## 1 Introduction
After that, we employ the Taguchi method which involves establishing an orthogonal simulation array, applying an S/N ratio and ANOVA to investigate the effects of cutting parameters on surface roughness. Finally, we compare our result with experiments and make evaluations. There are two key components in our work. The first one is to establish a reliable and accurate numerical cutting model, and the second one is to come up with a method to evaluate the variation trend of surface roughness with different cutting parameters. As for the first component, most of the traditional numerical models apply the Finite Element Method (FEM) which bears problems in handling with large deformations and material fragmentations during the cutting process and sometimes leads to simulation breakdowns caused by excessive mesh distortion [8; 9; 10; 11]. At the same time, the simulation result is sensitive to different ways of generating the mesh, which affect the accuracy of the simulation [14]. Another problem of FEM is that it is not capable of deriving the surface roughness from the simulated surface since FEM simulates the cutting process, including chips formation, through setting chip separation criteria and deleting elements [9]. To avoid these problems, we applied Smoothed Particles Hydrodynamic (SPH) method, a Lagrangian meshfree method, to establish the numerical cutting model. SPH divides material into individual particles with independent properties, such as density, mass and speed, in the process of simulation instead of generating mesh for materials and cutting tools. Compared with FEM, its adaptivity can be obtained at the early stage of approximation of field variables, and its formula is not affected by the distribution of particles. Thus, SPH is capable of handling large deformation, which always occurs during the cutting process, and at the same time, naturally simulates the process of chip separation. Previous studies have proven that SPH can simulate cutting processes effectively [8; 9; 10; 11; 15; 16]  
It is well known that the Johnson-Cook (JC) model [17] and Johnson-Cook damage [18; 19] model are the most popular constitutive material laws in describing metal behavior. High strain and high strain rates, however, always occur in Ti-6 AL-4V machining process, and under this condition, the dynamic mechanical properties of the material, such as strain softening and dynamic recrystallization mechanisms of Ti-6 AL-4V materials, cannot be exactly described by JC law. This paper, hence, appliesHyperbolic Tangent (TANH) constitutive law, which was proposed by [PERSON] [20] and later further developed by the [PERSON] and [PERSON] [21] to describe dynamic mechanical properties of Ti-6 AL-4V material. The TANH constitutive model not only considers those problems which are mentioned above, but also describes the process of dynamic recrystallization mechanisms which also always occurs in the cutting Ti-6 Al-4V process [22]. In addition, an improved SPH algorithm is adopted through adding modified schemes for approximating density (density correction) and kernel gradient approximation (kernel gradient correction) in this work, which has been proven to be very efficient in improving the accuracy of a cutting model [15]. Since the traditional SPH cannot exactly reproduce linear functions in the entire problem domain, in its initial form particle summation formulation, the SPH does not exactly reproduce a constant near the boundary because of the loss of symmetry in the smoothing operation. The second component involves the evaluation of the variation trend of surface roughness with different cutting parameters. The SPH algorithm adopted in this paper naturally simulates the separation of chips from the workpiece. Each individual particle carries independent attributes, such as density, mass, speed, and location.