# Smoothed Particle Hydrodynamics Simulation of Orthogonal Cutting with Enhanced Thermal Modeling
## 5 Results & Discussion
### Application: Orthogonal Metal Cutting
#### 5.2.2 Temperature Distribution  
The temperature distribution after \(l_{c}=2\) mm is displayed in Figure 7 to provide some qualitative insights into the thermal aspects of this metal cutting simulation. The left image of this figure is produced by running a simulation with the standard thermal model expressed in Equation (12), where no heat loss boundary condition is included. The middle image in Figure 7 is the result of a simulation including the proposed enhancements outlined in Equations (8) and (13). The chip temperature computed by the enhanced model is slightly lower than the standard model. This is because the open boundaries in the standard thermal model are perfectly isolated and the surface heat loss is ignored. More fundamentally, the essence of this marginal difference between the temperature distributions in Figure 7 can be associated with the constitutive modeling parameters and thermo-physical aspects of Ti6 Al4V. To better show the impact of the enhanced thermal model on simulation results, therefore, cutting experiments at lower speeds and/or materials with higher  
Figure 6: Summary of the measured and predicted forces for the cutting test. Forces predicted by SPH with different coefficients of friction are plotted in the bar chart, where the proposed thermal model is utilized. Impact of \(\mu\) on the thrust forces is higher than the cutting forces, demonstrating the most accurate result when \(\mu=0.65\) is used. thermal conductivity (e.g., AISI 1045) need to be considered. It is conjectured that running high-resolution SPH simulation of cutting chip formation can also help improve this issue. Next, the chip shapes of these two models are superimposed with two solid colors for a visual comparison. Ignoring the heat loss boundary condition by the standard model (i.e., the red particles in Figure 7) is the source of slightly more chip curling compared to the present enhanced model (i.e., the gray particles in Figure 7). Clearly, the chip becomes hotter when heat is not lost through its open surfaces. The thermal model in metal cutting has an indirect effect on force prediction, while its impact on the temperature field is direct, and perhaps more significant. Therefore, it is beneficial to demonstrate the improvements gained by the proposed model via a quantitative comparison. For this purpose, an orthogonal cutting experiment conducted by [PERSON] et al. [41] is taken into account, where temperature measurements are available. The case study pertains to machining a Ti6 Al4V workpiece at a cutting speed of \(v_{c}=20\) m/min, an uncut chip thickness of \(t_{u}=0.1\) mm, and a rake angle of \(\gamma=0^{\circ}\). The rake face temperature (\(T_{\text{RF}}\)) in this setting is about 680 K. Please note that \(v_{c}=20\) m/min is the lowest speed available in [41], deliberately chosen here to provide more time for thermal conduction in the chip formation zone. As the runtime associated with this relatively low cutting speed is almost 16x longer than the previous test at \(v_{c}=318.5\) m/min, these SPH simulations are carried out at a lower resolution and terminated after a cut distance of \(l_{c}=0.3\) mm. Shown in Figure 8 are the SPH results employing different thermal models, as well as a comparison of the rake face temperatures. The bar chart in this figure compares the predicted temperatures with the experimentally measured data from [41], which can, in turn, verify the correctness of the proposed thermal model. The red and blue bars are the arithmetic mean temperature of particles located inside the indicated black frames at the rake face, corresponding to 905 K and 744 K, respectively. Using the enhanced thermal model decreases the overprediction error of \(T_{\text{RF}}\) from 33% to 9% and leads to a more accurate simulation. This improvement is gained by the more realistic thermal boundary conditions in the proposed model and the utilization of a higher-order Laplacian operator. Figure 7: Distribution of the temperature after 2 mm of cut.