**4.1 Sanding ridge caused by loss of abrasive**

This defect is caused by a portion of the abrasive in an abrasive machining operation separating from the backing of the abrasive belt. This is often caused by the belt striking a foreign object in the surface of the workpiece. The result is a ridge which forms on the surface of the workpiece. Figure 16 shows a photograph of a cabinet door with two sanding ridges on it. This results in a defect that is localized in one location of the surface of the workpiece; but is also considered stationary in that it occurs along the entire length of the surface as well as subsequent workpiece surfaces. This defect is very similar to a machining defect that is caused by a nick in a blade on a moulder, planer, or router. The surface profile for the sanding ridge shows the ridges very clearly (see Figure 17, left). The frequency plot (Figure 17, right) shows very little information or periodicity. The harmonic wavelet plot (see Figure 18) also shows no periodicity but does show the two sanding ridges and the location (in time) where they occur. The wavelet coefficients are negligible over most of the plot; with the two peaks caused by the two sanding ridges clearly shown at both ends of the scan. The advantage of the harmonic wavelet transform is that it shows both time and frequency information together in a single plot. The HWT clearly shows the two peaks and **when** they occurred as well as the fact that no significant periodicity exists on the surface.

Fig. 16. Photograph of specimen with sanding ridges caused by loss of abrasive

This section will show the results of using the HWT for various surfaces. In review, the surface quality assessment system is being designed to assist wood product manufacturers in monitoring their machining operations and alert them if the operation or the product quality changes during the machining process. To that end, the system must be able to scan the surface, analysis the data and make a decision on the state of the operation in an acceptable time frame. Information in the frequency domain can be limited to below 50 marks per inch since very high spatial frequencies are not of importance to the manufacturer. However, higher frequencies still must be included in order to detect the

This defect is caused by a portion of the abrasive in an abrasive machining operation separating from the backing of the abrasive belt. This is often caused by the belt striking a foreign object in the surface of the workpiece. The result is a ridge which forms on the surface of the workpiece. Figure 16 shows a photograph of a cabinet door with two sanding ridges on it. This results in a defect that is localized in one location of the surface of the workpiece; but is also considered stationary in that it occurs along the entire length of the surface as well as subsequent workpiece surfaces. This defect is very similar to a machining defect that is caused by a nick in a blade on a moulder, planer, or router. The surface profile for the sanding ridge shows the ridges very clearly (see Figure 17, left). The frequency plot (Figure 17, right) shows very little information or periodicity. The harmonic wavelet plot (see Figure 18) also shows no periodicity but does show the two sanding ridges and the location (in time) where they occur. The wavelet coefficients are negligible over most of the plot; with the two peaks caused by the two sanding ridges clearly shown at both ends of the scan. The advantage of the harmonic wavelet transform is that it shows both time and frequency information together in a single plot. The HWT clearly shows the two peaks and **when** they occurred as well as the fact that no significant

Fig. 16. Photograph of specimen with sanding ridges caused by loss of abrasive

**4. Results of surface scans** 

localized defects in the frequency domain.

periodicity exists on the surface.

**4.1 Sanding ridge caused by loss of abrasive** 

Fig. 17. Profile (left) and frequency spectrum (right) of specimen with sanding ridges caused by loss of abrasive

### **4.2 Surface with varying frequency of knife marks**

This section shows a situation in which the knife marks occurring on the surface change in frequency along the length of the surface. This type of surface defect could be due to slippage occurring in the feed works of the machining operation or a slowing of the cutterhead rpm due to motor overload. This type of defect may be both non-stationary (among different workpieces) as well as non-stationary within a workpiece. Figure 19 shows a photograph of this type of surface characteristic. The surface profile (Figure 20, left) shows the varying wavelengths as well as the varying amplitudes on the surface of the workpiece. The frequency spectrum (Figure 20, right) shows the difference in the amplitude of the two frequencies as well as the difference in the spatial frequencies. The harmonic wavelet plot (Figure 21) shows the predominant frequency extending across the majority of the surface scan but changing in amplitude but also with varying frequencies present like a chirp. This plot also shows how the frequency changes along the length of the surface.

The Use of the Wavelet Transform to Extract

**5. Decision making scheme** 

one used in this research.

periodic.

Additional Information on Surface Quality from Optical Profilometers 119

The final step in developing an on-line surface quality monitoring system was the decision making scheme to determine if an unacceptable condition is present. As mentioned before, one of the objectives was to be able to determine from the data if a surface defect is periodic versus non-periodic and stationary versus non-stationary in nature. This aids the operator in

As discussed previously, the time-frequency plots provide information on the magnitude of the surface defect as well as determining if the defect is stationary or non-stationary. There are two approaches to interpreting the time-frequency plots. The first approach is to treat the time-frequency plot as an image and use standard image analysis techniques to determine the magnitude and shape of any "peaks" or "ridges" in the plot. A small diameter "blob" of the color representing a high mean-square value would represent a severe localized defect; whereas a long smear or ridge of the same color would represent a severe periodic condition. Since only the lower periodic frequencies (i.e. less than 50 knife marks per inch) are of interest for machined wood surfaces, the higher frequencies can be combined together for analysis of both non-periodic and localized defects. The second approach is to simply look at the data array representing the time-frequency plot of the harmonic wavelet analysis. For the examples shown, a surface profile generated by 16384 data points resulted in a time-frequency plot array of 15 x 4096 with the 15 columns representing the 15 frequency bandwidths (bins) of the HWT. This second approach was the

The first step in classifying a defect is to determine whether the surface defect is periodic, non-periodic, localized, or a combination of two or more of these categories. One approach is to view the periodic, non-periodic, and localized defects on an x, y, z plot. Since three parameters are required to describe a point in three space, the values of the three surface defect categories would indicate where in space the current specimen falls. A perfectly smooth surface would be at the origin of the plot. As a surface develops greater surface defects (regardless of the type or category of defect), the value on the plot moves further away from the origin. If the value for a periodic defect is higher than the value for the non-periodic defect then the surface in question is more periodic than non-

There are several methods of determining where along the three-space defect category axes a surface defect falls. One way is to conduct traditional time and frequency analysis and determine the best surface descriptor for the type of defect of interest in each category. The three surface descriptors would then be plotted in three-space with the magnitude of the

From the time-frequency plots it can be seen the HWT can differentiate between extreme conditions and can provide the user with comprehensive information about the type of surface that has been scanned. The difference between the periodic and non-periodic situations can be determined by setting a threshold and then counting the number of data excursions above the threshold to indicate that the signal has a periodic component. A single threshold crossing could indicate a scratch or other localized defect. Since only periodic components below 50 marks per inch are typically of interest, only lower frequency bins would need to be monitored for periodic components. The frequency bins representing

defect (surface descriptor) being normalized before being plotted.

determining the cause of the surface defect and what remedial action to take.

Fig. 19. Photograph of surface with varying frequency of knife marks

Fig. 20. Profile (left) and HWT (right) of surface with varying frequency of knife marks

Fig. 21. Harmonic wavelet transform of surface with varying frequency of knife marks
