# An Innovative Method for Forming Balls by Cross Rolling

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Analysis

_{F}is the yield stress, MPa; ε is the effective strain, -; T is the temperature, °C; and $\dot{\epsilon}$ is the strain rate, s

^{−1}.

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

^{2}·K and the friction factor was set to 0.8. The billet was a cylindrical rod of 90 mm in diameter and 520 mm in length, preheated to the temperature of 1100 °C. Two variations of the proposed rolling method were investigated: rolling with the use of flat tools and rolling with the use of two rolls.

#### 2.1. Rolling Process with the Use of Flat Tools

#### 2.2. Rolling Process with the Use of Two Rolls

## 3. Experiment

## 4. Conclusions

- The proposed cross rolling method can be used to form six balls at the same time, each ball with a diameter of 100 mm. When rolling six balls with a diameter of 100 mm, the minimal length of the rolls should be equal to 800 mm. If the rolls have a smaller width, the number of simultaneously produced balls should be decreased.
- The proposed cross rolling process for producing balls can be performed either with two flat tools or with the use of two rolls. Rolling mills equipped with two rolls are more widely available on the market. When the rolling process is performed with the use of rolls, the rolling mill should also be equipped with two guides to maintain the correct position of the billet in the working space of the machine.
- The accuracy of produced balls is not very high. The shape and dimensions of balls produced by the proposed method meet the requirements for balls used as grinding media in ball mills. The dimensional tolerance of balls for grinding media is ±3 mm.
- Balls produced by cross rolling with two rolls have higher shape and size accuracy, as the workpiece is precisely positioned in the working space of the rolling mill. An incorrect position of the billet can lead to various defects, such as underfill of one of the side balls, overfill due to a skew position of the billet, and the occurrence of cracks in the centre line of the balls.
- The proposed rolling method for producing 100 mm diameter balls is characterized by high throughput, amounting to 7.2 t/h for the two-roll variation of the process. The use of rolling mills equipped with two rolls prevents idle running of the tools that would lead to a lower efficiency of the rolling process. The throughput of the rolling process also largely depends on the efficiency of billet heating.
- The temperature of produced balls is high enough to perform quenching without material reheating. If the temperature of produced balls is too high, the balls should be subjected to slow cooling on the conveyors transporting them to the quenching tank. On the other hand, the temperature cannot be too low, as this will prevent a correct realization of the quenching process.
- The proposed cross rolling process for producing 100 mm diameter balls can be realized using commercial rolling mills available on the market. As a result, the cost of implementing the new manufacturing technique will be reduced. Moreover, rolling mills of this type can be used for rolling other axisymmetric parts, which will contribute to higher manufacturing flexibility of a production company.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Geometric model of the rolling process for producing six balls of 100 mm in diameter with the use of flat tools.

**Figure 3.**Workpiece shape progression during the cross rolling process for six balls with a diameter of 100 mm, and the distribution of temperature (in °C).

**Figure 4.**Shape of 100 mm diameter balls produced by cross rolling with flat tools and the distribution of temperature (in °C); the balls are shown in the order from ball in the middle (

**left**) to ball at the side (

**right**).

**Figure 5.**Distribution of the temperature (in °C) inside 100 mm diameter balls produced by cross rolling with flat tools; the balls are shown in the order from ball in the middle (

**left**) to ball at the side (

**right**).

**Figure 6.**Distribution of effective strains inside 100 mm diameter balls produced by cross rolling with flat tools; the balls are shown in the order from ball in the middle (

**left**) to ball at the side (

**right**).

**Figure 7.**Distribution of the damage function (according to the Cockcroft–Latham ductile damage criterion) inside 100 mm diameter balls produced by cross rolling with flat tools; the balls are shown in the order from ball in the middle (

**left**) to ball at the side (

**right**).

**Figure 8.**Variations in the radial and tangential forces in the cross rolling process for producing six balls with a diameter of 100 mm.

**Figure 9.**Geometric model of the cross rolling process for producing six balls of 100 mm in diameter with the use of two rolls.

**Figure 11.**Workpiece shape progression during the cross rolling process for producing six balls with a diameter of 100 mm, and the distribution of temperature (in °C).

**Figure 12.**Shape of 100 mm diameter balls produced by cross rolling with two rolls and the distribution of temperature (in °C); the balls are shown in the order from ball in the middle (

**left**) to ball at the side (

**right**).

**Figure 13.**Distribution of the temperature (in °C) inside 100 mm diameter balls produced by cross rolling with two rolls; the balls are shown in the order from ball in the middle (

**left**) to ball at the side (

**right**).

**Figure 14.**Distribution of effective strains inside 100 mm diameter balls produced by cross rolling with two rolls; the balls are shown in the order from ball in the middle (

**left**) to ball at the side (

**right**).

**Figure 15.**Distribution of the damage function (according to the Cockcrof–Latham ductile damage criterion) inside 100 mm diameter balls produced by cross rolling with two rolls; the balls are shown in the order from ball in the middle (

**left**) to ball at the side (

**right**).

**Figure 16.**Variations in the force parameters when producing six balls with a diameter of 100 mm by cross rolling with the use of two rolls.

**Figure 17.**One of the tools used in the experimental cross rolling process for producing six balls with a diameter of 40 mm.

**Figure 18.**Production of six balls with a diameter of 40 mm by cross rolling with the use of flat tools: billet is positioned on the lower tool (

**top**); advanced stage of the rolling process (

**centre**); and produced balls leave the machine rolling down into the container (

**bottom**).

**Figure 19.**Steel balls of 40 mm in diameter produced by cross rolling, obtained from the experimental tests.

**Figure 20.**Variations in the tangential force in the rolling process for producing six balls with a diameter of 40 mm.

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**MDPI and ACS Style**

Pater, Z.; Tomczak, J.; Bulzak, T.
An Innovative Method for Forming Balls by Cross Rolling. *Materials* **2018**, *11*, 1793.
https://doi.org/10.3390/ma11101793

**AMA Style**

Pater Z, Tomczak J, Bulzak T.
An Innovative Method for Forming Balls by Cross Rolling. *Materials*. 2018; 11(10):1793.
https://doi.org/10.3390/ma11101793

**Chicago/Turabian Style**

Pater, Zbigniew, Janusz Tomczak, and Tomasz Bulzak.
2018. "An Innovative Method for Forming Balls by Cross Rolling" *Materials* 11, no. 10: 1793.
https://doi.org/10.3390/ma11101793