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.     

Establishing circle and circular-cylinder references using computational geometric techniques

Form deviations of cylindrical features present in the manufactured parts are measured using coordinate measuring machine (CMM) and expressed as circularity or cylindricity errors evaluated using appropriate reference features. In the present work, computational geometric techniques are used to establish a circle as reference feature, and a heuristic algorithm is proposed to get a unique convex inner hull. Using the concept of equi-distant lines and diagrams, minimum circumscribed (MC), maximum inscribed (MI), and minimum zone (MZ) circles are established. For the first time, algorithms purely based on computational geometric concepts have been developed in the present work to arrive at MC, MI, and MZ circular cylinders. As the algorithms and the implementation details are explained with simple data sets, the practitioners can easily understand these methods and implement them in CMMs for the evaluation of circularity and cylindricity errors. The algorithms are also tested on larger datasets, and in all cases, accurate results are obtained in less than a second.     

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.     

计算几何在测试计量技术中的应用--求解最大内接圆

本文介绍了采用计算几何知识求解最大内接圆的新方法,该方法摆脱了传统的用坐标及函数处理几何问题的常规,从图形的崭新思路分析了最大内接圆的准确中心,并且提出了一种删除无关数据点的原则、可将采样点数减至十分之一以下。相应算法的运算时间比以往的算法快１５倍以上。     

三维焊缝形貌信息的变基准测量数据处理方法

为了实现大型航空航天薄壁结构件的精密激光焊接,在研制开发＂5＋2＂轴激光焊接测量系统的基础上,提出了一种变基准测量数据处理方法,通过齐次坐标变换,将表达在局部测量基准下的三维焊缝形貌信息转换到统一的机床基准下,建立了三维焊缝的几何模型,并对机床几何误差进行了分析与补偿。以某型号航空航天结构模拟件为例,通过在线测量、数据处理、几何建模以及编程加工进行验证,结果表明该方法能够满足实际加工的要求。     

Measurement point prediction of flatness geometric tolerance by using grey theory

The objective of this study is to improve the efficiency in achieving accurate and speedy inspection when coordinate measuring machine (CMM) is used to measure geometric tolerance. The grey prediction in grey theory was applied in developing the algorithm for predicting the number of measuring points required for measuring geometric tolerance in this article. The said algorithm was used to plan the number of measuring points of the next workpiece and to predict the geometric tolerance dimension of the next workpiece. This step provided better foundation for on line inspection to determine the number of measuring points required for measurement inspection of the next workpiece. Besides, it can predict whether the geometric tolerance of the next workpiece conform with the geometric tolerance dimension marked on the design drawing. This algorithm is used to determine whether the manufacturing process requires modification, in an attempt to save human and material resources and improve failure rate.In this paper, the said algorithm refers to the flatness measurement point algorithm in a plane of the workpiece. In planning for the increase of measuring points, this algorithm is bound by the principle of keeping the measurement scope a rectangular shape by adding a row of measuring points. When the prediction value exceeds the designation dimensions range, immediate inspection of the manufacturing process is needed. The concept of on line inspection of the addition of measuring points is also incorporated together with the grey prediction model and concept of standard deviation model in an effort to develop the said algorithm.Experimental data were also introduced to verify the flatness geometric tolerance measuring points algorithm for the flatness geometric tolerance in a workpiece plane. The objective is to reach a balance between the smallest number of measuring points possible required for inspection and inspection accuracy. Consequently, one can avoid using too many measuring points, which increases the inspection time, while achieving the required measurement accuracy.     

Robust generalized numerical inspection fixture for the metrology of compliant mechanical parts

Free-form non-rigid parts form the essence of today’s automotive and aerospace industries. These parts have different shapes in free state due to their dimensional and geometric variations, gravity and residual strains. For the geometric inspection of such compliant parts, special inspection fixtures are used in combination with coordinate measuring systems (CMM) and/or optical data acquisition devices (scanners). In our previous work, a general procedure was developed to eliminate the use of inspection fixtures. We measured the similarities between CAD model and scanned data by taking the advantage of the geodesic distance metric. Then, using finite element non-rigid registration, we deformed the CAD model into range data to find the geometric deviations. Here, we apply a new method to robustify the generalized numerical inspection fixture. We filter out points causing incoherent geodesic distances and demonstrate that our approach has several significant advantages, one being the ability to handle parts with missing range data. The other advantage of the method presented is its capacity to inspect parts with large deformations.     

6D MEASURING TECHNOLOGY AND METHOD OF COORDINATE TRANSFORMATIONS IN THE AUTOMOBILE BODY-IN-WHITE MEA

６ＤＭＥＡＳＵＲＩＮＧＴＥＣＨＮＯＬＯＧＹＡＮＤＭＥＴＨＯＤＯＦＣＯＯＲＤＩＮＡＴＥＴＲＡＮＳＦＯＲＭＡＴＩＯＮＳＩＮＴＨＥＡＵＴＯＭＯＢＩＬＥＢＯＤＹ－ＩＮ－ＷＨＩＴＥＭＥＡＳＵＲＥＭＥＮＴＷａｎｇＢａｏｇｕａｎｇ，ＺｈｕＭｅｎｇｚｈｏｕＴｉａｎｊ...     

