In this research, SKD11 steel is used as the workpiece material. This material is widely applied in mold manufacturing industries. Table 1 shows the chemical composition of SKD11 steel.¹⁰

The experimental set-up for thermal-assisted milling of SKD11 steel is shown in Fig. 1. Experiments were conducted on an MC500 milling machine without any lubricant or cooling. A cutting tool (APKT 1604PDR-GM, PRAMET, Czech Republic) with carbide inserts of diameter 40 mm was used. Induction temperature was created using 84 kHz of high-frequency power generated by magnetic induction heating equipment: induction power and frequency generator.

Fig. 1 
Experimental set-up (a) Schematic diagram and (b) experimental photograph

In this study, after each cutting experiment, the carbide inserts were replaced by new ones to avoid the influence of tool wear on the experimental results.

The cutting force was monitored by a piezoelectric force dynamometer (Kistler 9257B), which can measure three orthogonal cutting force components (Fx, Fy, and Fz). The dynamometer is connected to a charge amplifier for amplifying the output voltages, which are proportional to the measuring forces. Subsequently, an acquisition system with DASYlab 10.0 software is used to save the data on a computer.

In the magnetic induction heating process, induction heat is generated by modifying the induction current within the workpiece. Alternating current is applied to the coil to generate induction current within the workpiece. The intensity of the current is determined by the magnetic flux depending on the permeability (conductivity of the magnetic field) and resistivity of the material (electrical resistance of the electric current).

In general, a transient (time-dependent) heat transfer process in a metal workpiece can be described by the Fourier equation given as Eq. (1).

where T, ρ, c, and k are the temperature (^oC), density (g/cm³), specific heat (J/(kg.K)), and thermal conductivity of the material (W/(m.K)), respectively, and Q is the heat source density induced by the eddy currents per unit time on a unit volume. This heat source is determined by solving electromagnetic problems.

In most cases of TAM by induction heating, boundary conditions are heat losses due to radiation and convection. Hence, the boundary condition is expressed as Eq. (2).

where ∂T/∂n is the temperature gradient in a direction normal to the surface at the point under consideration; α, CS, and QS correspond to the convection surface heat transfer coefficient, radiation heat loss coefficient, and surface loss; and n is the boundary surface symbol.

Eq. (1) can be expressed in Cartesian coordinates as Eq. (3)

Eq. (3) with boundary conditions (Eq. (2)) represents the mathematical model of the heat transfer process in magnetic induction heating and heat transfer applications.

Lei Zhang¹⁴ applied the heat transfer equation to simulate the heat transfer process during magnetic induction heating using COMSOL finite element software. The effect of different parameters on the heat transfer process was also investigated.

In this study, the workpiece temperature is controlled by a hand-held digital contact thermometer (model 3527A from TSURUGA, Japan). The thermometer uses K type thermocouples with a temperature range of −99 to 1299^oC. The frequency of results displayed is 2 s⁻¹. In the range of 0 to 400^oC, the error of the device is ± (0.2% RDG + 0.5^oC).

The change in the thickness of the uncut chip due to plastic deformation is evaluated by the chip shrinkage coefficient (K), which depends on all the factors that affect the chip deformation: mechanical properties of the workpiece, geometry of the cutting tool, machining parameters, and other cutting conditions. If the volume of the metal block before and after deformation is constant, the chip width when the angle λ is small (λ < 30^o) varies insignificantly compared to the cut width. K is determined by Eq. (4).⁷

where L and L_f are the uncut chip and the actual chip length, respectively. Because of the difficulty in the determination of uncut chip length, the method of weight measurement is usually used as follows:

The cutting area is:

where Q and ρ are the mass of the chip (g) and destiny of the workpiece material (g/cm³), respectively.

Because the volume of the chip is constant, we have

where f_r and t are the feed rate (mm/rev) and cutting depth (mm), respectively.

By substituting Eqs. (6) in (4), K is determined as follows:

By substituting Eqs. (5) in (7), K is determined as follows:

In this study, chip length was measured using a 3D scanning method incorporating GOM Inspect Professional 3D data analysis software for high accuracy. The chips were scanned by ATOS Core 80 3D scanners on an ATOS ScanPort system (Fig. 2). This is an automated system that measures and tests small details with six kinematics combined movement around work points. The three motorized axes are the tilting, rotation, and linear axes. The three manual axes are an eccentric plate (eccentric adjustment with two degrees of freedom), a sensor axis (stepless rotation around sensor axis 0-90^°), and an adapter for height variation. ATOS Core 80 uses blue light technology, which provides high accuracy, and the scan results are not affected by ambient light owing to different light frequencies. Subsequently, GOM Inspect 3D data analysis software is used to analyze the data and measure the chip length as shown in Fig. 3.

