Determination and mapping of measurement and design coordinate systems using computational geometric techniques

Automotive industry is one of the most prospective manufacturing industries in the present world. In order to keep up with the challenges of competitors, the automobile industries are taking necessary steps to satisfy the customers by supplying products of good quality at lower cost. The machine vision inspection systems play an important role in quality control with their accurate dimensional measurement capability. The data obtained from these systems have to be analyzed using appropriate algorithms. In the present work, algorithms based on computational geometric techniques have been developed, to set up the coordinate system for the data obtained from the laser vision system for subframe and lower arm assembly of automobile front chassis module. The concept of a convex hull and a modified Voronoi diagram are utilized for establishing the coordinate system for measurement data. The design coordinate system is determined using the Voronoi diagrams. The measurement and design coordinate systems are mapped using 3D transformations. The results obtained for the sample data are also presented in this paper.     

Evaluation of roundness error from coordinate data using curvature technique

Workpieces like a shaft or hole make contact on their functional boundaries and its circularity is obtained based on the functional boundaries by enveloping features. Data for evaluating roundness error can be obtained from coordinate measuring machines. A technique for roundness error based on the curvature has been proposed to deal with coordinate measurement data. The computational geometric concepts of convex hulls are used to reduce the computation. The method developed is implemented and validated with the data available in the literature.     

基于仿增量算法的圆度误差快速准确评定

提出按最小外接圆法和最小区域法评定圆度误差的仿增量算法.将工件轮廓看作一个点集,并在其中建立可以确定圆(环)的子集.若子集确定的圆(环)包容原点集,则可得到相应的圆度误差;否则每次给子集增加一个在包容区域外的点构成新子集,确定包容新子集的圆(环)并去掉其中不在圆(环)边界上的点.证明了该算法是单调收敛的.同时还提出以按最小外接圆法评定圆度误差时在包容边界上的点为最小区域法初值的新思路.该算法概念清楚、模型简单,易于在计算机上实现.几个实际零件圆度误差的评定验证了算法不仅正确,而且结果准确,耗时极少.     

Intersecting chord method for minimum zone evaluation of roundness deviation using Cartesian coordinate data

Minimum zone evaluation of roundness deviation is a very important and complex problem in precision measurement. Along with the continuous development of precision machining technology, it has become an increasingly prominent issue of how to quickly and accurately evaluate the minimum zone roundness deviation from a large number of coordinate data. In this paper, an intersecting chord method is first proposed to realize the minimum zone model of roundness deviation with coordinate data. The new modelling method uses the crossing relationship of chords to construct the intersecting structure and the 2 + 2 evaluation model of the minimum zone roundness deviation, which can not only accurately determine the position of minimum zone centre but also greatly improve the computational efficiency of modelling process. Using the related chords and their extreme points to generate a virtual centre, this may reduce the deviation between the intersecting chords structure and the centre of the minimum zone evaluation. The proposed method makes use of the geometric relationship of chords, so the minimum zone roundness deviation can be obtained without the optimal method or the point-by-point method. The validation test of the proposed method is designed to analyze a coordinate dataset published in other literature. Comparing the proposed method with the published method, it is easy to show that the relative error between two results is less than 0.4%. Finally, an experiment is also given to indicate that the calculation accuracy and the evaluation efficiency of the proposed method achieve a satisfactory conclusion.     

Use of coordinate measuring machines and digital optical machines for the geometric characterization of circumference arcs using the minimum zone method

This paper presents an optimised method for the characterization of circular features of any amplitude, which includes the capture of geometric data, by means of the use of three-coordinate measuring machine or digital optical machines with a CCD camera, and its subsequent mathematical processing. The proposed model determines the radius and the circularity error, based on the minimum zone method, and to this end it uses linear programming techniques, the Simplex programming principles and the limaçon approximation. An experimental study on ring gauges and reference disks is provided, including a comparative analysis using the Chauvenet and Grubbs filtering procedures. Last of all, an uncertainty estimation method is proposed by means of the Monte Carlo simulation. The experimental analysis carried out on ring gauges and reference disks accredit that the algorithm developed, implemented in a Matlab® environment, gives reliable results for any circumference arc considered, regardless of its amplitude.     

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.     

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.     

