## 3 Results
### Remaining Useful Life (RUL) Prediction  
RUL is a critical metric in predictive maintenance and reliability analysis, serving to estimate the time remaining before a component or system experiences failure or necessitates maintenance. In this analysis, predictive models are employed to forecast the future wear of a tool based on various input characteristics, thus indirectly calculating the RUL by predicting the expected wear that will occur over time. Rather than determining the RUL directly, the focus is on predicting future tool wear, which can effectively serve as a proxy for RUL if wear is recognized as an indicator of the time until failure. To facilitate this analysis, the NUAA dataset is utilized due to its rich array of variables, which are essential for accurate predictions. In this approach, fixed values are applied, and a pre-trained Gradient Boosting model will assesses the tool's wear, ultimately allowing for the determination of the remaining useful life of the tool. This method harnesses the dataset's comprehensive features to enhance the reliability and accuracy of RUL predictions. The graph presented in Figure 9 closely resembles the graph generated from [PERSON]'s equation [22], with the \(Y\)-axis indicating the wear bandwidth as a function of time. It reveals three distinct zones, each representing specific wear levels and their corresponding severity for the cutting tool. The dataset demonstrates a wear range spanning from 0.049 mm to 0.31 mm, aligning well with the graph's scale and enabling the extraction of meaningful conclusions and physical interpretations from the mathematical results produced by the recently trained Gradient Boosting model. From the analysis of the correlation matrix, two parameters that exhibit a relatively somewhat strong relationship with tool wear are identified: spindle speed and feed per tooth. These parameters are input into the Gradient Boosting model, using mean values for  
Figure 9: Wear bandwidth over time [14]. the other variables, to calculate the time required to achieve the target wear levels. This analysis facilitates an approximate determination of the time it will take for the cutting tool to reach the specified wear thresholds corresponding to the three zones identified in the preceding graph (0.1 mm, 0.2 mm, and 0.3 mm). Importantly, even with variations in parameters, the predictive model can be continuously updated with real-time data, allowing for adjustments to the expected time. Consequently, operators will maintain precise awareness of when the cutting tool is projected to enter the dangerous wear zone, with a recommendation to replace the insert when wear values fall between 0.25 mm and 0.3 mm to ensure a high-quality finish on the machined product. While the NUAA dataset is derived from a specific insert and tool material, the findings can readily be extrapolated to other inserts if the materials are comparable. For instance, consider the insert model 345R-1375E-ML S30T (Sandvik Coromant, Sandviken, Sweden) [23], which is coated with titanium and designed for use with solid carbide parts, consistent with the materials specified in the chosen dataset. From its manufacturer's datasheet, the following values are obtained:  
* Feed per Tooth (\(f_{z}\)): 0.11 mm/rev; range: 0.07-0.20 mm/rev. * Cutting Speed (\(v_{c}\)): 140 m/min; range: 120-155 m/min. The value for \(f_{z}\) is directly incorporated into the code as a value. Subsequently, the cutting speed formula is applied, assuming a \(DC_{ap}\) (cutting diameter at the depth of cut) of 0.03 m to calculate the spindle speed, which, after rounding, yields a result of 1485 rpm. Upon inputting these parameters into the trained Gradient Boosting model, the following times are obtained:  
* For a wear value of 0.1 mm: Time: 0.06:40. * For a wear value of 0.2 mm: Time: 0.13:20. * For a wear value of 0.3 mm: Time: 0.48:20. To interpret these results, it is of great importance to reference [PERSON]'s equation and analyze the preceding graph.