Adaptive sampling for coordinate metrology

An iterative sampling process for dimensional measurement is presented. The strategy is based upon the use of surface normal measurement data to develop an interpolating curve between sample points. The interpolant is used to select subsequent measurement targets iteratively. The process is repeated until the measurement converges to a complete and accurate evaluation of the surface. The required sample size is proportional to part quality. The most accurate parts will require the least sample points; whereas, lower quality parts will require a greater number of total samples. The method is particularly applicable to measurement of complex surfaces with coordinate measuring machines (CMMs).     

Functionality-oriented evaluation and sampling strategy in coordinate metrology

This is a review on the evaluation criteria and sensing strategy used in coordinate metrology today. The necessity of basing future evaluation entirely on the test objective (product function, process control), the evaluation methods (algorithms) this requires, and the needed sampling strategy (including datapoint distribution) are described.     

A new free-form surface fitting method for precision coordinate metrology

Free-form surfaces are widely used in advanced optical and mechanical devices. In order to assess the form accuracy of free-form surfaces, it is needed to fit the measurement surface with the design template. To improve the fitting efficiency and accuracy, the fitting procedure is divided into two stages, rough fitting and final fitting. A new rough fitting method, called structured region signature is proposed. Structured region signature is a generalised global feature which represents the surface shape by a one-dimensional function. The template location occupying the best fitting signature is considered to be the correct initial position of the measurement surface. In the final fitting, the motion parameters are calculated iteratively using the Levenberg-Marquardt algorithm. Simulation and experiments are given to identify the validity of this method. It is demonstrated that the fitting accuracy is as high as 1:10⁶.     

Volumetric phase-measuring interferometer for three-dimensional coordinate metrology

We present a volumetric interferometer that has been specially designed to improve the measurement accuracy of the three-dimensional coordinate metrology by reducing excessive Abbe offsets. The interferometer is composed of two main parts; one is a three-dimensionally movable target and the other is a stationary two-dimensional array of photo-detectors. The target made of point diffraction sources emanates two spherical wavefronts, of which interference intensity is monitored by the photo-detectors. Applying phase shifting allows the phases of the photo-detectors to be precisely obtained, and the measured phases are fitted to a geometric model of multilateration so as to determine the xyz-location of the target by minimizing least square errors. A prototype built on a CMM demonstrates that the proposed interferometer is capable of measuring the xyz-coordinates of the probe with a volumetric uncertainty of less than 1.0 μm.     

Fiber deflection probe for small hole metrology

This paper presents the development of a new probing method for coordinate measuring machines (CMM) to inspect the diameter and form of small holes. The technique, referred to as fiber deflection probing (FDP), can be used for holes of approximately 100 μm nominal diameter. The expanded uncertainty obtained using this method is 0.07 μm (k = 2) on diameter. The probing system consists of a transversely illuminated fiber (with a ball mounted on the end) whose shadows are imaged using a camera. We can infer the deflection of the probe from the motion of the image seen by the camera, and we infer the position of the measured surface by adding the fiber deflection along x- and y-directions to the machine scale readings. The advantage of this technique is the large aspect ratio attainable (5 mm deep for a 100 μm diameter hole). Also, by utilizing the fiber as a cylindrical lens, we obtain sharp crisp images of the fiber position, thus enabling high resolution for measured probe deflection. Another potential advantage of the probe is that it exerts an exceptionally low force (ranging from a few micronewtons down to hundreds of nanonewtons). Furthermore, the probe is relatively robust, capable of surviving more than 1 mm over-travel, and the probe should be inexpensive to replace if it is broken. In this paper, we describe the measurement principle and provide an analysis of the imaging process. Subsequently, we discuss data obtained from characterization and validation experiments. Finally, we demonstrate the utility of this technique for small hole metrology by measuring the internal geometry of a 129 μm diameter fiber ferrule and conclude with an uncertainty budget.     

Assessment of sculptured surface milling strategies using design of experiments

Product manufacturing on CNC milling machine tools involves a number of machining parameters and tool geometries. In the case of sculptured or free-form surfaces the number of these parameters can be significantly large and vary according to surface complexity. Minimising the number of parameters is carried out through statistical elimination. Design of experiments (DoE) along with the respective statistical analysis of variance (ANOVA) constitutes a low-cost useful tool in determining sub-optimum values for all parameters involved in each milling strategy as well as the most significant of those parameters. DoE was implemented for a particular sculptured surface assessing a variety of roughing and finishing strategies of a CAM simulation software.     

