*3.1. Tool Breakage*

In cutting operations, process errors typically lead to an increase or decrease of the process force. For this reason, the process force is well suited for a sensitive and robust monitoring in machining. To determine the sensitivity of force measuring systems, material defects can be applied to the workpiece. Similar to tool breakage, missing material lead to a drop in the process force. This characteristic was used in order to compare the cutting force *Fc,SG*, which was determined by the feeling turret, and the cutting force *Fc,dyn*, which was measured with the dynamometer. A longitudinal turning process was carried out with a new tool for a cutting speed of 300 m/min and a feed rate of 0.1 mm. During machining, the depth of cut was reduced stepwise from 1 to 0.1 mm. This process was repeated 10 times. Afterward, a shaft was machined, which was prepared with a groove that had a width of 3 mm. The missing material causes a decrease in cutting force at each depth of cut, depicted in Figure 3.

The comparison of the two force measurement systems showed that they have an identical time behavior with regard to the signal change. The amplitude of the decreasing cutting force is also identical for both systems. Therefore, it can be concluded that both systems are highly sensitive to a change in cutting force due to tool breakage. However, by comparing the signals of the 10 good processes, it becomes clear that the cutting force *Fc,SG* has a lower signal-to-noise ratio (SNR).

$$\text{SNR} = \mu/\sigma \tag{5}$$

The SNR was determined for each depth of cut *ap* by the mean value of the amplitude μ and the standard deviation σ of the signal. The results of the SNR for both measuring systems are summarized in Table 3.


**Table 3.** Signal-to-noise ratio for the measured cutting force by using the dynamometer and feeling turret.

**Figure 3.** Longitudinal turning with and without a material defect for different depths of the cut.

The SNR was determined for each depth of cut *ap* by the mean value of the amplitude μ and the standard deviation σ of the signal. At an *ap* of 0.5 mm, *Fc,dyn* exhibits an SNR of 149. With a decreasing *ap*, the SNR also decreases further. For *ap* = 0.1 mm, the SNR is still 70. The measured cutting force by the dynamometer has the lowest SNR for *ap* = 1 mm with 46. The deviation to the other depths of cut is caused by different chip formation, which led to a higher vibration of the system. For *ap* = 1 mm, the *Fc,SG* shows a similar SNR with 40. However, with each reduction of *ap*, the signal-to-noise ratio decreases for the signal *Fc,SG*. For the depth of cut of *ap* = 0.1 mm, the SNR is 7 and, thus, lower by a factor of 10 compared to *Fc,dyn*. The repeatability of the individual measurements also shows a different quality for both signals. The evaluation of the 10 good processes demonstrates that the cutting force *Fc,SG* has larger variations between the measurements than *Fc,dyn*. With a depth cut of *ap* = 1 mm, the standard deviation σ*i* for the mean amplitudes of the different workpieces is for both systems being almost identical with approximately 15 N. By changing the process parameters to a lower *ap*, the standard deviation decreases for *Fc,dyn* to σ*i*= 1.7 N while σ*i*of *Fc,SG* is around 10 N.

If confidence limits are used to monitor the signal, the higher signal-to-noise ratio and variation of the mean amplitude leads to a widening of the statistical limits and, thus, to a decreasing monitoring sensitivity. In order to compare *Fc,SG* and *Fc,dyn* with regard to their qualification for confidence limit based monitoring, the feature of the normed bandgap (NB) was determined [26]. The normed bandgap

indicates the range in which the normalized signal has to be changed to trigger an alarm. For this purpose, the confidence limit was calculated based on the distribution of the signal around its long-term average. After eight processes, the limits had become close to the process. A further approximation was only possible in very small steps due to the high standard deviation of the measured signal. It can be assumed that 10 measurements are su fficient to generate the confidence limit and calculate the NB.

$$\text{NB} = \frac{k}{\overline{\overline{\mathbf{x}}}} = \frac{L\_{\text{np}} - \overline{\mathbf{x}}}{\overline{\overline{\mathbf{x}}}} \tag{6}$$

To evaluate the monitoring quality, the gap between the mean value *x* and the upper confidence limit *Lup* was evaluated. The distance *k* between *x* and *Lup* was normalized to the average. Figure 4 shows the confidence limits after 10 processes for the cutting forces *Fc,dyn* and *Fc,SG* and the comparison of the normed bandgap (NB) for both measuring systems.

**Figure 4.** Confidence limits and normed bandgaps for Fc,dyn and Fc,SG during a longitudinal turning process with di fferent depths of cut.

The sensitivity of the confidence limit, which is calculated based on the cutting force of the feeling turret, declines with decreasing force. This is reflected by the increasing normed bandgap. For an *ap* of 1 mm, both signal sources achieve a similar monitoring performance. At a normed bandgap of 0.3, a process error must result in a signal change of 30% to trigger the alarm. The ratio remains between NB = 0.1–0.2 for all examined depths of cut if the cutting force is measured with the dynamometer (Kistler, Winterthur, Switzerland). If the feeling turret is used, the normed bandgap for *ap* = 0.3 mm shows a maximum of NB = 0.8. The NB increases to 2 with a reduction of *ap* to 0.1 mm. Thus, the sensitivity of the dynamometer is higher by a factor of 10 compared to the feeling turret. The fact that the feeling turret has a significantly lower sensitivity at low process forces is based on the lower measurement resolution of the system relative to the dynamometer. This is primarily due to a higher signal-to-noise ratio, which has an increasing impact on the stochastic distribution of the signal for lower cutting forces. A generalized statement about the required NB of a signal cannot be made since each error is represented di fferently in the signal. However, based on the investigations, it is considered when no finishing operations can be monitored by the feeling turret. For roughing operations, on the other hand, a similar monitoring quality as with the dynamometer can be achieved.
