**4.1 Plastic deformation and chip formation in the precision machining titanium alloy**

The numerical analysis method applied to materials cutting process can be divided into two categories, namely, the elastic-plastic FEM and the rigid-plastic FEM. Furthermore, thermoelastic FEM and the thermo-rigid FEM are introduced if the temperature and the velocity are considered in the materials processing technology. The simulation results are almost same whether the problem analysed by either elastic-plastic FEM or rigid-plastic FEM if the size of the workpiece and the amount of discreted element are same for these two methods. The elastic-plastic FEM mainly applied to solve the residual stress and the elastic recovery while the rigid-plastic FEM cannot solve this type of problems as it ignored elastic deformation and thus it has higher solution efficiency.

In this research work, the commercial finite element analysis package (Advantedge®) is utilized to gain good understanding of the materials deformation behavior underlying machining of titanium alloy. Among the different alloys of titanium, Ti-6Al-4V is by far the most popular with its widespread use in the chemical, surgical, ship building and aerospace industry. The primary reason for wide applications of this titanium alloy is due to its high strength-to-weight ratio that can be maintained at elevated temperatures and excellent corrosion and fracture resistance. On the other hand, Ti-6Al-4V is notorious for poor machinability due to its low thermal conductivity that causes high temperature on the tool face, strong chemical affinity with most tool materials, which leads to premature tool failure, and inhomogeneous deformation by catastrophic shear that makes the cutting force

Analysis Precision Machining Process Using Finite Element Method 117

materials. The major drawback of this formulation, however, is that the chip thickness should be assumed and kept constant during the analysis, as well as the tool–chip contact length and contact conditions at the tool–chip and tool–workpiece interfaces. As the chip thickness is the major outcome of the cutting process that defines all other parameters of this process so it cannot be assumed physically. Consequently, the Eulerian formulation does not correspond to the real deformation process developed during a real metal cutting

0 0 <sup>0</sup>

*<sup>t</sup> ij ij ij ij V V <sup>p</sup> B S dV B S dV*

nodes, *B* is the geometry matrix in the case of finite strain conditions and the *B* is the

The corresponding mesh is refined in some region as severe plastic deformation may be induced under material surface which is shown in figure 5. The most fundamental and crucial characteristic of metal cutting process lies in the formation of chip. In reality, the chip is not exactly "cut" but "sheared" away from the work material which forms a clear distinction between machining plastic metal and other materials. Figure 6 shows the chip formation process during precision machining of titanium alloy. Chip formed with the tool approaching the material from the right side and the chip flow in curved fashion. When the original chip thickness or feed rate or depth of cut is compared with the chip thickness after cutting, the deformation can be clearly observed. This deformation is fundamental for the

> Material Titanium Size (*mm*) 0.4 0.01 0.1

Depth of Cut(*µm*) 5 Speed(*mm/s*) 200

℃

Temperature(

Table 1. FEM simulation parameters

Fig. 5. FE simulation model

Physical Property Elastic-Plastic Solid

) 20

*T T*

denotes the column vector of external force exerted at the discrete element

(31)

The Lagrangian formulation[16] under finite deformation is as follows:

**4.3 Finite element model and simulation results** 

additional item induced by the geometric nonlinear conditions.

process.

where *p* 

fluctuate and causes tool wear, thereby aggravating tool-wear and chatter. This poor machinability has limited cutting speed to less than 60 m/min in industrial practice. Numerical analysis of Ti-6Al-4V machining process using finite element method is of great importance on understanding the physical essence and optimizing the machining technique parameters.
