# Smoothed Particle Hydrodynamics Simulation of Orthogonal Cutting with Enhanced Thermal Modeling
## 6 Conclusions  
This paper presented a stabilized SPH framework for numerical simulation of orthogonal metal cutting with an enhanced thermal model. The numerical analysis consists of both thermal and mechanical effects by solving the heat equation in the whole system and considering the elasto-plastic behavior of the material. We found the agreement between the forces measured in the experiment and those predicted by SPH satisfactory, where the average error of force prediction (in both \(F_{c}\) and \(F_{t}\)) was smaller than 14% by comparing the numerical and experimental results. It was also shown that the temperature values obtained from the SPH simulation agree with the experimental measurement, leading to more accurate results with the proposed thermal model. The main contributions of this work to the SPH cutting models are summarized in the following. Figure 10: Comparison of chip shapes in different SPH resolutions, where \(v_{c}=241\) m/min, \(t_{u}=0.1\) mm, and \(r_{\beta}=0.005\) mm. The experimental photograph reprinted from [PERSON] et al. [42] Copyright (2021), with permission from Elsevier under License Number 4991260002261. Figure 9: Effect of SPH particles size on the chip shape, where \(\Delta x\) is the diameter of SPH particles. To account for the heat loss boundary condition in SPH cutting models, a new approach was proposed and subsequently applied to an orthogonal cutting problem. This approach incorporates an efficient surface detection algorithm, which was initially proposed for fluid flow applications [5]. An improved thermal model representing more realistic boundary conditions was presented as a result of this development. In addition to the constant temperature at fixed boundaries, heat loss in the forms of thermal convection and radiation was included. To ensure a second-order Laplacian operator in SPH, a corrected formulation (see the FMFS scheme in Equation (13)) was implemented for the first time in a metal cutting problem. This higher-order method allows us to solve the heat equation more accurately, especially in the presence of free surfaces. Future work opportunities can go in different directions. First, it would be necessary to conduct more experiments for temperature measurements in high-speed cutting. Another enhancement to this study, and perhaps applicable to much of the simulation literature, is determining all material and friction data by a unified numerical-experimental investigation (instead of assuming them from other work). Furthermore, the computational performance of the code needs to be enhanced by high-performance and parallel computing. This consideration is essential for high-resolution simulations of chipping and the 3D implementation of the present code. The following codes are openly available online: \"MFree IWF Cut Refine\" at [[https://doi.org/10.1016/j.ijmecsci.2019.06.045](https://doi.org/10.1016/j.ijmecsci.2019.06.045)]([https://doi.org/10.1016/j.ijmecsci.2019.06.045](https://doi.org/10.1016/j.ijmecsci.2019.06.045)) (link to Git repository: [[https://github.com/iwf-inspire/mfree_iwf-ul-cut-refine](https://github.com/iwf-inspire/mfree_iwf-ul-cut-refine)]([https://github.com/iwf-inspire/mfree_iwf-ul-cut-refine](https://github.com/iwf-inspire/mfree_iwf-ul-cut-refine))) and \"MFree IWF Thermal\" at [[https://doi.org/10.1007/s11831-019-09355-7](https://doi.org/10.1007/s11831-019-09355-7)]([https://doi.org/10.1007/s11831-019-09355-7](https://doi.org/10.1007/s11831-019-09355-7)) (link to Git repository: [[https://github.com/iwf-inspire/thermal_iwf](https://github.com/iwf-inspire/thermal_iwf)]([https://github.com/iwf-inspire/thermal_iwf](https://github.com/iwf-inspire/thermal_iwf))). M.A. : conceptualization, methodology, software, validation, formal analysis, investigation, data curation, visualization, writing, original draft preparation, and writing, review and editing. H.K. : software, data curation, and experiment. M.R. : conceptualization, methodology, and software. K.W. : supervision, revision, project administration, and funding acquisition.