超精密机床多尺度集成设计方法研究
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摘要
超精密机床应用于关系国家利益和安全的战略性产业中，其相关技术被我国以及美国、欧盟、日本等国家列为国家关键技术并予以重点资助和发展。超精密机床具有自己独特的特点：结构跨越了从纳米级到数百毫米级的多种空间尺度；结构之间的流体介质形成具有一定刚度和承载能力的流体膜结合面。由于超精密机床结构的特殊性，使得机床工作中位置、姿态及结合面的微小改变将对整机性能产生决定性影响。目前，超精密机床系统整体、关键部件的性能与结构及其结合面多种尺度参数间的映射关系尚未系统建立，设计中缺少对系统级性能的形成机理分析，缺乏建立在性能成因分析基础上的系统设计方法，不能应对超精密机床更高精度的设计挑战。基于此，本课题通过解析超精密机床空间尺度和功能尺度的本质特征，分析结构位置姿态宏微观变化、结构间结合面微观特性对超精密机床刚度、精度、热特性等性能的作用机理，提出超精密机床刚度、热性能和精度的多尺度集成设计方法，从而科学指导超精密机床系统设计，满足系统更高精度的设计追求。
课题将超精密机床的研究尺度分为三个层次：大尺度，核心尺度，小尺度。在大尺度上设定三个研究目标，分别为精度、刚度在工作空间中的变化规律和整机热特性的时空分析。在核心尺度中，基于运动学、动力学、传热学分析理论和空间统计学分析方法，将超精密机床各项设计参数与整机性能相关联，进而建立核心尺度与大尺度的映射关系。在小尺度上采用试验设计方法研究核心尺度参数的采样和敏度，构建核心尺度参数的取值准则。通过三个尺度的参数集成分析，获得超精密机床整体性能与各尺度设计参数的关联规律，从而确定超精密机床系统设计参数的选取准则，形成超精密机床刚度、精度、热特性及整机集成系统设计体系，用以指导高精度的超精密机床系统设计。
基于上述研究思想，建立超精密机床系统多尺度参数的刚度模型，研究微观表面结构、气浮刚度、结构刚度等本征多尺度特征对系统工作空间刚度的综合作用规律。采用空间统计学和Kriging方法，进行模态-位姿相关性分析，解析设计空间到特征状态空间的映射关系，进而获取设计目标机床在工作空间内的全部模态信息。以刚度模型和工作空间内的刚度分布规律为指导，构建刚度设计中结构、运动部件、结合面、微观表面结构等关键参数优化设计准则，形成超精密机床系统刚度多尺度设计方法，并给出超精密机床刚度多尺度特性分析设计的应用实例。
针对超精密机床整机热特性这一嵌入型多尺度问题，采用集总参数法预测强耦合分布，继而采用局部细化热阻网络法建立多尺度的超精密机床热特性分析模型，研究空间上的热分布特性和时间上的热传递规律。多尺度方法克服了传统热特性分析滞后的缺点，在设计之初进行热特性判断、提出热冷却要求，在详细设计阶段仿真获得机床热场分布，基于以上分析，建立热优化设计模型，形成超精密机床热特性多尺度设计体系。
在超精密机床系统精度特性研究中，以精度链端点矢量差值在工作空间的变化最小为设计目标，基于多体运动学理论建立误差分析模型，采用试验设计和效应分析，通过解析超精密机床部件体间误差、姿态误差和位置误差3类核心尺度误差参数主效应和交互效应，获得各误差对精度及精度保持性的作用规律，确定关键设计参数和精度分配准则，获得优化的定位精度及高的精度保持性。在此基础上，建立5轴超精密铣床的多元二次回归代理模型（160项参数项），与线性模型（38项参数项）、二次误差模型（741项参数项）比较分析各自的拟合精度，并进行系统精度与固有频率的空间相关性分析。这三部分的分析结果，提供了超精密机床系统精度设计的理论和方法支撑。
在完成刚度、精度和热性能多尺度设计和分析的基础上，建立刚度、精度和热性能集成设计的数学模型，搭建多尺度集成设计仿真平台，实现多种尺度数据传递，研究各相关因素和参数耦合对精度、刚度和热特性的综合影响规律。通过完成5轴超精密铣床实例集成设计与分析，与初始设计对比，集成设计能够在设计阶段更精确地获取性能参数，依据设计方法提供的优化设计指导准则，能够提高超精密机床的系统刚度、精度和热性能，对本文提出的设计方法实现实例验证。
Ultra-precision machine tools relate strongly to the strategies of national interestsand security, and their relevant technology are listed as the national key technologies bythe United States, European Union, Japan and other countries, and received special aidfor development. The ultra-precision machine tools have their own distinguishingfeatures: structures span the spatial scales from nanometers to hundreds of millimeter;fluid medium between structures form fluid membrane bound surface with a certainamount of stiffness and carrying capacity. The performance of ultra-precision machinetools is a function of structures and bound surface parameters, and the tiny change ofworking position, posture and bound surface will bring a decisive affection to the wholemachine performance. Currently the design method of ultra-precision machine toolslacks the mechanism investigation of the affecting from the motion of multi-scalestructures and bound surface micro changing to the performance of ultra-precisionmachine tools. So this project proposes a ultra-precision machine tools multi-scaleintegration design method, and through the analysis of the characteristics of spatialscales and function scales of ultra-precision machine tools, interpret the micro-macrochanging of structure position and posture, the interpret the affecting mechanism frommicro feature of structures bound surface to the stiffness, accuracy, thermalcharacteristics, etc., thus provide a scientific guidance to the whole machine design ofultra-precision machine tools including stiffness, accuracy and thermal characteristics.
