不确定性MDO在驱动桥壳轻量化设计中的应用
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摘要
轻量化设计技术的开发应用是提高汽车性能、降低汽车油耗、减少汽车尾气排放的有效措施。零部件的轻量化设计方案往往要满足使用过程中的多个性能约束,而各个性能约束又涉及多个学科领域,因此多学科设计优化的思想被引入进来,除此之外,在汽车的设计、制造和使用过程中广泛存在的不确定性因素不可避免地影响着轻量化设计方案的有效性。因此,基于不确定性的多学科设计优化方法已成为汽车重要部件轻量化技术的重点研究内容。
不确定性多学科设计优化方法融合了多学科设计优化思想和不确定性设计优化理论,其主要内容包括：系统分析与优化,学科分析与优化,试验设计,近似模型技术,不确定性建模与传递分析方法,可靠性约束等效处理方法,优化结果搜寻策略等。不确定性多学科设计优化可衍生出两类设计问题,即稳健性多学科设计优化问题和可靠性多学科设计优化问题。本文以某轻型载货汽车驱动桥壳为研究对象,以不确定性多学科设计优化理论为指导对驱动桥壳的轻量化设计开展了系统研究：
(1)将适合处理高维计算问题的稀疏网格方法应用于高维近似模型的建立过程,研究了其确定样本空间的方法和建立近似模型的过程,并以Haupt函数和NASA减速器设计优化实例验证了其在拟合高维近似问题时的效率和精度。
(2)建立驱动桥壳有限元模型,系统地归纳了驱动桥壳静强度试验和疲劳试验资料,将试验结果与有限元分析结果进行对比,验证了该有限元模型在仿真静强度和疲劳寿命方面的精度。补充进行了驱动桥壳的模态频率测试试验,并与有限元分析结果对比,最终获得了各指标仿真精度均符合要求的驱动桥壳有限元模型。
(3)建立了驱动桥壳轻量化设计的总体优化模型,以各设计变量的灵敏度分析为基础划分学科模型,分别界定各个学科的范围,确定不确定性多学科设计优化问题的数学描述,并初步建立了各个设计变量的不确定性分布模型。然后以学科划分为基础,分别建立了系统级和学科级不确定性多学科设计优化模型。
(4)为得到比较合理的驱动桥壳轻量化设计方案,以多学科优化软件Optimus为平台,利用有限元分析软件ANSYS Workbench得到的响应面数据,搭建基于协同优化方法的不确定性多学科设计优化工作流程,最终获得具有稳健性和可靠性的驱动桥壳轻量化设计最优解。
(5)轻型载货汽车其它关键部件的轻量化设计也会集成多种分析软件、多种试验设计方法、多种近似模型技术,本课题中提出的基于不确定性的多学科设计优化流程可以其轻量化方案的获取提供一定参考。
Development and application of lightweight design are effective measures to improve automobile performance and decrease fuel consumption and gas emission. Generally speaking, the process of lightweight design needs to meet a lot of performance indexes, so the multidisciplinary design optimization theory is introduced in, but the uncertainties which exist widely in the design, manufacture, and service process inevitably influence the effectiveness of the lightweight design scheme. So, the uncertainty-based multidisciplinary design optimization (UMDO) methods have been the significant trend of automobile components lightweight design.
Uncertainty-based multidisciplinary design optimization is the combination of multidisciplinary design optimization process and uncertainty-based design optimization process, its main contents include:systematical analysis and optimization, disciplinary analysis and optimization, design of experiment, approximate model technology, modeling and propagation analysis of uncertainties, equivalent modeling technologies of constraint reliability, etc.. UMDO have two derivative problems, which are robust multidisciplinary design optimization (RMDO) and reliability-based multidisciplinary design optimization (RBMDO). In this paper, the driving axle housing is used as research object to be studied systematically on the lightweight design according to the UMDO.
(1) The sparse grid method aiming at processing high dimensionality problems is introduced to the building of approximate model, and the determination method of sampling method and building process of approximate model using sparse grid method are stated. Then the Haupt function and NASA reducer design optimization examples are used to verify the efficiency and accuracy of sparse grid method in building high dimensionality approximate model.
(2) The finite element model of driving axle housing is built. Then the results of driving axle housing static strength and fatigue tests are summarized, and the modal frequency measuring test is added in. Through the contrast of finite element and tests results, the accuracy of finite element model of driving axle housing is verified.
(3) The systematical optimization model of lightweight design is built, and each discipline scope is defined according to the sensitivity analysis results of each design variables. Then the mathematical model of UMDO is built and uncertainty distribution model of each design variable is premised. Based on the results of disciplinary division, the UMDO model of system-level and discipline-level are built.
(4) In order to obtain a more reasonable lightweight design scheme, the UMDO workflow based on collaborative optimization method is set up in the MDO software Optimus. At last, the robust and reliable lightweight design scheme of driving axle housing is obtained.
