Automated visual inspection of geometric tolerance in circular components

In the manufacture of engineering products circular features are widely used. Roundness is one of the basic form errors encountered in circular features. The analysis of roundness error becomes crucial in the case of automated inspection. This paper presents mathematical models and algorithms to determine the roundness error in circular features using digital vision systems. Different approaches for determining out-of-roundness error are investigated and a proper approach is suggested. A methodology is proposed to determine the out-of-roundness error and number of lobes present in circular components. The proposed algorithm has been implemented and its reliability is reported in the paper     

Profile evaluation of radial Fresnel lens directly machined on roller molds by rotating-tool diamond turning

In Roll-to-Roll manufacturing of high-quality optical Fresnel lens films, a high-precision roller mold with super-fine surface quality is essential to precisely transfer the functional microstructures from the periphery roller surface onto the flexible substrate. Unfortunately, direct diamond turning of deep circular grooves on the periphery surface of a roller mold was considered infeasible. Recently, the team has developed a novel 4-axis interactive tool-workpiece motion, Rotating-tool diamond turning (RDT), as a solution to overcome this challenge. Experiments were conducted to justify the capability of the proposed RDT process by directly machining a radial Fresnel lens on a brass roller mold, but without precise 3D profile evaluation of the lens on the roller surface. On-machine measurement of the machined lens structures using 3D touch probe is not applicable because the diameter of the probe is relatively large to penetrate into steep grooves of the Fresnel lens. On the other hand, off-machine measurement using stylus profilometer will introduce inevitable alignment errors during the measurement and lead to mismatched machining and measurement coordinates, making it difficult to evaluate the 3D lens profile generated by the RDT process eventually. In this study, a compensation and comparison algorithm is presented to precisely evaluate the form error between the machined and designed features in a three dimensional manner. Alignment errors generated when positioning the roller mold on the stylus profilometer are investigated and quantified through analyzing the characteristics of this unique micro structure with Fresnel lens wrapped on the roller periphery. As a conclusion, the machined lens structure is compensated and restored to compare with the designed profile, and the form error is obtained with the sources of errors analyzed. Such profile compensation and comparison method can be applied in other measurement and characterization studies on evaluation of complex optical structures patterned on roller molds for Roll-to-Roll manufacturing of advanced functional films.     

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.     

用齿条刃边测头在机测量大型齿轮齿向误差

对渐开线齿轮廓面特性进行了映射分析 ,介绍了齿条刃边测头在机测量大型齿轮齿向误差的基本原理及测量方案 ,建立了齿向误差的数据评定模型 ,并给出了测量实例     

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.     

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.     

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.     

A design advisor for the optimal inspection of circularity tolerance

In the wake of growing importance for quality and the need to reduce inspection costs simultaneously, the need for a scientific method of selecting an optimum inspection strategy for coordinate measuring machine (CMM) based inspection has become very important. The inspection error resulting from CMM inspection is greatly affected by the profile irregularities and the sampling strategy, which includes sample size, sampling methods, and algorithms used for form evaluation. This paper describes a system that can recommend an optimal inspection plan based on the needs of the user. A design of experiments (DOE) based approach is used to relate the inspection error with sampling strategies. Surface irregularities are included in the form of lobes formed on the profile. A new two-way model is proposed that works in both directions between the sampling strategy and the performance metrics. The results indicate that the number of lobes and the sampling method used have little impact on the inspection error, while the sample size and form evaluation algorithms have a significant influence. An inspection plan advisor is presented, which provides an inspection plan based on the estimated shape and acceptable measurement error.     

