Method for cylindricity error evaluation using Geometry Optimization Searching Algorithm

According to the geometrical characteristics of cylindricity error, a method for cylindricity error evaluation using Geometry Optimization Searching Algorithm (GOSA) has been presented. The optimization method and linearization method and uniform sampling could not adopt in the algorithm. The principle of the algorithm is that a hexagon are collocated based on the reference points in the starting and the end measured section respectively, the radius value of all the measured points are calculated by the line between the vertexes of the hexagon in the starting and the end measured section as the ideal axes, the cylindricity error value of corresponding evaluation method (include minimum zone cylinder method (MZC), minimum circumscribed cylinder method (MCC) and maximum inscribed cylinder method (MIC)) are obtained according to compare, judgment and arranged hexagon repeatedly. The principle and step of using the algorithm to solve the cylindricity error is detailed described and the mathematical formula and program flowchart are given. The experimental results show that the cylindricity error can be evaluated effectively and exactly using this algorithm.     

具有二重机制的生物地理优化算法及圆柱度 误差评定研究*

生物地理学优化算法(Biogeography-base optimization, BBO)是一种新型的智能算法,因其参数少、易于实现等优点而受到学界的广泛关注和研究,并显示出了广阔的应用前景。为了提高算法的优化性能,对BBO算法提出一种改进。改进的算法在将差分优化算法(Differential evolution, DE)中的局部搜索策略同BBO算法中的迁移策略相结合的基础上,针对迁移算子和变异算子分别做出改进,并通过基准函数的测试证明了改进后的算法在迭代过程中种群进化、寻优能力以及算法的收敛性能得到进一步提升。尝试将改进了的生物地理学优化算法应用于圆柱度误差评定。依据国家标准,结合最小区域法,以圆柱度误差数学模型为目标函数,该算法实现了误差评定优化求解。通过该寻优结果与其他方法的评定结果的比较,验证了该种算法的可行性和正确性及其优越性。     

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。     

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.     

基于多目标优化的空间直线度误差评定

根据最小区域定义及数学规划理论,建立了空间直线度评定的非线性规划模型,指出了这模型实质上是多目标优化的问题并将该优化问题转化成单目标优化问题。由于该非线性规划模型还是凸的、二次的,因此提出了用逐次二次规划的解法（SQP法）来实施。SQP法在评定过程中保留了模型中的非线性信息,对初始参数的要求低,且稳定、可靠、效率高。几个算例的结果均满足凸规划全局最优判别准则,这就有力的验证了上述结论。     

FORM ERROR EVALUATION OF CIRCLES BASED ON A FINELY-DESIGNED GENETIC ALGORITHM

A genetic algorithm(GA)-based new method is designed to evaluate the circularity error of mechanical parts. The method uses the capability of nonlinear optimization of GA to search for the optimal solution of circularity error. The finely-designed GA (FDGA) characterized dynamical bisexual recombination and Gaussian mutation. The mathematical model of the nonlinear problem is given. The implementation details in FDGA are described such as the crossover or recombination mechanism which utilized a bisexual reproduction scheme and the elitist reservation method; and the adaptive mutation which used the Gaussian probability distribution to determine the values of the offspring produced by mutation mechanism. The examples are provided to verify the designed FDGA. The computation results indicate that the FDGA works very well in the field of form error evaluation such as circularity evaluation.     

基于误差转换的汽车曲轴圆度及圆柱度误差评价数学模型构建研究

针对国内汽车曲轴轴颈圆度误差、圆柱度误差检测普遍存在的效率低、精度低等问题,建立基于误差转换的平面曲线和空间曲线误差数学模型,结合圆和圆柱的数学表达建立满足最小包容条件的圆度和圆柱度误差评定数学模型,并采用遗传优化算法计算出符合最小评定要求的曲轴轴颈形位误差,解决了理想包容要素位姿参数不精确的问题。同时,建立基于图像域的汽车曲轴轴颈形状误差检测试验台,针对测量过程中连杆轴颈沿主轴颈公转运动,从而导致连杆轴颈图像域检测数据存在坐标不归一问题,以曲轴法兰端特征孔为基准,通过模板匹配特征与孔边缘提取实现了连杆轴颈圆度和圆柱度测量数据空间坐标归一化处理。以某型号发动机曲轴为例进行大样本误差检测试验,并与三坐标测量机测得的结果进行对比,数据分析表明提出的曲轴轴颈形状误差检测方法的精度为1μm,且重复检测误差在0.1μm以内,证明了其理论上的正确性及实践操作的可行性。     

