4.1. Measurement Experiments Using a Raw Data Transmission Method

Machining experiments were conducted in which tangential and radial accelerations were measured at 24 kHz (0.042 ms interval) and transmitted to a PC in real time via Wi-Fi. A WA80J8V36R grinding wheel (Noritake Co., Ltd.) was used. The workpiece speed was set to 0.22 m/s, the depth of cut to 2 μm, and a single pass was performed under down-cut conditions. Prior to the experiments, the grinding wheel was carefully balanced, and sufficient zero-cut passes were performed. The received radial and tangential acceleration signals are presented in Figs. 5(a) and (b). After the experiments, frequency analyses of the radial and tangential acceleration data were performed on a PC, and the results are shown in Figs. 6(a) and (b). In the frequency analysis, data were acquired up to 12 kHz; however, Figs. 6(a) and (b) display only up to 6 kHz because of the low amplitudes in the higher-frequency range. From Figs. 5(a) and (b), a clear distinction can be observed between the acceleration signals during idle rotation and grinding. Peaks corresponding to the wheel rotation period of 0.02 s were evident in both the radial and tangential directions. In addition, the radial acceleration exhibited a larger amplitude. In the frequency-domain results shown in Figs. 6(a) and (b), no characteristic peaks other than those associated with the rotational frequency of the wheel were observed. To observe the variations in acceleration in real time, the accumulated absolute value of acceleration \(A\) was calculated using Eq. (1) and displayed on a PC monitor. Here, \(\Delta t\) denotes the sampling interval of the acceleration measurement (0.042 ms), \(a(n\Delta t)\) is the acceleration at time \(n\Delta t\), \(A\) is the accumulated absolute acceleration value, and \(N\) is the number of samples used for accumulation.

Figure 7 shows the temporal variation of the accumulated value obtained by setting the number of samples to \({N=480}\), corresponding to the grinding wheel rotational period \({T=0.02}\) s, so that the acceleration is accumulated once every period. In the raw data transmission method, in which all sampled acceleration data are stored directly on a PC, the computational load on the PC becomes substantial. Therefore, instantaneous acceleration values are not shown in real-time displays. Instead, the accumulated values that require far fewer display updates are presented to reduce the PC load. It is evident from the figure that the magnitude of the acceleration during grinding was successfully captured and that the radial acceleration was greater than the tangential acceleration. Using the same experimental setup (as in Fig. 6), the grinding depth was varied among 2, 4, and 6 μm.

Figure 8 illustrates the relationship between the accumulated absolute acceleration and the grinding force. Fig. 8(a) focuses on the radial acceleration versus the normal force \(F_{n}\), while Fig. 8(b) presents the tangential acceleration versus the tangential force \(F_{t}\). In both cases, the respective acceleration values exhibit a linear relationship with their corresponding grinding forces. Notably, the acceleration values obtained by extrapolating the regression lines to zero force in Fig. 8(a) exceeded the idling level (Fig. 7), confirming an increase in vibration upon contact.

The proposed system enables the estimation of both \(F_{n}\) and \(F_{t}\) through acceleration measurements provided that calibration is performed beforehand under specific grinding conditions.

4.2. Measurement Experiments Using an Edge-Computing Method

Measurement experiments were conducted using an edge-computing approach. In this method, all computations are performed within the developed device, and only the processed results are transmitted to a PC via Wi-Fi. An autoencoder was used to calculate the anomaly scores during the experiment. The architecture of the autoencoder is illustrated in Fig. 9. The input layer consisted of 128 data points, the hidden layer comprised three stages, and the output layer also contained 128 data points. A rectified linear unit (ReLU) function is used as the activation function. The input data for the autoencoder were obtained from the tangential acceleration measured at a sampling frequency (Fs) of 48 kHz with a fast Fourier transform (FFT) size (\(N\)) of 1,024. Frequency analysis was performed on the microcontroller within the developed device, and 128 data points up to 6,000 Hz were used, corresponding to a frequency resolution of \({\Delta f}\) (\(=\) Fs/N) of 46.9 Hz. A Hamming window with 50% overlap was applied during the FFT processing. A moving average process was applied to the FFT results to improve the signal-to-noise ratio and reduce random noise. The number of input data points was limited to 128 owing to memory constraints of the microcontroller. The frequency range used for the data analysis can be arbitrarily selected up to 24 kHz by modifying the program ²⁷. Normal data for training the autoencoder were obtained from the acceleration signals measured while the grinding wheel rotated with the supplied coolant. Seventy datasets were used for training, and 30 were used for evaluation, with a total acquisition time of approximately two minutes. Anomaly scores were calculated using the root mean square error (RMSE), determined using Eq. (2), where \(n\) is the number of data points, \(x_{i}\) is the FFT-processed acceleration data, and \(x_{o}\) is the output generated by the autoencoder. Fig. 10 shows ten examples of frequency-domain data used for training. A distinct peak is observed near 50 Hz, corresponding to the rotational speed of the grinding wheel.

