421: based on the initialized population, all Pareto optimal solutions are obtained and stored to a set outside the initialized populationIn (a) and (b);
s422: at the collectionIs selected randomly->The Pareto optimal solutions form a current population;
s423: selection among the current populationHybridizing and mutating male parent and producing +.>A new individual;
s424: adding the new individuals based on the generated individuals to the current population to form an intermediate population;
s43: generating a new generation population;
carrying out local search on the intermediate population by utilizing the corrected SPSA algorithm to generate a new generation population substitution initialization population;
s44: obtaining optimal geometric parameters;
judging whether the new generation population meets the shutdown criterion;
s441: when the new generation population meets the shutdown criterion, terminating evolution, outputting all the generated Pareto optimal solutions and the current new generation population, and obtaining the optimal geometric parameters of the vehicle body section under the action of the current loading point;
s442: when the newly generated population does not satisfy the convergence condition, the flow goes to S42.
The beneficial effects of the application are as follows:
the application constructs a truss type vehicle body structure geometric simplified model into a chain type beam structure mathematical model which is easy to modify and calculate quickly, has no grid, is simplified and is fully parameterized, constructs a functional relation of deformation of a loading point in a loading direction relative to a vehicle body section geometric dimension parameter and a vehicle body bending stiffness calculation expression, constructs an optimization model relative to the vehicle body section geometric dimension parameter by taking the vehicle body mass as an objective function and the vehicle body bending stiffness as a constraint condition, and further adopts a random gradient genetic algorithm to solve and obtain the optimal vehicle body performance so as to lighten the vehicle body mass, improve the vehicle body stiffness and realize the light design of the vehicle body; compared with the traditional finite element analysis method, the modeling time can be reduced, the calculation efficiency is improved, and the cost is saved.
Drawings
FIG. 1 is a flow chart of the present application;
FIG. 2 is a schematic diagram of a body skeleton of an electric vehicle;
FIG. 3 is a schematic illustration of a simplified geometric model of a truss body structure;
FIG. 4 is a schematic diagram of the overall skeleton construction relationship;
FIG. 5 is a schematic view of a cross-section of a beam unit;
FIG. 6 is a schematic diagram of a model of a stochastic gradient genetic algorithm;
FIG. 7 is an exploded view of the construction of a simplified geometric model of a truss body structure in example 2;
FIG. 8 is an exploded view of the left side chain beam structure of example 2;
fig. 9 is a schematic view of a skeleton chain structure 1 in example 2;
FIG. 10 is a schematic view of a skeleton chain structure 2 in example 2;
FIG. 11 is a schematic view of a skeleton chain structure 3 in example 2;
FIG. 12 is a schematic view showing convergence of the random gradient genetic algorithm in example 2 to obtain the optimal geometric parameters of the cross section of the vehicle body;
FIG. 13 is a schematic view of a finite element model of the bending stiffness of the vehicle body in example 2;
fig. 14 is a schematic view showing a finite element model simulation structure of the bending rigidity of the vehicle body in example 2.
Reference numerals:
1. left side wall; 2. a right side wall; 3. and a cross beam.
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
It is noted that various aspects of the embodiments are described below within the scope of the following claims. It should be apparent that the aspects described herein may be embodied in a wide variety of forms and that any specific structure and/or function described herein is merely illustrative. Based on the present disclosure, one skilled in the art will appreciate that one aspect described herein may be implemented independently of any other aspect, and that two or more of these aspects may be combined in various ways. For example, an apparatus may be implemented and/or a method practiced using any number of the aspects set forth herein. In addition, such apparatus may be implemented and/or such methods practiced using other structure and/or functionality in addition to one or more of the aspects set forth herein.
Furthermore, in the following description, specific details are provided for the purpose of providing a thorough understanding of the examples, and it will be apparent to one skilled in the art that the specific meaning of the terms described above in the present application will be practiced with specificity.
