Mechanistic modeling of cutting forces. Orthogonal Cutting Data Base for Titanium Alloy Ti6AI4V

where T_s is the average shear plane temperature and k[_nt (i.e., ^0.7) is an empirical correction factor that accounts for temperature variations along the chip-tool contact zone. For an accurate analysis, both the plastic layer thickness (8h_c) and Z_t must be measured with a microscope that has a large magnification (such as a SEM). Our experiments indicated that the thickness of the plastic layer on the rake face is observed to be between 5 and 10% of the deformed chip thickness- (8/h_c & 0.05-0.1). The contact length can be estimated approximately by assuming that the resultant cutting force acts in the middle of the contact length and parallel to the stress-free chip boundary. From the geometry of orthogonal cutting (Fig. 2.3), the chip-rake face contact length can be approximately predicted as

fcsin(0c + A* -«!•)■                                                       ,₀o_QN

i_t - ----------- ;—------------- ~-------- .                                                                                                       U.od)

Sin <p_c cos p_a

The prediction of temperature distribution at the tool-chip interface is very important in determining the maximum speed that gives the most optimal material removal rate without excessive tool wear. The binding materials within the cutting tools may be weakened or diffused to the moving chip material at their critical diffusion or melting temperature limits. The fundamental machin-ability study requires the identification of a maximum cutting speed value that corresponds to the critical temperature limit where the tool wears rapidly. By using the approximate solutions summarized above, one can select a cutting speed that would correspond to a tool-chip interface temperature (7j_nt) that lies just below the diffusion and melting limits of materials present in a specific cutting tool. The detailed and fundamental scientific and experimental treatment of the cutting process is covered in Oxley [4].

It is difficult to predict the shear angle and stress in the shear plane and the average friction coefficient on the rake face using the standard material properties obtained from tensile and friction tests. For an accurate and realistic modeling, such fundamental parameters are identified from orthogonal cutting tests, where the deformed chip thickness and feed and tangential cutting forces are measured using cutting tools with a range of rake angles. The influence of uncut chip thickness and cutting speed is also considered by conducting experiments over a wide range of feeds and cutting speeds.

The relationships shown in Table 2.1 are identified from statistical analysis of more than 180 orthogonal cutting tests conducted using tungsten carbide (WC) cutting tools and TieAUV titanium alloy work material. A set of turning experiments resembling orthogonal cutting was conducted on titanium

tubes (TifiAUV) with tools of different rake angles at different feeds and cutting speeds. The diameter of the tube was 100 mm and the cutting-speed range was 2.6 to 47 m/min. Cutting forces in the tangential (F_t) and feed (Ff) directions were measured with a force dynamometer. Two sample orthogonal cutting test results are shown in Figure 2.4. Small steps in cutting conditions were used to increase the reliability of the measured forces. It should be noted that the measured forces may include both the forces due to shearing and a tertiary deformation process "ploughing" or "rubbing" at the flank of the cutting edge. Thus the

measured force components are expressed as a superposition of shearing and edge forces:

F_t = F_tc + F_te,

(2.34)

The tests have been repeated a number of times at different feeds and cutting speed to ensure the statistical reliability of measurements. The edge forces are obtained by extrapolating the measured forces to zero chip thickness. It can be seen that the edge forces do not vary significantly with cutting speeds for the particular titanium alloy used here. The average edge force coefficients i£"_te and Kfe represent the rubbing forces per unit width. The chip compression ratio (r_c), shear stress r_s, shear