There are several methods for volumetric hardness measurement * of grinding balls*. The method for hardenability determining, namely, the method of end hardening with a hardness measurement interval from 1.5mm to 3mm (GOST 5657-69) takes as the basis of all methods.

Hardenability — the steel ability of tempering at a certain depth from the surface to the center.

We will consider the 4 most common methods for the volumetric hardness measurement of grinding balls in this article:

**1. The method of volumetric hardness determination proposed in DSTU 3499-97 / DSTU 8538: 2015.**

This method consists of hardness measurement at all radius parts of grinding balls, averaging the values and determining the hardness by the formula:

**VH= 0,289 Тsurf+ 0,436 Т0,25 + 0,203Т0,5 + 0,063Т0,75 + 0,009 Тc**

Where:

VH — volumetric hardness of grinding balls;

Тsurf – surface hardness of grinding balls;

Т0,25 — hardness at 0,25 of the radius depth;

Т0,5 — hardness at 0,5 of the radius depth;

Т0,75 — hardness at 0,75 of the radius depth;

Тc – hardness at center of grinding ball;

**The hardness measurement scheme**

**2. The second method of volumetric hardness measurement used in Bulgaria.**

Measurement and calculation takes place by zones (4 zones correspond to radius parts as at DSTU 3499-97 / DSTU 8538: 2015, but measurements provide by center of zones).

The volumetric hardness determination calculates by the formula:

**VH = (48.8 * T1 Zone + 29.6 * T2 Zone + 15.2 * T3 Zone + 5.6 * T4zone + 0.8 * Center) / 100**

**The hardness measurement scheme**

This method has a small deficiency, because it isn’t takes into account the surface hardness of grinding balls.

**3. The third method used in Turkey.**

This method consists of the hardness measurement from the surface to the center with **R/12 **step (for example: the radius **R** is 30 mm for a 60mm grinding ball, then **R** divide into 12 dimensions and get a 2.5 mm pitch).

The volumetric hardness determination calculates by the formula:

**VH = 22,97%*****Т**_{1zone}**+19,16% ****Т**_{2 zone}** +15,68% ****Т**_{3 zone}** +12,56% ****Т**_{4 zone}** +9,78% ****Т**_{5 zone}** +7,35% ****Т**_{6 zone}** +5,27% ****Т**_{7 zone}** +3,53% ****Т**_{8 zone}** +2,14% ****Т**_{9 zone}** +1,1% ****Т**_{10 zone}** +0,41% ****Т**_{11 zone}** +0,06% ****Т**_{12 zone}

Where: **T1 — 12 zones** — the hardness value at each zone of grinding ball from the surface to the center, measured at one radius.

**The hardness measurement scheme**

This method has small deficiencies, because measurements perform at the same radius and don’t exclude the spotted hardness presence.

**The fourth method of volumetric hardness measurement used in Czech Republic.**

This method is similar to the previous one: measurement and calculation occurs by zones (10 zones with a layout from the surface A to the center J, the radius equal 1).

1 |
А |

2 |
В |

3 |
С |

4 |
D |

5 |
E |

6 |
F |

7 |
G |

8 |
H |

9 |
I |

10 |
J |

The volumetric hardness determination calculates by the formula:

**VH** = 0,271***А**+0,217***В**+0,169***С**+0,127***D** +0,091***Е**+0,061***F** +0,037***G** +0,019***Н**+0,007***I** +0,001***J**

**The hardness measurement scheme**

Summarizing, we can say all methods analogous and lead to the same goal – determination the hardened layer depth from the surface to the center of grinding ball.

Steel grinding balls with cross-cutting hardenability (i.e. high volumetric hardness) have the same structure and, as a result, the same properties (yield strength, relative narrowing and toughness) through the entire section, provides high operational properties: the ability to wear resist during work in the mill and the grinding balls reduce consumption per one ton of raw materials.