Example 1
FIG. 1 shows a cross section optimization method based on a full parameterized vehicle body mathematical model, wherein a truss type vehicle body structure geometric simplified model is constructed into a grid-free, simplified and full parameterized chain beam structure mathematical model which is easy to modify and calculate quickly by utilizing a transmission matrix, a functional relation of deformation of a loading point in a loading direction relative to a vehicle body cross section geometric dimension parameter and a vehicle body bending stiffness calculation expression are constructed, an optimization model is constructed relative to the vehicle body cross section geometric dimension parameter by taking the minimum vehicle body mass as an objective function and the vehicle body bending stiffness as a constraint condition, and then a random gradient genetic algorithm is adopted to solve and obtain optimal vehicle body performance so as to reduce the vehicle body mass, improve the vehicle body stiffness and realize the light design of the vehicle body. The method specifically comprises the following steps:
s1: constructing a truss type vehicle body structure geometric simplified model;
as shown in fig. 2 and 3, the process of constructing the truss type vehicle body structure geometric simplified model specifically includes:
s11: selecting a main bearing beam of a vehicle body based on a truss-type vehicle body;
s12: based on the main bearing beam of the vehicle body, simplifying the main bearing beam to establish a truss type vehicle body structure geometric simplified model;
s13: based on a truss type vehicle body structure geometric simplified model, main feature points and main feature data of a vehicle body structure are extracted according to the shape of a vehicle body of a passenger vehicle, and coordinates of each main feature point are recorded in a global coordinate system.
The method is characterized in that a beam with small influence on the performance of the vehicle body due to the arrangement of accessories such as batteries is not considered when a main bearing beam of the vehicle body is selected; meanwhile, when the truss type vehicle body structure geometric simplified model is built, a plurality of sections of straight beams are adopted for the curved beams to approximate.
S2: decomposing a truss type vehicle body structure geometric simplified model into a plurality of chain beam structures, establishing a full-parameterized chain beam structure mathematical model by adopting a transfer matrix method, and constructing a functional relation of deformation of a loading point in a loading direction relative to geometric dimension parameters of a vehicle body section and a calculation expression of vehicle body bending rigidity; the specific process comprises the following steps:
s21: decomposing the truss type vehicle body structure geometric simplified model into a plurality of parts, and decomposing each part into a chain type beam structure with a plurality of framework beams;
the truss type vehicle body structure geometric simplified model can be regarded as formed by coupling a plurality of chain type beam structures, as shown in fig. 4, the truss type vehicle body structure geometric simplified model is decomposed step by step from the whole to the part according to the principle of simplified design, a plurality of chain type beam structures with simpler forms can be obtained after the decomposition, mathematical models of the chain type beam structures are overlapped upwards in a layer-by-layer combination mode, and the chain type structures have coupling relations and corresponding boundary conditions.
S22: based on a single chain beam structure, a transmission matrix equation of the single chain beam structure is obtained by adopting a transmission matrix method;
the calculation expression of the transfer matrix equation of the single chain beam structure is as follows:
；
in the method, in the process of the application,is->Beam unit number in individual chain beam structure +.>,/>Is->Leftmost beam unit number in the individual chain beam structure +.>Is->The rightmost beam unit number in the individual chain beam structure +.>，/>The total number of the chain beam structures in the part; />Is->A coordinate conversion matrix of each beam unit; />Is->A field matrix of individual beam elements; />Is->Dot transfer matrix of left and right state vectors of each beam unit>、/>、/>Node->External load at the location; />Is->The rightmost state vector in the individual beam cell; />Is->The leftmost state vector in the beam element.
S23: obtaining unknown load vectors at coupling points in each chain beam structure, constructing corresponding boundary conditions, and obtaining a mathematical model of a single chain beam structure;
the mathematical model for obtaining the single chain beam structure according to the boundary conditions is as follows:
；
in the method, in the process of the application,is->Mechanical property set of individual beam unit sections, +.>；/>The deformation of the loading point in the loading direction is used;
wherein,for the cross-sectional area of the beam unit, the expression is calculated as:
；
the moment of inertia of the beam unit section in the Y-axis direction is calculated as:
；
the moment of inertia of the beam unit section in the X-axis direction is calculated as:
；
in the method, in the process of the application,、/>、/>the wall thickness, the wall height and the wall width of the beam unit section respectively form geometric dimension parameters of the beam unit section>I.e. +.>。
In an embodiment, the beam unit cross-sectional shape of the vehicle body approximates a thin-walled rectangular cross-section, as particularly shown in fig. 5.
S24: based on unknown load vectors of all coupling points in each part, constructing a functional relation of the coupling points, and calculating a state vector of any node by combining a mathematical model of a corresponding chain beam structure;
s25: based on the coupling relation and the topological relation of each chained beam structure, a functional relation of the deformation of the loading point in the loading direction relative to the geometric dimension parameter of the vehicle body section and a calculation expression of the bending rigidity of the vehicle body are constructed.
