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Research Papers: Design and Analysis

Inverse Solution for Bolt Preload Using Surface Deformation

[+] Author and Article Information
A. Zaki

Department of Mechanical Engineering,
Fastening and Joining Research Institute (FAJRI),
Oakland University,
Rochester, MI 48309

S. A. Nassar

Fellow ASME
Department of Mechanical Engineering,
Fastening and Joining Research Institute (FAJRI),
Oakland University,
Rochester, MI 48309

S. Kruk, M. Shillor

Department of Mathematics and Statistics,
Oakland University,
Rochester, MI 48309

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received February 3, 2013; final manuscript received December 21, 2016; published online April 24, 2017. Assoc. Editor: Reza Adibiasl.

J. Pressure Vessel Technol 139(4), 041206 (Apr 24, 2017) (9 pages) Paper No: PVT-13-1030; doi: 10.1115/1.4035695 History: Received February 03, 2013; Revised December 21, 2016

In this paper, an inverse biharmonic axisymmetric elasticity problem is solved by invoking measured out-of-plane surface deformation values at discrete locations around a preloaded bolt head, in order to calculate the underhead contact stress and joint clamp load that would have caused that out-of-plane surface deformation. Solution of this type of inverse problem promises to improve the automation process of bolted joint system assembly, especially in critical and safety-related applications. For example, a real-time optically measured joint surface deformation can be utilized for automating process control of bolted joint assembly in a reliable fashion. This would be a significant reliability improvement as compared to the commonly used method in mass production using torque-only control method in which there is wide scatter in the torque–tension correlation due to the normal scatter in frictional variables. Finite element analysis (FEA) method is used to validate the inverse problem solution provided in this paper.

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References

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Figures

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Fig. 1

The geometric model of bolted model

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Fig. 3

Deformation variation with radial location for various levels of clamp load F (M8 bolt: case 1)

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Fig. 4

Axisymmetric FEA model

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Fig. 5

Output displacement u(r) variation with the number of measured data points M

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Fig. 6

Out-of-plane deformation w(r) versus number of paired eigenvalues N (case 1: F=6 kN)

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Fig. 7

Model out-of-plane deformation w(r) compared to the model input wm

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Fig. 8

Out-of-plane deformation w(r) versus number of paired eigenvalues N (case 2: F=6 kN)

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Fig. 9

Normal force Fz under the bolt head versus number of paired eigenvalues N (case 2: F=6 kN)

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Fig. 10

Out-of-plane deformation w (r) versus number of paired eigenvalues N (case 3: F=6 kN)

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Fig. 11

Model out-of-plane deformation w(r) compared to the model input wm

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