1. Introduction
In mineral processing, the integration of High-Pressure Grinding Rolls (HPGR) and ball mills has emerged as a pivotal strategy for enhancing grinding efficiency and reducing energy consumption. Traditional comminution circuits often rely on multi-stage crushing followed by ball mill grinding. However, the inherent characteristics of “lean, fine, and complex” ores in modern mining operations demand innovative solutions to achieve higher throughput and lower specific energy consumption.
The ball mill, a cornerstone of grinding circuits, requires precise selection to match operational demands. Historically, the Bond Work Index (WiWi) has been the gold standard for ball mill sizing. However, industrial practices reveal significant discrepancies between theoretical calculations and actual performance when HPGR is integrated into the circuit. This paper addresses these discrepancies by introducing a synergistic coefficient (KK) to refine the Bond formula, thereby improving the accuracy of ball mill selection in HPGR-ball mill hybrid systems.
2. Problem Statement
2.1 Limitations of Traditional Bond Formula
The Bond Work Index equation, expressed as:W=10×Wi(1P80−1F80)W=10×Wi(P801−F801)
where WW = grinding work (kWh/t), F80F80 = feed size (μm), and P80P80 = product size (μm), assumes uniform particle size distribution and overlooks the microstructural changes induced by HPGR.
In HPGR-ball mill circuits, HPGR generates finer feed (F80F80 = 3–5 mm vs. 8–10 mm in traditional circuits) and introduces micro-cracks in ore particles, reducing the ball mill Work Index by 5–15%. Despite these advantages, theoretical ball mill capacity calculations using the Bond formula consistently underestimate actual throughput by up to 30%.
2.2 Case Study: Luoyang Molybdenum Plant
A retrofit project at Luoyang Molybdenum Plant replaced tertiary crushing with HPGR, reducing F80F80 from 8 mm to 3.2 mm. Post-retrofit data revealed a 45.8% increase in ball mill throughput (350 t/h vs. 240 t/h), yet Bond-based predictions only estimated 310 t/h (Table 1).
Table 1: Performance of Φ4.8 m × 7.0 m Ball Mill Before and After HPGR Integration
| Parameter | Pre-Retrofit | Post-Retrofit (Theoretical) | Post-Retrofit (Actual) |
|---|---|---|---|
| Motor Power (kW) | 2,460 | 2,460 | 2,465 |
| F80F80 (μm) | 8,000 | 3,200 | 3,200 |
| -0.074 mm Content (%) | 62–66 | 60–64 | 60–64 |
| Specific Energy (kWh/t) | 12.46 | 11.64 | 11.64 |
| Throughput (t/h) | 240 | 310 | 350 |
The gap between predicted (310 t/h) and actual (350 t/h) throughput underscores the need for a revised methodology.
3. Methodology: Synergistic Coefficient (KK)
3.1 Particle Size Distribution Analysis
HPGR products exhibit distinct size distributions compared to crushed feed. At identical P80P80, HPGR generates higher proportions of fine particles (e.g., -170 μm content increased by 17% in Luoyang’s case). These pre-liberated fines bypass grinding, directly contributing to final product yield.
Table 2: Feed Size Distribution Comparison
| Particle Size (mm) | Cumulative Passing (%) | |
|---|---|---|
| Crushed Feed | HPGR Feed | |
| 0.075 | 5.56 | 14.16 |
| 0.180 | 12.25 | 30.74 |
| 2.000 | 32.90 | 66.04 |
| 5.000 | 54.23 | 88.90 |
3.2 Deriving the Synergistic Coefficient (KK)
The synergistic coefficient (KK) quantifies the incremental throughput gain from HPGR-induced fines:K=1+ΔFinesTotal FeedK=1+Total FeedΔFines
For Luoyang’s case, ΔFines=17%ΔFines=17%, yielding K=1.17K=1.17. The corrected ball mill capacity (QcorrectedQcorrected) becomes:Qcorrected=QBond×KQcorrected=QBond×K
Applying this to Luoyang’s data:Qcorrected=310×1.17=363 t/h (vs. actual 350 t/h)Qcorrected=310×1.17=363t/h(vs. actual 350t/h)
The 3.7% error validates KK’s efficacy.
4. Results and Validation
4.1 Case Study 1: Luoyang Molybdenum Plant
Using K=1.17K=1.17, the revised ball mill capacity calculation aligns closely with field data (Table 3).
Table 3: Revised vs. Actual Throughput (Luoyang)
| Metric | Theoretical (Bond) | Revised (K=1.17K=1.17) | Actual |
|---|---|---|---|
| Throughput (t/h) | 310 | 363 | 350 |
| Error (%) | -11.4 | +3.7 | — |
4.2 Case Study 2: Jiangxi Copper Plant
A similar retrofit using GM100-30 HPGR achieved:
- Pre-retrofit throughput: 65 t/h (Bond prediction).
- Post-retrofit actual throughput: 90 t/h.
- Revised calculation (K=1.23K=1.23): 91.7 t/h (error: 1.9%).
Table 4: Revised vs. Actual Throughput (Jiangxi)
| Metric | Theoretical (Bond) | Revised (K=1.23K=1.23) | Actual |
|---|---|---|---|
| Throughput (t/h) | 83.0 | 91.7 | 90.0 |
| Error (%) | -7.8 | +1.9 | — |
5. Conclusion
- Ball mill selection in HPGR-ball mill circuits requires accounting for particle size distribution shifts induced by HPGR. The traditional Bond formula, focusing solely on F80F80, underestimates throughput by up to 30%.
- Introducing the synergistic coefficient (KK) corrects for fines bypassing grinding, reducing calculation errors to <5%.
- Industrial validations at Luoyang and Jiangxi plants confirm KK’s robustness, making it indispensable for optimizing ball mill sizing in modern grinding circuits.