## 4 Analysis of Results
### Application Example  
To illustrate the operation of the proposed algorithm, the machining of a component with the geometric characteristics shown in Figure 13 is defined.  
The manufacturing conditions of the test piece are shown in Table 4.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Description** \\ \hline \(V_{c}\) [m/min] & 16.0–30.0 & Recommended cutting speed for the work material \\ \(F_{v}\) [m/min] & 60.0 & Recommended cutting tool feed rate \\ \(k_{s}\) [MPa] & 1700.0 & Specific cutting pressure for mild steel \\ \(P_{\epsilon}\) [W] & 746.0 & Electrical power supplied to the machine tool \\ \(\rho_{T}\) [Adm] & 0.75 & Machining process efficiency factor \\ \(R_{a}\) [mm] & 0.002 & Roughness of machined surfaces in general \\ \(S_{y}\) [MPa] & 250.0 & Yield strength of the test material \\ \(S_{u}\) [MPa] & 400.0 & Ultimate strength of the test material \\ \hline \hline \end{tabular}
\end{table}
Table 4: Requested manufacturing properties: mild steel.  
Figure 12: Proposed algorithm for cutting speed search.  
Figure 13: Prototype of test piece to be machined: mild steel.  
These parameters were input into the processed algorithm (see Appendix A), producing the following graphs for a speed range defined by the cutting tool manufacturer and given the machine tool's constraints:  
For the cutting tool nose radius, recommended to meet the surface roughness restriction, Figure 14 illustrates its variation with respect to cutting speed.  
Figure 15 shows the comparison of machining time with respect to cutting depth and stress derived from the machining process \(S_{\theta_{c}}\) when the cutting speed varies within the range recommended by the cutting tool manufacturer.  
Figure 16 shows the depth of cut applied compared to the number of passes required to reach the requested machining size and the time consumed in this process.  
Figure 14: Behavior of the cutting tool nose radius.  
Figure 15: Machining time, stress applied to the process, and cutting depth.  
Figure 17 shows the comparison between the machining time, the average electrical power consumed by the electric motor, and the average energy consumed by the process.  
To measure the behavior of the proposed method, a comparison is made with the test piece defined in [20] and the parameters obtained between both methods are compared. Table 5 shows the properties reported by the author together with the properties necessary to carry out the simulation with the developed model, such as specific cutting pressure \(k_{s}\) and electric motor power \(P_{e}\).  
Figure 16: Machining time, number of cutting passes, and cutting depth.  
Figure 17: Electrical power, average energy consumed, and machining time.  
The geometry of the piece machined by the author in [20] is characterized only by the outer diameter because single-pass cuts are made in his experiment. For the model proposed in this article, it is necessary to define a diameter \(d_{m}\) to characterize the maximum load due to the stress concentrator; a smaller diameter \(d_{m}=58\) mm will be proposed arbitrarily in order to perform the calculation and analysis of the maximum load applied to the workpiece, thereby trying to replicate, with the model itself, the design of its working conditions.  
From the development of the problem posed and taking into consideration the cutting speed \(V_{c}\) reported by the author, the values shown in Table 6 were obtained.