S251: constructing a functional relation between the deformation of the loading point in the loading direction and the geometric dimension parameter set of the vehicle body section;
deformation of loading point in loading directionWith the carBody section geometry parameter set +.>The functional relation of (2) is:
；
wherein,is->The set of geometrical parameters of the individual beam unit sections, i.e.>；
S252: the method comprises the steps of constructing a calculation expression of the bending rigidity of the vehicle body, and specifically:
；
in the method, in the process of the application,applying a force in a loading direction for the loading point; />Is the bending rigidity of the vehicle body under the current whole vehicle skeleton chain.
S3: taking the minimum mass of the vehicle body as an objective function and the bending rigidity of the vehicle body as a constraint condition, and establishing an optimization model related to geometric dimension parameters of the chain beam structure; the mathematical expression is as follows:
；
；
in the method, in the process of the application,the weight of the vehicle body; />Is->The length of the individual beam units; />The density of the aluminum alloy material of the automobile body; wherein (1)>、/>Are all known amounts; />The maximum value of the deformation of the loading point in the loading direction; />、/>Respectively the minimum value and the maximum value of the wall height of the cross section of the beam unit; />、/>Respectively the minimum value and the maximum value of the wall width of the cross section of the beam unit; />、/>Is the minimum value and the maximum value of the wall thickness of the cross section of the beam unit.
S4: and obtaining optimal geometric dimension parameters of the cross section of the vehicle body under the action of the current loading point based on a random gradient genetic algorithm, and solving the optimal vehicle body performance under the whole vehicle frame beam.
As shown in fig. 6, the process of obtaining the optimal geometric parameters of the vehicle body section based on the random gradient genetic algorithm specifically includes the following steps:
s41: initializing a population;
s411: determining population sizeHybridization probability, mutation probability;
s412: determining parameters of local searches；
S413: setting an orthogonal test and randomly generating an initialization population;
s42: constructing an intermediate population;
s421: based on the initialized population, all Pareto optimal solutions are obtained and stored to a set outside the initialized populationIn (a) and (b);
s422: at the collectionIs selected randomly->The Pareto optimal solutions form a current population;
s423: selection among the current populationHybridizing and mutating male parent and producing +.>
S424: adding the new individuals based on the generated individuals to the current population to form an intermediate population;
s43: generating a new generation population;
carrying out local search on the intermediate population by utilizing the corrected SPSA algorithm to generate a new generation population substitution initialization population;
s44: obtaining optimal geometric parameters;
judging whether the new generation population meets the shutdown criterion;
s441: when the new generation population meets the shutdown criterion, terminating evolution, outputting all the generated Pareto optimal solutions and the current new generation population, and obtaining the optimal geometric parameters of the vehicle body section under the action of the current loading point;
s442: when the newly generated population does not satisfy the convergence condition, the flow goes to S42.
Example 2
In the embodiment, a section optimization method based on a full-parameterized vehicle body mathematical model is provided, and is used for realizing a lightweight design of a vehicle body with optimal rigidity performance and minimum vehicle body mass.
Based on example 1, the constructed truss body structure geometric simplified model is decomposed into a plurality of parts. In the present embodiment, as shown in fig. 7, the constructed geometric simplified model of the truss type vehicle body structure is decomposed into three parts of a left side frame 1, a right side frame 2, and 11 cross members 3.
In this embodiment, left side wall 1 is selected as the subject to be studied and decomposed intoAnd the skeleton beams are numbered. As shown in fig. 8, the left side wall 1 is decomposed into 3 skeleton beams, i.e., each skeleton beam is numbered +.>，/>And marks the coupling point, the node number and the beam unit number of each skeleton beam, namely 17 nodes and 17 beam units. Wherein, skeleton roof beam 1, skeleton roof beam 2, skeleton roof beam 3 are chain beam structure.
As shown in fig. 9, among them, for the frame girder 1,
the transmission equation of the skeleton beam 1 is constructed, and the expression is as follows:
；
it can be seen that only the load column vectors at the coupling points, i.e. at nodes 1, 2, 6、/>、/>Is an unknown number.
The boundary conditions are as follows:
；
；
in the method, in the process of the application,is the leftmost state vector of the 1 st beam unit in the skeleton beam 1, +.>The state vector at the rightmost side of the 7 th beam unit in the skeleton beam 1; />、/>Force applied at nodes 0, 7, < >>Is another known parameter vector.