(5) The UMDO workflow in this project can provide a reference for the other key parts optimization process which integrate multiple analysis softwares, DOE methods, approximate model technologies, etc..
不确定性多学科设计优化方法融合了多学科设计优化思想和不确定性设计优化理论,其主要内容包括：系统分析与优化,学科分析与优化,试验设计,近似模型技术,不确定性建模与传递分析方法,可靠性约束等效处理方法,优化结果搜寻策略等。不确定性多学科设计优化可衍生出两类设计问题,即稳健性多学科设计优化问题和可靠性多学科设计优化问题。本文以某轻型载货汽车驱动桥壳为研究对象,以不确定性多学科设计优化理论为指导对驱动桥壳的轻量化设计开展了系统研究：
(1)将适合处理高维计算问题的稀疏网格方法应用于高维近似模型的建立过程,研究了其确定样本空间的方法和建立近似模型的过程,并以Haupt函数和NASA减速器设计优化实例验证了其在拟合高维近似问题时的效率和精度。
(2)建立驱动桥壳有限元模型,系统地归纳了驱动桥壳静强度试验和疲劳试验资料,将试验结果与有限元分析结果进行对比,验证了该有限元模型在仿真静强度和疲劳寿命方面的精度。补充进行了驱动桥壳的模态频率测试试验,并与有限元分析结果对比,最终获得了各指标仿真精度均符合要求的驱动桥壳有限元模型。
(3)建立了驱动桥壳轻量化设计的总体优化模型,以各设计变量的灵敏度分析为基础划分学科模型,分别界定各个学科的范围,确定不确定性多学科设计优化问题的数学描述,并初步建立了各个设计变量的不确定性分布模型。然后以学科划分为基础,分别建立了系统级和学科级不确定性多学科设计优化模型。
(4)为得到比较合理的驱动桥壳轻量化设计方案,以多学科优化软件Optimus为平台,利用有限元分析软件ANSYS Workbench得到的响应面数据,搭建基于协同优化方法的不确定性多学科设计优化工作流程,最终获得具有稳健性和可靠性的驱动桥壳轻量化设计最优解。
(5)轻型载货汽车其它关键部件的轻量化设计也会集成多种分析软件、多种试验设计方法、多种近似模型技术,本课题中提出的基于不确定性的多学科设计优化流程可以其轻量化方案的获取提供一定参考。
Development and application of lightweight design are effective measures to improve automobile performance and decrease fuel consumption and gas emission. Generally speaking, the process of lightweight design needs to meet a lot of performance indexes, so the multidisciplinary design optimization theory is introduced in, but the uncertainties which exist widely in the design, manufacture, and service process inevitably influence the effectiveness of the lightweight design scheme. So, the uncertainty-based multidisciplinary design optimization (UMDO) methods have been the significant trend of automobile components lightweight design.
Uncertainty-based multidisciplinary design optimization is the combination of multidisciplinary design optimization process and uncertainty-based design optimization process, its main contents include:systematical analysis and optimization, disciplinary analysis and optimization, design of experiment, approximate model technology, modeling and propagation analysis of uncertainties, equivalent modeling technologies of constraint reliability, etc.. UMDO have two derivative problems, which are robust multidisciplinary design optimization (RMDO) and reliability-based multidisciplinary design optimization (RBMDO). In this paper, the driving axle housing is used as research object to be studied systematically on the lightweight design according to the UMDO.
(1) The sparse grid method aiming at processing high dimensionality problems is introduced to the building of approximate model, and the determination method of sampling method and building process of approximate model using sparse grid method are stated. Then the Haupt function and NASA reducer design optimization examples are used to verify the efficiency and accuracy of sparse grid method in building high dimensionality approximate model.
(2) The finite element model of driving axle housing is built. Then the results of driving axle housing static strength and fatigue tests are summarized, and the modal frequency measuring test is added in. Through the contrast of finite element and tests results, the accuracy of finite element model of driving axle housing is verified.
(3) The systematical optimization model of lightweight design is built, and each discipline scope is defined according to the sensitivity analysis results of each design variables. Then the mathematical model of UMDO is built and uncertainty distribution model of each design variable is premised. Based on the results of disciplinary division, the UMDO model of system-level and discipline-level are built.
(4) In order to obtain a more reasonable lightweight design scheme, the UMDO workflow based on collaborative optimization method is set up in the MDO software Optimus. At last, the robust and reliable lightweight design scheme of driving axle housing is obtained.
(5) The UMDO workflow in this project can provide a reference for the other key parts optimization process which integrate multiple analysis softwares, DOE methods, approximate model technologies, etc..
引文
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[6]克莱恩B.轻量化设计-计算基础与构件结构[M].北京：机械工业出版社,2010.
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