Hole-Drilling Residual Stress Profiling With Automated Smoothing

[+] Author and Article Information
Gary S. Schajer

Department of Mechanical Engineering, University of British Columbia, Vancouver, Canada V6T 1Z4

J. Eng. Mater. Technol 129(3), 440-445 (Mar 28, 2007) (6 pages) doi:10.1115/1.2744416 History: Received June 12, 2006; Revised March 28, 2007

An effective procedure is presented that allows stable hole-drilling residual stress calculations using strain data from measurements taken at many small increments of hole depth. This use of many strain measurements is desirable because it improves the data content of the calculation, and the statistical reliability of the residual stress results. The use of Tikhonov regularization to reduce the noise sensitivity that is characteristic of a fine-increment calculation is described. This mathematical procedure is combined with the Morozov criterion to identify the optimal amount of regularization that balances the competing tendencies of noise reduction and stress solution distortion. A simple method is described to estimate the standard error in the strain measurements so that the optimal regularization can be chosen automatically. The possible use of a priori information about the trend of the expected solution is also discussed as a further means of improving the stress solution. The application of the described method is demonstrated with some experimental measurements, and realistic results are obtained.

Copyright © 2007 by American Society of Mechanical Engineers
Topics: Stress , Errors , Drilling
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Figure 1

Schematic diagram of the bent-beam residual stress specimen

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Figure 2

Hole-drilling relieved strains versus depth. The data points are measured values. The lines are the backcalculated strains corresponding to the fixed principal direction regularized stresses in Fig. 4.

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Figure 3

Computed residual stresses: light (noisy) lines=unregularized results; bold (smooth) lines=regularized results; dashed (straight) lines=theoretical results. The upper three lines show the axial (X) stresses and the lower three lines show the transverse (Y) stresses.

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Figure 4

Computed principal direction versus depth: light line=unregularized results; bold lines=regularized results

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Figure 5

rms shear strain misfit qrms versus regularization factor α0 for the bent-beam specimen

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Figure 6

Strain misfits due to noise removal and to stress profile distortion



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