The transfer equation and boundary conditions of the above-described frame girder 1 are noted as:
；
similarly, as shown in fig. 10, with respect to the frame girder 2,
the transmission equation of the skeleton beam 2 is constructed, and the expression is as follows:
；
it can be seen that only the load column vectors at the coupling points, i.e. at nodes 1, 6, 9、/>、/>Is an unknown number.
The boundary conditions are as follows:
；
；
in the method, in the process of the application,is the leftmost state vector of the 8 th beam unit in the skeleton beam 2, +.>A state vector at the rightmost side of the 15 th beam unit in the framework beam 2; />、/>Force applied at nodes 1, 6, respectively, < >>Is another known parameter vector.
The transfer equation and boundary conditions of the above-described frame girder 2 are noted as:
；
similarly, as shown in fig. 11, with respect to the frame girder 3,
the transmission equation of the skeleton beam 3 is constructed, and the expression is as follows:
；
it can be seen that only the load column vectors at the coupling points, i.e. at nodes 2, 9、/>Is an unknown number.
The boundary conditions are as follows:
；
；
in the method, in the process of the application,is the leftmost state vector of the 16 th beam unit in the skeleton beam 3, +.>A state vector at the rightmost side of the 17 th beam unit in the skeleton beam 3; />、/>Force applied at nodes 2, 9, respectively, < >>Is another known parameter vector.
The transfer equation and boundary conditions of the above-described frame beam 3 are written as:
；
based on the above, it can be known that the left side wall 1 shares the nodes 1, 2, 6, 9 as coupling points, and the functional relation of all the coupling points is as follows:
；
in the method, in the process of the application,、/>the forces exerted at the joint 1 in the frame beams 2, 1, respectively, +.>、/>The forces exerted at the joints 2 in the skeleton beams 2, 3, respectively, +.>、/>The forces exerted at the joint 1 in the frame beams 2, 1, respectively, +.>、/>The forces at the node 1 in the skeleton beam 3 and the skeleton beam 2 are respectively applied; />、/>、/>、/>The coordinate transformation matrices of the 1 st, 2 nd, 6 th and 9 th beam units are respectively provided.
And the functional relation of all coupling points is recorded as:
；
the transfer equation, boundary condition and coupling point functional relation of the simultaneous skeleton beams are as follows:
；
the state vector of any node can be obtained.
And the transfer function of the skeleton beams of other parts of the vehicle body can be obtained by the same method, and the bending rigidity of the vehicle body under the whole vehicle skeleton chain can be obtained based on the coupling relation and the topological relation of each part.
Taking the left side wall as an example, as shown in fig. 9, a node 4 is set as a loading point, which has a vertically downward loading force, namely. I.e. the deformation of the loading point in the loading direction +.>And the geometric dimension parameter set of each beam unit section->The functional relation of (2) is:
；
the calculation expression of the bending rigidity of the vehicle body is as follows:
；
in this embodiment, the geometric parameters of the 17 beam unit sections forming the left side are selected as parameter variables, the mass minimization is an objective function, and the bending stiffness of the vehicle body is a constraint condition, and an optimization model of the geometric parameters of the chain beam structure is established, specifically:
；
；
for the single-objective optimization problem, solving a global optimal solution by adopting a random gradient genetic algorithm to obtain optimal geometric dimension parameters.
As shown in fig. 12, the convergence of the objective function shows that the optimal mass of the vehicle body is 0.052 ton, and the geometric parameters of the cross section of the optimized beam unit are shown in the following table.
Table 1 geometric parameters of the optimized beam unit section
；
Substituting the optimized geometric parameter results of the beam unit section into the deformation of the loading point in the loading directionIn the calculation expression of (a), namely:
；
in this embodiment, the left side wall 1 and the right side wall 2 are symmetrical parts, that is, the deformation of the right side wall 2 is the same as the deformation of the left side wall 1, so that the average deformation of the whole vehicle, that is, the deformation of the whole vehicle, can be represented by the deformation of the left side wall 1 under the loading action of the loading point loadingIs that。
The calculation expression of the bending rigidity of the vehicle body is as follows:
；
in the conventional method, as shown in fig. 13, finite element analysis is performed on a truss type vehicle body structure geometric simplified model, so that the displacement of loading points of a left side wall and a right side wall in the loading direction is respectively 0.456mm and 0.467mm, and the bending rigidity of the vehicle body obtained by the finite element analysis can be obtainedThe calculated expression of (2) is:
；
the simulation analysis results of the bending rigidity of the vehicle body in the finite element analysis are shown in fig. 14.
