Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model
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This document describes a simulation of a semi-autogenous grinding (SAG) mill using a circular-disk based model. The simulation models the mill as circular disks representing the mill liner and calculates interaction forces between particles to model particle motion over time. Simulation results show the distribution of particles and grinding modes like cascading and cateracting for different mill parameters like the number of disks, disk radius, and rotation speed. The program can simulate SAG mill operation and provide insight into how particle motion is affected by adjustable mill design parameters.
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Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model
- 1. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model R. Sari1, P. M. Widartiningsih2, M. A. Martoprawiro3, L. Hendrajaya4, S. Viridi4* 1Master Program in Computational Science 2Master Program in Physics 3Chemistry Department 4Physics Department Corresponding author: dudung@fi.itb.ac.id 10 – 12 July 2017 Bandung, Indonesia Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung Jalan Ganesha 10, Bandung 40132, Indonesia International Conference on Computation in Science and Engineering
- 2. ICCSE 2017R.Sari, et. al. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model Outline Introduction Model Results and Discussion Conclusion Question & Answer
- 3. ICCSE 2017R.Sari, et. al. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model Introduction Cascading Cataracting Centrifuging Impact zone Empty zone Abrasion zone Rotation Dead zone
- 4. ICCSE 2017R.Sari, et. al. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model Mill Model 𝜔 𝑀 (𝑥 𝑀, 𝑦 𝑀) 𝑅 𝑀 𝐷𝐿 𝑖 = 𝑁𝐿 𝑖 = 1 𝜔 𝑀 𝑔 𝑥 𝑦 𝑧 (𝑥 𝑀, 𝑦 𝑀) Δ𝜃 𝑅 𝑀 𝑅 𝑀 𝑖 𝑖 + 1 𝐷𝐿 = 2𝑅 𝑀 sin 𝜋 𝑁𝐿 𝜃𝑖+1 = 𝜃𝑖 + 𝜔 𝑀 𝑡
- 5. ICCSE 2017R.Sari, et. al. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model Mill Model 𝐷𝐿 = 2𝑅 𝑀 sin 𝜋 2 = 2𝑅 𝑀 𝐷𝐿 = 2𝑅 𝑀 sin 𝜋 3 = 3𝑅 𝑀 𝐷𝐿 = 2𝑅 𝑀 sin 𝜋 4 = 2𝑅 𝑀 𝐷𝐿 = 2𝑅 𝑀 sin 𝜋 6 = 𝑅 𝑀 𝐷𝐿 = 2𝑅 𝑀 sin 𝜋 𝑁𝐿 NL = 2 DL RM NL = 3 DLDL DL RM NL = 4 RM DL DLDL DL NL = 6 DL DL DL DL DL DL RM
- 6. ICCSE 2017R.Sari, et. al. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model Interaction Forces Gravitational Force 𝐺𝑖 = −𝑚𝑖 𝑔 𝑒 𝑦 Normal Force 𝑁𝑖𝑗 = 𝑘 𝑁 𝜉𝑖𝑗 − 𝛾 𝑁 𝑑𝜉𝑖𝑗 𝑑𝑡 𝑟𝑖𝑗 Drag Force 𝐷𝑖 = −𝑐 𝐷 𝑣𝑖 Acceleration of particle can be obtained from sum of all working forces Σ 𝐹 𝑎𝑖 = 1 𝑚𝑖 𝐹 𝑎𝑖 = 1 𝑚𝑖 𝐺𝑖 + 𝐷𝑖 − 𝑗=1 𝑁 𝐿 𝑁𝑖𝑗 + 𝑗=1 𝑗≠𝑖 𝑁 𝐺 𝑁𝑖𝑗 The motion can be solved using Euler method 𝑣 𝑡 + ∆𝑡 = 𝑣 𝑡 + 𝑎(𝑡)∆𝑡 𝑥 𝑡 + ∆𝑡 = 𝑥 𝑡 + 𝑣(𝑡)∆𝑡 𝜔 𝑀 𝑖 𝑖 𝑗 𝑁𝑖𝑘 𝐺𝑖 𝑁𝑗𝑖 𝐷𝑖 𝐷𝑖 𝑘
- 7. ICCSE 2017R.Sari, et. al. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model Simulation Liner Grains 𝐺𝑖 𝜔 𝑀 𝑖 = 1 𝑖 = 20
- 8. ICCSE 2017R.Sari, et. al. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model Number of Liner 𝑁𝐿 = 20 𝑁𝐿 = 30 𝑁𝐿 = 50 𝑅 𝑀 = 50, 𝑁 𝐺 = 25
- 9. ICCSE 2017R.Sari, et. al. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model Radius of Mill 𝑅 𝑀 = 35 𝑅 𝑀 = 40 𝑅 𝑀 = 50 𝑁𝐿 = 20, 𝑁 𝐺 = 25
- 10. ICCSE 2017R.Sari, et. al. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model Results 𝑡 = 0 𝑠 𝑡 = 2 𝑠 𝑡 = 3 𝑠 𝑡 = 4 𝑠 𝑡 = 6 𝑠 𝑡 = 8 𝑠 𝑡 = 10 𝑠 𝑡 = 12 𝑠 𝑁𝐿 = 20 𝑁 𝐺 = 25 𝑅 𝑀 = 40 𝜔 𝑀 = 0.8
- 11. ICCSE 2017R.Sari, et. al. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model Results Impact zone 21 abrasion 25 rolling 26 abrasion 36 fall down (dead zone) 42 abrasion 44 normal force > gravitation force 45 cascading 𝑡 = 6 𝑠 𝑡 = 8 𝑠
- 12. ICCSE 2017R.Sari, et. al. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model Conclusion The built program can be used to simulate SAG Mill with adjustable number of liner and mill’s radius. The simulation results an acceptable distribution of grains when the grinding occurs, especially for cascading and cateracting mode. Further research, the size of grains can be varied in order to approach the real condition.
- 13. ICCSE 2017R.Sari, et. al. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model References 1. Faizin N, Hendrajaya L, Viridi S and Alfisyah M 2016 Spektra: J. Fis. Aplikasi. 1 157 2. Schäfer J, Dippel S and Wolf D E 1996 J. Phys. I France 6 5 3. Seinfeld J H, Lapidus L and Hwang M 1970 Ind. Eng. Chem. Fundamen. 9 266 4. Viridi S and Kurniadi R 2017 Komputasi Fisika 3: Simulasi dan Visualisasi Fisika dengan JavaScript, Departemen Fisika, FMIPA, Institut Teknologi Bandung, pp. 289 – 294 doi: 10.13140/RG.2.2.35065.67680
- 14. ICCSE 2017R.Sari, et. al. Simulation of Semi-Autogenous Grinding (SAG) Mill using Circular-Disks-based Model Thank You