# Thermal Behavior of a Rod during Hot Shape Rolling and Its Comparison with a Plate during Flat Rolling

## Abstract

**:**

## 1. Introduction

## 2. Experimental Procedure and Numerical Simulation

#### 2.1. Experiment Using Off-line Rolling Simulator

_{o}and A

_{f}are the areas of initial and final cross section, respectively. The reduction of height of a plate during flat rolling was selected to have a same average effective strain with the rod during shape rolling. The average effective strain of a rod during shape rolling was calculated using the model proposed by Lee et al. [24] that is based on the equivalent rectangle approximation method, which transforms a non-rectangular cross section shape into a rectangular shape, and the average effective strain (ε

_{p}) is calculated as follows:

_{1}and ε

_{2}are simply obtained by calculating the reduction ratio of width and height in equivalent rectangle approximation, respectively. In case of plate rolling, the ratio of ε

_{1}and ε

_{2}is very small in nature, and thus the average effective strain is represented as follows:

_{2}is calculated by the reduction ratio of height as follows:

_{i}and H

_{f}are the height of initial and final plate, respectively. The final height of a plate was chosen using Equation (3), as shown in Figure 4a.

#### 2.2. Numerical Simulation

_{p}, k, and Q are the density, specific heat capacity, thermal conductivity of a workpiece, and volumetric rate of heat generation arising from the plastic deformation, respectively. Thermal properties of a workpiece such as thermal conductivity and specific heat were chosen from the library data provided by DEFORM FE software. That is, k and ρC

_{p}values were approximately 31 W·m

^{−1}K

^{−1}and 4.3 N·mm

^{−2}K

^{−1}, respectively. To solve the above governing equation, the boundary conditions for a workpiece are expressed as follows:

_{a}, and T

_{R}are emissivity, Stefan–Boltzmann constant, ambient temperature, and roll temperature, respectively. Ambient and roll temperature is 25 °C, and ε is assumed to be 0.7. h

_{conv}and h

_{cond}are the convective heat transfer coefficient and conductive heat transfer coefficient, respectively, which is discussed in the next section. The shear friction coefficient of 0.6 was selected in the roll-workpiece interface [10,25,26], and other process parameters were identical to the experimental conditions, as given in Figure 4 and Table 1.

## 3. Results

#### 3.1. Measured Temperature of a Workpiece with Area

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

^{−2}K

^{−1}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.

^{−2}K

^{−1}.

## 4. Discussion

#### 4.1. Effect of Conduction Heat Transfer in the Workpiece-roll Interface

#### 4.2. Effect of Heat Generation due to Plastic Deformation

## 5. Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Schematic description showing the roll design and the measurement points of temperature using thermocouples: (

**a**) cross section of flat rolling, (

**b**) cross section of rod rolling, and (

**c**) cross section of the longitudinal direction of the rod.

**Figure 5.**Measured temperature profiles of (

**a**) the plate during flat rolling and (

**b**) the rod during shape rolling with area.

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

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

**Figure 10.**Contour maps of effective strain of (

**a**) plate, (

**b**) rod, and (

**c**) comparison of profiles of effective strain along the horizontal and vertical directions of a workpiece.

Parameters | Value | |
---|---|---|

Workpiece | Material | AISI 1020 |

Initial temperature of workpiece | 1150 °C | |

Rolling mill | Rolling speed | 10 RPM |

Roll diameter | 400 mm | |

Temperature of roll | 21 °C | |

Process conditions | Reduction ratio of height of plate | 25.5% |

RA per pass of rod | 20.2% | |

Surrounding temperature | 21 °C |

Contact Conduction (kWm ^{−2}K^{−1}) | Convection (Wm ^{−2}K^{−1}) | Ratio of Mechanical Work to Heat | Rolling Type | Reference |
---|---|---|---|---|

5 | 10 | - | Shape rolling | [30] |

10 | 10 | - | Shape rolling | [31] |

24 | 2.33 | 0.9 | Round-oval | [2] |

72 | 2.33 | 0.9 | Square-diamond | [2] |

4.8 | 30 | - | Shape rolling | [32] |

40 | 10 | - | Flat rolling | [33] |

45–85 | - | 0.85–0.95 | Flat rolling | [10] |

54–71 | - | - | Flat rolling | [34] |

7.6–17.6 | - | - | Flat rolling | [35] |

20–45 | Flat rolling | [36] |

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**MDPI and ACS Style**

Hwang, J.-K.
Thermal Behavior of a Rod during Hot Shape Rolling and Its Comparison with a Plate during Flat Rolling. *Processes* **2020**, *8*, 327.
https://doi.org/10.3390/pr8030327

**AMA Style**

Hwang J-K.
Thermal Behavior of a Rod during Hot Shape Rolling and Its Comparison with a Plate during Flat Rolling. *Processes*. 2020; 8(3):327.
https://doi.org/10.3390/pr8030327

**Chicago/Turabian Style**

Hwang, Joong-Ki.
2020. "Thermal Behavior of a Rod during Hot Shape Rolling and Its Comparison with a Plate during Flat Rolling" *Processes* 8, no. 3: 327.
https://doi.org/10.3390/pr8030327