Fig. 2 
The ATOS scan port system

Fig. 3 
Result of chip length measurement

Figs. 4(a)-4(d) show the chip morphology of the milling of SKD11 steel with machining parameters (V = 235 m/min, f = 305 mm/min, and t = 1.5 mm) at room temperature and 200, 300, and 400^oC, respectively. Continuous chips are formed by the plasticity characteristics of the workpiece material. However, a chip’s color is completely different in traditional machining than that in TAM. In traditional machining, a chip’s color is dark purple due to the heat generated and transferred from the heating sources to the chip. However, in TAM, the color of a chip is much brighter because the cutting temperature was pre-elevated, thereby causing more uniform heat transfers to the chip.

Fig. 4 
Chip morphology during conventional machining (a) and TAM at 200^oC (b), 300^oC (c), and 400^oC (d)

Fig. 5 shows the experimental results of the dependence of cutting force on the cutting speed at elevated temperatures. Table 2 presents the cutting force and chip shrinkage coefficient values at various cutting speeds and temperatures. The results show that the cutting force reduces remarkably during TAM at 200^oC compared to that during conventional machining. The cutting force reduces when the temperature is increased to 300 and 400^oC. ΔF is the percentage of cutting force reduction determined using Eq. (9). The maximum ΔF is 65.1% during TAM at 400^oC and a 235 m/min of cutting speed (V). Hence, higher the temperature (T), lower is the cutting force (F). The strength and hardness of a material reduce because of the effect of elevated temperatures during heating. The bonding force between metal atoms becomes weak, thereby making the cutting process easy. The main reason is the softening effect caused by heating the workpiece material during the machining process. In general, the temperature of the primary shear zone increases when (V) increases. Hence, (F) is reduced by decreasing the flow stress in the primary shear zone. Besides, when (V) increases, the contact area between the rake surface of a tool and chip is reduced leading to decreasing frictional force.

Fig. 5 
The cutting force depends on cutting speed (V) and temperature (T)

where Y_T and Y_R are the cutting force or chip shrinkage coefficient during TAM and conventional machining, respectively.

Fig. 6 presents the effect of cutting speed (V) and elevated temperature (T) on the chip shrinkage coefficient. The effect of (V) on the chip shrinkage coefficient is the same as that on the cutting force; thus, the chip shrinkage coefficient decreases when (V) increases. On the other hand, when temperature increases, the chip shrinkage coefficient also increases. The increase in the chip shrinkage coefficient (ΔK) is determined using Eq. (9). The results show that the maximum ΔK is 31.7% during TAM at 400^oC and the cutting speed of 235 m/min. Because the material is softened under the influence of elevated temperature, the bonding between atoms becomes weak; thus, the arrangement of the metal lattice can be destroyed easily. Hence, a workpiece material will be easily deformed if the chip shrinkage coefficient is high.

Fig. 6 
The chip shrinkage coefficient depends on cutting speed (V) and temperature (T)

In this study, cutting parameters such as cutting speed (V), feed rate (f), cutting depth (t), and elevated temperature (T) are selected. Their optimal values (V, f, t, and T) will be chosen for the objective function of cutting force and chip shrinkage coefficient. Besides, the contribution percentage of the parameters will be assessed by the ANOVA method.

Taguchi proposed the signal to noise (S/N) ratio as the representative value to choose level, which is the best noise control. The S/N ratio considers both the mean and variation depending on the behavior of the target. The simplest form of the S/N ratio is the ratio of the mean (signal) to the standard deviation (noise). Because the optimization study for the objective function is the cutting force and chip shrinkage coefficient, the S/N ratio with smaller is better criteria is chosen. The formula for calculating the S/N ratio is given in Eq. (10)¹⁵:

where n is the number of repeated experiments and ∑i=1nyi2 is the sum of the square of all the results for each experiment.

