Research Papers

A Finite-Element Boundary Condition Setting Method for the Virtual Mounting of Compliant Components

[+] Author and Article Information
Gad N. Abenhaim

Department of Mechanical Engineering,
Université de Sherbrooke,
2500, Boulevard de l’Université,
Sherbrooke, QC J1K 2R1, Canada
e-mail: gad-noriel.abenhaim@usherbrooke.ca

Alain Desrochers

Department of Mechanical Engineering,
Université de Sherbrooke,
Sherbrooke, QC J1K 2R1, Canada
e-mail: Alain.Desrochers@usherbrooke.ca

Antoine S. Tahan

Department of Mechanical Engineering,
École de technologie supérieure (ÉTS),
Montreal, QC H3C 1K3, Canada
e-mail: antoine.tahan@etsmtl.ca

Jean Bigeon

G-SCOP Laboratory,
Grenoble INP–Université Joseph Fourier,
46 Avenue Félix Viallet,
Grenoble Cedex 1 38031, France
e-mail: Jean.Bigeon@grenoble-inp.fr

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received September 29, 2014; final manuscript received May 27, 2015; published online September 14, 2015. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 15(4), 041005 (Sep 14, 2015) (8 pages) Paper No: JCISE-14-1308; doi: 10.1115/1.4031152 History: Received September 29, 2014; Revised May 27, 2015

Using finite-element analysis (FEA) to numerically mount compliant components onto their inspection fixture is an approach proposed by researchers in the field of computational metrology. To address the shortcomings of the underlying principle of current methods, this paper presents a boundary displacement constrained (BDC) optimization using FEA. The optimization seeks to minimize the distance between corresponding points, in the scanned manufactured part and the nominal model, that are in unconstrained regions. This is done while maintaining that a distance between corresponding points in constrained regions (i.e., fixing points) remains within a specified contact distance. At the same time, the optimization limits the magnitude and direction of forces on boundary. In contrast to the current methods, postprocessing of the point cloud is not required since the method uses information retrieved from the FEA of the nominal model to estimate the manufactured part’s mechanical behavior. To investigate the performance of the proposed method, it is tested on ten (10) free-state simulated manufactured aerospace panels that differ in their level of induced deformation. Results are then compared to those obtained using the underlying principles of current methods.

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Abenhaim, G. N. , Desrochers, A. , and Tahan, A. S. , 2012, “ Nonrigid Parts’ Specification and Inspection Methods: Notions, Challenges, and Recent Advancements,” Int. J. Adv. Manuf. Technol., 63(5–8), pp. 741–752. [CrossRef]
ASME-Y14.5, 2009, Dimensioning and Tolerancing, American Society of Mechanical Engineers, New York.
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Weckenmann, A. , and Gabbia, A. , 2006, “ Testing Formed Sheet Metal Parts Using Fringe Projection and Evaluation by Virtual Distortion Compensation,” Fringe, Springer, Berlin/Heidelberg/New York, pp. 539–546.
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Abenhaim, G. N. , Desrochers, A. , Tahan, A. S. , and Lalonde, J. , 2013, “ Aerospace Panels Fixtureless Inspection Methods With Restraining Force Requirements: A Technology Review,” SAE Technical Paper No. 2013-01-2172.
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Fig. 1

Example of an aerospace panel: (a) mounted on its inspection fixture before the measurement process and (b) in a free-state (Source: Bombardier Aerospace)

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Fig. 2

Schematic representation of the method

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Fig. 3

Nominal model with: double red circles representing 38 datum targets of A, 2 datum targets B, and 1 datum target C. Dashed yellow lines represent the location of the two beams setup (i.e., the boundaries) used to simulate the part's free-state shapes.

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Fig. 4

Color-map with its distribution of the distance in millimeters between the ninth deformed model (F(9)o) and the undeformed FE mesh (i.e., induced deformation)

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Fig. 7

Shape errors in millimeters of the predicted ninth deformed model F(9)o: (a) using the underlying principle of current methods and (b) using the proposed FE–BDC optimization method

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Fig. 8

The eight regions used to evaluate the quality indicators. Light gray dots represent the nodes of the nominal mesh. Blue and red dots represent the closest nodes to the 1896 points in unconstrained regions selected by the manufacturer’s metrology department to evaluate the part’s profile. Blue and red areas identify the eight regions (R1R8) used to evaluate the algorithm’s performance.

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Fig. 9

Overall and per region evaluation of the algorithm error for each synthetic model case study. Bars represent the MAE, while the dots (○) and triangle (∇) symbols, respectively, represent the RMSE and Q3 quality indicators. The three quality indicators are in millimeters. Red and light blue bars represent, respectively, the errors obtained using the proposed and the current methods. The position of the bars is associated to the G values of the synthetic models, that is, the bars represent, from left to right, the cases where G equals 1 up to 10.

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Fig. 10

Shapes errors with respect to the distance between the synthetic and nominal model. Blue dots connected by the solid blue line and the dashed blue line represent, respectively, the maximum distance between the synthetic and nominal model before (solid) and after (dashed) being aligned using rigid registration. The distance units are in millimeters and are associated to the right vertical axis. Bars represent the overall MAE of the FE–BDC optimization method for each synthetic model G. The overall MAE units are in millimeters and are associated to the left vertical axis.

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Fig. 5

Distances in millimeters between the nodes of the undeformed mesh and the nominal position of the 41 datum targets

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Fig. 6

Schematic representation of boundary condition settings used for each method. Bottom mesh represents the nominal mesh with being a datum target position, a node B*, and the blue △ a set of nodes B. Upper mesh represents a synthetic model F(G)• with the yellow ∇ being the nodes B(G)•. Red and yellow arrows represent the boundary setting using, respectively, the current methods and the FE–BDC optimization method.

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Fig. 11

The bar histogram illustrates, for each synthetic model, the maximal estimated force on restrained regions from the first and second reverse FEA (black and gray), the current methods (blue), and the proposed method (red); values are in Newton.



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