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Research Papers

Fuzzy Sensitivity Analysis in the Context of Dimensional Management

[+] Author and Article Information
Thomas Oberleiter

Applied Mechanics,
Friedrich-Alexander-University
Erlangen-Nürnberg,
Erlangen 91058, Germany
e-mail: thomas.oberleiter@fau.de

Björn Heling

Engineering Design,
Friedrich-Alexander-University
Erlangen-Nürnberg,
Erlangen 91058, Germany
e-mail: heling@mfk.fau.de

Benjamin Schleich

Engineering Design,
Friedrich-Alexander-University
Erlangen-Nürnberg,
Erlangen 91058, Germany
e-mail: schleich@mfk.fau.de

Kai Willner

Applied Mechanics,
Friedrich-Alexander-University
Erlangen-Nürnberg,
Erlangen 91058, Germany
e-mail: kai.willner@fau.de

Sandro Wartzack

Engineering Design,
Friedrich-Alexander-University
Erlangen-Nürnberg,
Erlangen 91058, Germany
e-mail: wartzack@mfk.fau.de

Manuscript received March 29, 2018; final manuscript received July 11, 2018; published online August 14, 2018. Assoc. Editor: Siu-Kui Au.

ASME J. Risk Uncertainty Part B 5(1), 011008 (Aug 14, 2018) (7 pages) Paper No: RISK-18-1017; doi: 10.1115/1.4040919 History: Received March 29, 2018; Revised July 11, 2018

Real components always deviate from their ideal dimensions. This makes every component, even a serial production, unique. Although they look the same, differences can always be observed due to different scattering factors and variations in the manufacturing process. All these factors inevitably lead to parts that deviate from their ideal shape and, therefore, have different properties than the ideal component. Changing properties can lead to major problems or even failure during operation. It is necessary to specify the permitted deviations to ensure that every single product nevertheless meets its technical requirements. Furthermore, it is necessary to estimate the consequences of the permitted deviations, which is done via tolerance analysis. During this process, components are assembled virtually and varied with the uncertainties specified by the tolerances. A variation simulation is one opportunity to calculate these effects for geometric deviations. Since tolerance analysis enables engineers to identify weak points in an early design stage, it is important to know the contribution that every single tolerance has on a certain quality-relevant characteristic, to restrict or increase the correct tolerances. In this paper, a fuzzy-based method to calculate the sensitivity is introduced and compared with the commonly used extended Fourier amplitude sensitivity test (EFAST) method. Special focus of this work is the differentiation of the sensitivity for the total system and the sensitivities for the subsystems defined by the α-cuts of the fuzzy numbers. It discusses the impact of the number of evaluations and nonlinearity on sensitivity for EFAST and the fuzzy-based method.

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References

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Figures

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Fig. 1

Methodology of tolerance management

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Fig. 2

Fuzzy number and its α-cut

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Fig. 3

Fuzzy number with additional points

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Fig. 5

Vector loops of one way clutch

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Fig. 6

Probability distribution of the pressure angle

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Fig. 7

Change of sensitivity (EFAST-method)

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Fig. 8

Change of sensitivity (fuzzy-method)

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Fig. 9

Absolut deviation of fuzzy based method from EFAST method for two different tolerances

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