面向设计的铁道车辆动力学建模与灵敏度分析
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摘要
产品的设计过程是一个设计-分析-优化-设计的动态闭环过程,现有的CAD和CAE由于追求的目标不同,产品的设计与分析相对独立。同时,产品在不同的工程应用领域中,其分析模型也是各不相同,即使在相同的领域,由于分析的粒度和复杂度不同,对分析模型的要求也不同,这使得设计模型不能较好地适应后续分析模型的需求。同时,对分析模型仿真求解,获得结果,如何将分析结果存在的问题反馈到设计模型的这一过程中,缺乏统一的模型描述语言去显示、表达这个过程,影响了设计进程朝着设计目标推进。本论文结合工程分析集成、基于特征的集成和基于产品描述标准的集成,提出了一个完整的产品设计分析集成框架和集成策略。对框架中,面向设计的复杂产品动力学分析子系统层进行了详细研究,其主要研究工作和研究成果如下：
(1)对现有设计分析集成进行研究,提出了一个完整的产品设计分析模型HPDA (Holistic Product Design and Analysis model)。该模型由四个视图组成,即系统层、子系统层、部件层和组件层,分别描述了不同设计阶段的设计过程和设计信息,符合自顶向下的设计过程,支持模块定义和重用。重点对子系统层进行了研究,引用了Peak的研究成果MRA表达框架,并在此基础上提出添加面向设计的动力学求解模型、灵敏度分析模型和优化模型,扩展MRA表达框架,使其成为满足复杂多体系统产品设计-分析-再设计的广义集成框架GMRA (Generalized MRA)。
(2)定义了GMRA基于STEP标准的描述方法,采用面向对象的EXPRESS和EXPRESS-G语言,对复杂多体系统进行建模分析。提出了基于特征的语义集成表示方法,以复杂铁道车辆为研究对象,通过将其进行基于多体系统特征和轮轨接触特征的分解,获得车辆模型的基元分析特征,从而为铁道车辆设计模型到分析模型,分析模型到求解方法,再到设计模型循环设计的一体化描述奠定了基础。
(3)将多体系统理论与轮轨接触理论相结合,把铁道车辆分解为由车体、转向架、轮对、悬挂力元、铰约束、轨道等组成的多体系统。对多体系统理论进行研究,在已有的研究成果上,采用基于欧拉四元数的笛卡尔坐标法描述多体系统动力学模型,并对典型铰约束进行了建模,采用第一类拉格朗日方程建立铁道车辆的动力学方程,采用违约稳定增广法对所建立的动力学方程进行数值求解。为了真实地反映轮轨接触状态,采用Hertz非线性弹性接触理论计算轮轨法向力,采用迹线法求解轮轨空间接触几何参数。对轮轨蠕滑力的求解,先采用Kalker线性理论进行初步计算,然后采用沈氏定理进行修正。车辆的激励主要由轨道的不平顺性产生,介绍了常见轨道功率谱密度表示的轨道不平顺。为了分析、评价铁道车辆的动力学品质,对车辆动力学性能指标进行了分析。
(4)基于多体系统理论与轮轨接触理论,采用面向对象方法,开发了铁道车辆动力学计算包GVDS,并用ADAMS、NUCARS、SIMPACK等商业软件初步验证了GVDS的准确性和可靠性,实现了GMRA构架中求解方法(SMM)模型的数值计算工作。
(5)基于第一类拉格朗日方程建模方法,建立了多体系统灵敏度分析模型,推导了一阶灵敏度分析的直接微分公式和伴随变量公式,并对多体系统约束、质量、广义力进行基元特征灵敏度建模,通过求解这些基元灵敏度特征模型,并映射到直接微分法和伴随变量法中,实现了GMRA构架中一般多体系统灵敏度分析模型的数值计算工作。
(6)将轮轨力用典型的弹簧阻尼力进行描述。通过对弹簧-阻尼力进行基于基元灵敏度分析特征建模,获得轮轨力的灵敏度分析模型,实现了GMRA构架中灵敏度分析(SAM)模型的数值计算工作,为实现铁道车辆的动力学性能优化奠定基础。
通过开展上述研究得出,任何复杂机械产品本质上都可以看作是多体系统。通过分析建立了动力学领域描述分析对象拓扑构型的基元特征模型,建立了基于多体理论的灵敏度分析基元特征模型,建立了铁道车辆独有的轮轨基元特征、轮轨接触特征模型。这些基元特征,是构建复杂机械产品的最小要素。同时,这些基元特征也是设计模型向分析模型映射的主要要素。因此,理论上可以通过组合这些基元分析特征实现对任意复杂机械产品面向动力学设计的描述。
Product design is a circulate redesign process from the design-analysis-optimization and redesign. CAD and CAE play an important role in the design process of the products and they are relatively independent. Because of the different application fields of product, many different analysis works, such as dynamics analysis, FEA and so on, have to be done. The product design model needs to be transformed different analysis models according to the different analysis purposes. And due to the different analysis complexity, the analysis models are different even in the same analysis field. The design model, therefore, is unable to meet the follow-up demands of the analysis models well. Meanwhile, how to feedback the existing problems of the analysis result to the design model lacks the unified model language to describe this course of expression. It influences the automated design process. Based on analyses, features and describing standard of product integrations, a HPDA (Holistic Product Design and Analysis model) is proposed to define design and analysis at different levels, to enhance engineering design and analysis interoperability and to integrate the design methods and tools across multiple engineering domains. The main research work and study results are as follows in this dissertation:
(1) HPDA is constructed with four levels (system, subsystem, machine and component), which is well supported by Top-Down design method. At each level, design and analysis models are integrated under a GMRA (Generalized Multi-Representation Rrchitecture) which supports design, analysis and optimization appropriately. The subsystem level is mainly researched. Design oriented SMM (Solution Method Model), SAM (Sensitivity Analysis Model) and optimization Technology are added in the GMRA. According to this model, the dynamics performance of the product can be designed and verified.
