Monte carlo method for the uncertainty evaluation of spatial straightness error based on new generation geometrical product specification

Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product specification(GPS) requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on "The Guide to the Expression of Uncertainty in Measurement(GUM)". In order to compute spatial straightness error(SSE) accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization(QPSO) is proposed to solve the minimum zone SSE and Monte Carlo Method(MCM) is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function(PDF) for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine(CMM) is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.     

新一代产品几何技术规范(GPS)对制造业的影响

介绍了产品几何技术规范(GPS)的发展概况,归纳出新一代GPS体系倡导功能公差理念、按计量学设计公差、体现并行工程思想、实现与CAx系统有效集成等4大特点,分析了新一代GPS体系将给制造业带来的积极影响,探讨了目前的研究方向,提出了加快中国GPS标准应用平台建设的若干建议。     

新一代产品几何技术规范(GPS)体系中不确定度理论及应用技术的研究

不确定度理论及应用技术是新一代GPS标准体系中的关键技术之一。新一代GPS利用不确定度的量化统计特性和经济杠杆调节作用,实现产品设计、制造和检测/认证全过程资源配置的优化。     

Adaptive Monte Carlo and GUM methods for the evaluation of measurement uncertainty of cylindricity error

Measurement uncertainty is one of the most important concepts in geometrical product specification (GPS). The “Guide to the expression of uncertainty in measurement (GUM)” is the internationally accepted master document for the evaluation of uncertainty. The GUM method (GUMM) requires the use of a first-order Taylor series expansion for propagating uncertainties. However, when the mathematical model of measurand is strongly non-linear the use of this linear approximation may be inadequate. Supplement 1 to GUM (GUM S1) has recently been proposed based on the basis of probability density functions (PDFs) using the Monte Carlo method (MCM). In order to solve the problem that the number of Monte Carlo trials needs to be selected priori, adaptive Monte Carlo method (AMCM) described in GUM S1 is recommended to control over the quality of the numerical results provided by MCM.The measurement and evaluation of cylindricity errors are essential to ensure proper assembly and good performance. In this paper, the mathematical model of cylindricity error based on the minimum zone condition is established and a quasi particle swarm optimization algorithm (QPSO) is proposed for searching the cylindricity error. Because the model is non-linear, it is necessary to verify whether GUMM is valid for the evaluation of measurement uncertainty of cylindricity error. Then, AMCM and GUMM are developed to estimate the uncertainty. The procedure of AMCM scheme and the validation of GUMM using AMCM are given in detail. Practical example is illustrated and the result shows that GUMM is not completely valid for high-precision evaluation of the measurement uncertainty of cylindricity error if only the first-order terms in the Taylor series approximation are taken into account. Compared with conventional methods, not only the proposed QPSO method can search the minimum zone cylindricity error precisely and rapidly, but also the Monte Carlo simulation is adaptive and AMCM can provide control variables (i.e. expected value, standard uncertainty and lower and higher coverage interval endpoints) with an expected numerical tolerance. The methods can be extended to the evaluation of measurement uncertainty of other form errors such as roundness and sphericity errors.     

现代产品几何技术规范(GPS)体系的理论基础及关键技术研究

针对传统的几何公差体系存在的突出问题，着重研究探讨新一代GPS标准体系的构成原理、基本准则、内在规律及应用特点；在此基础上，对该体系的理论基础及关键技术进行深入地研究和探讨，揭示并阐述其“一条主线(规范，模型)、两种关联(不确定度与操作算子)、三个创新(基于统计优化的不确定度理论及拓展技术、基于对偶性的模型与操作技术、基于应用数学的数字化描述技术)”的构造模式规律及本质特征；进一步明确新一代GPS体系在实现“功能—规范—检验，认证”全过程统—规范和数字化描述与集成控制方面的关键性(支撑)技术基础；并提出建立我国GPS体系的应对策略。     

现代产品几何技术规范(GPS)体系及应用分析

现代产品几何技术规范GPS(dimensional geometrical product specification and verification)是ISO／TC213针对产品的设计与制造而规定的一系列宏观和微观的几何技术规范，是所有机电产品的技术标准与计量规范的基础。随着全球经济的发展和科学技术的进步，尤其是随着CAD／CAM／CAQ(computer aided design／computer aided manufacture／computer aided quality)的应用和发展，新工艺、新技术、新材料的应用以及加工精度从微米到纳米的提高，ISO／TC213 GPS也随之发生了巨大的变化，已经由以几何学为基础的第一代GPS，发展到以计量学为基础的第二代GPS。文中在阐述ISO／TC213 GPS标准体系的形成、特点及发展趋势的基础上，对其构成思路及矩阵模型进行深入分析和研究，进一步揭示出其新一代GPS标准体系的构造模式规律及本质特征。     

基于GPS的圆度、圆柱度误差数字化计量方法研究

基于对数字化计量过程中关键操作技术的研究,给出圆度、圆柱度误差计量的操作算子构成策略及选用原则,并针对传统的几何误差评定中随意性大、评定参数单一、效率低下等不足,提出现代几何误差计量中以"高效、规范"为目标的多元化评定思想.并通过实例说明该数字化计量思想的运作模式及其工程价值,进一步明确基于GPS(geometrical product specification)的数字化计量方法对于实现误差评定的数字化、规范化和高效化是至关重要的,同时,对于促进国家(际)标准的发展及有效应用也具有十分重要的意义.     

