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Research Papers

Comparison of Uncertainty Analyses for Crankshaft Applications

[+] Author and Article Information
I. Elishakoff

Department of Ocean and Mechanical Engineering,
Florida Atlantic University,
Boca Raton, FL 33431-0991

C. M. Fu, B. Y. Ni, X. Han

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,
College of Mechanical and Vehicle Engineering,
Hunan University,
Changsha City 410082, China

C. Jiang

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,
College of Mechanical and Vehicle Engineering,
Hunan University,
Changsha City 410082, China
e-mail: jiangc@hnu.edu.cn

G. S. Chen

School of Mechanical Engineering,
Nanjing University of Science and Technology,
Nanjing City 210094, China

1Corresponding author.

Manuscript received May 19, 2014; final manuscript received January 17, 2015; published online October 2, 2015. Assoc. Editor: Alba Sofi.

ASME J. Risk Uncertainty Part B 1(4), 041002 (Oct 02, 2015) (14 pages) Paper No: RISK-14-1023; doi: 10.1115/1.4030436 History: Received May 19, 2014; Accepted April 27, 2015; Online October 02, 2015

In this paper, four convex models (interval, parallelepiped, ellipsoidal, and super-ellipsoidal analyses) are introduced to describe the available data on uncertainty parameters for the engine’s crankshaft. The paper first evaluates the smallest area, such as box, ellipse, parallelogram, and super ellipse, which enclose the available data. Then, the Tchebycheff inequality is employed to inflate the uncertain domain to address the problem of forecasting data, i.e., variables taking values beyond the recorded uncertain data, as a limited amount of samples are used to construct the convex models. The minimum areas before and after the inflation are evaluated. Subsequently, the maximum stresses before and after the inflation of uncertain domain based on the areas of the convex models are obtained. The domain that predicts the minimum of the maximum stresses is declared as the best bounding figure, along with the attendant uncertainty model.

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References

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Figures

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Fig. 1

Interval model (2D case)

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Fig. 2

Parallelepiped convex model (2D case)

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Fig. 3

Ellipsoid convex model (2D case)

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Fig. 4

Super-ellipsoid convex model (2D case)

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Fig. 5

Crankshaft model for a specific type of engine

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Fig. 6

Half-crank model: (a) The 3D model and (b) the FEM

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Fig. 7

Uncertainty domains corresponding to the manufacturing class M(1,2) and associated four convex models (solid line = before inflation; dashed line = after inflation): (a) Rectangle, (b) parallelogram, (c) ellipse, and (d) super ellipse

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Fig. 8

Uncertainty domains corresponding to the manufacturing class M(1,3) and associated four convex models (solid line = before inflation; dashed line = after inflation): (a) Rectangle, (b) parallelogram, (c) ellipse, and (d) super ellipse

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Fig. 9

Uncertainty domains corresponding to the manufacturing class M(1,4) and associated four convex models (solid line = before inflation; dashed line = after inflation): (a) Rectangle, (b) parallelogram, (c) ellipse, and (d) super ellipse

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Fig. 10

Uncertainty domains corresponding to the manufacturing class M(1,5) and associated four convex models (solid line = before inflation; dashed line = after inflation): (a) Rectangle, (b) parallelogram, (c) ellipse, and (d) super ellipse

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Fig. 11

Uncertainty domains corresponding to the manufacturing class M(2,3) and associated four convex models (solid line = before inflation; dashed line = after inflation): (a) Rectangle, (b) parallelogram, (c) ellipse, and (d) super ellipse

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Fig. 12

Uncertainty domains corresponding to the manufacturing class M(2,4) and associated four convex models (solid line = before inflation; dashed line = after inflation): (a) Rectangle, (b) parallelogram, (c) ellipse, and (d) super ellipse

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Fig. 13

Uncertainty domains corresponding to the manufacturing class M(2,5) and associated four convex models (solid line = before inflation; dashed line = after inflation): (a) Rectangle, (b) parallelogram, (c) ellipse, and (d) super ellipse

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Fig. 14

Uncertainty domains corresponding to the manufacturing class M(3,4) and associated four convex models (solid line = before inflation; dashed line = after inflation): (a) Rectangle, (b) parallelogram, (c) ellipse, and (d) super ellipse

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Fig. 15

Uncertainty domains corresponding to the manufacturing class M(3,5) and associated four convex models (solid line = before inflation; dashed line = after inflation): (a) Rectangle, (b) parallelogram, (c) ellipse, and (d) super ellipse

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Fig. 16

Uncertainty domains corresponding to the manufacturing class M(4,5) and associated four convex models (solid line = before inflation; dashed line = after inflation): (a) Rectangle, (b) parallelogram, (c) ellipse, and (d) super ellipse

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Fig. 17

Minimum-area rectangle described by the rotation coordination

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Fig. 18

Minimum-area parallelogram described by the rotation coordination

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Fig. 19

Minimum-area super ellipse and its circumscribed rectangle

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Fig. 20

von Mises stress contour under rectangle-shaped uncertainty domain

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Fig. 21

von Mises stress contour under parallelogram-shaped uncertainty domain

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Fig. 22

von Mises stress contour under ellipse-shaped uncertainty domain

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Fig. 23

von Mises stress contour under super ellipse shaped uncertainty domain

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