The comparison of the finite element analysis method and the method of the application can be known as follows: compared with a finite element analysis method, the method reduces the mass of the whole vehicle by 30%, increases the bending stiffness of the whole vehicle, ensures that the mass of the body of a colleague with the optimal stiffness performance of the whole vehicle is the lightest, and has shorter modeling time and higher calculation efficiency in the actual operation process.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present application. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the present application have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the application, and that variations, modifications, alternatives and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the application.
Claims (8)
1. A section optimization method based on a full-parameterized vehicle body mathematical model is characterized by comprising the following steps:
s1: constructing a truss type vehicle body structure geometric simplified model;
s2: decomposing a truss type vehicle body structure geometric simplified model into a plurality of chain beam structures, establishing a full-parameterized chain beam structure mathematical model by adopting a transfer matrix method, and constructing a functional relation of deformation of a loading point in a loading direction relative to geometric dimension parameters of a vehicle body section and a calculation expression of vehicle body bending rigidity;
s3: taking the minimum mass of the vehicle body as an objective function and the bending rigidity of the vehicle body as a constraint condition, and establishing an optimization model related to geometric dimension parameters of the chain beam structure;
s4: and obtaining optimal geometric dimension parameters of the cross section of the vehicle body under the action of the current loading point based on a random gradient genetic algorithm, and solving the optimal vehicle body performance under the whole vehicle frame beam.
2. The cross-section optimization method based on the full-parametric vehicle body mathematical model according to claim 1, wherein in S1, the process of constructing the truss type vehicle body structure geometric simplified model specifically comprises:
s11: selecting a main bearing beam of a vehicle body based on a truss-type vehicle body;
s12: based on the main bearing beam of the vehicle body, simplifying the main bearing beam to establish a truss type vehicle body structure geometric simplified model;
s13: based on a truss type vehicle body structure geometric simplified model, main feature points and main feature data of a vehicle body structure are extracted according to the shape of a vehicle body of a passenger vehicle, and coordinates of each main feature point are recorded in a global coordinate system.
3. The section optimization method based on the full-parameterized vehicle body mathematical model according to claim 1, wherein in S2, the process of decomposing the truss type vehicle body structure geometric simplified model into a plurality of chain beam structures, establishing the full-parameterized chain beam structure mathematical model by adopting a transfer matrix method, and constructing the deformation of the loading point in the loading direction and the calculation expression of the vehicle body bending stiffness specifically comprises the following steps:
s21: decomposing the truss type vehicle body structure geometric simplified model into a plurality of parts, and decomposing each part into a chain type beam structure with a plurality of framework beams;
s22: based on a single chain beam structure, a transmission matrix equation of the single chain beam structure is obtained by adopting a transmission matrix method;
s23: obtaining unknown load vectors at coupling points in each chain beam structure, constructing corresponding boundary conditions, and obtaining a mathematical model of a single chain beam structure;
s24: based on unknown load vectors of all coupling points in each part, constructing a functional relation of the coupling points, and calculating a state vector of any node by combining a mathematical model of a corresponding chain beam structure;
s25: based on the coupling relation and the topological relation of each chained beam structure, a functional relation of the deformation of the loading point in the loading direction relative to the geometric dimension parameter of the vehicle body section and a calculation expression of the bending rigidity of the vehicle body are constructed.
4. The cross-section optimization method based on the full-parametric vehicle body mathematical model according to claim 2, wherein in S22, the calculation expression of the transfer matrix equation of the single chain beam structure is:
；
in the method, in the process of the application,is->Beam unit number in individual chain beam structure +.>,/>Is->Leftmost beam unit number in the individual chain beam structure +.>Is->The rightmost beam unit number in the individual chain beam structure +.>，/>The total number of the chain beam structures in the part; />Is->A coordinate conversion matrix of each beam unit; />Is->A field matrix of individual beam elements; />Is->Dot transfer matrix of left and right state vectors of each beam unit>、/>、/>Node->External load at the location; />Is->The rightmost state vector in the individual beam cell; />Is->The leftmost state vector in the beam cell.
