*2.4. Monitoring*

The confidence limits for monitoring tool breakage were calculated by performing 10 longitudinal turning operations. The measured cutting forces were used to calculate the upper *Lup* and lower *Llow* confidence limits. Thus, the confidence estimator approach according to Brinkhaus was used [24]. The confidence limits were updated after each process based on the expected mean value *x* standard deviation σ, and a safety value *Csaftey* for each running measurement value *i*. The safety value influences

the distance between *x* and the confidence limits. A safety value of *Csaftey* = 6 was used, which is usually the default setting of a monitoring system.

$$L\_{\text{up, low}}(i) = \overline{\mathfrak{X}}(i) \mp \mathbb{C}\_{\text{safe}\,\text{ty}} \cdot \sigma(i) \tag{1}$$

In order to take account of temporal fluctuations, the confidence limit was calculated for a function *h*(*i*). This function determines an envelope for the expected value *x*(*i*), which allows a time lag for a specified time *K*. During the investigations, *K* was set to 100 ms. Based on this value, no false alarms occurred after four processes in the teach-in phase.

$$\begin{array}{l} h\_{\text{up}}(i) = \max(\mathbf{x}(i-K), \dots, \mathbf{x}(i+K)) \\ h\_{\text{low}}(i) = \min(\mathbf{x}(i-K), \dots, \mathbf{x}(i+K)) \end{array} \tag{2}$$

According to the combination of Equations (1) and (2), the shift of time and amplitude was taken into account when calculating the confidence limits. The values of *h* and σ were calculated by a moving average to allow dynamic weighting of the di fferent measurements.

$$\begin{array}{l} L\_{up}(i) = \overline{h}\_{up}(i) + \mathsf{C}\_{safety} \cdot \sigma(h\_{up}(i))\\ L\_{low}(i) = \overline{h}\_{low}(i) - \mathsf{C}\_{safety} \cdot \sigma(h\_{low}(i)) \end{array} \tag{3}$$

For detecting the currently machined material, the material-specific cutting force *MatFc* was monitored [25]. In this approach, the cutting force *Fc* was normalized by the material removal rate *Qw*. The material removal rate was calculated online using a dexel-based cutting simulation. Input parameters for the simulation were the axis positions from the machine control. A material compound was subsequently monitored on the basis of a defined boundary surface.

$$Mat\_{Fc} = F\_c / Q\_w \tag{4}$$

#### **3. Results and Discussion**
