# Smoothed Particle Hydrodynamics Simulation of Orthogonal Cutting with Enhanced Thermal Modeling
## 5 Results & Discussion
### Application: Orthogonal Metal Cutting
#### 5.2.1 Force Prediction and Chip Shape  
Among the provided experimental dataset, the highest cutting speed of \(v_{c}=318.5\) m/min was chosen for the SPH models of this paper to attain the shortest simulation time. The elapsed time per 2 mm cut distance is in the range of 29 h for this \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Body** & **Property** & **Symbol** & **Unit** & **Value** \\ \hline \multirow{6}{*}{Tool} & Clearance angle & \(\alpha\) & deg & 7 \\  & Rake angle & \(\gamma\) & deg & 0 \\  & Cutting edge radius & \(r_{\beta}\) & mm & 0.0028 \\  & Speed & \(v_{c}\) & m min\({}^{-1}\) & 318.5 \\  & Heat conductivity & \(k\) & W m\({}^{-1}\) K\({}^{-1}\) & 88 \\  & Specific heat capacity & \(c_{p}\) & J kg\({}^{-1}\) K\({}^{-1}\) & 292 \\ \hline \multirow{6}{*}{Workpiece} & Length & \(l_{x}\) & mm & 3 \\  & Height & \(l_{y}\) & mm & 0.3 \\  & Uncut chip thickness & \(t_{u}\) & mm & 0.1 \\  & Cut distance & \(l_{c}\) & mm & 2 \\  & Density & \(\rho\) & kg m\({}^{-3}\) & 4430 \\  & Young’s modulus & \(E\) & GPa & 113.8 \\  & Poisson ratio & \(v\) & – & 0.35 \\  & Heat conductivity & \(k\) & W m\({}^{-1}\) K\({}^{-1}\) & 7.3 \\  & Specific heat capacity & \(c_{p}\) & J kg\({}^{-1}\) K\({}^{-1}\) & 580 \\  & Reference temperature & \(T_{r}\) & K & 300 \\  & Melting temperature & \(T_{m}\) & K & 1878 \\  & Coeff. of friction & \(\mu\) & – & 0.35 \\  & Pt. of plastic work into heat & \(\chi\) & – & 90\% \\  & Pt. of frictional work into heat & \(\eta\) & – & 100\% \\ \hline \multirow{3}{*}{All} & Convection coeff. & \(h_{c}\) & W m\({}^{-2}\) K\({}^{-1}\) & 50.0 \\  & Emissivity coeff. & \(e\) & – & 0.30 \\ \cline{1-1}  & Stefan–Boltzmann constant & \(\sigma\) & W m\({}^{-2}\) K\({}^{-4}\) & \(5.67\times 10^{-8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental and numerical parameters for the cutting test, according to the works in [17; 19]. Thermo-physical properties required for thermal convection and radiation are taken from the works in [38]. Figure 4: Configuration of orthogonal metal cutting problem and a closeup of the force diagram. cutting speed, with a single core of Intel(r) i5-469 at 3.50 GHz. Furthermore, the orthogonal cutting experiment was conducted by setting a rake angle of \(\gamma=0^{\circ}\) in order to obtain a state, where the thrust force (\(F_{t}\) in Figure 4) is mainly caused by the friction between the rake face and the sliding chip. For the experimentation, we conducted turning operations as orthogonal cutting tests on a Ti6 Al4V cylinder with a diameter of about 70 mm and a wall thickness of 2 mm. The insert in its holder was held on the tool turret of the CNC turning machine. Both cutting and feed forces (\(F_{c}\) and \(F_{t}\)) were measured with a 3D Kistler piezoelectric force sensor. The numerical simulation is first validated by comparing the predicted forces with the experimental measurements. Figure 5 plots the evolution of these forces during 2 mm of this cutting process. An average of the predicted forces is calculated at the stationary zone, after almost 10% of the simulation time is elapsed. These average forces are listed in Figure 6, showing that both \(F_{c}\) and \(F_{t}\) computed from the simulation compare very well with the experimental data. The percent errors given in parentheses in this table shows an average of approximately 14% overprediction for \(F_{c}\) and 9% underprediction for \(F_{t}\). According to the thrust force plot in Figure 5, the overall maximum discrepancy between the experimental and numerical results produces an error of 53% underprediction for SPH with the reference model (see the red line at about 1.2 mm cutting length). When using the proposed model, this value is reduced to 45% and occurs slightly before 1.5 mm of the cutting length. At first glance, this discrepancy may not be within an acceptable range for some applications such as precision machining.