基于改进遗传算法的圆度误差评定

提出了一种应用遗传算法计算满足最小区域法的圆度误差的新思路,并对传统的遗传算法提出了一些改进,理论上可以获得全局最优解。仿真结果表明,该方法可以在变量的全局范围内有效、正确的评价圆度误差。     

Roundness error evaluation algorithm based on polar coordinate transform

A new method for roundness error evaluation using polar coordinate system, named as polar coordinate transform algorithm (PCTA), was presented in this paper. The algorithm first allocates a circular region around the least square circle center following certain rules, then calculates the polar radius for all measured points by translating polar coordinate system to each point in the region in turn, and finally obtains minimum circumscribed center point, maximum inscribed center point and minimum zone center point from comparing each polar radius relative to each polar coordinate system. With accurate center point, the algorithm could give more accurate roundness evaluation. In the paper, the process of PCTA was described in detail including the algorithm formula and flowchart. Theoretical calculation and testing results show that PCTA can evaluate roundness error effectually and accurately.     

Conicity error evaluation using sequential quadratic programming algorithm

Form error evaluation plays an important role in processing quality evaluation. Conicity error is evaluated as a typical example in this paper based on sequential quadratic programming (SQP) algorithm. The evaluation is carried out in three stages. Signed distance function from the measured points to conical surface is defined and the cone is located roughly by the method of traditional least-squares (LS) firstly; the fitted cone and the measured point coordinates are transformed to simplify the optimal mathematical model of conicity error evaluation secondly; and then optimization problem on conicity error evaluation satisfying the minimum zone criterion is solved by means of SQP algorithm and kinematic geometry, where approximate linear differential movement model of signed distance function is deduced in order to reduce the computational complexity. Experimental results show that the conicity error evaluation algorithm is more accurate, and has good robustness and high efficiency. The obtained conicity error is effective.     

电磁轴承转子表面圆度误差对系统的影响

通过对转子表面圆度误差的机理分析,建立了圆度误差的数学模型,并实验验证了数学模型的正确性。分析讨论了圆度误差对采用PID控制策略的电磁轴承系统的控制精度的影响。研究结果表明:圆度误差会使转子作周期振动,当圆度误差信号的频率等于系统固有频率时,振动幅值较大,在这个频率后随频率的增加振动幅值减小。     

A new strategy for circularity problems

The evaluation of circularity based on the minimum zone criterion as a non-linear and non-convex problem, which requires a substantial amount of computational effort in general, is investigated. A new strategy for improving the computational efficiency by collecting data points at the farthest and nearest locations from current minimum radial separation center until all collected data points meet the optimum criterion is proposed. A number of mathematical models developed in this paper indicate that the minimum circularity can be determined by using a small number of critical data points. The validated results show that the proposed strategy offers an effective way to identify the critical data points at the early stage of computation and gives an efficient approach to solve the circularity problems, especially when the number of data point is large.     

Applying particle swarm optimization algorithm to roundness error evaluation based on minimum zone circle

Minimum zone circle (MZC) method and least square circle (LSC) method are two most commonly used methods to evaluate roundness, but only the MZC method complies with the standard definition and can obtain the minimum roundness error value. The determination of the center of MZC is a nonlinear optimization problem which is suitable to be solved by particle swarm optimization (PSO) algorithms. In this paper, the standard PSO algorithm was introduced and theory analysis about the impact of value selection of some important parameters, such as inertia weight ω, on the algorithm’s stability and convergence was carried on so as to provide basis for giving these parameters better values. Furthermore, the superiority of making ω decrease linearly with iterations was verified through a computation experiment in terms of stability and accuracy, compared with the other three cases of ω = 1, 0.5, 0. Based on the analysis, the novel PSO algorithm, with ω decreasing linearly from 0.9 to 0.4 and the LSC center as the initial positions of the particles, is implemented to obtain MZC-based roundness errors of sampling points collected from circular section profiles by a coordinate measuring machine (CMM). By comparing the novel PSO–MZC results with the LSC-based results, it is concluded that the former are a little smaller than the latter, which verifies that the novel PSO algorithm is feasible to calculate roundness error and the fact that a LSC-based one is generally larger than a MZC-based result; the values of the two roundness errors are both related to sample size and increase with an increase in the sample size with a decreasing increment.     

球面圆线定位提高工件圆度的分析研究

通过设计合理的球面与锥面的运动、尺寸参数,利用球面圆线中心自定位的特点,建立两球面圆线中心联线,替代传统锥顶中心线,使高精密磨削加工的圆度等级提高。     

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.     

基于遗传算法的球度误差评定

首先对球度公差评定问题进行了综述.然后根据圆度公差的数学定义,引申提出球度公差最小区域条件下的评定模型,并给出遗传算法的适应度函数.随后给出算法实现中的中的关键问题.最后用实例对算法进行了检验,计算结果表明基于遗传算法的球度误差优化算法不仅符合最小区域的条件,而且易于理解和实现,能够获得全局最优解,保证了高精度、高效率.     

一种利用坐标测量机实现圆度误差评价的方法

针对直角坐标系下圆周截面形状误差评价,介绍了一种圆柱体截面圆度误差的测量与评定方法.在研究了圆度误差定义及测量方法的基础上,建立了基于三坐标测量机的最小外接圆圆度误差三维评测模型.利用双截面最小二乘拟合轴线调整坐标系位置,减少了位姿误差对测量结果的影响.对模型进行坐标系统一转换,使得变换后的模型能更适用于计算机数据处理.然后在坐标变换的前提下,提出了一种利用几何关系搜索最小外接圆圆心的方法,开发了相应的数据分析软件.实验和数据证明,此算法优于传统最小外接圆算法,实现了在直角坐标系下三坐标测量机对圆度误差的最小外接圆法评价.     

