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Manufacturing industries require a right-first-time paradigm to remain competitive. Variation simulation (VS) is a key tool to predict variation of the final shape of flexible assemblies, allowing to reduce defects and waste. VS models involving compliant sheet-metal parts commonly integrate physics-based simulation with statistical approaches (usually Monte Carlo simulation). Although increasingly used as a backbone of synthesis techniques for (stochastic) optimization of assembly systems, the main roadblock of VS methods is the intense computational costs due to time-intensive simulations and high-dimensional design space. Driven by the need of time reduction, this paper presents an innovative real-time physics-based VS model of assembly systems with compliant sheet-metal parts. The proposed methodology involves a non-intrusive reduced-order model (niROM), empowered by a novel adaptive sampling procedure for dataset generation, and a cross-validation-based optimized radial basis function (RBF) formulation for interpolation. Demonstrated through two case studies—(i) a remote laser welding operation to predict mechanical distortions, with two input parameters, and (ii) the assembly of an aircraft vertical stabilizer with five input parameters—the methodology achieves accurate real-time results, with up to a 43% improvement in accuracy compared to traditional sampling techniques. Findings highlight the critical influence of the sampling strategy and the number of input parameters on ROM accuracy. Better results are reached by employing adaptive sampling in combination with optimum RBF, which additionally disengages the user from the choice of the interpolation settings. This study unlocks new avenues in the field of variation simulation and dimensional/quality monitoring by narrowing the gap between any advanced CAE solver and VS models with real-time physics-based simulations. [ABSTRACT FROM AUTHOR]

In the digital measuring environment, to solve the problem of sampling point planning on the aero-engine blade profile, two requirements should be satisfied: adapting geometry features and keeping the sampling point spacing. Therefore, this paper proposes an adaptive sampling method, which can flexibly increase or decrease the sampling points according to the curvature. Firstly, according to the geometric characteristics of blade profile, an adaptive sampling method based on the equal moment theory is established. Secondly, a parameterized model based on non-uniform rational B-spline (NURBS) is used to represent the geometry of the blade profile, and the Hausdorff distance is used to evaluate the error of the fitting curve. Finally, two cases verify the effectiveness and accuracy of the proposed method. In the simulation, the relationship between the adaptability and the error of the proposed method is analyzed by taking the Sine function as an example. It is obtained by numerical calculations that the error reached the minimum when the adaptive degree r is 0.75. In the actual blade measurement experiment, compared with other methods, the deviation between the reconstructed blade cross-section curve by the proposed method and the theoretical curve is minimum. [ABSTRACT FROM AUTHOR]

The paper describes a general adaptive sampling methodology useful in multivariate optimization involving finite element analysis that typically requires a long time. The proposed adaptive sampling method was obtained by starting from a model-based statistical methodology developed to design an adaptive inspection plan for the geometric control of mechanical parts. The novelty of the new kriging adaptive sampling procedure consists in overcoming some critical issues, such as the reduction of the estimation time to have an efficient tool for quick application. The others are related to how to set up a kriging-based adaptive sampling, how to choose the stopping rule, and how to remove the dependence on the statistical variability. These issues are the subject of this work to develop a useful tool for multivariate optimization. By improving the methodology in these aspects, it was possible to obtain a feasible and useful instrument for the application in a quick sampling procedure within the inspection process. After this enhancement process, the method is sufficiently general to be extended in the multivariate optimization field that requires a multi-factorial finite element analysis. To demonstrate this, an illustrative real case study from an industrial application is presented and it was found that the proposed method reduces significantly the time required to reach the optimal solution. [ABSTRACT FROM AUTHOR]

Dimensional inspection of engineering components comprising free-form surfaces demands accurate measurement of a large number of discrete points, such that the actual shape may be fully characterized. This paper presents an on-machine verification (OMV) measurement planning strategy for CAD-based measurement of such components on five-axis machines. The main shortcoming of the conventional methodology with coordinate measuring machines (CMMs) has been identified to do with relation to repetitive position error. However, by employing the CAD model and on-machine platform, the proposed methodology maximizes the measurement accuracy, and such problem does not exist. The steps are as follow: adaptive sampling strategy is used to obtain effective measured points, probe path optimization, verification, post-processing, and measurement. The OMV process of surface on ' S'-shaped test piece is implemented, and the obtained deviation is compared with another set of data measured on a coordinate measurement machine. [ABSTRACT FROM AUTHOR]