First, the variation in the RMSE caused by the rotation of the grinding wheel during idling was measured. The experimental results are shown in Figs. 11(a)–(c). Fig. 11(a) shows the temporal change in the rotational speed of the grinding wheel, whereas Fig. 11(b) shows the corresponding change in the RMSE. In this experiment, a stop command was issued, causing the rotational speed to gradually decrease from 3,000 min\(^{-1}\) until the wheel came to a complete halt. After remaining stationary for 20 s, a start command was applied to initiate rotation. The results indicated that the anomaly scores increased as the rotational speed approached zero. Fig. 11(c) presents the RMSE measurement results within a spindle speed range of 1,000 to 3,000 min\(^{-1}\). The figure shows that the variation in the RMSE was minimal within this range. These results indicate that while the developed device is capable of detecting a complete spindle stop, it is not sensitive enough to detect changes in the rotational speed within the range of 1,000 to 3,000 min\(^{-1}\).

Next, the progression of the RMSE during grinding was measured. The experiment was conducted under the same conditions as those shown in Fig. 5 using a single-pass grinding operation. Fig. 12(a) presents the RMSE transmitted to a PC via Wi-Fi for depths of cut 2 μm and 6 μm. The normal grinding force \(F_{n}\) measured using a dynamometer is shown in Fig. 12(b), whereas the tangential grinding force \(F_{t}\) is shown in Fig. 12(c). As shown in Fig. 12(a), the RMSE remained low in the non-contact state but increased during grinding. Furthermore, increasing the depth of cut from 2 μm to 6 μm causes the RMSE to increase accordingly. It took 0.2 s for the RMSE to reach its peak value, owing to the application of the moving average. Notably, the RMSE value may not reach its peak if the grinding time is shorter than this duration.

The relationship between the grinding forces and the peak RMSE resulting from larger infeed depths was investigated. Experiments were conducted at infeed depths of 2, 4, and 6 μm. Figs. 13(a) and (b) show the relationship between the normal grinding force \(F_{n}\) and the peak RMSE and between its amplitude \(\Delta F_{n}\) and this value, respectively. Similarly, Figs. 13(c) and (d) present the relationship between tangential grinding force \(F_{t}\) and its amplitude \(\Delta F_{t}\). From Fig. 13, it is evident that both the grinding forces and their amplitudes increase with increasing infeed depth. A linear relationship is observed between the peak RMSE and these forces. These findings suggest that the magnitude of the grinding forces can be estimated using the peak RMSE measured using the developed system under the same grinding conditions.

Next, the changes in the RMSE owing to the grinding-wheel condition were measured. After dressing the wheel, a grinding experiment was performed with an infeed depth of 2 μm until a total infeed of 2 mm was reached. The workpiece was moved only in the left-right direction at a speed of 0.05 m/s. Fig. 14(a) shows the relationship between the total infeed and RMSE, whereas Fig. 14(b) presents the RMSE variation at the beginning of grinding and immediately before reaching a total infeed of 2 mm. Fig. 14(c) illustrates the relationship between the total infeed and normal grinding force \(F_{n}\). Both Figs. 14(a) and (c) indicate that the RMSE and normal grinding force increase as the total infeed increases. In addition, Fig. 14(b) clearly distinguishes the RMSE waveform during the contact and non-contact conditions. An RMSE value of approximately 0.1 corresponds to the non-contact state in which the wheel is not engaged with the workpiece. From Fig. 14(b), it is evident that the RMSE during grinding differs significantly between the initial stage and immediately before reaching a total infeed of 2 mm. These results demonstrate that the developed system can detect changes in grinding-wheel conditions.