This project takes research of ultra-precision machine tools into three levels:macro-scale, core-scale, and micro-scale. And three research goals are set tomacro-scale design, and they are the varying rules of accuracy and stillness, and thespatial analysis of the whole machine thermal characteristics. In core-scale, based on thekinematics, dynamics, heat transfer theory and spatial statistics method, relate thedesign parameters to the whole machine performance, and thus establish the mappingrelation between core-scale to macro-scale. In micro-scale, investigate the samplingmechanism and acuteness of the core-scale parameters, and build the tuning rules ofcore-scale-parameters. Through parameters seamless integration analysis of the threescales, obtain the relating rules between ultra-precision machine tools and multi-scaledesign parameters, thus determine the selecting rules of ultra-precision machine toolsdesign parameters, and finally guide the design process.
Based on the antecedent thought, establish the whole machine stiffness model ofultra-precision machine tool systems, in order to investigate the integrated affectingrules from the multi-scale feature, such as surface micro structures, air bearing stiffness,structural stiffness, to the whole machine spatial stiffness. With the stiffness model based spatial statistics and Kriging method, parse out the design space to thecharacteristics of the state space mapping relationship, and analyze the modal-pose toget machine processing space modal information to guide the system stiffness design.
Aiming at the fact that the whole machine thermal characteristics is a strongcoupling embedded multi-scale problems, adopt lumped parameter method to predictthe strong coupling distribution, and then establish the ultra-precision machine toolsthermal characteristics analyzing model based on local refining thermal resistancenetwork method, to investigate the spatial thermal distribution characteristics and thetemporal thermal transmission rules. The multi-scale method overcomes the weaknessof lagging in traditional thermal characteristics analysis, since it conduct thermalcharacteristics prediction in elementary design process, and propose coolingrequirement, and simulate the machine thermal distribution in detailed design process.
In the research of the conjunction between various scale parts with their boundingsection, the positioning accuracy and the precision preserve, take the minimum spatialchanging of the difference value between the endpoint vectors of accuracy chain, as thedesign goal. Build error analyzing model based on multi-body kinematics theory, andadopt experimental design and effect analysis, solve the affecting rules from the varyingof3core-scale parameters, the verticality error, the tilt angular error and the straightnesserror. According the influence level from the former parameters to accuracy, determinekey design parameters, and provide theoretical support to ultra-precision machine toolsdesign. On this basis, build multi-parameter quadratic regression model for5-axis (160parameters), and compare the model with linear model (38parameters) and secondaryerror (741parameters), and obtain the optimized positioning accuracy and accuracypreserve, and validate the constraint settings of parameters during design process.
