接头柔度参数化概念车身建模及其改进PSO算法的优化应用
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摘要
本文首先根据车身结构接头的特性及提取原则,建立了一种角接弹簧-刚梁简化接头模型,并通过算例验证了此模型的正确性和有效性;其次,以某车型为例建立了车身简化模型,并对模型分别进行静刚度分析和低阶模态分析,通过与HYPERWORKS软件建立的详细模型对比,结果表明本文建立的车身简化模型可以较准确地描述详细车身性能;随后,建立了车身简化模型优化问题的数学模型,直接对单元的力学特性进行优化;此外,提出一种基于正交试验设计和模拟退火思想的改进PSO算法——OPSO算法,并通过测试函数和10杆桁架结构算例验证本文提出OPSO算法的可行性和有效性。
最后,将本文提出的OPSO算法应用于包含梁单元、板单元和接头单元的概念车身结构中,分别进行静力学和频率优化,优化结果表明:OPSO算法可在有限次迭代中找出满足全部约束条件的优化结果,且与标准PSO算法相比结果精度更好,寻优效率更高,从而证明了OPSO方法对解决工程实际优化问题是着实有效的。
The concept design which is about the car properties, outline and inner decorations, is used to describing the car’s commissioning in the future. It is used to analyzing and optimizing the body structure, choosing the type of the body structure, defining structure parameters, calculating modal response and so on. It’s hard to remedial the design defects in the concept design, so this step is very important in the whole design. The concept design can shorten the period of the whole design, decrease the blindness of the design and improve efficiency. Also, it can determine 70% of the whole cost in the end of this step leading to more reliable results.
Establishing a simplified model of the body structure correctly is very important in the study and the difference between the simplified models is the joints. As it is used to be the intersection of loading-carrying members, the joints are the key part of the body structure. Since modeling a joint is a complex process, it’s necessary to find an accurate but simple modeling method of joint. If we don’t take it care, it will bring about the reduction of joint stiffness, low NVH properties, the increase of the stress and strain level, as well as the decrease of fatigue life. So it is significant to study the principle of joint design and quick establishment of mathematical model.
Not only the exact body simplified structure, but also the weight reduction and high stiffness should be considered. Now it has become one of the hotspots. The traditional mathematical model is hard to solve large practical engineering problem with massive elements and variables. Therefore, establish correct mathematical model and find a way to solve large optimization problems are worth to do.
This paper researches about the concept car body structure with the aim at establishing the simplified joint model quickly and exactly. Also, optimize the concept car body composed of beam elements, plate elements and joint elements, and all of the optimization is based on the software“CAE analysis and optimization of the concept body structure”proposed in our laboratory. Finally realize the process of CAE analysis step by step.
The paper mainly does the following work:
1) The method of extracting joints, the principle of establishing joints detailed models, the flexibility and mechanical properties are discussed in this paper. Take Joint C as an example to calculate the errors of simplified models in nine conditions. The terms“characteristic direction”and“characteristic system”are defined and used to deal with the coupling phenomenon between different rotation degrees. Finally, the validity of the simplified model is proved.
2) According to different processing methods of joints in body structure, this paper establishes simplified body model with detailed joints(Model 1), one with rigid joints(Model 2) and one withΔ-rotational spring and rigid beam joint(Model 3). Finally, compare the results of the three simplified body models under bending and tensional conditions in order to discuss joints’effect on the whole body stiffness.
3) Body structure optimization aims at weight reduction and high stiffness. The design variables contain the sectional area, the bending inertia moment, the twisting inertia moment of beam elements, sheet thickness of plate elements and joint stiffness. The traditional method is used to transform the mechanical characteristic parameters into geometric parameters. In this method, the variation of the inertia moment has no effect on the objective of weight, and only relates with the strain energy. Therefore, under the action of minimal strain energy, the inertia moments are respectively the upper bound of each restriction interval, and such results do nothing to the optimization. In order to solve this problem, we transform the objective functions into the restrictions and so the mechanical characteristic parameters can be optimized directly.
4) Because body structure optimization is a multiple objective problem with massive variables, the traditional optimization method can not get the optimal solution. So after comparing the features of several improved PSO methods, this paper proposes an improved PSO method named OPSO method to solve this problem. The main idea of OPSO method is the initialization of particles based on orthogonal experiments, and also combined with the theory of simulated annealing. Some acceptance criteria e can be established in order to accept new solutions whereΔE < e. Larger value of inertia weight is good to avoid local minimum as well as smaller value is good to convergence. The best way to find global minimum is to get high ability of exploration in the primer and high ability of convergence later. The OPSO method adjusts the value of inertia weight adaptively.
5) As we know, the OPSO method distributes the initial particles by orthogonal experiments. A general orthogonal table can only solve the problems with no more than 20 factors under 2 to 5 levels. However, it only can be found in existing references and not suitable for complex problems. The orthogonal tables proposed in this paper can solve the problems with more than 2000 factors under 2 to 15 levels at least and the amount of experiments in orthogonal experiments is up to 3000. Furthermore, more large orthogonal tables can be constructed if they are required.