用圆柱铣刀与不可展直纹面的二阶切触及蒸汽机车排汽叶轮加工

把微分几何中曲线与曲面之间的“切触”概念应用于不可展直纹面的数控加工，提出用圆柱铣刀的外圆在五坐标联动中加工的最不可展直纹面最佳切触条件。并应用于蒸汽机车排汽叶轮加工。     

Determining the cutting conditions for sculptured surface machining

This paper deals with a new method for determining cutting conditions for the machining of 3D sculptured surface shapes with a ball endmill. Since the interaction area between workpiece and cutting tool changes during ball endmill machining, the cutting conditions have to be changed accordingly. To determine the spindle speed, the tool-workpiece contact area is obtained from the depth of cut, path interval, and cutter contact (CC) data. The spindle speed is determined so that the tangential cutting speed of the centroid of the tool-workpiece contact area becomes the value suggested in the machining data handbook. The feedrate is determined so that the material removal rate is maximised within the range of the cutting-force constraint. The practical feasibility of the proposed scheme has been verified through experiments performed on a workpiece with sculptured surfaces. The test result shows that the new method can be used to increase the tool life, and improve the production rate.     

基于从明暗恢复形状的雕塑曲面三维形状重构

在从明暗恢复形状问题(由物体二维灰度图象提取其表面高度值的问题)的基本原理和数学模型的基础上,提出了一种求解该问题的算法,利用变分原理和有限差分方法得到了算法的迭代方程。这里将该算法应用于雕塑曲面的三维形状重构,通过对人工合成图象的计算及数控加工实验证明了该算法具有一定的实用价值。     

复杂曲面CNC加工技术的曲面包络逼近原理

针对当前数控加工技术以“点”去除方式加工复杂曲面效率很低的缺陷,提出了以“线”去除方式加工复杂曲面的CNC制造技术的曲面包络逼近原理。论述了以曲面活动标架思想描述和控制刀具相对工件运动的微分几何方法,建立了刀具包络面以最小误差逼近目标加工曲面的刀具运动优化模型。最后,以一个点啮合齿面的数控加工实例论证了该方法的精确性和可行性。     

3D surface form error evaluation using high definition metrology

This paper presents an approach to evaluate 3D surface form error of machined surface using high definition metrology that can measure millions of data points representing the entire surface. A data preprocessing method was developed to convert the mass data into a height-encoded and position-maintained gray image. With the converted image, a modified gray level co-occurrence matrix method was adopted to extract 3D surface form error characteristics, including entropy, contrast and correlation. Entropy measures the randomness of surface height distribution. Contrast indicates the degree of surface local deviations. Correlation could be used to identify different machining techniques. These characteristics can be used with flatness together to evaluate 3D surface form error of large complex surface.     

A universal spline filter for surface metrology

In this study, a novel fractional spline filter is proposed for surface metrology. The filter combines arbitrary order fractional spline function with variational principle, and is endowed with an adjustability of transition characteristic. If the order is high enough, the fractional spline filter can obtain more step-edge-like cut-off characteristic of the low-pass filter, and it can also realize the transmission characteristic of the Gaussian filter with high accuracy if the order equals to two. In addition, if the approximation parameter is set to zero, this filter will be simplified to a form of ordinary spline filter. Therefore, this fractional spline filter is called the universal spline filter. In order to reduce the computation time, the universal spline filter is calculated by a fast Fourier transform (FFT) algorithm. Furthermore, for practical use, an improved method prior to the FFT algorithm is proposed to suppress the end effect. Finally, the efficiency of the whole algorithm in comparison with the ordinary spline filter is demonstrated by the experiments, and it is also shown that the universal spline filter is able to alleviate the end effect significantly.     

基于坐标测量机的自由曲面检测采样策略

为了实现自由曲面快速精确的检测和评定,研究了检测过程涉及的采样策略。提出采用随机Hamersley采样、简单随机采样和列系统采样3种方法设置自由曲面上的测量点。采用拟粒子群算法优化变换参数,实现被测曲面与设计曲面之间的定位,采用曲面细分法搜索设计模型上与被测点距离最近点以计算自由曲面轮廓度误差。为了对基于坐标测量机(CMM)在不同采样策略下的检测结果进行比较,采用非均匀有理B样条生成零件设计模型,选择相同的加工工艺在不同的加工中心加工多个零件得到粗糙度不同的自由曲面。最后,使用CMM在所设计的采样策略下实测零件,用提出的方法计算零件的轮廓度误差,并与CMM内置软件的计算结果进行比较。实验结果显示:选择随机Hammersley采样法和中等采样点数的采样策略检测效果最佳,不仅测量精度高,而且耗时少、成本低。应用提出的方法计算自由曲面轮廓度误差时,其精度比由CMM内置软件计算结果高10%~22%,表明提出的方法适用于自由曲面零件轮廓度误差的快速精确检测与评定。     

A quick deviation zone fitting in coordinate metrology of NURBS surfaces using principle component analysis

