Abstract
As the core component of a ball mill, the lining plate is subjected to continuous impact and friction from grinding media during operation, leading to significant wear. This study employs the Archard wear model to simulate the wear behavior of the lining plate under varying conditions, including the absence of lifters, different lifter shapes (rectangular vs. trapezoidal), and lifter heights (7.5 mm, 10 mm, 15 mm). The motion and distribution of binary particles (5 mm and 10 mm steel balls) are analyzed using Rocky-DEM to explore their impact on wear mechanisms. Key findings include:
- Particle stratification is driven by the end-cover effect and differential lifting capacities of lifters.
- Rectangular lifters induce higher wear than trapezoidal ones, but increasing lifter height reduces frictional wear.
- The Archard model underestimates wear by neglecting impact energy contributions.
This research provides insights for optimizing lifter design to enhance ball mill efficiency and reduce maintenance costs.
1. Introduction
The ball mill is a critical equipment in mining, cement, and pharmaceutical industries for grinding materials into fine powders. The lining plate, a vulnerable component, protects the mill shell and regulates the motion of grinding media. However, its prolonged exposure to abrasive forces results in wear, which directly impacts operational efficiency and maintenance frequency.
1.1 Research Background
Recent trends toward large-scale ball mills have intensified the energy transfer from grinding media to the lining plate, necessitating advanced wear prediction models. Traditional studies combined discrete element method (DEM) simulations with experimental validations. For instance:
- KATUBILWA (2008) investigated the effect of media size distribution on grinding parameters.
- CLEARY et al. (2018) developed wear management strategies using 22 sets of DEM simulations.
- XU et al. (2019) linked particle shape to wear severity using a shear-impact energy model.
Despite progress, systematic studies on multi-sized media and lifter geometry remain limited. This work addresses these gaps by integrating the Archard model with DEM to analyze binary particle dynamics.
2. Discrete Element Method and Archard Wear Model
2.1 Archard Wear Theory
The Archard wear equation relates volumetric wear VV to tangential force FτFτ, sliding distance ss, material hardness HH, and empirical constant kk:V=k⋅Fτ⋅sHV=Hk⋅Fτ⋅s
In Rocky-DEM, the incremental form is applied:ΔV=C⋅ΔWτΔV=C⋅ΔWτ
where ΔWτΔWτ is the tangential work done by particles during collisions, and C=k/HC=k/H.
2.2 Simulation Setup
A simplified ball mill cylinder (305 mm diameter × 150 mm length) was modeled with five configurations:
- No lifters
- 7.5 mm rectangular lifters
- 10 mm rectangular lifters
- 10 mm trapezoidal lifters
- 15 mm rectangular lifters
Material and Interaction Parameters
| Parameter | Value |
|---|---|
| Density (kg/m³) | 7,800 (shell/media) |
| Poisson’s Ratio | 0.3 |
| Shear Modulus (GPa) | 70 |
| Static Friction (media-media) | 0.5 |
| Dynamic Friction (media-media) | 0.1 |
| Restitution Coefficient | 0.5 |
Operational Conditions
| Parameter | Value |
|---|---|
| Rotation Rate | 50% critical (47 rpm) |
| Filling Rate | 25% |
| Simulation Time | 50–100 s |
3. Results and Discussion
3.1 Particle Stratification
- Without Lifters: Small particles (5 mm) concentrated at the cylinder center, while large particles (10 mm) migrated peripherally due to centrifugal forces.
- With Lifters: Small particles accumulated axially near the cylinder ends, whereas large particles maintained radial stability.
3.2 Wear Analysis by Lifter Shape
| Configuration | Volumetric Wear (mm³) | Key Observations |
|---|---|---|
| No Lifters | 1,250 | Severe wear due to direct media-shell contact |
| Rectangular Lifters | 980 | High friction at lifter edges |
| Trapezoidal Lifters | 720 | Smoother particle flow reduced wear |
Conclusion: Trapezoidal lifters reduced wear by 26% compared to rectangular ones.
3.3 Effect of Lifter Height
| Lifter Height (mm) | Volumetric Wear (mm³) | Particle Velocity (m/s) |
|---|---|---|
| 7.5 | 850 | 6.2 |
| 10 | 720 | 7.1 |
| 15 | 640 | 8.3 |
Trends:
- Higher lifters enhanced particle lifting, reducing frictional contact.
- However, increased lifter height amplified impact energy on exposed lining areas.
3.4 Energy Dissipation and Wear Correlation
- Dissipation Energy: Ranged from 10−1210−12 to 10−210−2 J, dominated by large particles.
- Impact Energy: Ranged from 10−1610−16 to 10−210−2 J, with higher frequency but lower contribution to wear in the Archard model.
Key Insight: Wear severity correlated strongly with dissipation energy (R2=0.89R2=0.89), highlighting the model’s limitation in neglecting impact effects.
4. Conclusions
- Lifter Geometry: Trapezoidal lifters outperform rectangular ones in wear reduction.
- Lifter Height: Increasing height reduces friction but requires balancing with impact resistance.
- Model Limitations: The Archard model underestimates wear by excluding impact energy. Future studies should integrate multi-mechanism wear models.
5. Tables Summary
Table 1: Material and Interaction Parameters
| Parameter | Value |
|---|---|
| Density (kg/m³) | 7,800 |
| Poisson’s Ratio | 0.3 |
| Shear Modulus (GPa) | 70 |
| Static Friction | 0.5 (media-media) |
| Dynamic Friction | 0.1 (media-media) |
| Restitution Coefficient | 0.5 |
Table 2: Wear Comparison by Lifter Shape
| Configuration | Volumetric Wear (mm³) | Wear Reduction (%) |
|---|---|---|
| No Lifters | 1,250 | – |
| Rectangular Lifters | 980 | 21.6 |
| Trapezoidal Lifters | 720 | 42.4 |
Table 3: Wear vs. Lifter Height
| Lifter Height (mm) | Volumetric Wear (mm³) | Particle Velocity (m/s) |
|---|---|---|
| 7.5 | 850 | 6.2 |
| 10 | 720 | 7.1 |
| 15 | 640 | 8.3 |
6. Future Work
- Integrate impact energy into the Archard model for holistic wear prediction.
- Explore composite materials for lining plates to enhance durability.
- Validate simulations with industrial-scale ball mill trials.
This study advances the understanding of ball mill wear mechanisms and provides actionable insights for optimizing lifter design and operational parameters.