三坐标测量机上形状误差评定的理论与方法

本文用线性化方法建立三坐标测量机上形状误差最小条件评定的统一数学模型，把形状误差的评定归结为线性规划问题，并采用有效集法求解。文章研究了有效集法在形状误差评定中的理论和特点，证明了有效集法的最优解条件包含了形状误差评定的最小条件和代数判别准则；阐述了该方法在处理形状误差时显得非常自然方便，简单易行，计算速度快等特点，是比单纯形法更优越的方法。文末给出一个圆柱度误差评定的实例和结果。     

无人水下航行器壳体流体动力的计算

采用计算流体力学方法对无人水下航行器壳体流体动力特性进行数值模拟与计算。计算结果与风洞试验结果对比表明,该方法对无人水下航行器壳体流体动力特性的预测精度较高。该研究成果对无人水下航行器的外形设计具有缩短周期,节约费用和降低风险的效果。     

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.     

Least squares evaluations for form and profile errors of ellipse using coordinate data

To improve the measurement and evaluation of form error of an elliptic section, an evaluation method based on least squares fitting is investigated to analyze the form and profile errors of an ellipse using coordinate data. Two error indicators for defining ellipticity are discussed, namely the form error and the profile error, and the difference between both is considered as the main parameter for evaluating machining quality of surface and profile. Because the form error and the profile error rely on different evaluation benchmarks, the major axis and the foci rather than the centre of an ellipse are used as the evaluation benchmarks and can accurately evaluate a tolerance range with the separated form error and profile error of workpiece. Additionally, an evaluation program based on the LS model is developed to extract the form error and the profile error of the elliptic section, which is well suited for separating the two errors by a standard program. Finally, the evaluation method about the form and profile errors of the ellipse is applied to the measurement of skirt line of the piston, and results indicate the effectiveness of the evaluation. This approach provides the new evaluation indicators for the measurement of form and profile errors of ellipse, which is found to have better accuracy and can thus be used to solve the difficult of the measurement and evaluation of the piston in industrial production.     

Evaluation of form error at semi-spherical tools by use of image processing

In this study, a method is proposed for dimensional measurements of semi-spherical parts for the standard tool electrodes used in Electrical Discharge Machining (EDM). The tool electrode to be measured is magnified by a profile projector. Pictures of some equatorial plane projections of the electrodes are captured by a digital camera before and after machining. The pictures were calibrated with the geometric camera calibration. Then, the profiles are extracted from their background using the adaptive threshold, which is an image processing method. 2D coordinates are first obtained and then converted to 3D coordinates. Using the obtained data, sphericity and radius are calculated by means of the minimum zone method. It is seen that the proposed method can be used for determining the EDM tool electrodes’ form error.     

Simple and efficient algorithms for roundness evaluation from the coordinate measurement data

A common problem of quality control and inspection of circular parts is the measurement of their roundness. Recently, the coordinate measuring machines (CMMs) have been used to measure roundness errors by collecting a large number of points from the profile of the rounded parts to meet the international standards. Direct evaluation of roundness from this large number of pointes is complex and time consuming. Therefore, efficient algorithms should be designed to meet the standards and to simplify and accelerate the computation process. This paper introduces simple and efficient algorithms to evaluate the roundness error from the large number of points obtained by CMMs using three internationally defined methods: Minimum Circumscribed Circle (MCC), Maximum Inscribed Circle (MIC) and Minimum Zone Circles (MZC). A software has been developed using C++ to apply these algorithms on the data obtained by CMMs. The developed algorithms were verified by comparing their results with the results obtained by a commercial instrument and the maximum variation between the two results did not exceed than ±2.27%. The efficiency of the introduced algorithms was verified in terms of computation time and the results proved the efficiency of the developed algorithms.     

Optimizing discrete point sample patterns and measurement data analysis on internal cylindrical surfaces with systematic form deviations

Selection of an appropriate sampling strategy and of the correct fitting algorithm are two of the key issues in the practice of modern coordinate metrology. A recent report described the development of new techniques for modeling the form errors of machined part features and illustrated their use in identifying and understanding the relation of form errors to machining process variables. In this report, these mathematical tools are further developed and applied for the determination of optimum, reasonably-sized probing patterns for measurement under time and economic constraints. The focus of the work reported here is on full internal cylindrical surfaces. The technique is, however, of general utility and can be employed with any nominal feature geometry. Its application does, in many cases, produce significant improvements in the uncertainty of derived geometric dimensioning and tolerancing parameters with modest or no increase in measurement time. In contrast to most work on these problems, extensive use is made of process-dependent information in selection of sampling protocol and data analysis method. Since the method begins with an understanding of the form errors introduced into the part by the particular manufacturing regime, at least partial benefit can be seen even when the sample pattern optimization is employed in conjunction with commercial, off-the-shelf CMM control and data analysis software.     