6) According to calculating the text function and 10-bar truss structure, the feasibility and effectiveness of the OPSO method has been proved. Finally, the OPSO method is applied to the concept car body structure composed of beam elements, plate elements and joint elements. Then statics optimization and dynamics optimization has been done. Compared with the optimal solutions respectively solved by the OPSO method and standard PSO method, the results solved by the OPSO method is more optimal and effectively in finite iterations. And they also satisfy the constraint conditions. So the OPSO method has the ability to solve the practical problems well.
最后,将本文提出的OPSO算法应用于包含梁单元、板单元和接头单元的概念车身结构中,分别进行静力学和频率优化,优化结果表明:OPSO算法可在有限次迭代中找出满足全部约束条件的优化结果,且与标准PSO算法相比结果精度更好,寻优效率更高,从而证明了OPSO方法对解决工程实际优化问题是着实有效的。
The concept design which is about the car properties, outline and inner decorations, is used to describing the car’s commissioning in the future. It is used to analyzing and optimizing the body structure, choosing the type of the body structure, defining structure parameters, calculating modal response and so on. It’s hard to remedial the design defects in the concept design, so this step is very important in the whole design. The concept design can shorten the period of the whole design, decrease the blindness of the design and improve efficiency. Also, it can determine 70% of the whole cost in the end of this step leading to more reliable results.
Establishing a simplified model of the body structure correctly is very important in the study and the difference between the simplified models is the joints. As it is used to be the intersection of loading-carrying members, the joints are the key part of the body structure. Since modeling a joint is a complex process, it’s necessary to find an accurate but simple modeling method of joint. If we don’t take it care, it will bring about the reduction of joint stiffness, low NVH properties, the increase of the stress and strain level, as well as the decrease of fatigue life. So it is significant to study the principle of joint design and quick establishment of mathematical model.
Not only the exact body simplified structure, but also the weight reduction and high stiffness should be considered. Now it has become one of the hotspots. The traditional mathematical model is hard to solve large practical engineering problem with massive elements and variables. Therefore, establish correct mathematical model and find a way to solve large optimization problems are worth to do.
This paper researches about the concept car body structure with the aim at establishing the simplified joint model quickly and exactly. Also, optimize the concept car body composed of beam elements, plate elements and joint elements, and all of the optimization is based on the software“CAE analysis and optimization of the concept body structure”proposed in our laboratory. Finally realize the process of CAE analysis step by step.
The paper mainly does the following work:
1) The method of extracting joints, the principle of establishing joints detailed models, the flexibility and mechanical properties are discussed in this paper. Take Joint C as an example to calculate the errors of simplified models in nine conditions. The terms“characteristic direction”and“characteristic system”are defined and used to deal with the coupling phenomenon between different rotation degrees. Finally, the validity of the simplified model is proved.
2) According to different processing methods of joints in body structure, this paper establishes simplified body model with detailed joints(Model 1), one with rigid joints(Model 2) and one withΔ-rotational spring and rigid beam joint(Model 3). Finally, compare the results of the three simplified body models under bending and tensional conditions in order to discuss joints’effect on the whole body stiffness.
3) Body structure optimization aims at weight reduction and high stiffness. The design variables contain the sectional area, the bending inertia moment, the twisting inertia moment of beam elements, sheet thickness of plate elements and joint stiffness. The traditional method is used to transform the mechanical characteristic parameters into geometric parameters. In this method, the variation of the inertia moment has no effect on the objective of weight, and only relates with the strain energy. Therefore, under the action of minimal strain energy, the inertia moments are respectively the upper bound of each restriction interval, and such results do nothing to the optimization. In order to solve this problem, we transform the objective functions into the restrictions and so the mechanical characteristic parameters can be optimized directly.
4) Because body structure optimization is a multiple objective problem with massive variables, the traditional optimization method can not get the optimal solution. So after comparing the features of several improved PSO methods, this paper proposes an improved PSO method named OPSO method to solve this problem. The main idea of OPSO method is the initialization of particles based on orthogonal experiments, and also combined with the theory of simulated annealing. Some acceptance criteria e can be established in order to accept new solutions whereΔE < e. Larger value of inertia weight is good to avoid local minimum as well as smaller value is good to convergence. The best way to find global minimum is to get high ability of exploration in the primer and high ability of convergence later. The OPSO method adjusts the value of inertia weight adaptively.
5) As we know, the OPSO method distributes the initial particles by orthogonal experiments. A general orthogonal table can only solve the problems with no more than 20 factors under 2 to 5 levels. However, it only can be found in existing references and not suitable for complex problems. The orthogonal tables proposed in this paper can solve the problems with more than 2000 factors under 2 to 15 levels at least and the amount of experiments in orthogonal experiments is up to 3000. Furthermore, more large orthogonal tables can be constructed if they are required.
6) According to calculating the text function and 10-bar truss structure, the feasibility and effectiveness of the OPSO method has been proved. Finally, the OPSO method is applied to the concept car body structure composed of beam elements, plate elements and joint elements. Then statics optimization and dynamics optimization has been done. Compared with the optimal solutions respectively solved by the OPSO method and standard PSO method, the results solved by the OPSO method is more optimal and effectively in finite iterations. And they also satisfy the constraint conditions. So the OPSO method has the ability to solve the practical problems well.
引文
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