Table 3 presents the parameters with their corresponding levels. The three selected parameters (V, f, and t) combined with the heating temperature contributed to the greatest effect on the cutting process. Table 4 shows the orthogonal array L9 according to the Taguchi method. The experimental results of the cutting force and chip shrinkage coefficient with the S/N ratio of each corresponding experiment are calculated using Eq. (10) and shown in Table 5. ANOVA result for the cutting force (F) is presented in Table 6. As observed, the percentage contribution of the cutting depth (t) is the highest at 67%, while that of the supported temperature (T) and feed rate (f) are lower at 13.6 and 12.2%, respectively. The cutting speed (V) has a negligible effect on the cutting force with a contribution percentage of 7.2%. Fig. 7 shows the S/N ratio response. The optimal conditions for F are A3B1C1D3 with V = 280 m/min, f = 230 mm/min, t = 0.5 mm, and T = 400^oC.

Fig. 7 
Mean of S/N ratios of the factors considering F

Table 7 presents the ANOVA result for the chip shrinkage coefficient (K). The results show that the percentage contribution of the feed rate (f) was the highest at 82.7%, while that of the supported temperature (T) and cutting speed (V) are lower at 11.7 and 4.6%, respectively. The cutting depth (t) has negligible effect on the chip shrinkage coefficient with a contribution percentage of 1.1%. The S/N ratio response is shown in Fig. 8. The optimal conditions for K are A2B3C1D1 with V = 235 m/min, f = 380 mm/min, t = 0.5 mm, and T = 200^oC.

Fig. 8 
Mean of S/N ratios of the factors considering K

The cutting force and chip shrinkage coefficient models depend on the technological parameters (V, f, and t) and supported temperature for the machining process (T) and are described by Eqs. (11) and (12), respectively.

where a₁ and a₂ are coefficients; b_1, c_1, d₁, e₁ and b_2, c_2, d₂, e₂ are the exponents determined from the experiments; and F is the synthetic cutting force analyzed by the three cutting force components (Fx, Fy, and Fz) according to Eq. (13).

In this study, the Gauss–Newton method is used to construct a nonlinear regression function of the cutting force and chip shrinkage coefficient models. This method is applied in the nonlinear regression tool of Minitab 17 software. The results of cutting force and chip shrinkage coefficient presented in Tables 4 and 5, respectively, obtained from the experiments and the orthogonal array L9 are used as input data for the method. The values of the coefficients and exponents are listed in Table 8.

The nonlinear regression functions of the cutting force and chip shrinkage coefficient during the TAM of SKD11 steel are given by Eqs. (14) and (15), respectively.

To evaluate the accuracy of the cutting force and chip shrinkage coefficient models, extra experimental data was used as shown in Fig. 9, where: experiment 1, 2, 3 (Ex-1, Ex-2, Ex-3) were performed at the fixed feed rate of 305 mm/min and the fixed cutting depth of 1.5 mm while the cutting speed and elevated temperature were corresponding at (235 m/min, 300^oC), (190 m/min, 400^oC) and (280 m/min, 200^oC), respectively. The results show that the graph, which is built using the experimental data, is similar to the one built using the numerical data. Hence, the cutting force and chip shrinkage coefficient models represented by Eqs. (14) and (15), respectively, have high accuracy.

Fig. 9 
Comparing the experimental and numerical of the cutting force and the chip shrinkage coefficient value

By using Eqs. (14) and (15) and the Maple software tool, Figs. 10 and 11 were also built to present the relationship between the cutting force/chip shrinkage coefficient and the machining parameters at elevated temperatures. Fig. 10 shows that when the temperature for the machining process is high, the cutting force is low. Figs. 10(a)-10(c) show the cutting force at fixed (V), (f) and (t), respectively, and the slope of the cutting force graph is maximum when changing (t). Hence, cutting depth has the greatest effect on the cutting force. Fig. 10(c) shows the slope of the cutting force graph when the change in (V) is higher than that in (f). This means that the contribution percentage of (V) is higher than that of (f) on the cutting force (F).

Fig. 10 
The relationship between the cutting force (F) and technological parameters (The graphs are labeled 1, 2, 3 in order of roughness graph at 200^oC, 300^oC, and 400^oC)

Fig. 11 
The relationship between chip shrinkage coefficient (K) and machining parameters (The graphs are labeled 1, 2, 3 in order of roughness graph at 200^oC, 300^oC, and 400^oC)

Fig. 11 presents the relationship between the chip shrinkage coefficient (K) and machining parameters and shows that high temperatures lead to large chip shrinkage coefficient values. Figs. 11(a) and 11(c) are graphs of the chip shrinkage coefficient at fixed (V) and (t), respectively, indicating the increasing chip shrinkage coefficient with changing (f). Thus, (f) makes a major contribution to (K). Fig. 11(c) is the chip shrinkage coefficient graph at a fixed (f) showing that (f) and (t) have negligible influence on K.