(2) GMRA is defined based on describe method of STEP standard, and an object-oriented language EXPRESS and EXPRESS-G are used for modelling and analysis of complicated multibody system. The description of the features based semantics integration is proposed to describe the complicated multibody system. Regard complicated railway vehicle as the research object, decompose the vehicle model to the smallest analyzable element to obtain the smallest analyzable feature. These can be foundations to implement the circulate redesign process, which is from design model to analysis model and then from analysis model to solution method model and more to redesign model.
(3) Railway vehicle systems consist of a large number of bodies that include carbodies, bogies, wheelsets, suspension elements, and other components. These bodies are interconnected by mechanical joints. Therefore, the multibody system dynamics and wheel-rail contact theory are combined to model and analyze the railway vehicle dynamics. The railway vehicle can be divided into carbody, bogie, suspension force element, constraints, track and so on. Cartesian coordinates with Euler parameters are used to describe the multibody system model. The railway vehicle system dynamics equations are built by the first kind Lagrange Equation. The constraint violation stabilization and augmented approaches are used to solve the differential-algebraic equations. In order to describe the contact feature of wheel and rail, nonlinear Hertz elasticity contact theory is adopted to compute the normal force of wheel and rail. The trace-line method is applied for contact geometry parameters. For the creep force of wheel and rail, the Kalker's linear theory is used to solve initially and then the Shen's Theory is used to revise them. The excitation of the vehicle is mainly produced by track irregularity. And the track irregularity can be expressed by power spectrum density of the track. The frequent characteristic of the power spectrum density must be transformed into time characteristics which is sutable for solving the track irregularity by Inverse Fourier Transform. In order to evaluate the railway vehicle dynamics capacity, the performance index has been researched.
(4) Based on the multibody system theory and wheel-rail contact theory, the railway vehicle compute package named GVDS is developed by object oriented method, and the accuracy and the reliability of GVDS have been verified by commercial software, such as ADAMS, NUCARS, SIMPACK, etc. And the model of SMM in GMRA has been implemented.
(5) Differential-algebraic equations of the multibody system, which include the design variable, are constructed based on The First Kind Lagrange Equation. The direct differentiation and adjoint variable methods are applied for the design sensitivity analysis of multibody system, and the sensitivity analysis of constraint, mass and generalized force are modeled. Some case studies have been done and the accuracy has been demonstrated. So, the sensitivity analysis model (SAM) in the GMRA is carried out.
(6) Because the nonlinear Hertz elasticity theory is applied for the wheel-rail force calculation, the wheel-rail force can be described by spring-damper force and the sensitivity analysis of the spring damper force can be modeled. The sensitivity model of wheel-rail force can be achieved for performance optimization of the railway vehicle.