一种复杂二次曲面轮廓度评定方法

为了建立复杂二次曲面轮廓度评定中计算机数据处理的理论模型和实现方法,提出了一种不要求满足小误差假设、不使用微分线形化评定二次曲面轮廓度的方法。该方法首先通过最小二乘法得到一个初始二次曲面,然后用模式搜索对初始二次曲面系数进行调整,直到找到满足最小区域原则的理想二次曲面,其目标函数值作为被测曲面的轮廓度。在计算过程中使用坐标变换将一般型的二次曲面化为标准型,既简化了轮廓度的计算,而且被测曲面可以在测量范围内任意放置。对抛物面轮廓度评定表明目标函数随着模式搜索的进行逐渐减小,模式搜索得到的抛物面轮廓度值比用最小二乘法得到的轮廓度值小得多,因此该方法更好地反映了被测二次曲面表面形状误差。     

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.     

圆弧齿廓谐波齿轮传动齿形设计中的几个问题

谐波齿轮传动采用圆弧齿廓后,可以改善柔轮齿根的应力状况和传动的啮合质量,提高承载能力和扭转刚度。本文首先计算出柔轮采用圆弧齿廓时,刚轮与之共轭的理论齿廓,通过用拟合圆弧对其进行逼近,得到拟合误差的变化规律;最后指出在开发双圆弧齿廓谐波齿轮传动时,应首先合理确定波发生器形式和柔轮径向变形量系数。     

Comprehensive assessment algorithm for calculating CEP of positioning accuracy

This study aims to evaluate the inertial navigation systems’ performance. To this end, we comprehensively investigate 12 methods for calculating the circular error probability (CEP). Using data processing techniques, we classify these methods into three categories: parameterization of one-dimensional variables, computation of bi-normal random variables, and numerical integration. From these methods, we develop algorithms and programs, which are subsequently applied in evaluating the positioning accuracy of navigation systems. Using the algorithms and programs, we perform simulations to evaluate applicability and evaluation accuracy under the same initial conditions. Practical test data are employed to validate the results. Using the comparison of the methods as bases, we put forward a comprehensive practical method regarding sample number and evaluation accuracy. Our results serve as a theoretical reference for the development of different approaches to assessing inertial positioning accuracy in accordance with applicable standards.     

Roundness modeling of machined parts for tolerance analysis

Out-of-roundness of circular and cylindrical parts can greatly affect assembly accuracy. At present, the ASME Y14.5M-1994 specifies circularity tolerance based on two extreme circular boundaries to confine the highest peak and the lowest valley of a roundness profile; however, the profile variations within the two extreme boundaries are not accounted for. In this paper, we propose a harmonic roundness model using Fourier series expansion. In addition, a cutting profile model has been developed to illustrate the relationship between the radial error motion of a spindle and the resultant part profile. This relationship is then used to provide physical meanings to the harmonics generated by the proposed roundness model for a part profile, in particular those caused by fractional frequency spindle error motions. The proposed harmonic model has been verified statistically by a large number of real profiles produced by both turning and cylindrical grinding processes. The proposed roundness model is expected to provide insights into the advanced tolerance analysis of circular and cylindrical parts.     

Profile error evaluation of free-form surface using sequential quadratic programming algorithm

Profile error of free-form surface is evaluated in this paper based on sequential quadratic programming (SQP) algorithm. The optimal localization model is established with the minimum zone criterion firstly. Subsequently, the surface subdivision method or STL (STeror Lithography) model is used to compute the point-to-surface distance and the approximate linear differential movement model of signed distance is deduced to simplify the updating process of alignment parameters. Finally, the optimization model on profile error evaluation of free-form surface is solved with SQP algorithm. Simulation examples indicate that the results acquired by SQP method are closer to the ideal results than the other algorithms in the problem of solving transformation parameters. In addition, real part experiments show that the maximum distance between the measurement points and their corresponding closest points on the design model is shorter by using SQP-based algorithm. Lastly, the results obtained in the experiment of the workpiece with S form illustrate that the SQP-based profile error evaluation algorithm can dramatically reduce the iterations and keep the precision of result simultaneously. Furthermore, a simulation is conducted to test the robustness of the proposed method. In a word, this study purposes a new algorithm which is of high accuracy and less time-consuming.     

