# Smoothed Particle Hydrodynamics Simulation of Orthogonal Cutting with Enhanced Thermal Modeling
## 1 Introduction  
Metal cutting is one of the essential processes throughout engineering designs and manufacturing industries. In order to reduce costs and increase productivity, it is necessary to improve understanding of the metal cutting problem. As there is a wide range of design variables (e.g., tool wear, workpiece temperature, process forces, chip shape, or surface quality) and diverse physical phenomena; nonetheless, the reliability of empirical and analytical models for metal cutting is limited. In this view, computer-based simulations using numerical methods appear as an invaluable alternative to study metal cutting problems with deeper insights. In addition to the well-known Finite Element Method (FEM), the family of particle-based methods is another numerical approach frequently used for cutting simulations. Unlike FEM, however, these methods do not require re-meshing as they are mesh-free. This interesting feature of particle methods makes them a suitable choice for metal cutting applications. In particular, the Smoothed Particle Hydrodynamics (SPH) method, introduced independently by [PERSON] et al. [1] and [PERSON] [2] in 1977, sees a broader spectrum of applications in this context. SPH is known as a well-established numerical tool for modeling fluid dynamics. Examples include the application in impact [3] and shockwave [4] simulations, complex free-surface problems [5], and thermal simulation of multiphase flows by [6, 7]. The utilization of SPH in more industrially-oriented fields of application can also be found in the literature. Examples in laser-based manufacturing problems are the modeling of material removal in [8, 9] and pulsed-laser ablation of aluminum in [10]. Between 2007 and 2015, numerous researchers applied SPH to metal cutting and the chip formation, including the high-speed cutting [11, 12] and 3D single-grain [13] models using commercial software packages, as well as the developments in [14, 15] using anin-house code. These papers do not consider the heat transfer from the workpiece to the tool, while the experimental evidence has shown that a significant proportion of heat in metal machining operations transfers from the chipping zone to the cutting tool [16]. More recently, the concept of parallel computing on Graphics Processing Units (GPU) has been introduced to both 2D [17] and 3D [18] SPH cutting simulations to boost the computational performance. [PERSON] et al. [19] employed this GPU-accelerated approach for inverse parameter identification and proposed a temperature-dependent coefficient of friction in SPH cutting models. Furthermore, a tailor-made framework for the multi-resolution SPH simulation of orthogonal cutting tests was published by [20]. It is worth mentioning that the computer codes utilized by these recent works are open source. Although previous studies have demonstrated some excellent results in the capability of SPH to simulate metal cutting processes, none of them accounts for heat loss boundary conditions in their thermal model. More specifically, the issue with ignoring the heat transfer from the workpiece to the tool in SPH models (e.g., in [13; 20]) was addressed by some recent works in [17; 19]. However, the thermal modeling approach in these papers also suffers from two shortcomings: (1) Utilizing an inconsistent Laplacian operator that deteriorates the solution accuracy near the boundaries. (2) Neglecting the convective and radiative heat loss from the system. Consequently, we intend to develop a comprehensive thermal model for SPH cutting simulations that resolve these issues and account for all these effects. In this work, a numerical simulation framework is developed that can increase the reliability of available mesh-free cutting models in their thermal modeling approach. As the first task, boundary particles are identified by a robust surface detection algorithm [5] borrowed from the CFD community.