Measurement uncertainty assessment for virtual assembly

IF 0.8 Q4 INSTRUMENTS & INSTRUMENTATION Journal of Sensors and Sensor Systems Pub Date : 2021-04-22 DOI:10.5194/JSSS-10-101-2021
M. Kaufmann, I. Effenberger, M. Huber
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引用次数: 3

Abstract

Virtual assembly (VA) is a method for datum definition and quality prediction of assemblies considering local form deviations of relevant geometries. Point clouds of measured objects are registered in order to recreate the objects’ hypothetical physical assembly state. By VA, the geometrical verification becomes more accurate and, thus, increasingly function oriented. The VA algorithm is a nonlinear, constrained derivate of the Gaussian best fit algorithm, where outlier points strongly influence the registration result. In order to assess the robustness of the developed algorithm, the propagation of measurement uncertainties through the nonlinear transformation due to VA is studied. The work compares selected propagation methods distinguished from their levels of abstraction. The results reveal larger propagated uncertainties by VA compared to the unconstrained Gaussian best fit. 1 Current trends in dimensional metrology and state-of-the-art datum definition and uncertainty assessment As quality demands on products increase, tolerance specifications for parts become more and more complex. With these challenging geometrical specifications, verification algorithms are required that represent the geometrical system more precisely. According to Nielsen (2003), in the last few decades, dimensional tolerances shrank due to improved manufacturing systems. However, the form deviations could not be reduced by the same extent. Therefore, their consideration should be intensified. A main deficit in the current International Organization for Standardization (ISO) standard for datum definition, ISO 5459 (Deutsches Institut für Normung e.V., 2011), is the lack of consideration of local form deviations for datum features. A datum feature is defined as a “real (non-ideal) integral feature used for establishing a single datum” (Deutsches Institut für Normung e.V., 2017, p. 2). Datum systems composed of three datum features mathematically define a coordinate system. This allows the definition of tolerance zones for extrinsic tolerances (Weißgerber and Keller, 2014). About 80 % of all measurement tasks require datum systems, so a further function-oriented datum system definition has a strong impact on geometrical verification. Hence, an assessment of the uncertainty for datum systems is of broad interest. Figure 1 shows a datum definition, where three perpendicular associated planes are considered in a nested approach. The primary datum constrains 3 degrees of freedom (DOF), the secondary datum 2 DOF and the tertiary datum 1 DOF (Gröger, 2015). 1.1 Concept of the virtual assembly In this paper, measurement data of physical objects are gathered from measurements using industrial computed tomography (CT). Registration is the action of aligning a data set relatively to another according to a datum definition in a common coordinate system. Virtual assembly (VA) comprises the consideration of local form deviations in the datum system computation. As shown in Fig. 1a, through VA, the physical workpiece contact is simulated by computing the contact points. The registration for VA is mathematically stated as an optimization problem, as introduced in Weißgerber and Keller (2014). In the following, matrices are marked as boldface capital, vectors in boldface italic, and scalar Published by Copernicus Publications on behalf of the AMA Association for Sensor Technology. 102 M. Kaufmann et al.: Measurement uncertainty assessment for virtual assembly Figure 1. Datum definition by nested registration, using associated planes (a), registration approach according to the default case in the current standard, (b) and registration approach according to virtual assembly (c). values in roman formatting. The signed distances dsig,i of i ∈ 1. . .N , i ∈ N, corresponding pairs of points { p1,i,p2,i } , with p1,i ∈ P 1 and p2,i ∈ P 2 determine the clearance between the surfaces to register. P 1 and P 2 are point sets of surfaces 1 and 2, respectively, as presented in Fig. 1b and c. The objective function f of the optimization problem is as follows: f ( tx, ty, tz,φ,θ,ψ )
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虚拟装配的测量不确定度评定
虚拟装配是一种考虑相关几何形状局部偏差的装配件基准定义和质量预测方法。对被测物体的点云进行配准,以重建物体的假想物理装配状态。通过VA,几何验证变得更加精确,从而越来越以功能为导向。VA算法是高斯最优拟合算法的非线性约束衍生,其中离群点对配准结果影响很大。为了评估所开发算法的鲁棒性,研究了测量不确定性通过非线性变换的传播。该工作比较了从抽象级别区分的选定传播方法。结果表明,与无约束高斯最佳拟合相比,VA传播的不确定性更大。随着产品质量要求的提高,零件公差规格也变得越来越复杂。由于这些具有挑战性的几何规范,需要更精确地表示几何系统的验证算法。根据尼尔森(2003),在过去的几十年里,尺寸公差缩小由于改进制造系统。然而,形式偏差却不能同样程度地减少。因此,应加强对它们的考虑。当前国际标准化组织(ISO)的基准定义标准ISO 5459 (Deutsches Institut fr Normung e.v., 2011)的一个主要缺陷是缺乏对基准特征的局部形式偏差的考虑。基准特征被定义为“用于建立单个基准的实(非理想)积分特征”(Deutsches Institut fr Normung e.v., 2017, p. 2)。由三个基准特征组成的基准系统在数学上定义了一个坐标系。这允许定义外部公差的公差区(Weißgerber and Keller, 2014)。大约80%的测量任务需要基准系统,因此进一步面向功能的基准系统定义对几何验证具有重要影响。因此,对基准系统的不确定性进行评估具有广泛的意义。图1显示了一个基准定义,其中以嵌套的方式考虑了三个相互垂直的相关平面。主基准约束3个自由度,次基准约束2个自由度,次基准约束1个自由度(Gröger, 2015)。1.1虚拟装配的概念在本文中,物理对象的测量数据是从工业计算机断层扫描(CT)测量中收集的。配准是根据通用坐标系中的基准定义,将一个数据集相对于另一个数据集对齐的动作。虚拟装配(VA)包括在基准系统计算中考虑局部形状偏差。如图1a所示,通过VA,通过计算接触点来模拟工件的物理接触。正如Weißgerber和Keller(2014)所介绍的那样,VA的配准在数学上被表述为一个优化问题。下图中,矩阵用黑体大写标记,向量用黑体斜体标记,标量由哥白尼出版社代表美国医学会传感器技术协会出版。通过嵌套注册来定义数据,使用关联平面(a),根据当前标准中的默认情况注册方法,(b)和根据虚拟汇编(c)注册方法。罗马格式的值。有符号距离设计,i (i∈1,n,i∈N),对应点{p1,i,p2,i}对,其中p1,i∈p1,i∈p1, p2,i∈p2,确定要注册的曲面之间的间隙。p1和p2分别是曲面1和2的点集,如图1b和c所示。优化问题的目标函数f为:f (tx, ty, tz,φ,θ,ψ)
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来源期刊
Journal of Sensors and Sensor Systems
Journal of Sensors and Sensor Systems INSTRUMENTS & INSTRUMENTATION-
CiteScore
2.30
自引率
10.00%
发文量
26
审稿时长
23 weeks
期刊介绍: Journal of Sensors and Sensor Systems (JSSS) is an international open-access journal dedicated to science, application, and advancement of sensors and sensors as part of measurement systems. The emphasis is on sensor principles and phenomena, measuring systems, sensor technologies, and applications. The goal of JSSS is to provide a platform for scientists and professionals in academia – as well as for developers, engineers, and users – to discuss new developments and advancements in sensors and sensor systems.
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