A Brief Analysis of Grinding Mill Steel Ball Size Distribution

It is well known that the hourly output of a grinding mill is influenced by numerous factors, including the grinding process flow and the performance of associated auxiliary equipment (such as classifiers and pre-crushers), the characteristics of the feed material (including its type and blend ratio, particle size distribution, total moisture content, grindability, etc.), the desired fineness, internal mill ventilation, the shape and positioning of the partition plates, the working profile of the lining plates, the grinding-media filling ratio and gradation, the mill speed, as well as operational practices and system-wide control of the grinding process. How, then, can the grinding-media filling level and gradation be optimized to achieve the highest possible grinding efficiency? Drawing on theoretical knowledge and practical experience in production, I would like to share my personal views for your reference and consideration.

First, the average ball diameter for each chamber of the mill is determined based on the feed particle size; next, the mill filling ratio and charge weight are set according to the grinding process flow; finally, the gradation of steel balls of various sizes is back-calculated from the charge weight and the average ball diameter.

1. Relationship between the average particle size of feed material and the average diameter of wear-resistant steel balls (empirical data)

2. Determine the filling ratio of the grinding media in each chamber. Furthermore, for the same mill, the filling ratio in the front chamber should be 1%–2% higher than that in the rear chamber to facilitate material flow within the mill.

3. Calculate the effective volume of each chamber of the mill based on its specifications, and then determine the charge weight for each chamber using the filling ratio and the density of the grinding balls.

The effective volume, or the effective internal space of the mill, refers to the interior volume of the mill’s cylindrical shell excluding the lining plates. It can be calculated using the formula: V = π · Di² · L, where Di is the effective diameter of the cylinder and L is the effective length.

Loading capacity = ρ × ψ × V (where ρ is the density of steel balls, 4.65 t/m³; ψ is the filling ratio; and V is the effective volume).

4. Determine the maximum ball diameter Dmax

5. Once the average ball diameter and the mill’s charge volume have been determined, the steel-ball gradation can be back-calculated using the average-ball-diameter formula. The principle for determining the steel-ball gradation is to use fewer large and small balls and more medium-sized balls, with particular emphasis on the gradation in the first chamber.
There are two formulas for the average particle diameter: formula a and formula b.

aa: Coarse average particle diameter formula: D平=

Bb: Exact average particle diameter formula: D_avg =

Generally, the average particle diameter calculated using method a is 2–3 units higher than that calculated using method b, and the initial internal grinding formulation should be more accurate when determined by method b.

D平—Average ball diameter of steel ball gradation, mm

D1, D2, D3—ball diameters in various specifications, in mm

G1, G2, G3—mass t of steel balls with diameters D1, D2, and D3, respectively.

T1, T2, T3—number of balls per ton when the ball diameters are D1, D2, and D3, respectively.

Overview of Forged Steel Ball Parameters

6. After the grinding mill has been charged with steel balls according to the specified gradation, start the mill and feed material. One hour later, take a sample of the mixed product from the mill outlet for fineness analysis. The general requirements are as follows: the fineness of the milled product should be maintained within the range of 35%–45%; the circulating load ratio should be 80%–300% (for closed-circuit grinding); the separator efficiency should be reduced to approximately 60%–65%. Based on the test results, make fine adjustments to the steel-ball gradation until the crushing capacity of the coarse-powder compartment (or multiple compartments) is balanced with the grinding capacity of the fine-powder compartment.

7. The feed particle size to the mill should be reduced as much as possible (subject to the capacity of the crusher). For blended feeds, the moisture content of the material entering the mill should be minimized, and the particle size should be kept relatively stable. The ball charge gradation in the mill should also be maintained at a stable level. While ensuring that the crushing capacity of the first chamber remains normal, the average ball diameter should be reduced as much as possible to increase the specific surface area of the material and improve product quality.

8. During the winter and spring seasons, the moisture content in the air surrounding the milled material differs: generally, the spring season features higher moisture, calling for a larger average ball diameter in the gradation, whereas the winter season has drier air with lower moisture, necessitating a smaller average ball diameter in the gradation.

Example: Take the φ2.2×6.5 m cement mill as an example (the company currently has a total of five φ2.2×6.5 mills).

Ⅰ Effective length of the silo: L1 = 2.5 m; effective internal diameter Di = 2.12 m (average lining plate thickness 40 mm);

Effective volume: V1 = 1 × Di² × L1 = ×2.122 ×2.5 = 8.825 m³

II. Effective length of the silo: L2 = 3.75 m; effective internal diameter Di = 2.12 m (average lining plate thickness: 40 mm).

Effective volume: V2 = ×Di²×L2 = ×2.122×3.75 = 13.237 m³

Average particle diameter:

Bin I: 76.4 (calculated using method a); calculated using method b: the average particle diameter is 73.78.

Steel ball gradation:

Warehouse I: φ90/2T; φ80/6T; φ70/5T; φ60/1T;

Bin II: φ50/5T; φ40/6T; φ30/8.5T;

Average ball diameter in Bin II: φ38 (Bin II aims to minimize the average ball diameter to increase the specific surface area).

Of course, an appropriate ball-size distribution is only one factor in enhancing the mill’s output and product quality. The steel-ball grading is not static; it should be adjusted in accordance with the mill’s operating conditions, with continuous fine-tuning during production until the mill achieves optimal grinding efficiency.