商用车车架拓扑优化轻量化设计方法研究
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摘要
众所周知,重型商用车的高水平振动将影响驾乘人员乘坐舒适性、运载货物的安全性和道路条件。汽车设计师极大关注汽车结构的优化设计,即提高商用车零部件的刚度和强度并减轻其结构重量。商用车零部件的轻量化设计变得越来越重要,已成为汽车工业重要研究的主题。用于汽车零部件轻量化设计的优化方法可分为三种：尺寸、形状和拓扑优化。
在尺寸优化中,其设计变量为材料参数(如弹性模量E和密度ρ)和尺寸参数(如杆梁的横截面尺寸、转动惯量,板的厚度,弹性支承刚度,两部件之间的联接刚度等)。在形状优化中,其设计变量为边界点的坐标,为计及网格的变化,有基向量法和摄动向量法两种方法可以应用。
拓扑优化用来确定结构的最优形状和质量分布。拓扑优化计算每一单元的材料特性并改变材料分布,在一定的约束条件下实现优化目标。目前人们已经认识到,与拓扑结构不变的优化方法相比,拓扑优化能极大地改进结构设计。因此,拓扑优化方法受到了极大的重视并取得了快速发展。例如,拓扑优化的均匀化方法和密度法已广泛应用于商用车的结构设计。在密度法中每一个单元仅有一个表示材料密度的变量。在均匀化法中,对2D壳单元有两个尺寸变量,对3D块体元有三个尺寸变量。每个单元的附加变量就是其方位角。
近年来,上述三种优化方法已成功用于商用车零部件优化设计并取得了很大的成功。然而,上述三种优化方法很难处理自由度和设计变量巨大的有限元模型优化问题。迄今为止,大多数结构优化研究仅限于处理商用车单一零部件的优化问题。很少见到有关在整车装配环境下零部件优化方面的研究报导。
应当说明的是,即使作用在整车上的载荷是已知的,但作用在每个零部件(如驾驶室、车架等)上的载荷多半是未知的。因为在整车装配环下各零部件之间存在弹性动态耦合关系,每个零部件的边界条件也很难精确给出。在此情况下,单一零部件的优化仅能给出不精确结果,还可能是毫无意义的结果。因此,即使单一零部件的设计是优化的,但整车装配环境下可能不再是优化的。也就是说,零部件的单独优化设计不等同于在整车装配环境下的优化。为了得到整车性能的优化,必须在整车装配环境下对零部件进行优化设计。为此目的,本文讨论在整车装配环境下商用车车架的轻量化优化设计问题,包括简化的建模方法和更有效的拓扑优化方法,解决在整车装配环境下,零部件大规模优化问题。本文完成的主要研究工作如下：
回顾并综述了结构优化方法在商用车零部件设计中的应用,论述了单一零部件的尺寸、形状和拓扑优化的国内外研究现状,指出了大规模优化问题遇到的困难以及本文要讨论的问题。
讨论了车架刚度对商用车乘坐舒适性和货物运输安全性的影响。由于不平道路激励引起的商用车高水平振动将影响乘坐舒适性和货物运输的安全性。为此,建立了整车有限元模型,分析了车架振动的加速度功率谱密度(PSD)均方根值(RMS)。为了说明车架刚度对乘坐舒适性和货物安全性的影响,给出了两种不同车架刚度在4种激励作用下驾驶员座椅地板和货厢中心的PSD和RMS。结果表明,当车架的刚度提高时,驾驶员座椅地板和货厢的PSD和RMS均较大的降低(频率为14-26Hz),从而改善了驾乘舒适性和货物安全性。此结论可为后续改进车架设计提供参考。
对商用车结构进行了拓扑优化及拓扑灵敏度分析。首先,回顾了结构静态位移和模态频率的灵敏度分析方法和拓扑优化方法(均匀化法和密度法)。然后,针对大规模结构优化所产生的困难,提出了商用车零部件结构优化的新概念和新方法。把结构在外载荷作用下的应变能定义为结构刚度的逆测度,提出了基于子结构单元和超单元的结构静态拓扑修改灵敏度的新概念,并给出了相应的结构静态拓扑优化的方法。把振动特征值λr定义为模态刚度,提出了子结构基于单元和超单元拓扑修改的模态刚度灵敏度的概念,同时建立了相应的动态拓扑优化方法。应用所提出方法,计算了商用车架的静态扭转和弯曲刚度灵敏和车架的扭转模态和弯曲的模态刚度灵敏度。这些拓扑修改灵敏度信息可用来改进车架的设计。
在整车装配环境下商用车车架的优化设计过程中。讨论了包括多体系统模拟、模态综合和结构模态缩减等结构响应分析方法,并指出,这些方法很难用来处理在整车装配环境下商用车的零部件的优化问题。针对大规模结构优化所带来的计算困难,提出了在整车装配环境下车架优化设计的新方法。应用主模态缩减和静态缩减方法,提出了基于整车分析的动态子结构缩减方法。在此基础上,建立了在整车装配环境下车架的动态拓扑优化方法。所提出的分析方法已应用于商用车车架的设计。结果表明,所提出的方法是正确的和有效的。在计算中,得到了车架中每个元件的模态刚度灵敏度及车架模态刚度对整车的贡献。
最后,给出了论文研究的主要结论以及商用车优化设计需要进一步研究的问题。
It is well known that the excessive levels of vibration in heavy trucks negatively affect driver comfortability, cargo safety and road condition. The automotive designers pay great attention to optimize the vehicle structure, that is, to increase stiffness and strength and to reduce weight. Weight optimizing structural components for heavy trucks is becoming more and more important.Therefore the structural optimization has been the subject of numerous studies and widely used to develop the truck. The optimal methods used in the automotive component design can be divided into three types, size, shape and topology optimization.
In the size optimization, the design variables are the used material parameters such as the elastic module(E) and density(ρ), and the size parameters such as the cross sectional area of a beam, bending moment of inertia, the thickness of a plate, an elastic support with spring stiffness and an connector of stiffness between two components, etc. In the shape optimization, the design variables are the coordinates of the boundary node points. In order to account for mesh changes, the basis vector approach and the perturbation vector approach, are used.
