# MOIRA-UNIMORE Bearing Data Set for Independent Cart Systems
## 4 Fault Injection Methodology
Specifically, by assuming a beam quality factor \(M^{2}\) of 1.5 and a laser beam diameter (measured at \(1/e^{2}\) intensity) of \(D_{0}=14\,\mathrm{mm}\) on the lens, the following calculations were performed:  
* Rayleigh length \(z_{f}\), as the distance from the beam waist, where the beam radius is increased by a factor of the \(\sqrt{2}\): \[z_{f}=\frac{\pi\Big{(}\frac{D_{0}}{2}\Big{)}^{2}}{M^{2}\lambda}\approx 100\ \mu \mathrm{m}\] (1)
* Depth of field (D.O.F.) as the distance on either side of the beam waist, \(D_{0}\), over which the beam diameter grows by 5% \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Unit of Measure** & **Value** \\ \hline Wavelength, \(\lambda\) & nm & 1064 \\ \hline Average Output Power, \(P\) & W & 13.32 \\ \hline Pulse Frequency, \(f\) & kHz & 300 \\ \hline Pulse energy, \(E\) & \(\mathrm{\SIUnitSymbolMicro J}\) & 44.4 \\ \hline Pulse duration, \(\tau\) & ps & 10 \\ \hline Pulse fluence, \(F\) & \(\mathrm{J/cm^{2}}\) & 56.56 \\ \hline Line spacing, \(s\) & \(\mathrm{\SIUnitSymbolMicro m}\) & 5 \\ \hline Marking speed, \(v_{s}\) & m/s & 1 \\ \hline Number of passes on each groove, \(p\) & & 150 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Laser parameters used during experiments. Figure 5: Positioning of bearings on an ad hoc support. The operating principle of the multi-altitude approach for progressive focusing is explained in the enlarged image. \[\text{D.O.F.}=\pm 0.08\pi D_{0}^{2}M^{2}\lambda\approx 118\ \upmu\text{m} \tag{2}\]  
The relatively small depth of field (D.O.F.) of our laser, calculated at 118 \(\upmu\)m, made it impossible to damage the bearing components in a single laser pass. As a result, a multi-pass approach was adopted. This method involves focusing the laser beam on a specific target area of the component to be damaged. The process is defined by achieving the desired depth in the focused region, while areas outside the focal zone remain untreated due to insufficient energy deposition for proper material ablation. Consequently, the processing area is confined to a rectangle with a height equal to the previously calculated depth of field. Regions outside this height remain unprocessed because the laser beam is out of focus. To achieve the required depth incrementally, the height of the galvanometric head was adjusted, and the \(X\) position was compensated for by advancing the \(XY\) table. By refocusing the laser on a lower area, additional ablation could be performed. This process was repeated continuously until the desired damage geometry was achieved, with a depth tolerance of \(\pm 0.15\) mm from the nominal shape. To address the limitations discussed earlier, the bearings were fully disassembled. This allowed individual components to be exposed, enabling precise and controlled fault injection. Disassembly eliminated obstructions, such as balls between the inner and outer races, which previously hindered access to the target areas. As a result, more accurate and well-defined flat-bottom grooves were created using the multi-pass strategy described above. The final fault dimensions and geometry were characterized using an optical microscope (Model: Nikon LV100 ND). By adjusting the depth of focus, detailed measurements were obtained. Further methodological details on fault characterization can be found in [36]. Figure 6 shows a microscopic view of some faults created without disassembling the bearings. As can be observed, the depth of the faults varies inconsistently, a result of the challenges previously discussed. Figure 6: Microscopic view of bearing faults: (**a**) Incipient version IR fault of bottom bearing, (**b**) Incipient version OR fault of bottom bearing, (**c**) Laser version 0.5 OR fault of top bearing, (**d**) Laser version 1.0 OR fault of bottom bearing, (**e**) Laser version 0.5 IR fault of bottom bearing.