基于NURBS曲面拟合的特大型齿轮齿廓偏差评定

在中等尺寸齿轮测量中,通常以轴线作为测量的基准,但对特大型齿轮来说,要精确获取其轴线存在较大困难。为了特大型齿轮特征线测量问题,本文提出并采用了三维测量与评定的方法。首先利用激光跟踪仪进行被测齿轮的粗定位,获取被测齿轮与三维平台的相对位置关系;然后利用所设计的三维平台在被测齿面获取大量的数据点,对这些数据点进行NURBS曲面拟合,建立真实齿面的三维参数化模型;最后将所建立的参数化模型与理论模型相比较得到齿廓等偏差。实验结果表明,该方法在解决特大型齿轮特征线测量方面具有较好的可行性。     

NC toolpath generation for arbitrary pockets with Islands

This paper presents an efficient algorithm for generating cutter paths for the NC milling of arbitrary pockets with multiple islands. In this algorithm, the pocket border and island profiles are made up of concave or convex segments comprising linear and circular arc elements. For the generation of NC tool paths, the algorithm is divided into four stages, namely, profile pre-processing stage, offset calculation, determination of the termination condition, and determination of the path sequence. Compared with the other pocketing algorithms, the main aspect of this work is that the pocket border and island profiles are pre-processed in the first stage of the algorithm. Making use of contour bridges in the profile pre-processing stage, the island profiles are connected to the pocket border profile to form a closed path. This then simplifies the calculations in cutter offsets and eliminates the problem of nesting which occurs in some other pocketing algorithms.     

Designing small samples for form error estimation with coordinate measuring machines

We propose a method for designing inspection plans of small size for use in form error evaluation of parts from batch or mass production using coordinate measuring machines. The method exploits a priori information coming from large sample inspection of one or a few parts of the lot. It is based on a regression model fitted to the large sample. The model is used twice. First, it provides the dominant pattern of the surface. Then, the deviations from the model that are relevant to form error are captured by weighting the points of the convex-hull of the large sample with the regression residuals. Based on two case studies, we show that the method provides a good accuracy in the estimation of straightness and flatness with very few measurement points. Comparative results also indicate that the method outperforms both the typical sampling schemes used in industry (random sampling, latin hypercube sampling), which do not exploit a priori information, and a recently proposed method using the same kind of a priori information.     

一种基于多方法的多传感器数据融合算法研究

提出了一种基于多方法的多传感器数据融合算法,分批估计融合求得单传感器最优估计值,然后依据权值最优分配原则进行分组自适应加权融合处理.通过对多热电偶测温的实测数据分析表明,与算术平均值法、单传感器分批估计和自适应加权相结合的算法以及单传感器分批估计和多传感器分批估计相结合的算法相比,绝对误差分别降低3.52℃,1.28℃和1.227℃,相对误差分别降低0.294％,0.107％和0.102％.     

The containment model for composite positional tolerance evaluation

The composite positional tolerance evaluation problem for planar point features and circular tolerance zones is defined and characterized under necessary and sufficient conditions. This model is then generalized to the circular feature case, and the solution to the circular feature–circular tolerance zone problem is characterized analogous to the point feature model. The circular feature–circular tolerance zone problem is formulated as a containment model and solved as a constrained nonlinear program. The three-dimensional spherical containment model is also formulated and numerical examples are used to illustrate the methodology in the two- and three-dimensional cases.     

基于工件弹性变形的薄型非球曲面(玻璃)零件加工方法研究

针对传统非球曲面加工技术存在对设备依赖度高及加工效率较低等问题,研究了薄型非球曲面零件的弹性变形加工法,并基于材料弹性变形特性,将非球曲面加工转变为平面加工。通过理论计算及ABAQUS有限元仿真确定了平板玻璃工件在均匀压力及周边简支条件下的弹性变形面型,并对工件进行了弹性变形加工实验;加工面型与理论面型误差的最小均方根、峰谷值分别为1.66μm与2.80μm,验证了使用弹性变形加工方法进行薄型非球曲面零件加工的有效性。