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Estimation of the Specific Energy Requirement for Size Reduction of Solids in Ball Mills

  • V. K. GuptaEmail author
  • Mofid Hussain
Technical Paper

Abstract

Design engineers generally use Bond Work Index and Bond energy equation to estimate specific energy requirements for ball milling operations. Morrell has proposed different equations for the Work Index and specific energy, which are claimed to have a wider range of application. In this paper an attempt has been made to provide a comparison of these two approaches and bring out their shortcomings. It has been shown that it is possible to develop a modified approach based on the well proven Kapur energy-size relationship and the size-mass balance mathematical modelling approach. Several important points have been illustrated using our own experimental data and a large amount of relevant data available in the literature.

Keywords

Ball mill Size reduction Energy-size relationship Work Index Specific energy requirement 

Abbreviations

A

Constant in Eq. (10)

B(x,v)

Breakage distribution function

c

Constant in Eq. (15)

C

Constant in Eq. (8)

C1

Constant in Eq. (16)

C2

Constant in Eq. (22)

C3

Constant in Eq. (23)

\(C_{1}^{i}\)

C1 value for i-th time interval

\(C_{1}^{*}\)

Average of C1 values for two time intervals

D

Constant in Eq. (25)

E

Specific energy required for size reduction

Er

Error function defined in Eq. (21)

F(y,t)

Cumulative weight fraction finer than size y at time t

g(x)

A function defined in Eq. (5)

G

Grindability in Bond test

k(x)

Specific breakage rate for particles of size x

K1

Constant in Eq. (18)

K2

Constant in Eq. (19)

m(y,t)

Relative mass frequency function in particle size at time t

n

Total number of size intervals

q

Constant in Eq. (25)

r

Constant in Eq. (25)

S

Size of the openings of the test mesh in µm

t

Grinding time

V

An unknown function of α in Eq. (26)

W

Specific energy in Bond equation

WB

Bond Work Index

\(W_{B}^{*}\)

Defined in Eq. (26)

WM

Morrell Work Index

\(W_{H}\)

Holmes Work Index

xf

Size at which 80% of the fresh feed to the grinding circuit passes

xi

Size of the openings of the lower sieve of the i-th size interval

xp

Size at which 80% of the grinding circuit product (classifier overflow) passes

x80

Particle size corresponding to F = 0.8

Xf

Size in micron at which 80% of the new feed to ball mill passes

Xp

Size in microns at which 80% of the last cycle test sieve undersize product passes

y

Particle size

yf

80% passing size of the mill feed for batch operation

yp

80% passing size of the mill product for batch operation

z

Particle size

Z1

Similarity distribution function in Eq. (12)

Z2

Similarity distribution function in Eq. (14)

Greek Symbols

α

Exponent in Eq. (2) and Eq. (15)

μ1

First moment of particle size distribution

Subscripts

i

Indices for particle size interval

f

Mill feed

p

Mill product

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Copyright information

© The Indian Institute of Metals - IIM 2016

Authors and Affiliations

  1. 1.Department of Fuel and Mineral EngineeringIndian School of MinesDhanbadIndia

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