**6. Results and Discussion**

In this section, the results and discussion of the workpiece assessment and the digital signal processing will be presented, which focus on the correlation of the material removal of the grinding process with the statistics herein applied to the ultrasound signals.

### *6.1. Workpiece Assessment*

The variation of masses and weights of the workpieces, measured by a precision scale, before and after the grinding passes, are shown in Table 2. Before the grinding tests, each workpiece underwent the standardization operation, which consists of grinding passes across the workpiece surface (with a depth of cut of 5 μm); the operation was repeated until uniform contact was achieved between the workpiece surface and the grinding wheel surface. After the standardization operation and the grinding passes, the workpiece mass decreases due to the material removal during the grinding process. It is worth mentioning that the mass decrease is due to the standardization and grinding passes. Thus, workpiece 2 had a smaller decrease in mass than workpiece 1 and 3 because the standardization operation was performed with fewer grinding passes than for the other workpieces (1 and 3).


**Table 2.** Variation of masses and weights of the workpieces.

The volume of material removed is shown in Figure 5. There is an increase in the volume of material removed according to the number of grinding passes and the selected depth of cut, as expected. The volume of material removed is obtained by Equation (7).

$$Q\_w(p) = p \ast a\_p \ast l\_w \ast b\_w \tag{7}$$

where *Qw* is the volume of material removed in mm3, *p* is the number of grinding passes, *ap* is the depth of cut in mm, *lw* is the workpiece length in mm and *bw* is the workpiece width in mm, as presented in Figure 5a. The volume of material removed as a function of the number of passes is shown in Figure 5b.

**Figure 5.** (**a**) Schematic for grinding process with cutting parameters; (**b**) material removal volume as a function of the grinding pass.

## *6.2. Signal Processing and Selection of Frequency Bands*

The emitted and received signals used to evaluate the workpieces are shown in Figure 6. It is observed in Figure 6a,b that the emitted and received signals have five packages (#1, #2, #3, #4, #5), respectively. The amplitude of each emitted package decreases as the frequencies increases; this behavior can be explained by the arrangement of the impedance between the DAQ (chirp signal emitter) and the emitter PZT. The PZT capacitive elements caused a voltage decrease at higher frequencies, as observed in Campeiro et al. [68]. Regarding the received packages in Figure 5b, it is observed that some frequencies propagated with greater effectiveness; this behavior is justified by the material characteristics that play a very important role in the propagation of waves. It is worth mentioning that the emission packages started with amplitudes of 10 V and finished with amplitudes of 3 V, whereas the received packages started with amplitudes of 200 mV, having in certain times amplitudes of 50 mV. This significant attenuation is due to the energy loss through the PZTs' intrinsic characteristics, the workpiece holder medium, interfaces (PZTs/holder; workpiece/holder), coupling medium, workpiece medium, amplifier and cables. However, despite the high energy loss of the ultrasound signal for the setup used in this work, the results will later show that the received signal preserved the process characteristics under study. The procedure for the emitted and received packages shown in Figure 6 was repeated for each grinding pass at each selected depth of cut.

**Figure 6.** (**a**) Emitted signals packages and (**b**) received signals packages.

The statistics used in the analysis of the received packages are shown in Figure 7. It is worth mentioning that, in order to show the statistics together, it was necessary to normalize the values. However, the analyses, such as the mean and standard deviations, were performed with the raw unfiltered signals without the normalization procedure. The analyses were performed for each package considering the mean values of these statistics (RMS and Counts). Subsequently, a total mean value and standard deviation, with respect to all packages, was calculated.

**Figure 7.** Statistics used to analyze the received packages—root mean square (RMS) and Counts.

The RMS mean and standard deviation values (unfiltered signals) for each grinding pass at each depth of cut are shown in Figure 8. In Figure 8a it can be seen that the result of the RMS mean value without material removal showed a greater amplitude compared to the results of the grinding passes 1 and 2. This non-linear behavior hinders the implementation of this system in the diagnosis of material removal during the grinding process. In relation to Figure 8b,c, a growth tendency is observed as the grinding passes occur; however, the difference of the RMS mean values between the 2nd and 3rd grinding pass for the 20 μm depth of cut is very small, making it difficult to identify the grinding pass and thus, being unattractive for practical implementation. In the same way, this analysis can be applied to the RMS mean values of the 1st and 2nd grinding passes for the 30 μm depth of cut in which there is a small difference, making it difficult to identify this grinding passes. It is worth mentioning that the standard deviations, compared to the RMS mean values, were very small, around 1%, for all the observed conditions. This behavior characterizes the consistency and repeatability of the emission and reception signals used in the proposed technique.