The topology optimization is used to affirm an optimized shape and material distribution for a given structure. The topology algorithm calculates the material properties for each element,and alters the material distribution to optimize the defined objective function under given constrains. It has been recognized that topology optimization can more greatly improve the structure design than fixed-topology optimization. Up to date significant progress has been made with a variety of different approaches. For example, homogenization or a density method has been widely used to solve the topological optimization problem of trucks. For the density method, each element has one variable representing its material density. For the homogenization method which is limited to 2-D and 3-D elements, there are two size variables for each shell element and three void size variables for each solid element, and an additional variable for each element is the void orientation angel.
In recent years, all three optimal methods described above have been widely applied to the component design of the truck and significant successes have been achieved. However, for the optimal problems of the large scale finite element model with a large number of degree of freedom and design variable, the difficulties arise and three methods described above are difficult to deal with. Up to date, most of the optimizations are limited to deal with the individual component of the truck. A few studies can be found for the optimization under full truck assembly.
It should be pointed out that even though the loads on the full truck are usually known, the loads on each component, such as cab, body and frame, are rarely known. Since there exist the elastic and dynamic coupling relations between components under the assembly environment of the truck, it is difficult to obtain the boundary conditions of each component. In this case, the optimization for the individual component may not only give inaccurate result but also may be meaningless, if exact loads and boundary conditions can not be given. As can be seen that even through the optimal design for the individual component is obtained, the design of full assembly truck may not be optimal, In other words, the optimization of the individual is not equal to the optimization of full assembly truck. Therefore, it is necessary to discuss the optimization of the component under full truck assembly environment in order to obtain the optimal performances of the full truck. To this end, this paper presents the optimization of the frame under full truck assembly environment including the simplified modeling and more effective topological optimal method for solving the large scale optimal problems of components under full truck assembly environment. The main contents of this paper are studied as following:
A review on the applications of structural optimal method to the component design of the truck is given. The state-of-the-arts of the size, shape and topological optimizations for the individual component of trucks is presented. The difficulties resulting from the large scale optimal problems of the structure and problems to be discussed in this paper are also given.