Evaluation of the tolerance zone using discrete measured points plays a critical role in today’s manufacturing, metrology, and many industrial applications. The deviation zone is typically evaluated using a fitting method that locates an ideal desired geometry corresponding to a set of measured points while a function of the Euclidean distances of the measured points to the ideal surface becomes minimum. This paper presents a quick and reliable algorithm called Dynamic Principle Component Alignment (DPCA) for fitting complex surfaces to the coordinate metrology measured points using the information that is dynamically generated by Principal Component Analysis (PCA) of the measurement data and the corresponding fitted geometry. The developed algorithm efficiently eliminates the necessity for applying commonly used optimization methods for the fitting (localization) process, which decreases the computational cost and uncertainty of the evaluation process. Moreover, DPCA is very reliable and practical in coordinate metrology with large data sets in processes such as laser scanning and other optical methods. The results show that the proposed methodology more accurately finds fitting parameters in comparison with the other commonly used methods while the computational cost is considerably reduced.     

Combined reparameterization-based spiral toolpath generation for five-axis sculptured surface machining

Reparameterization-based toolpath generation methods are usually adopted for machining triangular meshes, trimmed surfaces and compound surfaces. The quality of the reparameterization has an important effect on that of the surface. In this paper, a combined reparameterization procedure is introduced to generate an optimal mapping between the designed surface and a specified planar circular region with relatively less distortion both in length and in angle. Then, for five-axis sculptured surface machining the mathematical model of spiral guide path with maximum path interval is constructed in the circular region. Cutter contact paths are obtained by inversely mapping the guide path onto the designed surface. Under constraints of gouging and collision, continuous and optimal cutter orientations are subsequently calculated. Finally, the results of simulation and experiment of the machining process are given to illustrate the feasibility and applicability of the proposed method.     

采用光学测棒的三目视觉坐标测量系统的理论研究

本文提出了一种基于手持式测量棒的三目视觉坐标测量系统。文中阐述了该系统的结构设计理论及测量原理，引入了一种全新的采用冗余差分技术的测量棒的结构．并且对其结构特点．及其实现自标定的原理进行了详细的分析。     

Improved measure of workpiece surface deterioration during turning using non-contact vision method

The surface finish quality of a machined workpiece is commonly measured using the average roughness parameter, R_a. This parameter, however, is insensitive to the lateral changes undergone by the surface in the feed direction as a consequence of tool wear. In this work, the effectiveness of four methods of workpiece surface analysis, namely autocorrelation, cross-correlation, and two new methods, called lateral material shift (LMS) ratio and profile slope ratio (PSR) analyses are investigated. Dry machining experiments were carried out on 316 stainless steel. Images of tool nose and workpiece profiles were captured using digital camera, and the edges were extracted using sub-pixel edge detection. In the autocorrelation approach, each workpiece profile was correlated with a shifted version of the same profile. In the cross-correlation approach, the workpiece profiles at different stages of machining were correlated with a reference profile generated using the unworn tool edge. In the LMS ratio method, the material shift ratios were determined from each waveform on the workpiece profile at various stages of tool wear, while in the PSR method the slopes at the right and left part of the waveform were compared. Among the four methods, the LMS ratio method produced the best correlation with tool flank wear with the maximum R-squared value of 0.9461, while average roughness R_a showed no correlation at all with both major and nose flank wear.     

An improved tool path discretization method for five-axis sculptured surface machining

The genetic algorithm (GA) is a heuristics, and commonly used to solve combinational problems. It has been proven to have high effectiveness and efficiency in many application areas. However, a successful GA application requires adapting the algorithm to the characteristics of a problem. In the past decades, various articles on single machine earliness and tardiness (SET) problem using a heuristic approaching have been published. Yet, there are few research addressing the area of the SET problem with distinct due dates and ready times for jobs. In this paper, a designed GA, modified optimal timing procedure, which starts the searching with a feasible solution obtained by applying the EXP-ET rule developed by Ow and Morton is developed for the SET problem. Computational results in the provided experiment show that the designed GA improves the SET solution in both quality and efficiency.     

Exudates segmentation using inverse surface adaptive thresholding

This paper presents a new approach to detect exudates and optic disc from color fundus images based on inverse surface thresholding. The strategy involves the applications of fuzzy c-means clustering, edge detection, otsu thresholding and inverse surface thresholding. The main advantage of the proposed approach is that it does not depend on manually selected parameters that are normally chosen to suit the tested databases. When applied to two sets of databases the proposed method outperforms methods based on watershed segmentation and morphological reconstruction. The proposed method obtained 98.2 and 90.4 in terms of sensitivity for Standard Diabetic Retinopathy Database – Calibration Level 1 (DIARETDB1) and a local dataset provided by National University Hospital of Malaysia (NUHM), respectively.