Analysis and Synthesis of Engineering Surfaces in Bridge Manufacturing and Design - Manufacturing Systems Processes - page 37

FIGURE 1.19 Karhunen-Loève analysis of surfaces from Part #2.

surface analysis tool: a Fourier transform analysis of the surface profile reveals a structure which is no
longer random in nature ( Fig. 1.18 ) ; however, the distinction in frequency components is not clear using
the Fourier-based analysis. Remedial actions by designers can only be taken if the information received
from the manufacturers is clear and unambiguous.
To obtain a clearer picture, we next analyze the same surface ( Fig. 1.18 ) using the Karhunen-Loève
transform technique. This analysis results in two eigenvectors, which are identified as the two dominant
components, shown in Fig. 1.19 . The sinusoidal component is clear and distinct, as shown with the
accompanying Fourier transform. This provides an unambiguous way of detecting the correct frequency
component corresponding to the low-frequency waveform on part surfaces. The waveform corresponds
to the roller chatter frequency identified from vibrational measurements [68]. By collecting vibrational
measurements from the roller mechanism, the designer can match the waveform frequency to the roller
chatter frequency. Monitoring both submechanisms will provide a means to assure that the magnitude
of the surface fault pattern is below an unacceptable threshold. The threshold levels can be set by the
customer specifications. When this threshold is exceeded, the fault pattern is deemed severe; the remedial
action taken by the designer is to look into ways of redesigning the roller mechanism. This systematic
surface analysis procedure provides a means to understand the potential fault mechanisms in the man-
ufacturing process under investigation. This information is conveyed to the designer, who then imple-
ments remedial measures to prevent or eliminate the potential problems. This analysis can be carried
out for different surfaces to determine and categorize the different fault mechanisms affecting surface
quality during part production [68].
Finally, to investigate the potential of a priori prediction of the fault mechanisms, we compute an
estimate of the surface patterns on the Selective Laser Sintering parts. The reconstruction is shown in
Fig. 1.20 , as compared to the original profile measurement. The reconstructed profile compares to the
original profile fairly closely. The designers can use such tools to predict what the fault patterns will look
like, given the manufacturing specifications. For example, if the surface roughness is the important
criterion for a satisfactory profile, designers may decide to build the part as is, without eliminating the
low-frequency waveform identified earlier.
This simple design example using a real industrial problem illustrates the potential of the Karhunen-
Loève analysis technique in integrating the design and manufacturing phases. The potential of such an
implementation is invaluable for our idealistic vision of automated design and manufacturing. Automated