The effect of frame stiffness on the ride comfort and the cargo ride safety is discussed. As can be seen that excessive levels of vibration in commercial vehicles, due to excitation from the road irregularities, can lead to cargo damage and safety problems. Therefore a finite element model of full vehicle was established. The computation algorithm for acceleration power spectral density (PSD) and root mean square (RMS) are also given. In order to show the effect of frame stiffness on the ride comfort and cargo ride safety, two frames with different stiffness were given in the computations of PSD and RMS of the drivers and body vertical accelerations for four excitation cases. The computed results showed that when the stiffness of the frame is increased, the values of RMS the driver and body are decreased significantly at the frequency band 14～26Hz, which can effectively improve the ride comfort and cargo ride safety. This conclusion can be used to improve the design of frame as a valuable guide.
The topological optimization and topological sensitivity analysis of the truck structure are presented in this paper. Firstly, the sensitivity analysis methods for the static displacements and modal frequencies, and the topological optimal methods which including, the homogenization and the density methods, are reviewed, And then, focusing on difficulties of resulting from the optimal design problems in large scale finite element model of the complex structure, a new conceptions and new methods for the topology optimization design of the truck component are developed. The strain energy resulting from the loads applied to the structure is defined as the inverse measurement of the stiffness of the structure. The new conception of the static sensitivity for topological modification based on the element and superelement is presented and the corresponding static topological optimal method is developed for structures. The eigenvaluesλr can be defined as the modal stiffness. The modal stiffness sensitivities based on the element and super element(substructure) are presented for the topological modification, and the corresponding dynamic topological optimal method are developed. By using the present methods for sensitivity computation the static topological modification sensitivities of the torsional and bending stiffness of the truck frame, and the modal stiffness sensitivities of the torsional and bending modes are obtained. The topological modification sensitivities can be to improve the frame design as a valuable guide.
In the discussion of the optimal design of the truck frame under full vechiche assembly environement, the response analysis methods including multi-body system simulation, component mode synthesis and structural reduction are discussed. It is pointed out that it is difficult to use these methods to deal with the optimal design of the truck component under full vehicle assembly environment. By considering, difficulty resulting form the optimal problem with large scale degrees of freedom and design variables, the new methods for the optimization of the frame under full vehicle assembly environment are developed. Using the normal mode reduction and the static reduction, the dynamic substructural reduction and the dynamic topological optimization method are developed for the frame design under full vehicle assembly environment. The present method is applied to the design of the truck frame, and the obtained results indicate that the proposed method is valid and effective. The sensitivities of the modal stiffness of each component and the modal stiffness of the frame to the full vehicle are obtained from the computations.
Finally, the conclusions are drawn and problems to be further investigated are also presented for the truck.
在尺寸优化中,其设计变量为材料参数(如弹性模量E和密度ρ)和尺寸参数(如杆梁的横截面尺寸、转动惯量,板的厚度,弹性支承刚度,两部件之间的联接刚度等)。在形状优化中,其设计变量为边界点的坐标,为计及网格的变化,有基向量法和摄动向量法两种方法可以应用。