Coordinate measurement machines (CMMs) have been widely used in inspecting mechanical parts with higher accuracy. Both the distribution and the number of the sampled points on measurand have an important effect on the efficiency and quality of the measurement of CMMs. In this paper, an adaptive sampling method is proposed for inspection planning on CMM for free-form surface. The points are iteratively sampled from a form error model, which is constructed by superimposing appropriate form errors on the nominal data. Moreover, a modified algorithm is introduced to determine the deviation of two point sets for the improvement of the inspecting accuracy, and the inspection uncertainty is also analyzed. A comparison is performed between the proposed method and the two well-known sampling methods, which are the equi-parametric method and the patch mean Gaussian curvature-based method, both simulated and experiment results show the effectiveness and robustness of this method. [ABSTRACT FROM AUTHOR]

The two most important factors in sampling during coordinate verification of a surface are the number of measuring points that accurately represent the surface and the distribution of those points. Three algorithms are developed in this paper for sampling of free-form surfaces at a patch scale (not the entire surface). The three developed algorithms take each patch on the surface as a separate unit and distribute the points within the patch in two steps, namely, sample the most critical points that depend on maximum and minimum Gaussian curvature of each patch and add more points depending on the overall distribution of the most critical points distributed on the surface. In each step of sampling, the maximum difference between the CAD model and the surface created using those sampled points is obtained, and an optimum number of measuring points is determined. This minimizes sampling effort and (non-value-added) measurement time. A comparison is performed between the three proposed algorithms and two well known sampling techniques: the equiparametric approach and the patch-size-based sampling method. The proposed algorithms distribute the points in each patch based on a specific plan. The results show that the developed algorithms help select an efficient number of sampling points. [ABSTRACT FROM AUTHOR]

The parts with freeform surfaces are extensively employed in the production industries. Consequently, the quality inspection of sculptured surfaces becomes increasingly important. Typically, the Coordinate Measuring Machine (CMM) is utilized for inspection of these irregular geometries because of its precision. Certainly, the complex and non-rotational geometry makes it difficult to obtain the freeform surfaces. The meticulous analysis will indeed require the explicit reconstruction of the measuring surface. In view of the fact that only a well-chosen sample of inspection points and their locations can accurately define the measurand, the development of an appropriate sampling strategy becomes crucial. This work proposes a novel adaptive sampling plan for the precise extraction of surface form. It recursively and adaptively computes the relevant sampling scheme to achieve an effective inspection using the CMM. The input to the algorithm is a random sample size depending on the inspection point spacing and measuring surface dimensions. This algorithm employs a knot vector–based segmentation, followed by curvature-based grading of the segmented patches. A newly established formulation is utilized to assign a specific sample size for each segment. The points within each patch are allocated by exploiting distinct point distribution algorithms. This algorithm intends to abbreviate the variance between the reference and generated surface obtained through the specific sampling plan. Indeed, the befitting sampling policy provides the least error between the two surfaces. The outcome in the present study demonstrates that the proposed algorithm can significantly reduce the inspection points as well as maintain the precision of surface modeling. [ABSTRACT FROM AUTHOR]

The components with freeform surface are widely used in industrial fields. The machining quality of freeform surface becomes increasingly significant. Coordinate measuring machine (CMM), as a conventional dimensional measuring instrument, is commonly used to inspect freeform surface. The sampling strategy, consisting of distribution of sampling points and sample size, is important to the effectiveness and accuracy of the measurements performed on CMM. The present work aims at proposing an improved adaptive sampling strategy based on a machining error model (MEM) for freeform surface inspection on CMM. The machining error model is built to determine the distribution of sampling points adaptively. In addition, Hammersley sequence is adopted to address the aliasing problem. Experiments are performed to compare presented strategy with four well-known sampling strategies. Results prove that the MEM is valid and the present strategy is reliable and effective. [ABSTRACT FROM AUTHOR]

This research investigates adaptive sampling for determining form errors found in milled parts. Adaptive sampling saves time and cost because it lowers the number of inspection points. Optimizing the inspection points improves the productivity of the manufacturing process. Primarily, the workpiece errors are modeled in milling flat plates using a consideration of process variables. The model force is applied, theoretically, using finite element software on a flat plate to obtain the workpiece deflection at specific points. The cutter deflection and the workpiece deflection are added to obtain the dimensional error on the flat plate. This model error becomes the basis for a search procedure to determine the locations of maximum error. The ensuing optimum sampling heuristic supposes that if the tolerance zone for a specific area is high, there is a high likelihood of finding points of high dimensional errors in its vicinity. The tolerance zone obtained thus is compared to that obtained using a uniform grid of points. Experimental results indicate that a finite reduction in the number of sample points can be achieved using this knowledge-based search. [ABSTRACT FROM AUTHOR]