The Counts mean values and the standard deviations (unfiltered signals) for each grinding pass at each depth of cut are shown in Figure 9. As in the behavior shown by the RMS results, the application of the Counts statistic was not effective in identifying a linear growth pattern between the grinding passes. The depth of cuts of 20 μm (Figure 9b) and 30 μm (Figure 9c) showed a non-linear behavior. In Figure 9b it is observed that the Counts mean value of the undamaged workpiece is higher than the Counts mean values for the 1st and 2nd grinding pass. Regarding Figure 9c, the Counts mean value of the workpiece without damage had a very close result in relation to the 1st and 2nd grinding pass, however, it was higher than the Counts mean value of the 3rd grinding pass. Finally, regarding Figure 9a with a 10 μm depth of cut, an increasing pattern was observed, however, the difference between the 1st and 2nd grinding pass was small, similar to the behavior shown by the RMS mean values at the depth of cut of 20 μm (Figure 8b) and 30 μm (Figure 8c). The standard deviations, when compared to the mean values, were very small, around 1%, similar to the values found in the RMS results, shown in Figure 8. Again, the behavior of the presented results emphasizes the consistency and repeatability of the technique used in this work. Both statistics (RMS and Counts) did not show a regular tendency in the diagnosis of material removal, thus a spectral analysis of the received signals for each grinding pass was performed in order to find the frequency bands that are more strongly related to the process conditions.

**Figure 8.** RMS mean and standard deviation values of the raw unfiltered signals at (**a**) 10 μm, (**b**) 20 μm and (**c**) 30 μm.

**Figure 9.** Counts mean and standard deviation values of the raw unfiltered signals at (**a**) 10 μm, (**b**) 20 μm and (**c**) 30 μm.

The mean spectrums for two workpiece conditions, without material removal and after the 3rd grinding pass, at each depth of cut, are shown in Figure 10. It can be seen in Figure 10 that the spectrums, in general, showed similar behavior, with higher spectral activity between 150 and 190 kHz.

**Figure 10.** Spectrum of two workpiece conditions at (**a**) 10 μm, (**b**) 20 μm and (**c**) 30 μm.

Furthermore, it is observed that the spectrum of the 3rd grinding pass at the three depth of cuts, 10 μm (Figure 10a), 20 μm (Figure 10b) and 30 μm (Figure 10c), presented the greatest amplitudes along most part of the spectrum when compared with the workpiece without material removal. By means of the frequency band selection criterion, presented in Section 5.2, the 37 to 46 kHz frequency band was selected and subsequently filtered into the received packages of the 10 μm depth of cut, as shown in the magnification of Figure 10a. For the 20 μm depth of cut, a frequency band from 135 to 144 kHz was selected, as shown in Figure 10b. Regarding the 30 μm depth of cut, a frequency band of 186 to 192 kHz was selected. The frequency bands magnifications of both depth of cuts (20 and 30 μm) are shown in Figure 10b,c, respectively. The RMS mean values and standard deviations of the filtered signals for each grinding pass at each depth of cut are shown in Figure 11. In contrast to the results observed in Figure 8, the filtered RMS values showed a uniform increase trend. An increase in the RMS values was identified according to the grinding passes. The increase in the RMS values was due to the behavior of the amplitude of the signals in the selected frequency bands. After the application of digital filters in the selected frequency bands and subsequent computation of the RMS statistic, an increasing trend was observed at all depths of cut (Figure 11a–c). This behavior can be explained by the signal amplitudes in the selected bands, that is, the changes in the workpiece (material removal) presented higher amplitude levels [26]. It is worth mentioning that the sample changed after each grinding pass and, as a consequence, the propagated waves also showed changes that are evidenced in the selected frequency bands. Thus, events produced during the grinding process that indicated changes in the workpiece structure, such as material loss, burning, high roughness and cracks, were evidenced in the selected frequency bands, allowing better diagnosis of the process. Finally, it is worth mentioning that the standard deviation values remained small, again showing the consistency and repeatability of the method. Thus, the appropriate selection of frequency bands is very important for the application of this technique.

**Figure 11.** RMS mean and standard deviation values of the raw filtered signals at (**a**) 10 μm; (**b**) 20 μm and (**c**) 30 μm.

The Counts and standard deviation values of the filtered signals for each grinding pass at each depth of cut are shown in Figure 12. As with the filtered RMS values shown in Figure 11, the mean Counts values for the same signals showed an increasing trend in all the conditions observed. However, it is worth mentioning that the depth of cut of 10 μm shown the best result for this statistic, whereas in the depths of cut of 20 and 30 μm the Counts presented a small improvement when compared to the optimal result obtained in the RMS application of Figure 11. Thus, the Counts and RMS statistics can be used together, with priority for the RMS due to the optimal results; the Counts statistic can be used with the purpose of validating the RMS results and strengthening the damage diagnosis system in the grinding process.

The percentages of difference between the mean RMS and Counts values of the unfiltered and filtered packages for two workpiece conditions, without material removal and after the 3rd grinding pass, at each depth of cut are shown in Figure 13. In Figure 13a it can be observed that the highest percentage variation is around 38% for the filtered signal and depth of cut of 10 μm. Similarly, the percentage of difference for the Counts mean values, shown in Figure 13b, presented the greatest difference at the same depth of cut, around 22%. Finally, the differences in the observed conditions are higher in the results of the mean RMS, denoting that the RMS statistic is more adequate for the application of this technique due to the better results.