拓扑优化用来确定结构的最优形状和质量分布。拓扑优化计算每一单元的材料特性并改变材料分布,在一定的约束条件下实现优化目标。目前人们已经认识到,与拓扑结构不变的优化方法相比,拓扑优化能极大地改进结构设计。因此,拓扑优化方法受到了极大的重视并取得了快速发展。例如,拓扑优化的均匀化方法和密度法已广泛应用于商用车的结构设计。在密度法中每一个单元仅有一个表示材料密度的变量。在均匀化法中,对2D壳单元有两个尺寸变量,对3D块体元有三个尺寸变量。每个单元的附加变量就是其方位角。
近年来,上述三种优化方法已成功用于商用车零部件优化设计并取得了很大的成功。然而,上述三种优化方法很难处理自由度和设计变量巨大的有限元模型优化问题。迄今为止,大多数结构优化研究仅限于处理商用车单一零部件的优化问题。很少见到有关在整车装配环境下零部件优化方面的研究报导。
应当说明的是,即使作用在整车上的载荷是已知的,但作用在每个零部件(如驾驶室、车架等)上的载荷多半是未知的。因为在整车装配环下各零部件之间存在弹性动态耦合关系,每个零部件的边界条件也很难精确给出。在此情况下,单一零部件的优化仅能给出不精确结果,还可能是毫无意义的结果。因此,即使单一零部件的设计是优化的,但整车装配环境下可能不再是优化的。也就是说,零部件的单独优化设计不等同于在整车装配环境下的优化。为了得到整车性能的优化,必须在整车装配环境下对零部件进行优化设计。为此目的,本文讨论在整车装配环境下商用车车架的轻量化优化设计问题,包括简化的建模方法和更有效的拓扑优化方法,解决在整车装配环境下,零部件大规模优化问题。本文完成的主要研究工作如下：
回顾并综述了结构优化方法在商用车零部件设计中的应用,论述了单一零部件的尺寸、形状和拓扑优化的国内外研究现状,指出了大规模优化问题遇到的困难以及本文要讨论的问题。
讨论了车架刚度对商用车乘坐舒适性和货物运输安全性的影响。由于不平道路激励引起的商用车高水平振动将影响乘坐舒适性和货物运输的安全性。为此,建立了整车有限元模型,分析了车架振动的加速度功率谱密度(PSD)均方根值(RMS)。为了说明车架刚度对乘坐舒适性和货物安全性的影响,给出了两种不同车架刚度在4种激励作用下驾驶员座椅地板和货厢中心的PSD和RMS。结果表明,当车架的刚度提高时,驾驶员座椅地板和货厢的PSD和RMS均较大的降低(频率为14-26Hz),从而改善了驾乘舒适性和货物安全性。此结论可为后续改进车架设计提供参考。
对商用车结构进行了拓扑优化及拓扑灵敏度分析。首先,回顾了结构静态位移和模态频率的灵敏度分析方法和拓扑优化方法(均匀化法和密度法)。然后,针对大规模结构优化所产生的困难,提出了商用车零部件结构优化的新概念和新方法。把结构在外载荷作用下的应变能定义为结构刚度的逆测度,提出了基于子结构单元和超单元的结构静态拓扑修改灵敏度的新概念,并给出了相应的结构静态拓扑优化的方法。把振动特征值λr定义为模态刚度,提出了子结构基于单元和超单元拓扑修改的模态刚度灵敏度的概念,同时建立了相应的动态拓扑优化方法。应用所提出方法,计算了商用车架的静态扭转和弯曲刚度灵敏和车架的扭转模态和弯曲的模态刚度灵敏度。这些拓扑修改灵敏度信息可用来改进车架的设计。
在整车装配环境下商用车车架的优化设计过程中。讨论了包括多体系统模拟、模态综合和结构模态缩减等结构响应分析方法,并指出,这些方法很难用来处理在整车装配环境下商用车的零部件的优化问题。针对大规模结构优化所带来的计算困难,提出了在整车装配环境下车架优化设计的新方法。应用主模态缩减和静态缩减方法,提出了基于整车分析的动态子结构缩减方法。在此基础上,建立了在整车装配环境下车架的动态拓扑优化方法。所提出的分析方法已应用于商用车车架的设计。结果表明,所提出的方法是正确的和有效的。在计算中,得到了车架中每个元件的模态刚度灵敏度及车架模态刚度对整车的贡献。
最后,给出了论文研究的主要结论以及商用车优化设计需要进一步研究的问题。
It is well known that the excessive levels of vibration in heavy trucks negatively affect driver comfortability, cargo safety and road condition. The automotive designers pay great attention to optimize the vehicle structure, that is, to increase stiffness and strength and to reduce weight. Weight optimizing structural components for heavy trucks is becoming more and more important.Therefore the structural optimization has been the subject of numerous studies and widely used to develop the truck. The optimal methods used in the automotive component design can be divided into three types, size, shape and topology optimization.
In the size optimization, the design variables are the used material parameters such as the elastic module(E) and density(ρ), and the size parameters such as the cross sectional area of a beam, bending moment of inertia, the thickness of a plate, an elastic support with spring stiffness and an connector of stiffness between two components, etc. In the shape optimization, the design variables are the coordinates of the boundary node points. In order to account for mesh changes, the basis vector approach and the perturbation vector approach, are used.
The topology optimization is used to affirm an optimized shape and material distribution for a given structure. The topology algorithm calculates the material properties for each element,and alters the material distribution to optimize the defined objective function under given constrains. It has been recognized that topology optimization can more greatly improve the structure design than fixed-topology optimization. Up to date significant progress has been made with a variety of different approaches. For example, homogenization or a density method has been widely used to solve the topological optimization problem of trucks. For the density method, each element has one variable representing its material density. For the homogenization method which is limited to 2-D and 3-D elements, there are two size variables for each shell element and three void size variables for each solid element, and an additional variable for each element is the void orientation angel.