According to the research, any complicated mechanical product can be regarded as multibody systems essentially. So, the smallest element feature model of multibody system has been built and the smallest sensitivity analysis feature and the specific wheel-rail smallest analysis feature are achieved. These smallest analyzable features are the smallest elements of analysis of mechanical product. And they are also the smallest elements for design model map into analysis model. So, any complicated mechanical product can be presented by composing the smallest analyzable element in theory.
(1)对现有设计分析集成进行研究,提出了一个完整的产品设计分析模型HPDA (Holistic Product Design and Analysis model)。该模型由四个视图组成,即系统层、子系统层、部件层和组件层,分别描述了不同设计阶段的设计过程和设计信息,符合自顶向下的设计过程,支持模块定义和重用。重点对子系统层进行了研究,引用了Peak的研究成果MRA表达框架,并在此基础上提出添加面向设计的动力学求解模型、灵敏度分析模型和优化模型,扩展MRA表达框架,使其成为满足复杂多体系统产品设计-分析-再设计的广义集成框架GMRA (Generalized MRA)。
(2)定义了GMRA基于STEP标准的描述方法,采用面向对象的EXPRESS和EXPRESS-G语言,对复杂多体系统进行建模分析。提出了基于特征的语义集成表示方法,以复杂铁道车辆为研究对象,通过将其进行基于多体系统特征和轮轨接触特征的分解,获得车辆模型的基元分析特征,从而为铁道车辆设计模型到分析模型,分析模型到求解方法,再到设计模型循环设计的一体化描述奠定了基础。
(3)将多体系统理论与轮轨接触理论相结合,把铁道车辆分解为由车体、转向架、轮对、悬挂力元、铰约束、轨道等组成的多体系统。对多体系统理论进行研究,在已有的研究成果上,采用基于欧拉四元数的笛卡尔坐标法描述多体系统动力学模型,并对典型铰约束进行了建模,采用第一类拉格朗日方程建立铁道车辆的动力学方程,采用违约稳定增广法对所建立的动力学方程进行数值求解。为了真实地反映轮轨接触状态,采用Hertz非线性弹性接触理论计算轮轨法向力,采用迹线法求解轮轨空间接触几何参数。对轮轨蠕滑力的求解,先采用Kalker线性理论进行初步计算,然后采用沈氏定理进行修正。车辆的激励主要由轨道的不平顺性产生,介绍了常见轨道功率谱密度表示的轨道不平顺。为了分析、评价铁道车辆的动力学品质,对车辆动力学性能指标进行了分析。
(4)基于多体系统理论与轮轨接触理论,采用面向对象方法,开发了铁道车辆动力学计算包GVDS,并用ADAMS、NUCARS、SIMPACK等商业软件初步验证了GVDS的准确性和可靠性,实现了GMRA构架中求解方法(SMM)模型的数值计算工作。
(5)基于第一类拉格朗日方程建模方法,建立了多体系统灵敏度分析模型,推导了一阶灵敏度分析的直接微分公式和伴随变量公式,并对多体系统约束、质量、广义力进行基元特征灵敏度建模,通过求解这些基元灵敏度特征模型,并映射到直接微分法和伴随变量法中,实现了GMRA构架中一般多体系统灵敏度分析模型的数值计算工作。
(6)将轮轨力用典型的弹簧阻尼力进行描述。通过对弹簧-阻尼力进行基于基元灵敏度分析特征建模,获得轮轨力的灵敏度分析模型,实现了GMRA构架中灵敏度分析(SAM)模型的数值计算工作,为实现铁道车辆的动力学性能优化奠定基础。
通过开展上述研究得出,任何复杂机械产品本质上都可以看作是多体系统。通过分析建立了动力学领域描述分析对象拓扑构型的基元特征模型,建立了基于多体理论的灵敏度分析基元特征模型,建立了铁道车辆独有的轮轨基元特征、轮轨接触特征模型。这些基元特征,是构建复杂机械产品的最小要素。同时,这些基元特征也是设计模型向分析模型映射的主要要素。因此,理论上可以通过组合这些基元分析特征实现对任意复杂机械产品面向动力学设计的描述。
Product design is a circulate redesign process from the design-analysis-optimization and redesign. CAD and CAE play an important role in the design process of the products and they are relatively independent. Because of the different application fields of product, many different analysis works, such as dynamics analysis, FEA and so on, have to be done. The product design model needs to be transformed different analysis models according to the different analysis purposes. And due to the different analysis complexity, the analysis models are different even in the same analysis field. The design model, therefore, is unable to meet the follow-up demands of the analysis models well. Meanwhile, how to feedback the existing problems of the analysis result to the design model lacks the unified model language to describe this course of expression. It influences the automated design process. Based on analyses, features and describing standard of product integrations, a HPDA (Holistic Product Design and Analysis model) is proposed to define design and analysis at different levels, to enhance engineering design and analysis interoperability and to integrate the design methods and tools across multiple engineering domains. The main research work and study results are as follows in this dissertation:
(1) HPDA is constructed with four levels (system, subsystem, machine and component), which is well supported by Top-Down design method. At each level, design and analysis models are integrated under a GMRA (Generalized Multi-Representation Rrchitecture) which supports design, analysis and optimization appropriately. The subsystem level is mainly researched. Design oriented SMM (Solution Method Model), SAM (Sensitivity Analysis Model) and optimization Technology are added in the GMRA. According to this model, the dynamics performance of the product can be designed and verified.