As demonstrated by Webster et al. [51], the 1 ms interval is best suited for calculating the RMS value in the monitoring of grinding processes. The same interval, corresponding to 4096 points, was applied in the Counts statistic. Thus, it is possible that this interval is not the most appropriate for this statistic, which explains the better result of the RMS statistic when compared to Counts. In addition, the choice of the most appropriate frequency band is crucial for the performance of the statistics. Therefore, other intervals and frequency bands can be studied in order to optimize the Counts statistics.

**Figure 12.** Counts and standard deviation values of the raw filtered signals at (**a**) 10 μm; (**b**) 20 μm and (**c**) 30 μm.

**Figure 13.** Percentage variation between the unfiltered and filtered signals of the workpiece without removal material and after the 3rd grinding pass—(**a**) RMS and (**b**) Counts values.

The correlations between the mean values of the statistics (RMS and Counts) and the volume of material removed are shown in Figure 14. The correlation analysis is performed by means of the coefficient of determination (*R*), where *R* = 1 represents a linear fit of 100% and *R* = 0 represents the complete lack of correlation between the values [21]. It can be observed that for the RMS statistic (Figure 14a), the *R* values were close to 1. Regarding the Counts statistic (Figure 14b), the coefficient of determination showed a high degree of correlation; however, the coefficient was lower than the coefficient found for the RMS statistic. At the 10 μm depth of cut, the RMS statistic presented an *R* of 0.9883 and the Counts statistic an *R* of 0.98794. Thus, the RMS was slightly better than the Counts in the estimation of the volume of material removed. At the depth of cuts of 20 and 30 μm, a higher sensitivity of the RMS statistic was observed when compared to the Counts statistic.

**Figure 14.** Correlation between the statistics and the volume of material removed (**a**) RMS and (**b**) Counts.

At 20 μm, the RMS had an *R* = 0.99517 while Counts had an *R* = 0.94788. Finally, at 30 μm the largest difference was observed, where the RMS presented an *R* = 0.99469 and Counts presented an *R* = 0.93441. Thus, in the application of this technique, the RMS statistic has a better performance than the Counts statistic, however, the high degree of correlation shows that both statistics can be used to indirectly determine the volume of material removed.

In a system where both statistics can be applied, it is possible to obtain results that confirm the material removal diagnoses, since both statistics showed the same increasing trend. It is worth mentioning that, in both statistics, the filtered signals produced a much greater percentage of change when compared to the unfiltered signals. Thus, the selection of frequency bands that best characterize the events occurred during the grinding process is very important for the application of the technique proposed in this work.

### **7. Conclusions**

The interest of the scientific community in ultrasound techniques has increased in recent years due to its wide range of applications. Thus, a new method of ultrasound wave monitoring is proposed in this study as an alternative to traditional ultrasound methods. The main advantage of this method is the use of low-cost transducers for the emission and reception of ultrasound waves in conjunction with traditional signal processing statistics, thus allowing the non-invasive monitoring of structures. Unlike traditional methods of ultrasound analysis, the method presented in this paper does not depend on reflections and wavelengths to identify damage. Moreover, the proposed method does not require the use of the traditional ultrasound parameters (wavelength, propagation velocity and time of flight) to detect changes in the structures. Finally, this method uses traditional statistics for monitoring the material removal volume in grinding, allowing the study of other statistics, indexes and parameters, such as RMSD and CCDM used in SHM.

A study of the frequency bands that best correlate with the workpiece characteristics during the grinding passes was performed. Thus, it can be concluded that the unfiltered RMS and Counts mean values have low sensitivity to the material removal changes and are not attractive for practical purposes. On the other hand, the RMS and Counts mean values of the filtered signals in the selected frequency bands showed excellent results, obtaining an increasing tendency according to the number of grinding passes that occurred in the tests. It is worth mentioning that the filtered RMS values presented the best results when compared with the Counts values in the same condition. The highest percentage changes between the workpiece without material removal and after the 3rd grinding pass for each depth of cut was observed for the mean RMS values. The frequency band selection and the interval period were determinant for the sensitivity of the statistics. In addition, the correlation analysis between the statistics (RMS and Counts) and the volume of material removed reinforced the results obtained, proving the viability of applying the chirp-through-transmission technique in the monitoring of material removal, as all the coefficients of determination were higher than 90%.

Nevertheless, the results presented in this work are preliminary and new studies must be conducted for improvements of the proposed technique with application in grinding, SHM as well as in other machining processes.

**Author Contributions:** Conceptualization, F.A.A. and P.R.A.; Formal analysis, T.G.L.; Methodology, F.A.A., R.G., M.A.A.V. and T.G.L.; Supervision, P.R.A. and E.C.B.; Writing—review & editing, F.A.A., P.R.A., M.A.A.V. and E.C.B.

**Funding:** This research was funded by the Sao Paulo Research Foundation (FAPESP), under grant #2017/18148-5 and National Council for Scientific and Technological Development (CNPQ), under grant 306435/2017-9 for supporting this research work.

**Acknowledgments:** The authors would like to thank the Norton Company for the grinding wheel donation.

**Conflicts of Interest:** The authors declare no conflict of interest.