In recent years, all three optimal methods described above have been widely applied to the component design of the truck and significant successes have been achieved. However, for the optimal problems of the large scale finite element model with a large number of degree of freedom and design variable, the difficulties arise and three methods described above are difficult to deal with. Up to date, most of the optimizations are limited to deal with the individual component of the truck. A few studies can be found for the optimization under full truck assembly.
It should be pointed out that even though the loads on the full truck are usually known, the loads on each component, such as cab, body and frame, are rarely known. Since there exist the elastic and dynamic coupling relations between components under the assembly environment of the truck, it is difficult to obtain the boundary conditions of each component. In this case, the optimization for the individual component may not only give inaccurate result but also may be meaningless, if exact loads and boundary conditions can not be given. As can be seen that even through the optimal design for the individual component is obtained, the design of full assembly truck may not be optimal, In other words, the optimization of the individual is not equal to the optimization of full assembly truck. Therefore, it is necessary to discuss the optimization of the component under full truck assembly environment in order to obtain the optimal performances of the full truck. To this end, this paper presents the optimization of the frame under full truck assembly environment including the simplified modeling and more effective topological optimal method for solving the large scale optimal problems of components under full truck assembly environment. The main contents of this paper are studied as following:
A review on the applications of structural optimal method to the component design of the truck is given. The state-of-the-arts of the size, shape and topological optimizations for the individual component of trucks is presented. The difficulties resulting from the large scale optimal problems of the structure and problems to be discussed in this paper are also given.
The effect of frame stiffness on the ride comfort and the cargo ride safety is discussed. As can be seen that excessive levels of vibration in commercial vehicles, due to excitation from the road irregularities, can lead to cargo damage and safety problems. Therefore a finite element model of full vehicle was established. The computation algorithm for acceleration power spectral density (PSD) and root mean square (RMS) are also given. In order to show the effect of frame stiffness on the ride comfort and cargo ride safety, two frames with different stiffness were given in the computations of PSD and RMS of the drivers and body vertical accelerations for four excitation cases. The computed results showed that when the stiffness of the frame is increased, the values of RMS the driver and body are decreased significantly at the frequency band 14～26Hz, which can effectively improve the ride comfort and cargo ride safety. This conclusion can be used to improve the design of frame as a valuable guide.
The topological optimization and topological sensitivity analysis of the truck structure are presented in this paper. Firstly, the sensitivity analysis methods for the static displacements and modal frequencies, and the topological optimal methods which including, the homogenization and the density methods, are reviewed, And then, focusing on difficulties of resulting from the optimal design problems in large scale finite element model of the complex structure, a new conceptions and new methods for the topology optimization design of the truck component are developed. The strain energy resulting from the loads applied to the structure is defined as the inverse measurement of the stiffness of the structure. The new conception of the static sensitivity for topological modification based on the element and superelement is presented and the corresponding static topological optimal method is developed for structures. The eigenvaluesλr can be defined as the modal stiffness. The modal stiffness sensitivities based on the element and super element(substructure) are presented for the topological modification, and the corresponding dynamic topological optimal method are developed. By using the present methods for sensitivity computation the static topological modification sensitivities of the torsional and bending stiffness of the truck frame, and the modal stiffness sensitivities of the torsional and bending modes are obtained. The topological modification sensitivities can be to improve the frame design as a valuable guide.
In the discussion of the optimal design of the truck frame under full vechiche assembly environement, the response analysis methods including multi-body system simulation, component mode synthesis and structural reduction are discussed. It is pointed out that it is difficult to use these methods to deal with the optimal design of the truck component under full vehicle assembly environment. By considering, difficulty resulting form the optimal problem with large scale degrees of freedom and design variables, the new methods for the optimization of the frame under full vehicle assembly environment are developed. Using the normal mode reduction and the static reduction, the dynamic substructural reduction and the dynamic topological optimization method are developed for the frame design under full vehicle assembly environment. The present method is applied to the design of the truck frame, and the obtained results indicate that the proposed method is valid and effective. The sensitivities of the modal stiffness of each component and the modal stiffness of the frame to the full vehicle are obtained from the computations.
Finally, the conclusions are drawn and problems to be further investigated are also presented for the truck.
引文
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