# Cutting Force Estimation Using Milling Spindle Vibration-Based Machine Learning
## 2 Relationship Between Tool Wear and Cutting Force
### Machining Experiments  
As shown in Figure 1a, a dynamometer was installed beneath the workpiece fixture of the 5-axis machining center to measure cutting forces, and an accelerometer was attached to the lateral surface of the spindle to capture vibration signals. Figure 1b provides an overview of the data acquisition (DAQ) system used to simultaneously collect cutting force and vibration data. The specifications of the sensors and the DAQ system are detailed in Table 1. During the data collection process, spindle vibration signals were recorded concurrently, and these data will be utilized in subsequent chapters to develop and refine the cutting force estimation model. Table 2 presents a comprehensive summary of the machining equipment, tools, workpieces, and machining parameters used in the experiment. The machining conditions were determined based on the material-specific guidelines provided by the tool manufacturer. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**List** & \multicolumn{3}{c}{**Specifications**} \\ \hline Dynamometer & Range Fx, Fy & kN & \(-\)5–5 \\ \cline{2-4} (9257B \& 5167A81 Kistler, Winterthur, Switzerland) & Sensitivity & pC/N & \(-\)7.5 \\ \cline{2-4}  & Analog output & V & \(-\)10–10 \\ \hline \multirow{3}{*}{Vibration sensor (8688A10 \& 5134B, Kistler)} & Range & g & \(-\)10–10 \\ \cline{2-4}  & Sensitivity & mV/g & 500 \\ \cline{2-4}  & Analog output & V & \(-\)5–5 \\ \hline \multirow{3}{*}{Data acquisition (DAQ) (PXle-1092 \& PXle-6363, NI, Austin, TX, USA)} & Analog input & V & \(-\)10–10 \\ \cline{2-4}  & Analog input & ADC resolution & bit & 16 \\ \cline{1-1} \cline{2-4}  & Sample rate & Sample/s & Max 2M \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of sensors and data acquisition system. Figure 1: Experimental setup of machining center and data acquisition system for cutting force spindle vibration monitoring: (**a**) Machining center configuration with sensor and tool dynamometer placement; (**b**) Data acquisition system with software interface and signal processing units. According to Equations (1) and (2), the spindle speed (\(V_{s}\)) was set to 1194 rpm (19.9 Hz), and the feed rate (\(V_{f}\)) was adjusted to 573 mm/min. The sampling frequency for both cutting force and acceleration signals was configured at 1 kHz, ensuring data acquisition at a rate more than 12 times higher than the tooth passing frequency of 79.6 Hz. \[V_{s}=\frac{V_{c}\times 1000}{\pi\times d_{t}} \tag{1}\]  
\[V_{f}=V_{t}\times n_{t}\times V_{s} \tag{2}\]  
where \(n_{t}\), \(d_{t}\), \(V_{c}\), and \(V_{t}\) represent the number of teeth, tool diameter, cutting speed, and feed per tooth, respectively. The machining path for the experiment was a linear pass along the x-axis for the first layer, as depicted in Figure 2a. After each pass, the tool advanced by the radial depth of cut (\(d_{t}\)) along the y-axis, repeating the same machining pattern. This process was repeated for a total of 33 passes, after which the tool returned to its initial position and moved by the axial depth of cut (\(d_{a}\)) along the z-axis to begin the second layer, continuing with 32 passes. As shown in Figure 2b, with each successive layer, the number of passes decreased by one, resulting in a stepped workpiece composed of seven layers (a total of 210 passes). Six workpieces were machined under identical conditions, and the side surface of each layer was examined under a microscope to monitor surface changes.