Figure 15 shows the experimental results obtained when the workpiece speed in the experiment of Fig. 14 was increased from 0.05 m/s to 0.22 m/s. As the workpiece speed increased, the maximum grain depth of the cut increased by 4.4 times. Fig. 15(a) shows the relationship between the total depth of cut and RMSE, whereas Fig. 15(b) illustrates the evolution of the RMSE at the beginning of grinding and immediately before the total depth of the cut reached 2 mm. Fig. 15(c) shows the relationship between the total depth of cut and the normal grinding force \(F_{n}\). A comparison of Figs. 15(a) and (c) with Figs. 14(a) and (c) shows that the RMSE was high in the early stages of grinding, although it may not have reached its peak because of the moving average processing. Similarly, the normal grinding force exhibited high values during the initial stage. Furthermore, even as the total depth of cut increased, both the RMSE and normal grinding force exhibited only minor variations.

Figure 16 shows the experimental results obtained when the depth of cut per pass in the experiment shown in Fig. 14 increased from 2 μm to 6 μm. As the depth of cut per pass increases, the maximum grain depth of the cut increases by 1.7 times. Fig. 16(a) shows the relationship between the total depth of cut and RMSE, whereas Fig. 16(b) illustrates the evolution of the RMSE at the beginning of grinding and immediately before the total depth of cut reached 2 mm. Fig. 16(c) shows the relationship between the total depth of cut and the normal grinding force \(F_{n}\). From Figs. 16(a) and (c), it can be observed that both the RMSE and normal grinding force exhibit larger values in the early stage of grinding compared to Fig. 14. Immediately before the total depth of cut reached 2 mm, both the RMSE and the normal grinding force exhibited almost the same values, as shown in Figs. 14 and 16. Furthermore, as shown in Figs. 16(b) and (c), no significant changes in the RMSE or grinding force were observed between the initial and final stages of grinding.

Based on the experimental results shown in Figs. 14–16, it is suggested that by observing the RMSE obtained from the developed system, changes in the grinding-wheel condition can be estimated at a level comparable to that achieved by measuring the grinding force.

To investigate the detection of grinding burns, grinding experiments were conducted under the conditions described in our previous studies to induce this phenomenon. A different grinding wheel, WA80N8V36R (Noritake Co., Ltd.), was used. The workpiece speed was set to 0.07 m/s, and the depth of cut was repeatedly varied in a sequence of 2 μm followed by a zero-cut. In this experiment, grinding burns occurred on the machined surface at a total cut of 0.85 mm, as shown in the photograph of the workpiece in Fig. 17(a), after which the experiment was terminated. Fig. 17(a) shows the relationship between the total depth of cut and the RMSE. Fig. 17(b) illustrates the evolution of the RMSE at the beginning and immediately before the end of machining. Fig. 17(c) shows the corresponding evolution of the normal grinding force \(F_{n}\). In Fig. 17(a), an abnormal RMSE waveform is observed when a grinding burn occurs at a total grinding depth of 0.85 mm. Additionally, abnormal values were observed in the RMSE waveform at the total grinding depths of 0.69 mm, 0.74 mm, and 0.79 mm. As the identification of grinding burns relies on the operator’s subjective evaluation, it remains uncertain whether the observed RMSE anomalies correspond precisely to the occurrence of burns in this experiment. In the waveform obtained immediately before the end of the grinding, as shown in Fig. 17(b), an abnormal RMSE pattern presumably associated with grinding burns was observed, indicating that a machining anomaly had already occurred at this stage. Based on the normal grinding forces shown in Fig. 17(c), the difference between the 2 μm depth of cut and the zero-cut is clearly visible at the beginning of machining. The abnormal grinding force was recorded immediately before the machining ended. The RMSE waveform exhibits the same trend as the grinding force waveform. It is expected that, as the amplitude of the grinding force increases, the vibration of the grinding wheel also increases. Although the specific reason for the increased force amplitude during grinding burn remains unidentified in this experiment, the increase in force amplitude appears to coincide with the increase in RMSE. In this experiment, the vibration increased with the occurrence of grinding burns. Therefore, grinding burns can also be detected by measuring the accumulated absolute acceleration, which is an indicator given by Eq. (1).