# Effects of Deformation Conditions on the Rolling Force during Variable Gauge Rolling

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## Abstract

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## 1. Introduction

## 2. Experimental Procedure

## 3. Results

## 4. Discussion

## 5. Conclusions

- The rolling force increases when the downward rolling is performed; however, upward rolling is associated with a continuous reduction in the rolling force.
- An abrupt change in the rolling force in the outlet sections of the downward and upward rolling was observed. It was found that this abrupt change in rolling force is a function of absolute thickness reduction, roll diameter and friction coefficients. This abrupt change in rolling force was called DRF.
- The reasons for these abrupt changes in rolling force were attributed to the changes in contact length and the vertical component of frictional forces.
- The dependence of contact length during downward and upward rolling on the wedge angle and roll diameter of TRBs was studied. It was found that both parameters have a great effect on contact length.
- The experimental data obtained from VGR of DP590 revealed that the abrupt change in the rolling force increases with increasing absolute thickness reduction.
- The data provided using FEM simulations showed that this abrupt change in the rolling force during VGR increases with increasing friction coefficients and roll diameter.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

TRB | Tailor rolled blanks |

VGR | Variable gauge rolling |

TTZ | Thickness transition zone |

DRF | Drop of rolling force |

$\theta $ | Bite angle in variable gauge rolling |

$\alpha $ | Bite angle in flat rolling |

$\phi $ | Thickness transition zone wedge angle |

${l}_{d}$ | Roll- specimen contact length |

Thickness ratio | Thickness of the thinner side/thickness of the thicker side |

$\Delta l$ | Changes in contact length |

$\stackrel{-}{Y}$ | Average yield stress |

$\mu $ | Friction coefficient |

w | Width of tailor rolled blanks |

${l}_{1}$ | Contact length in flat rolling |

${l}_{2}$ | Contact length in downward rolling |

R | Roll diameter |

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**Figure 1.**Variations of target thickness with rolling time for (

**a**) absolute thickness reduction of 0.2 mm and (

**b**) absolute thickness reduction of 1 mm.

**Figure 2.**Variations of real thickness with rolling time for (

**a**) absolute thickness reduction of 0.2 mm and (

**b**) absolute thickness reduction of 1 mm.

**Figure 3.**Rolling force vs. rolling time curves for (

**a**) absolute thickness reduction of 0.2 mm and (

**b**) absolute thickness reduction of 1 mm.

**Figure 7.**Schematic representation of variations of rolling force vs. rolling time during downward rolling.

**Figure 8.**Variations of rolling force with rolling time for (

**a**) downward rolling with absolute thickness reduction of 0.2 mm; (

**b**) upward rolling with absolute thickness reduction of 0.2 mm; (

**c**) downward rolling with absolute thickness reduction of 1 mm; and (

**d**) upward rolling with absolute thickness reduction of 1 mm.

**Figure 9.**Dependency of contact length during upward and downward rolling for (

**a**) absolute thickness reduction of 0.2 mm and (

**b**) absolute thickness reduction of 1 mm.

**Figure 11.**Simulation rolling force vs. experimental rolling force for friction coefficients of 0.14 and 0.17.

Elements | C | Si | Mn | Nb | Al | Cr | Fe |
---|---|---|---|---|---|---|---|

Wt % | 0.149 | 0.467 | 1.513 | 0.016 | 0.033 | 0.23 | Bal. |

Yield Stress, MPa | Ultimate Tensile Strength, MPa | Young Modulus, GPa | n | K, MPa | Total Elongation, % | Uniform Elongation, % | |
---|---|---|---|---|---|---|---|

DP590 | 486 ± 14 | 731 ± 18 | 207 | 0.125 ± 0.02 | 900 ± 20 | 27 ± 0.5 | 19 ± 0.5 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Shafiei, E.; Dehghani, K.
Effects of Deformation Conditions on the Rolling Force during Variable Gauge Rolling. *J. Manuf. Mater. Process.* **2018**, *2*, 48.
https://doi.org/10.3390/jmmp2030048

**AMA Style**

Shafiei E, Dehghani K.
Effects of Deformation Conditions on the Rolling Force during Variable Gauge Rolling. *Journal of Manufacturing and Materials Processing*. 2018; 2(3):48.
https://doi.org/10.3390/jmmp2030048

**Chicago/Turabian Style**

Shafiei, Ehsan, and Kamran Dehghani.
2018. "Effects of Deformation Conditions on the Rolling Force during Variable Gauge Rolling" *Journal of Manufacturing and Materials Processing* 2, no. 3: 48.
https://doi.org/10.3390/jmmp2030048