Evaluation of the form errors of axisymmetric components

The form errors of three-dimensional surfaces have an effect on the proper functioning of an assembly. Methods for evaluating form errors of surfaces of spherical and cylindrical components are available. However, in most machines and instruments the functional components are axisymmetric, e.g. spindles, and have varying geometry in the form of steps, tapers etc. Evaluation of the form errors at different zones on the component as well as a form error characteristic of the whole component is required in such cases. To do this coordinate data or circularity traces are obtained at different horizontal sections using a coordinate measuring machine or a roundness measuring instrument respectively and the required form error is then evaluated. Different algorithms developed for fitting the axis of the component which is the first step in the evaluation of form errors are described. The method of normal least-squares fitting was found to be superior to the general least-squares method.     

Nonrigid geometric metrology using generalized numerical inspection fixtures

Freeform surfaces have become an integral part of the automobile and aerospace industries. The parts with a very thin wall in proportion to their size are referred to as nonrigid (or flexible) parts. Generally, for the geometric inspection of such flexible parts, special inspection fixtures, in combination with coordinate measuring systems (CMM), are used because these parts may have different shapes in a free state from the design model due to dimensional and geometric variations, gravity loads and residual strains. A general procedure to eliminate the use of inspection fixtures will be developed. Presented methodology is based on the fact that the interpoint geodesic distance between any two points of a shape remains unchangeable during isometric deformation. This study elaborates on the theory and general methods for the metrology of nonrigid parts. We will merge existing technologies in metric and computational geometry, statistics, and finite element method to develop a general approach to the geometrical inspection of nonrigid parts.     

Circle fitting from the polarity transformation regression

Geometrical fitting is useful in different fields of science and technology, in particular least squares minimum (LSM) methods are widespread in contact probing for coordinate measuring machines, as well as a reference shape for surface metrology. We present a new intuitive and simple LSM algorithm for circle fitting, the polarity transformation regression. It is a non-linear algebraic method from a generic geometric transformation. We derive the explicit expression of the model estimators from the data points. Then, the algorithm is compared with other methods based on simulation and some literature data sets. The proposed algorithm presents a comparable accuracy, low computational effort and good behavior with outliers based on the initial test, outperforming other well-known algebraic methods in some of the studied data sets. The basis of the algorithm is finally suggested for other potential uses.     

三坐标测量机非刚性效应测量误差分布特征

本文采用坐标运动链系统分析法,研究三坐标测量机组成构件和运动副的各项基本误差与整机综合坐标测量误差间的关系,导出考虑构件和运动副非刚性效应的综合坐标测量误差数学表达式,并以移动桥式和固定桥式两种典型结构的三坐标测量机为例,进一步分析了非刚性效应坐标测量误差的空间分布特征,得出对三坐标测量机的综合非刚性效应坐标测量误差建模补偿有指导意义的新结论。     

The Application of Grey Theory to the Prediction of Measurement Points for Circularity Geometric Tolerance

The objective of this study is to improve the efficiency of achieving accurate and speedy inspection when a coordinate measuring machine (CMM) is used to measure circularity geometric tolerance. Grey prediction using grey theory was applied in developing the heuristic algorithm for predicting the number of measuring points required for measuring circularity geometric tolerance. The heuristic algorithm was used to plan the number of measuring points of the next workpiece and to predict the circularity geometric tolerance dimensions. This step provides a better foundation for on-line inspection to determine the number of measuring points required for measurement inspection of the next workpiece. It can also predict whether the circularity geometric tolerance of the next workpiece will conform with the circularity geometric tolerance dimension on the design drawing. This heuristic algorithm could also be used to determine whether the manufacturing process requires modification, in order to save human and material resources and reduce failure rate. In this paper, a circularity heuristic algorithm for deciding the number of measuring points for the circularity geometric dimension is proposed to reduce the angle between measuring points. In this heuristic algorithm, the addition of measuring points is determined by whether the predicted circularity value exceeded the scope of the grey interval. When more points are to be inspected, equiangular inspection is again performed. Once the predicted circularity value exceeds the limitation of the design drawing circularity geometric dimensions, the manufacturing process is examined immediately. The concept of adding measuring points for on-line inspection is combined with the grey prediction and the standard deviation concept to establish the circularity heuristic algorithm for deciding the number of the measuring points. Experimental data are also introduced to verify the measuring point algorithm for the circularity geometric dimension of a workpiece. The objective is to reach a balance between the smallest number of measuring points required for inspection and inspection accuracy. Consequently, it is possible to avoid using too many measuring points, which increases the inspection time, while achieving the required measurement accuracy. using too many measuring points, which increases the inspection time, while achieving the required measurement accuracy.     

