*3.1. Measured Temperature of a Workpiece with Area*

Figure 5a represents the measured temperature profiles of the plate with area during flat rolling. Temperature of all the surface areas decreased when the plate was extracted from the reheating furnace; in particular, the temperature of corner area decreased fast due to the higher radiation heat transfer. In contrast, the surface areas were cooled slowly compared to the corner area, stemming from their geometric condition of the radiation heat transfer, i.e., flat plane. The center area of the plate was cooled slowly because the size of the initial workpiece was relatively large. When the workpiece was contacted with the cold roll, the upper surface and corner areas of the plate cooled very sharply due to the higher conduction heat transfer between the roll and plate. On the other hand, the non-contact surface, i.e., side, was cooled slowly because no conduction heat transfer occurred between the roll and plate in this area. Meanwhile, the temperature of the center slightly increased due to the heat generation by the plastic deformation. After passing through the rolling section, the temperatures of all the areas were equalized due to the higher thermal conductivity of the workpiece. That is, the center area with a higher temperature acted as a heat source for the surface areas with a lower temperature.

Figure 5b shows the temperature profiles of the rod with area during shape rolling, i.e., round-oval pass. The upper surface area, i.e., the hard contact surface, was cooled very fast. In other words, the lowest temperature of the rod was lower than 600 ◦C. This was a very surprising result considering the location of thermocouple in the surface—the surface indicated 1.5 mm from the outer surface. It is reasonable to induce that the temperature of the outer hard contact surface could be dropped below 500 ◦C. This low temperature at the rod surface was very different from the result of the plate during flat rolling, which is discussed in the next section. Ideally, the surface area at the right side had a similar temperature profile to the surface area at the left side, but they had somewhat different temperature profiles because the rod may not have rolled symmetrically in this study. That is, the temperature discrepancy between the right side surface and left side surface can be attributed to the error in alignment of a workpiece during the shape rolling process, which is frequently observed in an industrial rod rolling process. All the surface temperatures were recovered after rolling, owing to the redistribution of heat within the rod. Meanwhile, the center temperature of the rod increased when the rod passed through the roll bite, which was the result of the heat generation by plastic work. It is worth noting that the rod exhibited a higher temperature rise compared to the plate at the center area during the rolling process.

On the basis of the comparison study of temperature profiles of the plate and rod with area, it was found that the temperature profiles were very different between the two rolling processes. The rod had a higher temperature deviation with area in comparison with the plate. In particular, the surface temperature of the rod was very different along the circumferential direction during shape rolling. For instance, the temperature of the outer surface could be dropped below 500 ◦C at the hard contact area of the rod with rolls, which can make different microstructures and mechanical properties among surface areas [2,27]. Furthermore, it could induce surface defects of a rod during shape rolling, i.e., surface flaws [1,28], abnormal grain growths [29], decarburizations, and martensite transformations in the surface area. Accordingly, it is necessary to analyze the rod temperature for at least the following four regions in order to fully understand the thermal behavior of the rod during hot shape rolling: center, hard contact surface, soft contact surface, and non-contact surface. This means that the 1D or 2D approaches, which are generally used in plate rolling, were insufficient to describe the thermal

behaviors of a rod during shape rolling. Overall, the center area had the maximum temperature in the both processes, and the minimum temperature appeared in the corner area during plate rolling and in the hard roll contact area during shape rolling.

**Figure 5.** Measured temperature profiles of (**a**) the plate during flat rolling and (**b**) the rod during shape rolling with area.

#### *3.2. Temperature Distribution of Workpiece by Numerical Simulation*

To have more useful information on the thermal behavior of the rod during shape rolling, a numerical simulation was conducted. During the hot rolling process, heat is transferred with several mechanisms as shown in Figure 6, which is summarized as follows:

(i) The heat of a workpiece is dissipated by radiation because the temperature of the workpiece is relatively high during the hot rolling process, for instance, 800–1200 ◦C.

(ii) Forced convection heat transfer takes the heat from a workpiece because the workpiece moves during the hot rolling process. Additionally, the workpiece loses the heat by natural convection heat transfer via the derived air flow originated from the density difference of air between the surface of a workpiece and ambient.

(iii) The contact between the hot workpiece and cold rolls makes a strong conduction heat transfer; therefore, the surface area of a workpiece is chilled in a very short time as the workpiece contacts the rolls.

(iv) Heat is generated in the deformation zone, i.e., roll bite zone, due to the plastic deformation.

(v) Frictional stress between workpiece and roll produces heat.

