Research Papers

On the Selection of Sensitivity Analysis Methods in the Context of Tolerance Management

[+] Author and Article Information
Björn Heling

Department of Mechanical Engineering,
Institute of Engineering Design,
Erlangen 91058, Germany
e-mail: heling@mfk.fau.de

Thomas Oberleiter, Kai Willner

Department of Mechanical Engineering,
Institute of Applied Mechanics,
Erlangen 91058, Germany

Benjamin Schleich, Sandro Wartzack

Department of Mechanical Engineering,
Institute of Engineering Design,
Erlangen 91058, Germany

Manuscript received March 16, 2018; final manuscript received May 24, 2019; published online June 18, 2019. Assoc. Editor: Sez Atamturktur.

J. Verif. Valid. Uncert 4(1), 011001 (Jun 18, 2019) (10 pages) Paper No: VVUQ-18-1009; doi: 10.1115/1.4043912 History: Received March 16, 2018; Revised May 24, 2019

Although mass production parts look the same at first sight, every manufactured part is unique, at least on a closer inspection. The reason for this is that every manufactured part is inevitable subjected to different scattering influencing factors and variation in the manufacturing process, such as varying temperatures or tool wear. Products, which are built from these deviation-afflicted parts, consequently show deviations from their ideal properties. To ensure that every single product nevertheless meets its technical requirements, it is necessary to specify the permitted deviations. Furthermore, it is crucial to estimate the consequences of the permitted deviations, which is done via tolerance analysis. During this process, the imperfect parts are assembled virtually and the effects of the geometric deviations can be calculated. Since the tolerance analysis enables engineers to identify weak points in an early design stage, it is important to know which contribution every single tolerance has on a certain quality-relevant characteristic to restrict or increase the correct tolerances. In this paper, four different methods to calculate the sensitivity are introduced and compared. Based on the comparison, guidelines are derived which are intended to facilitate a selection of these different methods. In particular, a newly developed approach, which is based on fuzzy arithmetic, is compared to the established high–low–median method, a variance-based method, and a density-based approach. Since all these methods are based on different assumptions, their advantages and disadvantages are critically discussed based on two case studies.

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Fig. 1

Methodology of tolerance management

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Fig. 2

Unconditional and conditional density functions

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Fig. 3

Fuzzy number and its α-cut

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Vector loops of one-way clutch

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Fig. 4

Fuzzy number with additional points

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Fig. 7

Probability distribution of the pressure angle

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Fig. 8

Results of the sensitivity analysis (case study 1)

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Fig. 9

Change of sensitivity for case study 1 (EFAST)

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Fig. 10

Change of sensitivity for case study 1 (density-based)

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Change of sensitivity for case study 1 (fuzzy-based)

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Fig. 12

Mounting of the racing seat holder

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Fig. 13

Schematic presentation of the base plate and resulting tilt angle of the bracket

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Fig. 19

Selection of sensitivity analysis method

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Fig. 14

Probability distribution of the tilting angle

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Fig. 15

Results of the sensitivity analysis (case study 2)

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Fig. 16

Change of sensitivity for case study 2 (EFAST)

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Fig. 17

Change of sensitivity for case study 2 (density-based)

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Fig. 18

Change of sensitivity for case study 2 (fuzzy-based)



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