Based on the above multi-scale analyzing method and principle of accuracy,stiffness and thermal characteristics, establish an integrated mathematical modelincluding stiffness, accuracy and thermal characteristics, and adopt the multi-scaleintegration design and simulation platform, achieve seamless data transmission amongmulti-scale parameters, to investigate the coupling effect of the performance relatedparameters, and explore the influence rules from the various factors and parameterschanging to the whole machine performance. Complete the integrated design andanalysis for a5-axis ultra-precision milling machine, and compared with the initialdesign, obtain more accurate performance parameters in design stage, and provideguidance principles to optimization design, and finally experimentally validate thedesign method proposed in this thesis.
课题将超精密机床的研究尺度分为三个层次：大尺度，核心尺度，小尺度。在大尺度上设定三个研究目标，分别为精度、刚度在工作空间中的变化规律和整机热特性的时空分析。在核心尺度中，基于运动学、动力学、传热学分析理论和空间统计学分析方法，将超精密机床各项设计参数与整机性能相关联，进而建立核心尺度与大尺度的映射关系。在小尺度上采用试验设计方法研究核心尺度参数的采样和敏度，构建核心尺度参数的取值准则。通过三个尺度的参数集成分析，获得超精密机床整体性能与各尺度设计参数的关联规律，从而确定超精密机床系统设计参数的选取准则，形成超精密机床刚度、精度、热特性及整机集成系统设计体系，用以指导高精度的超精密机床系统设计。
基于上述研究思想，建立超精密机床系统多尺度参数的刚度模型，研究微观表面结构、气浮刚度、结构刚度等本征多尺度特征对系统工作空间刚度的综合作用规律。采用空间统计学和Kriging方法，进行模态-位姿相关性分析，解析设计空间到特征状态空间的映射关系，进而获取设计目标机床在工作空间内的全部模态信息。以刚度模型和工作空间内的刚度分布规律为指导，构建刚度设计中结构、运动部件、结合面、微观表面结构等关键参数优化设计准则，形成超精密机床系统刚度多尺度设计方法，并给出超精密机床刚度多尺度特性分析设计的应用实例。
针对超精密机床整机热特性这一嵌入型多尺度问题，采用集总参数法预测强耦合分布，继而采用局部细化热阻网络法建立多尺度的超精密机床热特性分析模型，研究空间上的热分布特性和时间上的热传递规律。多尺度方法克服了传统热特性分析滞后的缺点，在设计之初进行热特性判断、提出热冷却要求，在详细设计阶段仿真获得机床热场分布，基于以上分析，建立热优化设计模型，形成超精密机床热特性多尺度设计体系。
在超精密机床系统精度特性研究中，以精度链端点矢量差值在工作空间的变化最小为设计目标，基于多体运动学理论建立误差分析模型，采用试验设计和效应分析，通过解析超精密机床部件体间误差、姿态误差和位置误差3类核心尺度误差参数主效应和交互效应，获得各误差对精度及精度保持性的作用规律，确定关键设计参数和精度分配准则，获得优化的定位精度及高的精度保持性。在此基础上，建立5轴超精密铣床的多元二次回归代理模型（160项参数项），与线性模型（38项参数项）、二次误差模型（741项参数项）比较分析各自的拟合精度，并进行系统精度与固有频率的空间相关性分析。这三部分的分析结果，提供了超精密机床系统精度设计的理论和方法支撑。
在完成刚度、精度和热性能多尺度设计和分析的基础上，建立刚度、精度和热性能集成设计的数学模型，搭建多尺度集成设计仿真平台，实现多种尺度数据传递，研究各相关因素和参数耦合对精度、刚度和热特性的综合影响规律。通过完成5轴超精密铣床实例集成设计与分析，与初始设计对比，集成设计能够在设计阶段更精确地获取性能参数，依据设计方法提供的优化设计指导准则，能够提高超精密机床的系统刚度、精度和热性能，对本文提出的设计方法实现实例验证。
Ultra-precision machine tools relate strongly to the strategies of national interestsand security, and their relevant technology are listed as the national key technologies bythe United States, European Union, Japan and other countries, and received special aidfor development. The ultra-precision machine tools have their own distinguishingfeatures: structures span the spatial scales from nanometers to hundreds of millimeter;fluid medium between structures form fluid membrane bound surface with a certainamount of stiffness and carrying capacity. The performance of ultra-precision machinetools is a function of structures and bound surface parameters, and the tiny change ofworking position, posture and bound surface will bring a decisive affection to the wholemachine performance. Currently the design method of ultra-precision machine toolslacks the mechanism investigation of the affecting from the motion of multi-scalestructures and bound surface micro changing to the performance of ultra-precisionmachine tools. So this project proposes a ultra-precision machine tools multi-scaleintegration design method, and through the analysis of the characteristics of spatialscales and function scales of ultra-precision machine tools, interpret the micro-macrochanging of structure position and posture, the interpret the affecting mechanism frommicro feature of structures bound surface to the stiffness, accuracy, thermalcharacteristics, etc., thus provide a scientific guidance to the whole machine design ofultra-precision machine tools including stiffness, accuracy and thermal characteristics.