现代产品几何技术规范(GPS)中基于对偶性的操作技术及其应用

揭示现代产品几何技术规范（geometrical product specification and verification，GPS）中规范过程和检验／认证过程的物象对应关系，以及其表面模型存在着对偶性、操作技术存在着共性的内在规律性；井以几何误差的检验／认证过程为例，阐述利用操作及算子技术实现GPS计量过程数字化的可能性及应用规律；进一步明确基于对偶性的表面模型、操作及操作算子技术，对于实现GPS设计与计量的统一性、与CAX的集成性和数字化功能是至关重要的。     

改进遗传算法与拟随机序列结合评定自由曲线轮廓度误差

为了高效率、高精度检测自由曲线和曲面零件并计算轮廓度误差,提出将改进遗传算法与拟随机序列结合来评定自由曲线轮廓度误差.首先,针对自由曲线因没有已知的解析表达式而常用离散点表示其轮廓的特点,采用非均匀有理B样条(NURBS)来表示自由曲线,并用改进遗传算法优化重建自由曲线;然后,应用拟随机Halton序列均匀产生参数值精确计算点到曲线最短距离.阐述了自由曲线重建时控制顶点及目标函数值的计算方法,确立了改进遗传算法重建自由曲线及采用拟随机序列生成参数值求解点到曲线最短距离的具体步骤.最后,针对仿真实例计算并实测零件曲线轮廓度误差.结果显示,自由曲线轮廓度误差评定精度高于99％,表明提出的方法算法简单、计算速度快、精度高,适于在工程计量中推广应用.     

新一代产品几何量技术规范(GPS)标准体系研究

新成立的国际尺寸与产品几何技术委员会(ISO/TC213)提出了新一代GPS标准体系,该标准体系由基础、全局、通用和补充GPS标准组成。新一代GPS标准为产品的设计、制造、检验与评估提供了一套完整的技术规范。分析了新一代产品几何量技术规范(GPS)的系统模型、标准体系、关键技术、目前的研究方向与内容,以及我国新一代GPS标准体系的建立途径。     

Fast genetic algorithm for roundness evaluation by the minimum zone tolerance (MZT) method

According to ISO 1101, “A geometrical tolerance applied to a feature defines the tolerance zone within which that feature shall be contained”.The main goal of the minimum zone tolerance (MZT) method is to achieve the best estimation of the roundness error, but it is computationally intensive. This paper describes the application of a genetic algorithm (GA) to minimize the computation time in the evaluation of CMM roundness errors of a large cloud of sampled points.Computational experiments have shown that by selecting the optimal GA parameters, namely a combination of the five genetic parameters related to population size, crossover, mutation, stop condition, and search space, the computation time can be reduced by up to one order of magnitude, allowing real-time operation.Optimization has been tested using seven CMM samples, obtained from different machining features. The performance of the optimized algorithm has been validated using four benchmark samples from the literature and with certified samples.     

基于遗传算法的机器零件圆柱度误差评定方法研究

为解决机器零件圆柱度误差在线评定过程复杂和精度较低的问题,将遗传算法应用于圆柱度误差在线评定方法的研究中。根据测量装置的工作原理,建立了圆柱度误差评定的数学模型,并对其进行了简化;采用实数编码和引入迁移算子的遗传算法对最小区域圆柱度误差进行了评定,通过设计圆柱度误差在线检测装置,利用Matlab和VC混合编程的方式,完成了圆柱度误差评定系统的构建,最后采用实验数据对系统性能进行了测试。研究结果表明,所构建的误差评定系统能够简化误差评定过程,并可满足机器零件精度检验的要求。     

粒子群优化算法及其在圆柱度误差评定中的应用

提出了将粒子群优化算法用于圆柱度误差评定的设想。对算法的基本原理和实现步骤做了具体阐述,给出了圆柱度误差评定的基本问题,及其优化目标函数及算法的适应度函数和编码方式,对算法进行了可行性和准确性验算。计算结果表明,该方法对于圆柱度误差评定这类具有复杂目标函数和较多参数的非线性优化问题有很好的计算性能,优于最小二乘法;与遗传算法和其它满足最小区域条件计算方法相比,计算精度略优于前者或者与前者相当,能够获得精度较高的结果,而突出优点是简单,易于实现而且计算效率较高。