(2) GMRA is defined based on describe method of STEP standard, and an object-oriented language EXPRESS and EXPRESS-G are used for modelling and analysis of complicated multibody system. The description of the features based semantics integration is proposed to describe the complicated multibody system. Regard complicated railway vehicle as the research object, decompose the vehicle model to the smallest analyzable element to obtain the smallest analyzable feature. These can be foundations to implement the circulate redesign process, which is from design model to analysis model and then from analysis model to solution method model and more to redesign model.
(3) Railway vehicle systems consist of a large number of bodies that include carbodies, bogies, wheelsets, suspension elements, and other components. These bodies are interconnected by mechanical joints. Therefore, the multibody system dynamics and wheel-rail contact theory are combined to model and analyze the railway vehicle dynamics. The railway vehicle can be divided into carbody, bogie, suspension force element, constraints, track and so on. Cartesian coordinates with Euler parameters are used to describe the multibody system model. The railway vehicle system dynamics equations are built by the first kind Lagrange Equation. The constraint violation stabilization and augmented approaches are used to solve the differential-algebraic equations. In order to describe the contact feature of wheel and rail, nonlinear Hertz elasticity contact theory is adopted to compute the normal force of wheel and rail. The trace-line method is applied for contact geometry parameters. For the creep force of wheel and rail, the Kalker's linear theory is used to solve initially and then the Shen's Theory is used to revise them. The excitation of the vehicle is mainly produced by track irregularity. And the track irregularity can be expressed by power spectrum density of the track. The frequent characteristic of the power spectrum density must be transformed into time characteristics which is sutable for solving the track irregularity by Inverse Fourier Transform. In order to evaluate the railway vehicle dynamics capacity, the performance index has been researched.
(4) Based on the multibody system theory and wheel-rail contact theory, the railway vehicle compute package named GVDS is developed by object oriented method, and the accuracy and the reliability of GVDS have been verified by commercial software, such as ADAMS, NUCARS, SIMPACK, etc. And the model of SMM in GMRA has been implemented.
(5) Differential-algebraic equations of the multibody system, which include the design variable, are constructed based on The First Kind Lagrange Equation. The direct differentiation and adjoint variable methods are applied for the design sensitivity analysis of multibody system, and the sensitivity analysis of constraint, mass and generalized force are modeled. Some case studies have been done and the accuracy has been demonstrated. So, the sensitivity analysis model (SAM) in the GMRA is carried out.
(6) Because the nonlinear Hertz elasticity theory is applied for the wheel-rail force calculation, the wheel-rail force can be described by spring-damper force and the sensitivity analysis of the spring damper force can be modeled. The sensitivity model of wheel-rail force can be achieved for performance optimization of the railway vehicle.
According to the research, any complicated mechanical product can be regarded as multibody systems essentially. So, the smallest element feature model of multibody system has been built and the smallest sensitivity analysis feature and the specific wheel-rail smallest analysis feature are achieved. These smallest analyzable features are the smallest elements of analysis of mechanical product. And they are also the smallest elements for design model map into analysis model. So, any complicated mechanical product can be presented by composing the smallest analyzable element in theory.
引文
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