基于坐标测量机和拟粒子群进化算法的圆柱度误差检测与评定

建立了任意位置下基于坐标测量机检测的圆柱度误差最小区域解的数学模型,提出了采用拟粒子群进化算法求解最小区域圆柱度误差新方法。该算法使用实数编码,由拟随机Halton序列产生粒子的初始位置和速度,基于浓缩因子法修改粒子的速度。为了验证算法的有效性,对文献中测量数据采用提出的方法进行圆柱度误差计算并将结果与多种算法计算结果进行比较,同时在加工中心加工大量轴类零件,使用三坐标测量机对零件进行实测,应用该进化算法计算最小区域圆柱度误差并与三坐标测量机给出的结果进行比较。实验结果均证实了提出的方法不仅优化速度快、计算精度高,而且算法简单,需设置参数少,便于推广应用。     

Application of several computing techniques for minimum zone straightness

This research deals with the application of several algorithms to calculate the minimum zone straightness. Generally, in the evaluation of the minimum zone value of form errors such as straightness, flatness, roundness, and cylindricity, nonlinear optimization techniques are usually applied. The problem with the nonlinear technique that depends on computing algorithm is that the computing time may be prolonged. Therefore, some linear search techniques that are relatively easy to program are applied for straightness in this article. Furthermore, the problem can also be linearized by considering the characteristics of the measured profile for straightness; thus, the reduction of computing time will be achieved. Then, the problems caused by the above consideration are clarified. Consequently, the convergence criteria and comparison of results by means of several computing methods are investigated. The relationship between flatness and straightness values in some machining conditions and the comparison with the least-squares values are studied.     

Precision modeling of form errors for cylindricity evaluation using genetic algorithms

A heuristic approach is proposed in this paper to model form errors for cylindricity evaluation using genetic algorithms (GAs). The proposed GAs method shows good flexibility and excellent performance in evaluating the engineering surfaces via measurement data involved with randomness and uncertainty. The numerical-oriented genetic operator is used as a basic representation for error modeling in the paper. The theoretical basis for the proposed Gas-based cylindricity evaluation algorithms is first presented. The performance of the method under various combinations of parameters and the precision improvement on the evaluation of cylindricity are carefully analyzed. One numerical example is presented to illustrate the effectiveness of the proposed method and to compare the Gas-based modeling results with those obtained by the least-squares method. Numerical results indicate that the proposed GAs method does provide better accuracy on cylindricity evaluation. The method can also be extended for solving difficult form error minimization and profile evaluation problems of various geometric parts in engineering metrology.     

基于MATLAB的圆柱度误差评定方法

针对圆柱度误差评定的特点,提出了一种基于MATLAB的圆柱度误差评定方法,同时建立了符合最小条件的目标函数数学模型.通过实际测量数据计算,该方法能收敛到最优解,而且计算稳定.该方法可以推广应用到其他形状误差的评定中.     

Multi-objective optimization and evaluation method of modular product configuration design scheme

Product configuration is one of the key technologies for mass customization. Traditional product configuration optimization targets are mostly single. In this paper, an approach based on multi-objective genetic optimization algorithm and fuzzy-based select mechanism is proposed to solve the multi-objective configuration optimization problem. Firstly, the multi-objective optimization mathematical model of product configuration is constructed, the objective functions are performance, cost, and time. Then, a method based on improved non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the configuration design optimization problem. As a result, the Pareto-optimal set is acquired by NSGA-II. Due to the imprecise nature of human decision, a fuzzy-based configuration scheme evaluation and select mechanism is proposed consequently, which helps extract the best compromise solution from the Pareto-optimal set. The proposed multi-objective genetic algorithm is compared with two other established multi-objective optimization algorithms, and the results reveal that the proposed genetic algorithm outperforms the others in terms of product configuration optimization problem. At last, an example of air compressor multi-objective configuration optimization is used to demonstrate the feasibility and validity of the proposed method.     