5. The cross-section optimization method based on the full-parametric vehicle body mathematical model according to claim 4, wherein in S23, the mathematical model for obtaining the single chain beam structure according to the boundary condition is:
；
in the method, in the process of the application,is->Mechanical property set of individual beam unit sections, +.>；/>The deformation of the loading point in the loading direction is used;
wherein,for the cross-sectional area of the beam unit, the expression is calculated as:
；
the moment of inertia of the beam unit section in the Y-axis direction is calculated as:
；
the moment of inertia of the beam unit section in the X-axis direction is calculated as:
；
in the method, in the process of the application,、/>、/>the wall thickness, the wall height and the wall width of the beam unit section respectively form geometric dimension parameters of the beam unit section>I.e. +.>。
6. The section optimization method based on the full-parametric vehicle body mathematical model according to claim 5, wherein in S25, the process of constructing a functional relation of the deformation of the loading point in the loading direction with respect to the geometric parameters of the vehicle body section and the calculation expression of the vehicle body bending stiffness based on the coupling relation and the topological relation of each chained beam structure specifically comprises the following steps:
s251: constructing a functional relation between the deformation of the loading point in the loading direction and the geometric dimension parameter set of the vehicle body section;
deformation of loading point in loading directionParameter set of geometric dimension of cross section of vehicle body +.>The functional relation of (2) is:
；
wherein,is->The set of geometrical parameters of the individual beam unit sections, i.e.>；
S252: the method comprises the steps of constructing a calculation expression of the bending rigidity of the vehicle body, and specifically:
；
in the method, in the process of the application,applying a force in a loading direction for the loading point; />Is the bending rigidity of the vehicle body under the current whole vehicle skeleton chain.
7. The cross-section optimization method based on the full-parametric vehicle body mathematical model as claimed in claim 6, wherein,
in the step S3, an optimization model of geometric dimension parameters of the chain beam structure is constructed by taking the vehicle body mass minimization as an objective function and the vehicle body bending rigidity as a constraint condition, and the mathematical expression is as follows:
；
；
in the method, in the process of the application,the weight of the vehicle body; />Is->The length of the individual beam units; />The density of the aluminum alloy material of the automobile body; wherein (1)>、/>Are all known amounts; />The maximum value of the deformation of the loading point in the loading direction; />、/>Respectively the minimum value and the maximum value of the wall height of the cross section of the beam unit; />、/>Respectively the minimum value and the maximum value of the wall width of the cross section of the beam unit; />、/>Is the minimum value and the maximum value of the wall thickness of the cross section of the beam unit.
8. The section optimization method based on the full-parametric vehicle body mathematical model according to claim 7, wherein in S4, the process of obtaining the optimal geometric parameters of the vehicle body section under the action of the current loading point based on the random gradient genetic algorithm specifically comprises the following steps:
s41: initializing a population;
s411: determining population sizeHybridization probability, mutation probability;
s412: determining parameters of local search;
s413: setting an orthogonal test and randomly generating an initialization population;
s42: constructing an intermediate population;
s421: based on the initialized population, all Pareto optimal solutions are obtained and stored to a set outside the initialized populationIn (a) and (b);
s422: at the collectionIs selected randomly->The Pareto optimal solutions form a current population;
s423: selection among the current populationHybridizing and mutating male parent and producing +.>A new individual;
s424: adding the new individuals based on the generated individuals to the current population to form an intermediate population;
s43: generating a new generation population;
carrying out local search on the intermediate population by utilizing the corrected SPSA algorithm to generate a new generation population substitution initialization population;
s44: obtaining optimal geometric parameters;
judging whether the new generation population meets the shutdown criterion;
s441: when the new generation population meets the shutdown criterion, terminating evolution, outputting all the generated Pareto optimal solutions and the current new generation population, and obtaining the optimal geometric parameters of the vehicle body section under the action of the current loading point;
s442: when the newly generated population does not satisfy the convergence condition, the flow goes to S42.
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| CN109255141A (en) * | 2017-12-18 | 2019-01-22 | 湖南大学 | A kind of body of a motor car forward direction conceptual design cross sectional shape optimization method |
| CN109344538A (en) * | 2018-10-30 | 2019-02-15 | 北京机械设备研究所 | A kind of body rail method in section design based on model validation technology |
| CN109800494A (en) * | 2019-01-14 | 2019-05-24 | 湖南大学 | Vehicle body forward direction conceptual design method based on thin wall section attribute |
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| CN109255141A (en) * | 2017-12-18 | 2019-01-22 | 湖南大学 | A kind of body of a motor car forward direction conceptual design cross sectional shape optimization method |
| CN109344538A (en) * | 2018-10-30 | 2019-02-15 | 北京机械设备研究所 | A kind of body rail method in section design based on model validation technology |
| CN109800494A (en) * | 2019-01-14 | 2019-05-24 | 湖南大学 | Vehicle body forward direction conceptual design method based on thin wall section attribute |
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