This project takes research of ultra-precision machine tools into three levels:macro-scale, core-scale, and micro-scale. And three research goals are set tomacro-scale design, and they are the varying rules of accuracy and stillness, and thespatial analysis of the whole machine thermal characteristics. In core-scale, based on thekinematics, dynamics, heat transfer theory and spatial statistics method, relate thedesign parameters to the whole machine performance, and thus establish the mappingrelation between core-scale to macro-scale. In micro-scale, investigate the samplingmechanism and acuteness of the core-scale parameters, and build the tuning rules ofcore-scale-parameters. Through parameters seamless integration analysis of the threescales, obtain the relating rules between ultra-precision machine tools and multi-scaledesign parameters, thus determine the selecting rules of ultra-precision machine toolsdesign parameters, and finally guide the design process.
Based on the antecedent thought, establish the whole machine stiffness model ofultra-precision machine tool systems, in order to investigate the integrated affectingrules from the multi-scale feature, such as surface micro structures, air bearing stiffness,structural stiffness, to the whole machine spatial stiffness. With the stiffness model based spatial statistics and Kriging method, parse out the design space to thecharacteristics of the state space mapping relationship, and analyze the modal-pose toget machine processing space modal information to guide the system stiffness design.
Aiming at the fact that the whole machine thermal characteristics is a strongcoupling embedded multi-scale problems, adopt lumped parameter method to predictthe strong coupling distribution, and then establish the ultra-precision machine toolsthermal characteristics analyzing model based on local refining thermal resistancenetwork method, to investigate the spatial thermal distribution characteristics and thetemporal thermal transmission rules. The multi-scale method overcomes the weaknessof lagging in traditional thermal characteristics analysis, since it conduct thermalcharacteristics prediction in elementary design process, and propose coolingrequirement, and simulate the machine thermal distribution in detailed design process.
In the research of the conjunction between various scale parts with their boundingsection, the positioning accuracy and the precision preserve, take the minimum spatialchanging of the difference value between the endpoint vectors of accuracy chain, as thedesign goal. Build error analyzing model based on multi-body kinematics theory, andadopt experimental design and effect analysis, solve the affecting rules from the varyingof3core-scale parameters, the verticality error, the tilt angular error and the straightnesserror. According the influence level from the former parameters to accuracy, determinekey design parameters, and provide theoretical support to ultra-precision machine toolsdesign. On this basis, build multi-parameter quadratic regression model for5-axis (160parameters), and compare the model with linear model (38parameters) and secondaryerror (741parameters), and obtain the optimized positioning accuracy and accuracypreserve, and validate the constraint settings of parameters during design process.
Based on the above multi-scale analyzing method and principle of accuracy,stiffness and thermal characteristics, establish an integrated mathematical modelincluding stiffness, accuracy and thermal characteristics, and adopt the multi-scaleintegration design and simulation platform, achieve seamless data transmission amongmulti-scale parameters, to investigate the coupling effect of the performance relatedparameters, and explore the influence rules from the various factors and parameterschanging to the whole machine performance. Complete the integrated design andanalysis for a5-axis ultra-precision milling machine, and compared with the initialdesign, obtain more accurate performance parameters in design stage, and provideguidance principles to optimization design, and finally experimentally validate thedesign method proposed in this thesis.
引文
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