基于面阵传感技术的圆柱度测量新方法

针对现行圆柱度测量方法的局限性和存在的问题,提出一种基于面阵传感技术的圆柱度测量新方法———多孔径重叠扫描拼接测量。该方法以数字光栅条纹投射技术为单视角测量手段,利用多孔径重叠扫描拼接技术实现各个单视角面形数据的精确融合拼接,从而获得零件的整个圆柱表面的面阵数据。文中给出圆柱度扫描拼接测量原理、拼接模型及算法,并通过对样品轴实测证明该方法的准确性和可行性。该方法具有非接触、高效、全场的特点,且能够满足新一代GPS(geometrical product specifications,产品几何技术规范)标准的采样要求,从而为圆柱度的精确评定提供可靠的数据信息。     

Accurate cylindricity evaluation with axis-estimation preprocessing

Evaluating cylindricity is a very important application in metrology. In this paper, we focus on cylindricity evaluation based on radial form measurements. The standard characterization of cylindricity is the notion of zone cylinder, i.e. the cylindrical crown contained between two coaxial cylinders with minimum radial separation and containing all the data points. Unfortunately, the construction of the zone cylinder is a very complex geometric problem, which can be formulated as a nonlinear optimization. Recently a new method (referred to here as the hyperboloid method) has been discussed, which avoids the direct construction of the zone cylinder of a point set, but approximates it with guaranteed accuracy through a computationally very efficient iterative process based on a linearization of the underlying problem. The iterations can be viewed as the construction of a sequence of “zone hyperboloids” tending to the desired “zone cylinder.” An important requirement of the method, however, is that the initial position of the cylindrical specimen axis be nearly vertical, since significant deviations from this condition essentially invalidate the process. It is the purpose of this paper to remove this shortcoming of the hyperboloid technique by providing a simple procedure for appropriately initializing the data (axis estimation). Axis estimation and the hyperboloid technique constitute an integrated methodology for cylindricity evaluation, which is currently the most effective. The theoretical foundations of the method are reviewed from a viewpoint that highlights its essential features and intuitively explains its effectiveness. The analytical discussion is complemented by experimental data concerning a few significant samples.     

基于遗传算法的回转体零件轮廓度误差评定方法

提出一种基于生物遗传算法的回转体零件轮廓度误差最小区域评定方法 ,以圆柱度误差评定为例 ,介绍了该算法的应用     

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.     

基于遗传算法的圆度误差评估

将遗传算法应用于圆度误差的评定.首先简介了误差评定背景和遗传算法及其特点.然后根据尺寸和公差的数学定义^[1]给出满足最小区域条件的圆度公差评定的数学模型和适应度函数.接着,以最小二乘解作为初始值,对圆度误差的遗传优化过程进行了详细的论述.最后用实例对算法进行验证.优化过程和实验结果显示了遗传算法在解决形状公差的评定这类非线性问题的优越性,通过并行搜索能最大限度地保证解的全局最优,计算精度高、效率高,且易于理解和实现.     

以线性逼近算法模式实现形状误差包容评定

根据形状误差定义及数学规划理论,建立形状误差包容评定的非线性规划模型,提出一种线性逼近算法摸式。其核心是利用线性规划模型的迭代运算,结合坐标变换去逼近非线性规划模型最优解。理论分析和大量计算表明算法能精确地评定形状误差,且快速收敛、计算稳定。     

A reliable method of minimum zone evaluation of cylindricity and conicity from coordinate measurement data

The form error evaluation of cylinders and cones is very important in precision coordinate metrology. The solution of the traditional least squares technique is prone to over-estimation, as a result unnecessary rejections may be caused. This paper proposes a reliable algorithm to calculate the minimum zone form errors of cylinders and cones, called a hybrid particle swarm optimization-differential evolution algorithm. The optimization is conducted in two stages, so that the program can hold a fast convergence rate, while effectively avoiding local minima. Experimental results demonstrate that the proposed algorithm can obtain very accurate and stable results for the calculation of cylindricity and conicity.     

面向大规模定制的装配线优化调度研究

针对大规模定制生产模式下汽车装配线调度存在的问题,提出一种多目标优化调度的方法,设计了相应的目标函数。提出一种多目标遗传算法,设计了相应的编码、选择和交换方案,在算法实现中对精英策略和选择机制进行了改进。仿真实验说明该算法可行有效,优于VEGA、PGA和NPGA等其他遗传算法。