All the heat transfer mechanisms need to be carefully considered to understand the thermal behavior of a workpiece and to improve the prediction accuracy of temperature in a workpiece. It is well known that heat transfer coefficient is dependent on several process parameters such as rolling speed, reduction ratio, lubrication condition, surface roughness of workpiece and roll, size and shape of a workpiece, and roll shape, which is the main reason why several researchers have used different values of parameter to simulate the hot rolling process, as summarized in Table 2. In this study, because the author was interested in the temperature distribution of plate and rod in the roll bite, the temperature near the roll bite was simulated during plate rolling and rod rolling. The contact heat transfer coefficient of 24 kW·m<sup>−</sup>2K−<sup>1</sup> was chosen to simulate the temperature distribution of both rod and plate, owing to the similar roll shape and process conditions in reference [2]. It should be noted that the rod and plate had a different heat transfer coefficient because of the different roll shape. However, it is difficult to find the optimum heat transfer coefficients of the two processes due to the limited experiments in this study. Accordingly, the same heat transfer coefficient was chosen for the two processes on the basis of the literature review (Table 2), and then the thermal behavior of the two processes was qualitatively compared.

Figure 7 shows the temperature distribution of the rolled workpieces calculated by the FE numerical analysis. Temperature was varied with rolling process and area. The center area had the highest temperature and the surface area tended to have the lowest temperature during hot rolling, which is consistent with the measured temperature profiles using thermocouples (Figure 5). In both rolling processes, the hard contact surface area with roll had the lowest temperature due to the high conduction heat transfer by roll contact, whereas the center area had the highest temperature originating from the relatively small heat loss during hot rolling process. The surface temperature was different between the plate and rod. The upper surface and lower surface of the plate had similar temperatures, whereas the rod had a temperature variation along the circumferential direction of the surface area. For more detailed information, the temperature distribution in the cross section of the rolled workpiece near the roll bite is presented in Figure 8. It is clear that the surface of the rod had a different temperature along the circumferential direction, which meant that the hard contact surface and soft contact surface with rolls experienced different thermal histories. The maximum temperature was similar between the two processes, but the minimum temperature was different in plate and rod—the minimum temperature of the plate was 668 ◦C, and that of the rod was 598 ◦C. Therefore, the temperature difference of the rod with area was higher than that of the plate, which is consistent with the result of measured temperature profiles using thermocouples. However, the deviation in temperature between the results of simulation and experiment was in existence. For instance, the surface temperature of the rod was estimated at 500 ◦C on the basis of the experiment, but the surface temperature of the rod was 598 ◦C from the numerical simulation, which was closely related to the selected heat transfer coefficient for the numerical simulation. That is, the heat transfer coefficient in this rolling condition was higher than the selected value of 24 kW·m<sup>−</sup>2K−1.

**Figure 6.** Schematic description showing the heat transfer mechanisms in a workpiece during the hot rolling process.

**Table 2.** Process parameters and values for heat transfer during the hot rolling process.


**Figure 7.** Comparison of contour maps of temperature during plate rolling and rod rolling.

**Figure 8.** Comparison of contour maps of temperature in the roll bite during plate rolling and rod rolling.

#### **4. Discussion**

The most interesting point of the present study is the fact that the rod rolling process caused higher temperature deviation of the rod with area in comparison with the plate rolling. In particular, the rolled rod experienced very low temperature at the surface area.

#### *4.1. E*ff*ect of Conduction Heat Transfer in the Workpiece-roll Interface*

It is well known that the conduction heat transfer between the cold roll and hot workpiece is proportional to the contact pressure [8,37]. That is, the heat transfer coefficient by the roll contact increased along the arc of roll contact and reached the steady-state maximum values, and then decreased until the separation of the workpiece and roll [7]. Figure 9 shows the distribution of effective stress during plate and rod rolling processes. The plate had a uniform distribution of effective stress in the surface area. In contrast, the rod exhibited an inhomogeneous distribution of effective stress on the surface area—the upper surface area had the maximum value, and the effective stress gradually decreased along the circumferential direction from the upper surface. This different behavior of effective stress on the surface area between flat rolling and shape rolling made a different contact heat transfer coefficient between the two processes, leading to the different thermal history. In other words, the higher contact pressure in the upper surface of the rod during shape rolling led to the higher temperature drop in the upper surface area and the inhomogeneous temperature distribution along the circumferential direction of the rod. It is worth mentioning that the contact heat transfer

coefficient also depended on rolling speed [7], reduction ratio [9], scale formation on the surface [35], and lubrication condition [7,36]. However, the effect of roll shape was only considered in this study because the other process parameters were set as identical in the two processes.