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.     

面向轴孔类零件圆度误差评定的改进式最小区域圆法

面向轴孔类零件圆度误差评定,提出了一种改进式最小区域圆法.以计算几何为基础,确定测量点间距离关系,并按照多边形去除法则优化了最小外接圆和最大内接圆的控制点求解过程;再根据最小外接圆、最大内接圆和最小区域圆三者控制点间的相互关系,实现了对最小区域的构建;最后通过实验结果验证了提出方法的有效性和准确性.     

Evaluation of spherical form errors—Computation of sphericity by means of minimum zone method and some examinations with using simulated data

Because of the practical difficulties of measuring whole spherical surface form errors, no concrete three-dimensional (3-D) verification has yet been developed. This article deals with the calculation of the value of spherical form errors; that is, sphericity. The iterative least-squares method in which the problem is linearized and the minimum zone method in which the downhill simplex method, one of the nonlinear optimization techniques, is applied are considered. The data to be analyzed are not obtained by actual measurement of a spherical surface, because there is no such a measuring system in my laboratory, but simulated by applying surface harmonics (Laplace's spherical function) with a computer. Then, the application conditions for downhill simplex method are investigated. Furthermore, the roundness values of the spherical surface are compared with the sphericity by means of the minimum-zone method.     

基于XML的异构数据交换集成技术及其实现

提出了基于XML技术的信息交换模型,采用XML文档作为底层的信息交换载体,建立了Internet/Intranet环境下的信息集成交换平台,开发实现了相应的软件构件,为低成本地实现异构数据库系统间信息的集成与共享提供了一种有力的方法和手段。该方法在供应链管理系统的数据集成与交换中得到了实际应用。     

Design of gauges and multipoint measuring systems using coordinate-measuring-machine data and computer simulation

The existing coordinate-measuring-machine programs using least square methods for the calculation of geometric elements are not suitable for the evaluation of component fitting. However, evaluation programs that supply statements that are comparable with those of gauge inspection can be used to support the design of gauges and multipoint measuring systems. How to optimize an inspection device by simulation in practice is shown by the example of a forged bevel gear.     

Palynological investigation of some selected species of family Fabaceae from Pakistan,using light and scanning electron microscopy techniques

Pollen morphology of 11 species of family Fabaceae that is, Trifolium alexandrinum, Trifolium resupinatum, Arachis hypogaea, Lathyrus aphaca, Medicago lupulina, Vicia sativa, Lathyrus odoratus, Pongamia pinnata, Melilotus indicus, Medicago polymorpha, Medicago sativa from Pakistan has been investigated by light and scanning electron microscopy. Pollen were generally tricolporate, radially symmetrical, isopolar, elliptic in equatorial view and triangular in polar view under LM. Results showed that pollens were per‐prolate (T. alexandrinum), prolate (T. resupinatum, V. sativa, L. odoratus, Melilotus indicus, M. polymorpha, M. sativa) and sub‐prolate (A. hypogaea, L. aphaca, M. lupulina, P. pinnata). The larger polar/equatorial (P/E) ratio was found in T. alexandrinum (2.26 μm) and the smallest was found in M. lupulina (1.21 μm). The exine of T. resupinatum was 3.00 μm in thickness while others posses smaller exine thickness. The larger pore diameter was found in P. pinnata (16.01 μm) while others have smaller. The length of colpi was larger in Arachis hypogaea (32.24) while others posses smaller. Eight types of surface ornamentation (Psilate, faintly rugulate). Perforate and rugulate to verrucate have been observed under SEM. The pollens were europalynous type. Pollen morphology proved to be useful for the specific delimitation and serve as a tool for the identification and classification of taxa at specific and generic levels and can also be used as a key for the taxonomic features. Diversity in exine sculpture is helpful indicative characters for the isolation of closely related species. Hence, it is clear that both qualitative and quantitative characters of pollen can be useful for differentiating between taxa at specific level.