基于加工中心的在机测量系统

开发了利用加工中心和自行开发的测量软件实现的坐标测量系统。在加工中心主轴上安装触发式测头,利用加工中心的高精度行走机构,运行在机测量软件生成的测量主程序和典型几何特征的测量宏程序,对在机加工的工件进行坐标测量;测头接触工件时产生触发电信号,数控系统记录此时的机床三个坐标值作为测点数据,测量完成后将所有的测点数据传送回测量软件;利用编制好的算法对工件实现尺寸、形状和位置误差的计算与评价,使加工中心实现坐标测量机的功能。     

Computational methodologies for evaluating form and positional tolerances in a computer integrated manufacturing system

In any manufacturing process, the manufactured parts always show some kind of variation in their geometric characteristics (e.g. form, size, orientation, and position). To achieve the desired part quality, these geometric characteristics need to be maintained within predetermined design limits as defined by tolerances. After a part is manufactured, it is then inspected to tolerance specifications. In industries, coordinate measuring machines (CMMs) and vision systems are widely used to accomplish the verification tasks. Owing to the lack of proper definitions and implementational details of the correct assessment criteria for different geometric characteristics, it is difficult to develop appropriate algorithms for the inspection software of the CMMs. Though the standards have used the concepts of the tolerance zones (TZs) [1] and minimum zones (MZs) [2] for other geometric (e.g. form, location, etc.) characteristics, the incompleteness in their definitions creates ambiguities in implementing the inspection procedures. It is necessary to develop rigorous definitions of the geometric characteristics (of manufactured parts) that are to be established from discrete, manufactured data points in terms of either TZs or MZs. It is also important to establish the required mathematical criteria for assessing those geometrical characteristics of the manufactured features. In this paper the concepts of TZ and MZ have been thoroughly investigated for establishing practical methodologies for part inspection.     

Determination of Best Objective Function for Evaluating Geometric Deviations

Laser scanning equipment and coordinate measuring machines are used to sample points from manufactured surfaces for inspection purposes. The sampled points are then used to evaluate the geometric deviations associated with the surface. The evaluation of geometric deviations involves an optimisation step which fits a substitute surface to the measured points, while minimising the error between the substitute surface and the measured points. The geometric deviation is equal to the difference between the maximum and the minimum normal distances between the fitted surface and the measured surface points. The choice of the objective function used in fitting the substitute surface affects the accuracy by which the geometric deviations are estimated. This paper presents a procedure for determining the best fitting function. It considers the trade-off between the accuracy of the estimation and the susceptibility to measurements and sampling errors. The proposed procedure has been verified for a number of geometric deviation types. Those results show that adopting a generic form for the fitting objective function may lead to large estimation errors with some geometric deviations, and that the proposed procedure reduces these errors significantly.     

Method for enhanced accuracy in machining curvilinear profiles on wire-cut electrical discharge machines

The present article describes a method for enhanced accuracy in machining components produced on CNC wire-cut electrical discharge machines. In this method, machining programs are generated on the basis of nominal geometric models of the produced objects, developed in CAD/CAM systems. After the initial machining, coordinate measurements are performed. On the basis of these measurement results, the values and distribution of the machining deviations are determined. The obtained information is then used to modify the nominal geometric models of the produced objects and to correct the machining programs. After that, the machining process and measurements are repeated. The method described in the present article was verified using the example of a curvilinear profile, produced with the use of a wire-cut electrical discharge machine.     

基于标准器的大尺寸测量系统坐标统一化方法

针对大尺寸测量系统坐标统一化过程中公共点的测量误差不可控制的问题,提出了利用可现场溯源的标准器取代传统的独立公共点的方法。设计了一种标准器,并用更高精度等级的三坐标测量机对标准器上各个目标点之间的空间几何位置关系进行标定,把这些几何位置关系作为约束条件。现场应用中多站大尺寸测量仪分别测量标准器上的目标点,计算出各个几何关系与通过标定的约束关系之差,将这个差值与设定的误差限进行比较,确定公共点的测量值是否有效。对该方法进行了理论分析和仿真证明。提出了7参数坐标配准算法对大尺寸测量进行空间坐标数据配准。用激光跟踪仪和激光雷达及4个标准器进行现场实验,实验结果与传统方法相比,坐标配准误差得到降低。为了进一步验证该方法的有效性,把一根经过检定的基准尺放置于测量空间的12个不同位置,使用标准器约束前后的两组坐标配准参数分别计算基准尺长度的平均值和标准差。实验结果表明,使用标准器约束方法能够提高大尺寸测量系统坐标统一化精度。     

摆线齿轮极坐标径向跟踪测量技术的研究

摆线齿轮的几何精度直接影响摆线齿轮减速机及摆线油泵等产品的性能。本文以极坐标测量原理为理论基础,研究采用极坐标径向跟踪测量技术的基于DSP(digital signal processor)和FPGA(field programmable gate array)数据采集、控制系统的摆线齿轮测量仪,通过USB接口和上位机进行通讯。根据数学模型,解决了测头实际接触位置的误差补偿问题。使用该仪器,可以对摆线齿轮的齿廓进行高效率、连续自动跟踪测量,以实现对摆线齿轮误差的测量和综合评定。