instrutech

Ball mill

INSTRUCTION MANUAL

BALL MILL

Introduction:

Reduction of particle size is an important operation in many chemical and other industries. The

important reasons for size reduction are:

Easy handling

Increase in surface area per unit volume

Separation of entrapped components

The operation is highly energy intensive; hence a variety of specialized equipment is available

for specific applications. The equipment may utilize one or more of the following physical

mechanisms for size reduction: (i) Compression, (ii) Impact, (iii) Attrition, (iv) Cutting. Estimation

of energy for the operation is important and is usually done by empirical equations. Enormous

quantities of energy are consumed in size reduction operations. Size reduction is the most

inefficient unit operations in terms of energy, as 99% of the energy supplied goes to operating

the equipment and producing undesirable heat and noise, while less than 1% goes in creating

new interfacial area. Reduction to very fine sizes is much more costly in terms of energy as

compared to relatively coarse products.

Sieving refers to the separation of a mixture of particles of different sizes using sieves each with

a uniform sized opening. Standard sieves of specified opening sizes are used. Sieves are stacked

with the sieve with the largest opening on the top and the material is separated into fractions

by shaking. The material between two sieves is smaller than the upper sieve opening but larger

than the smaller sieve opening.

Objectives:

1. To grind the given material to a smaller size using a ball mill and to obtain the size

distribution of the initial and final mixture by sieving.

2. To estimate the energy required for the grinding operation.

3. To analyze the results using available theories.

Theory and Analysis:

The minimum energy required for crushing is the energy required for creating fresh surface. In

addition, energy is absorbed by the particulate material due to deformation, friction, etc.,

which results in an increase of the material temperature. Defining the crushing efficiency as

ɳC=Surfaceenergy created

Energy absorbed bymaterial=es

(A¿¿wb−Awa)W n

(1)¿

Where es is the surface energy per unit area and W n is the energy absorbed. We can

experimentally find ɳC . The range of ɳC is between 0.06 – 1.00%. If ɳmis the mechanical

efficiency, the energy input is

W=es

(A ¿¿wb−Awa)ɳC ɳm

(SINCEW n=ɳmw)(2)¿

Finally, the grinding energy used per unit mass is

Wm

=6es

ηcηmρ p ( 1ϕb Dsb

− 1ϕaD sa )(3)

where m is mass of material being ground. In the above equation φ is the sphericity, Dsis the

surface volume diameter and the subscripts a and b refer to the initial and final states,

respectively.

Experiments show that the first term in Eq. (3) is not independent of Ds, and as a result the

above equation is difficult to use for analysis. Instead a number of empirical laws have been

proposed for calculation the energy requirements for crushing. The laws can be unified in a

differential form as follows:

d (Wm )=−kdDs

Dsn (4)

The different laws for the different values of the exponent are

n=1:Wm

=K K ln( D sa

D sb)(Kic k ' s law )(5)

n=2:Wm

=K R( 1Dsb

−1Dsa

) (Rittnger ' s Law )(6)

n=32:Wm

=KB( 1

√D80b

−1

√D80a) (Bond' s Law )(7)

Note that the definition of particle size in Bonds law is different: 80D= Particle size such that

80% by weight of the sample is smaller than it.

Bonds law is often written in terms of the work index (Wi) as,

Wm

=10W i( 1

√D80b

−1

√D80a)(8)

Where the work index is defined as the energy required per unit mass in kWh/ton to reduce an

infinitely large particles to D80=100 μm. In the above equation, unit of D80 is μm, of W is kWh

and of m is ton. Values of the work index: obtained from experiments for different materials are

given in the table below.

Material Wi (kWh/ton)

Basalt 20.41

Coke 73.8

Limestone 11.6

Mica 134.5

Glass 3.08

Calcined clay 1.43

Procedure:

1. Weigh the given sample and obtain the initial size distribution by sieving.

2. Grind the sample in the ball mill for 30 minutes noting the energy consumed during

grinding.

3. Measure the size distribution by sieving.

4. Note the RPM of ball mill.

5. Note readings and draw size distribution curves for

a. Cumulative size distribution.

b. Frequency size distribution.

c. Initial distribution and distributions obtained after sieving.

d. Calculate the surface volume diameter in each case.

e. Obtain the diameter D80 for all three distributions.

f. Obtain the coefficients of kk kR and the work index Wi for all runs.

g. Assuming reasonable values of ɳc and ɳc estimate es.