# The Effect of Process Parameters in Helical Rolling of Balls on the Quality of Products and the Forming Process

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Object of the Study

## 3. Test Stand and Experimental Tests

## 4. Experimental Results

_{a}) and along the axis perpendicular to the rolling axis (D

_{b}). The results indicate that the dimensional accuracy of the produced balls is very high. In the case of balls formed from the 40 mm-diameter rods, the tolerance range is +/− 0.2 mm. However, in the case of the balls formed from the billet preheated to higher temperatures, the connectors are not completely separated. The use of a smaller-diameter billet (39 mm) leads to producing relatively accurate balls (despite the presence of an approximately 0.3 mm deep ring-shaped groove on the tool circumference). The geometric accuracy of balls from the 41 mm-diameter billet is much lower. One can see that the balls are visibly flattened in the rolling axis even as much as 4.4 mm, which exceeds the acceptable deviation for balls used as grinding media [16].

## 5. Numerical Modelling of the Helical Rolling Process for Producing Balls

_{i}is the effective stress, MPa; and Δv is the slip velocity on contact surface, mm/s.

^{2}K, whereas that between the material and the environment was 0.35 kW/m

^{2}K. The billet was assigned the properties of C55 steel, the model of which was obtained from the material model library of the applied software [19], it was defined by the following dependence:

_{1}is the maximum principal stress, σ

_{i}is the effective stress, ε is the strain, and C is the Cockcroft-Latham damage criterion.

## 6. Summary and Conclusions

- the highest geometric accuracy of balls is achieved when the balls are formed from the 40 mm-diameter billet (i.e., the billet diameter is 3.5% smaller than that of the ball);
- the use of the billet with a diameter 6% smaller than that of the ball leads to underfill; however, the achieved geometric accuracy of the rolled part is sufficient is the ball is to be used in grinding media;
- the use of billet materials with the same or bigger diameter as that of the balls causes overfill and serious surface defects of the balls;
- the billet should be preheated to the lowest possible temperature to enable the quenching of produced balls immediately after the rolling process;
- when the billet preheating temperature is too high, it is difficult to separate produced parts and the connecting necks between produced balls cannot be completely removed;
- overfill resulting from too great a billet diameter and the application of a low preheating temperature of the tool lead to a sudden increase in the force parameters, which results in a lower service life of the tools;
- the high agreement between the experimental findings and the FEM results proves that numerical modelling can be used for analysis of complex metal forming processes.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Tools for forming balls mounted in the skew rolling mill: (

**a**) helical roll; (

**b**) upper and lower guides.

**Figure 4.**Rolling of balls in a helical rolling mill: (

**a**) billet is fed into the machine work space via sleeve; (

**b**) balls are removed from the machine work space via receiving chute.

**Figure 7.**Variations in the force parameters in helical rolling of balls: (

**a**) temperature versus radial force when billet diameter is 40 mm; (

**b**) temperature versus torque when billet diameter is 40 mm; (

**c**) billet diameter versus radial force when preheating temperature is 1000 °C; (

**d**) billet diameter versus torque when preheating temperature is 1000 °C.

**Figure 10.**Finite Element Method-simulated changes of workpiece shape in helical rolling and the distribution of effective strains.

**Figure 11.**FEM-simulated distribution of: (

**a**) effective strains; (

**b**) temperature; (

**c**) Cockcroft-Latham ductile damage criterion.

**Figure 12.**Distribution of the damage criterion according to Cockroft-Latham in the axial section of the semi product balls with a diameter bigger than nominal ∅41 mm.

**Figure 13.**Axial sections of the balls in helical rolling manufactured from the semi-finished product of various diameter: (

**a**) nominal ∅40 mm; (

**b**) smaller than nominal ∅39 mm; (

**c**) bigger than nominal ∅41 mm.

**Figure 14.**FEM-simulated variations in the force parameters in helical rolling of balls: (

**a**) radial force; (

**b**) torque.

Parameter | Value | Unit |
---|---|---|

Roll position in the mill stand | horizontal | - |

Nominal diameter of the rolls | 320 | mm |

Work length of the roll face | 400 | mm |

Minimum roll space | 300 | mm |

Maximum roll space | 350 | mm |

Shaft turn angle | +/−12 | deg |

Minimum rotational speed of the rolls | 15 | rpm |

Maximum rotational speed of the rolls | 30 | rpm |

Nominal torque per roll (15 rev/min) | 20 | kNm |

Nominal torque per roll (30 rev/min) | 10 | kNm |

Overall dimensions of the machine | 3.2 × 1.8 × 2.1 | m |

Machine weight | 17,500 | kg |

Engine power | 60/80 | kW |

Process/Billet Parameters | Ball Shape | Dimension D_{a}, mm | Dimension D_{b}, mm |
---|---|---|---|

T = 1000 °C d _{o} = 39 mm | 41.4 | 40.9 | |

T = 1000 °C d _{o} = 40 mm | 41.5 | 41.3 | |

T = 1150 °C d _{o} = 40 mm | 41.3 | 41.6 | |

T = 1000 °C d _{o} = 41 mm | 37.1 | 43.5 | |

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**MDPI and ACS Style**

Tomczak, J.; Pater, Z.; Bulzak, T.
The Effect of Process Parameters in Helical Rolling of Balls on the Quality of Products and the Forming Process. *Materials* **2018**, *11*, 2125.
https://doi.org/10.3390/ma11112125

**AMA Style**

Tomczak J, Pater Z, Bulzak T.
The Effect of Process Parameters in Helical Rolling of Balls on the Quality of Products and the Forming Process. *Materials*. 2018; 11(11):2125.
https://doi.org/10.3390/ma11112125

**Chicago/Turabian Style**

Tomczak, Janusz, Zbigniew Pater, and Tomasz Bulzak.
2018. "The Effect of Process Parameters in Helical Rolling of Balls on the Quality of Products and the Forming Process" *Materials* 11, no. 11: 2125.
https://doi.org/10.3390/ma11112125