Abstract
In addressing the challenges of unreasonable ball filling systems and suboptimal particle size composition in the grinding products of the Φ7.9 m × 13.6 m ball mill at Mirador Copper Mine, this study focuses on optimizing the initial and supplemental steel ball ratios. Through rigorous calculations and comparative experiments, a refined initial ball scheme—Φ80 mm, Φ60 mm, Φ50 mm, Φ40 mm, Φ30 mm with a mass ratio of 15:20:25:20:20—was proposed. Results demonstrated significant improvements: the yield of the -0.074 mm fraction increased by 4.11 percentage points, intermediate particle size (0.074–0.010 mm) yield rose by 2.05 percentage points, and the +0.20 mm fraction decreased by 6.24 percentage points. Furthermore, optimized supplemental ball ratios (Φ80 mm, Φ60 mm, Φ50 mm, Φ40 mm at 25:35:20:20) enhanced the -0.074 mm yield by 6.05 percentage points and reduced the +0.20 mm fraction by 8.87 percentage points. These advancements hold critical implications for improving copper recovery by refining particle size distribution and minimizing coarse copper losses in flotation tailings.
1. Introduction
The ball mill is a cornerstone of mineral processing, where grinding media (steel balls) directly influence energy transfer, ore fragmentation, and product granularity. Suboptimal ball size distribution can lead to insufficient impact energy (undersized balls) or overgrinding (oversized balls), both detrimental to equipment longevity and process efficiency. At Mirador Copper Mine, the first-stage ball mill exhibited inefficiencies: excessive +0.074 mm particles in flotation tailings, high copper losses, and elevated steel consumption (1.28 kg/t). This study aims to optimize the grinding media configuration to enhance particle size control, reduce steel consumption, and improve copper recovery.
2. Methodology
2.1 Sample Characterization
Feed ore, cyclone underflow, overflow, and ball mill discharge were analyzed for particle size distribution (Tables 1–3). Key observations:
- Cyclone underflow: 95.73% -5 mm, 9.64% -0.074 mm.
- Cyclone overflow: 56.82% -0.074 mm, 22.54% -0.010 mm.
- Ball mill discharge: 20.19% -0.074 mm, indicating low generation of target fines.
2.2 Initial Ball Ratio Optimization
Using the Duan’s semi-theoretical formula for ball size determination, the initial ball ratio was redesigned to target +0.20 mm coarse fractions (Table 4).
Table 1: Cyclone Underflow Particle Size Distribution
| Size Range (mm) | Individual Yield (%) | Cumulative Yield (%) |
|---|---|---|
| +10 | 1.39 | 100.00 |
| 10–8 | 1.33 | 98.61 |
| 8–5 | 1.55 | 97.28 |
| … | … | … |
Table 4: Calculated Initial Ball Ratio
| Size Range (mm) | Yield (%) | Target Ball Size (mm) |
|---|---|---|
| +2 | 10.84 | 80 |
| -2–0.90 | 13.71 | 60 |
| 0.90–0.45 | 17.21 | 50 |
| … | … | … |
The proposed ratio (Φ80:Φ60:Φ50:Φ40:Φ30 = 15:20:25:20:20) was tested against the original configuration (Table 5).
Table 5: Grinding Product Comparison (Initial Balls)
| Size Range (mm) | Original Yield (%) | Optimized Yield (%) |
|---|---|---|
| +0.90 | 0.16 | 0.06 |
| 0.90–0.45 | 0.72 | 0.40 |
| … | … | … |
2.3 Supplemental Ball Ratio Optimization
To counteract ball wear, supplemental ratios (Φ80:Φ60:Φ50:Φ40 = 25:35:20:20) were tested against single-size supplementation (Table 6).
Table 6: Grinding Product Comparison (Supplemental Balls)
| Size Range (mm) | Single-Size Yield (%) | Multi-Size Yield (%) |
|---|---|---|
| +0.90 | 0.01 | 0.16 |
| 0.90–0.45 | 0.14 | 0.68 |
| … | … | … |
3. Results and Discussion
3.1 Initial Ball Ratio Impact
The optimized ratio significantly improved grinding efficiency:
- -0.074 mm yield: +4.11 percentage points.
- 0.074–0.010 mm yield: +2.05 percentage points.
- +0.20 mm reduction: -6.24 percentage points.
The refined ball distribution enhanced impact energy distribution, ensuring balanced coarse fragmentation and fines generation.
3.2 Supplemental Ball Ratio Impact
Multi-size supplementation outperformed single-size:
- -0.074 mm yield: +6.05 percentage points.
- 0.074–0.010 mm yield: +3.14 percentage points.
- +0.20 mm reduction: -8.87 percentage points.
This approach maintained optimal media size distribution, mitigating the “over-filling” effect of oversized balls.
3.3 Economic and Operational Benefits
- Steel consumption: Reduced through balanced wear rates.
- Energy efficiency: Improved due to minimized overgrinding.
- Copper recovery: Enhanced by reducing coarse copper in tailings.
4. Theoretical Framework
The Duan’s semi-theoretical formula for ball size selection is expressed as:Db=K⋅F80k⋅(Wi⋅SGCs⋅ϕ)0.53Db=K⋅3kF80⋅(Cs⋅ϕWi⋅SG)0.5
Where:
- DbDb = Ball diameter (mm)
- F80F80 = 80% passing size of feed (mm)
- WiWi = Work index (kWh/t)
- SGSG = Specific gravity of ore
- CsCs = Critical speed fraction
- ϕϕ = Mill diameter (m)
This formula guided the initial ball size selection, ensuring alignment with ore characteristics and ball mill dynamics.
5. Conclusion
- Optimized initial ball ratios (Φ80:Φ60:Φ50:Φ40:Φ30 = 15:20:25:20:20) improved -0.074 mm yield by 4.11 percentage points.
- Multi-size supplemental ratios (Φ80:Φ60:Φ50:Φ40 = 25:35:20:20) further enhanced fines generation by 6.05 percentage points.
- The study underscores the critical role of ball mill media optimization in achieving target particle size distributions, reducing operational costs, and maximizing copper recovery.