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Review Article

Review and Comparison of Form Error Simulation Methods for Computer-Aided Tolerancing

[+] Author and Article Information
Xingyu Yan

Université de Bordeaux,
Institut de Mécanique et
d'Ingénierie (I2M), UMR5295,
Talence F-33400, France
e-mail: xyan@u-bordeaux.fr

Alex Ballu

Université de Bordeaux,
Institut de Mécanique et
d'Ingénierie (I2M), UMR5295,
Talence F-33400, France
e-mail: alex.ballu@u-bordeaux.fr

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received November 15, 2017; final manuscript received September 9, 2018; published online October 18, 2018. Assoc. Editor: Charlie C. L. Wang.

J. Comput. Inf. Sci. Eng 19(1), 010802 (Oct 18, 2018) (16 pages) Paper No: JCISE-17-1273; doi: 10.1115/1.4041476 History: Received November 15, 2017; Revised September 09, 2018

Computer-aided tolerancing (CAT) aims to predict and control geometrical and dimensional deviations in the early design stage. Former simulation models based on the translation and rotation of nominal features cannot fulfill engineering demands or cover the product lifecycle. Nonideal feature-based simulation methods are, therefore, drawing a great deal of research attention. Two general problems for non-ideal feature-based methods are how to simulate manufacturing defects and how to integrate these defects into tolerance analysis. In this paper, we focus on the first problem. There are already many manufacturing defect simulation methods. Although they are derived from different fields and have different names, they share common characteristics in application. In this study, we collected different simulation methods and classified them as random noise methods, mesh morphing methods, and mode-based methods. The theoretical backgrounds of these methods are introduced, and the simulation examples are conducted on a consistency model to show their differences. Criteria such as multiscale, surface complexity, measurement data integration, parametric control, and calculation complexity are proposed to compare these methods. Based on these analyses, the advantages and drawbacks of each method are pointed out, which may help researchers and engineers to choose suitable methods for their work.

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Sudret, B. , and Der Kiureghian, A. , 2000, “Stochastic Finite Element Methods and Reliability: A State-of-the-Art Report,” University of California Berkeley, Berkeley, CA, Report No. UCB/SEMM-2000/08.
Henke, R. P. , Summerhays, K. D. , Baldwin, J. M. , et al.  1999, “ Methods for Evaluation of Systematic Geometric Deviations in Machined Parts and Their Relationships to Process Variables,” Precis. Eng., 23(4), pp. 273–292. [CrossRef]
Ballu, A. , Mathieu, L. , and Dantan, J.-Y. , 2003, “ Global View of Geometrical Specifications,” Geometric Product Specification and Verification: Integration of Functionality, Springer, Dordrecht, The Netherlands, pp. 13–24.
ISO, 2011, “ Geometric Product Specification-General Concepts—Part 1: Model for Geometrical Specification and Verification,” International Organization for Standardization, Geneva, Switzerland, Standard No. 17450-1.
Kurokawa, S. , and Ariura, Y. , 2005, “ Evaluation of Shot Peened Surfaces Using Characterization Technique of Three-Dimensional Surface Topography,” J. Phys. Conf. Ser., 13, pp. 9–12. [CrossRef]
Samper, S. , Adragna, P.-A. , Favreliere, H. , and Pillet, M. , 2009, “ Modeling of 2D and 3D Assemblies Taking Into account Form Errors of Plane Surfaces,” ASME J. Comput. Inf. Sci. Eng., 9(4), p. 041005. [CrossRef]
ISO, 2012, “ Geometrical Product Specifications (GPS)—Surface Texture: Areal—Part 2: Terms, Definitions and Surface Texture Parameters,” International Organization for Standardization, Geneva, Switzerland, Standard No. 25178-2.
Chen, X. , Raja, J. , and Simanapalli, S. , 1995, “ Multi-Scale Analysis of Engineering Surfaces,” Int. J. Mach. Tools Manuf., 35(2), pp. 231–238.

Figures

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Fig. 1

Classification of simulation methods

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Fig. 2

Discrete rectangular surface model

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Fig. 3

Random Gaussian deviation in 1D and 3D: (a) 1D Gaussian and (b) 3D Gaussian

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Fig. 8

Form error simulation by second-order shape morphing on rectangular surfaces: (a) paraboloid and (b) cylinder

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Fig. 7

Form error simulation on cylinder surfaces: (a) banana, (b) concave, (c) convex, and (d) taper

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Fig. 6

Simulation result of random mesh morphing

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Fig. 5

Control points with sphere and ellipsoid influence hull

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Fig. 4

Result of 1D Gaussian simulation

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Fig. 9

Examples of Zernike polynomials [87]

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Fig. 10

Modes (u,v) of DCT used for simulation of form error

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Fig. 11

Manufacturing deviation simulation on the rectangular surface by DCT

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Fig. 12

Embedding a line mesh by its eigenvectors of Laplacian matrix: (a) initial position, (b) second eigenvector, (c) fourth eigenvector, and (d) tenth eigenvector

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Fig. 14

Manufacturing deviation simulation on the rectangular surface by graph Laplacian

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Fig. 13

Eigenvectors (modes) generated from graph Laplacian

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Fig. 17

Deformation patterns generated by eigenvectors corresponding to the five largest eigenvalues

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Fig. 18

Random field simulation result for different correlation lengths

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Fig. 15

Vibration modes used for deviation simulation

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Fig. 16

Simulation result by natural vibration modes

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Fig. 19

Decomposition modes by PCA-based method [106]

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Fig. 21

Possible and suggested simulation methods depending on precision demands

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Fig. 20

Possible and suggested methods depending on shape complexity

Tables

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