同轴度误差快速评定新算法

针对空间最小二乘拟合同轴度基准轴线算法效率较低的问题,提出一种同轴度误差快速评定新算法。根据空间最小二乘法拟合直线的思想,利用两次投影法,先将n个基准要素的轮廓圆心正截面投影到xo Y面上,求取拟合的基准轴线与xo Y面的交点,再将n个被测实际要素轮廓正截面圆心投影到xo Y面上,将三维问题转化为二维问题,进行同轴度误差评定。并对一组数据进行了MATLAB仿真,结果证明该算法准确,便捷且计算速度大幅度提高。     

Roundness: A closed form upper bound for the centroid to minimum zone center distance by worst-case analysis

The minimum zone tolerance (MZT) meets the ISO 1101 definition of roundness error: it determines two concentric circles that contain the roundness profile and such that the difference in radii is the least possible value.     

Evaluation of circularity from coordinate and form data using computational geometric techniques

Data for evaluating circularity error can be obtained from coordinate measuring machines or form measuring instruments. In this article, appropriate methods based on computational geometric techniques have been developed to deal with coordinate measurement data and form data. The computational geometric concepts of convex hulls are used, and a new heuristic algorithm is suggested to arrive at the inner hull. Equi-Distant (Voronoi) and newly proposed Equi-Angular diagrams are employed for establishing the assessment features under different conditions. The algorithms developed in this article are implemented and validated with the simulated data and the data available in the literature.     

A study on analyzing the problem of the spherical form error

Many methods to evaluate the form error of a sphere have been studied over the years. Most of these, such as the optimum methods, employed the approximate local solution to obtain the desired results. In this paper, three mathematical models are constructed to evaluate the solutions of the minimum circumscribed sphere, the maximum inscribed sphere, and the minimum zone sphere by directly resolving the simultaneous linear algebraic equations. Examples are given to verify that the model is admissible and reliable. These simple mathematical methods are verified to be useful for determining the exact solution.     

The min–max problem for evaluating the form error of a circle

There have been many studies to evaluate the form error of a circle. Most of them, such as the optimum methods and limacon model, employed the approximate solution to obtain the desired results. In this paper, three mathematical models depending on the method used to select the exact control points are constructed to evaluate the analytic solution of the minimum circumscribed circle, the maximum inscribed circle and the minimum zone circle by directly resolving the simultaneous linear algebraic equations. These new and simple mathematical methods are verified to be useful for determining the exact solution.     

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.     

Flatness error evaluation and verification based on new generation geometrical product specification (GPS)

New generation geometrical product specification (GPS) links the whole course of a geometrical product from the research, development, design, manufacturing and verification to its release, utilization, and maintenance. Measurement process is one of the most important part of verification/inspection in the new generation GPS. With the knowledge-intensive and globalization trend of the economy, unifying the evaluation and verification of form errors will play a vital role in international trade and technical communication. Considering the plane feature is one of the most basic geometric primitives which contribute significantly to fundamental mechanical products such as guide way of machine tool to achieve intended functionalities, the mathematical model of flatness error minimum zone solution is formulated and an improved genetic algorithm (IGA) is proposed to implement flatness error minimum zone evaluation. Then, two evaluation methods of flatness error uncertainty are proposed, which are based on the Guide to the Expression of Uncertainty in Measurement (GUM) and a Monte Carlo Method (MCM). The calculating formula and the propagation coefficients of each element and correlation coefficients based on GUM and the procedures based on MCM are developed. Finally, two examples are listed to prove the effectiveness of the proposed method. An investigation into the source and effects of different uncertainty contributors for practical measurement on CMM is carried out and the uncertainty contributors significant are analyzed for flatness error verification. Compared with conventional methods, the proposed method not only has the advantages of simple algorithm, good flexibility, more efficiency and accuracy, but also guarantees the minimum zone solution specified in the ISO/1101 standard. Furthermore, it accords with the requirement of the new generation GPS standard which the measurement uncertainty characterizing the reliability of the results is given together. And it is also extended to other form errors evaluation and verification.     

Novel cyclostationarity-based blind source separation algorithm using second order statistical properties: Theory and application to the bearing defect diagnosis

Among signal processing techniques, blind source separation (BSS) and the underlying mathematical tool of independent component analysis (ICA) are of continuously growing interest in the scientific community of various research domains. Vibration analysis is a potential application field of this quite recent technique.Actually, BSS methods aim to retrieve unknown source signals from a set of their observations coming to a matrix of sensors, without necessarily having any prior knowledge about the sources. In monitoring and diagnosis purposes, bearing defects constitute a problem for manufacturers who aim at predicting those faults as well as potential engines breakdowns. These defects may be the unknown sources one wants to estimate from a set of recorded signals by a matrix of accelerometers placed close to the rotating machine.It has been shown that these vibration signals are wide-sense cyclostationary [[11] R.B.Randall, J. Antoni, S. Chobsaard, The relationship between spectral correlation and envelope analysis in the diagnostics of bearing faults and other cyclostationary machine signals, Mechanical Systems and Signal Processing 15 (5) (2001) 945–962]. The new algorithm of BSS proposed in this work is based, precisely, on that property. Second-order statistics of such processes led us to a new separation criterion for blind source separation. The theoretical results of this study, simulation and experimental analysis are presented in here. Perspectives for future research conclude this paper.     

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。     

A fast and simple algorithm for evaluation of minimum zone straightness error from coordinate data

Various methods have been suggested in the past to determine the minimum zone straightness error, but suffer from various drawbacks. A new, fast and simple algorithm is proposed to calculate the straightness error from planar coordinate data. It guarantees the minimum zone solution. An example and test data are provided. Results of simulation experiments to establish the time computational complexity of the algorithm are also presented.