## 1 Introduction  
Ti-6 Al-4V is one of most popular titanium alloys in many engineering applications. It is an important material for modern mechanical components and equipment, especially in biomedical and aerospace systems, since it not only has superb corrosion resistance, but also has a high strength to weight ratio. Machining of Ti-6 Al-4V workpieces, however, is tricky, and it is very difficult to produce the desired components with the required shape and high-quality surface finishing. Cutting is the most popular and important way to fabricate titanium components. As the technology advances, more and higher requirements are necessary for cutting the titanium alloy, especially for quality surfaces. Surface roughness, as an effective measure to evaluate the quality of a surface, is affected by different settings of cutting parameters such as different cutting speed, rake angle and feed [1]. Thus, investigation of the effects and subsequent optimization of the cutting parameters on surface roughness is crucial and, currently, the Taguchi method is one of the most popular methods used. [2; 3; 4]. It first establishes orthogonal experiment to decrease the number of experiments and, further, to reduce experimental time. The surface roughness is then measured and recorded in these experiments, according to which the effectiveness of each combination of cutting parameters is evaluated and confirmed by Taguchi \(S\)/\(N\) ratios and the variance analysis (ANOVA) [4]. Finally, an optimal set of cutting parameters is found to achieve the lowest surface roughness. Previous research has conducted experiments to optimize cutting parameters to minimize the surface roughness value based on the Taguchi method [5; 6; 7; 8; 9; 10; 11; 12; 13]. [PERSON] and [PERSON] studied the influence of process parameters using the Taguchi method and provided optimized parameters by applying an uncoated tungsten carbide tool in the machining Al/SiCp metal matrix composite without adding cutting fluid [5]. [PERSON] and [PERSON] applied the Taguchi method to study the influence of cutting parameters on the metal removal rate [6]. [PERSON] studied the influence of cutting parameters on surface roughness, such as feed rate, cutting speed, and drill bit angle, and then the optimum levels of control factors are defined to reduce the surface roughness by applying S/N ratios [7]. Measuring surface roughness by conducting experiments is the current practice to study the effects of cutting parameters on surface roughness. It is, however, costly as well as time-consuming, involving a substantial waste of materials. This problem is not negligible especially for some material which is very expensive and very hard to cut such as titanium alloy. Even though the number of experiments can be decreased substantially by applying an orthogonal array of the Taguchi method, the costs and time taken for the experiments may not be acceptable. With the rapid development of computer technology, the advantages of numerical simulation of cutting processes attracts a lot of attention and has become an important means for analyzing the mechanism of cutting processes. This paper proposes an approach to investigate the effects of cutting parameters on surface roughness by combining the numerical simulation of the cutting process and the Taguchi method. Compared to other experiments, our approach is applicable to investigate the effects of cutting parameters with substantially reduced costs and time. This paper gives an example of turning to show how our method works. First, a cutting model is simplified as the orthogonal cutting model. Then a numerical simulation based on the SPH method is applied to simulate the cutting process as an alternative to the real cutting experiment. Furthermore, the surface roughness of this simulation model is calculated and the variation trend of surface roughness with different cutting parameters is evaluated.