Jan Svoboda. Magnetic Techniques for the Treatment of Materials

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290 CHAPTER 4. DESIGN OF MAGNETIC SEPARATORS

Figure 4.38: The dependence of the magnetic induction generated by a stron-

tium ferrite block 100×150 mm, on its depth O,onthesurfaceof

theblockandat15mmfromthesurface.

illustrates the variation of the magnetic induction on the surface of a drum with

the width e of the magnet block. It can be seen that for a constant width d =

10 mm of the gap, the maximum magnetic induction is achieved for the magnet

width of 100 mm. The ratio e@d = 10 is thus in disagreement with the empirical

rule-of-thumb mentioned earlier.

Figure 4.34 also shows that replacement of the air gap with a steel block

results in the reduction of the magnetic ﬁeld. Similar conclusions can be drawn

from Fig. 4.35, which displays the eect of the magnet width on the force index.

The eect of the width d of the air gap on the ﬁeld at various distances from

the drum surface is illustrated in Fig. 4.36. It can be seen that by increasing d,

for a constant value of the width of the magnetic block (i.e. with the ratio e@d

decreasing), the magnetic induction decreases, at least in the proximity of the

drum surface. At larger distances from the drum surface, e.g. at 50 mm, the

eect of the value of d (and thus of e@d) is diminishing. Similar trends can be

observed for the force index as shown in Fig. 4.37.

The results illustrated in Fig. 4.30 and Figs. 4.34 to 4.37 were obtained

for a drum with axial pole arrangement and with magnets magnetized radially.

The diameter of the drum was 600 mm and the depth O of the magnet stack

was 100 mm.

The eect of the depth of the magnet stack can be determined by using eq.

(4.30), which allows for the variation of the depth O , as shown in Fig. 4.9, and

for the calculation of the magnetic ﬁeld generated by such a magnet block, at

dierent distances }. Figure 4.38 illustrates such a dependence for a strontium

4.6. DESIGN OF A MAGNETIC ROLL 291

Figure 4.39: Magnetic induction on the roll surface, as a function of the magnet

ring thickness. The values of magnetic induction were obtained by

computer modelling [F18].

ferrite block, of dimensions 150 mm (Z ) × 100 mm (G). It can be seen that

the beneﬁt of increasing the depth of the magnet stack above 140 mm is limited.

The computer modelling also allowed for the development of new geometries

of the magnet arrangement, capable of producing a higher magnetic strength

and magnetic force [A13, S8]. Some of these new designs are proprietary and the

patents are still pending. Comparison of one such a design, with conventional

designs, is shown in Figs. 4.34 and 4.35.

4.6 Design of a magnetic roll

4.6.1 Basic concepts of design

The overall view of a magnetic roll separator is shown in Figs. 2.30 and 2.31.

The magnetic roll itself forms a part of a short conveyor fed by a vibratory

feeder. The conveyor belt is made of a thin high-tensile material, often with

antistatic coating. The belt is supported by second roll (idler). Roll separators

are usually of modular design allowing them to be stacked in any number of

passes of material. Typical speciﬁcations of such a roll separator are shown in

Table 4.6.

The e!ciency of separation is aected by the roll design and by several

operating variables: the number of separation stages, belt speed, splitter posi-

tion and belt loading. Most of these variables are determined by particle size

292 CHAPTER 4. DESIGN OF MAGNETIC SEPARATORS

Figure 4.40: Force index as a function of the magnet ring thickness, for thickness

of steel rings equal to 1 mm and 1.75 mm, on the roll surface and

at 15 mm from the surface.

Figure 4.41: Magnetic induction on the surface of a roll, as a function of thick-

ness of steel rings, for several thicknesses of permanent magnet

rings.

4.6. DESIGN OF A MAGNETIC ROLL 293

Table 4.6: Typical speciﬁcations of a permanent roll magnetic separator.

Parameter Speciﬁcation

Belt thickness minimum 0.12 mm

Roll diameter 72, 76, 100, 220 & 300 mm

Roll length 250, 500, 1000 and 1500 mm

Max. magnetic induction NdFeB: 1.9 T, SmCo: 1.5 T, SrFe: 0.5 T

distribution and magnetic properties of the feed and by the recovery vs grade

requirement.

4.6.2 Design parameters

Thicknesses of magnet and steel rings

As has been discussed in Section 2.3.3 and shown in Fig. 2.28, the roll consists

of discs or rings of permanent magnets, interleaved with mild steel rings. The

adjacent permanent magnet rings are arranged with the same polarity facing one

another, i.e. rings are arranged in a repulsive mode. The relative thicknesses

of the magnets and the steel rings aect the magnetic ﬁeld strength and its

pattern around the roll. This situation is depicted in Figs. 4.39, 4.40 and 4.41.

It can be seen that the magnetic induction on the surface of a roll increases

with increasing thickness of the magnet ring. At the same time it achieves

the maximum value for a certain, rather small, thickness of the steel rings.

With further increase in the thickness of the steel rings the magnetic induction

decreases. This is a consequence of the fact that the saturation magnetization

of steel is much greater than that of the permanent magnet material. If the

thickness of the steel exceeds a certain optimum value, the magnet ring does

not succeed in saturating the steel, as transpires from eq. (4.12).

As can be seen in Figs. 4.42 and 4.43, for thin steel and magnet rings, which

generate a high force index close to the roll surface, the reach of the magnetic

force drops dramatically away from the surface. The rate of decrease is much

smaller for thicker magnet rings and even more so for an NdFeB drum.

Optimization of the design of the magnetic roll consists not only of maximiz-

ing the magnetic induction and force index on the roll surface and at a suitable

distance from the roll, but also of matching the dimensions of the magnet and

steel rings thicknesses to the particle size distribution of the material to be sep-

arated. Distributions of the magnetic induction along the axes of NdFeB and

SrFe rolls are shown in Figs. 4.44 and 4.45. The magnetic ﬁeld (and magnetic

force) on the roll surface are the greatest in a relatively narrow region at the

interface between the magnet and steel rings. It can also be seen that the ﬁeld

and the force along the circumference of the magnet rings are very feeble, and

it is imperative, therefore, that no particles are continuously exposed to this

region of the roll.

The thickness of the magnet rings should thus be of magnitude similar to the

294 CHAPTER 4. DESIGN OF MAGNETIC SEPARATORS

Figure 4.42: Force index as a function of distance from the roll surface, for

various thicknesses of magnet rings. Steel ring thickness equals 1

mm.

Figure 4.43: Force index (in arbitrary units), for two conﬁgurations of NdFeB

rolls and an NdFeB drum, as a function of the distance from the

surface of the roll [F18].

4.6. DESIGN OF A MAGNETIC ROLL 295

Figure 4.44: Distribution of the magnetic induction on the surface on an Nd-

FeB roll with 3/1 conﬁguration (magnet thickness: 3 mm, steel

thickness: 1 mm).

Figure 4.45: Distribution of the magnetic induction on the surface of a SrFe roll

with 6/2 conﬁguration (magnet thickness: 6 mm, steel thickness:

2mm).

296 CHAPTER 4. DESIGN OF MAGNETIC SEPARATORS

Figure 4.46: The partition curves for the recovery of 4 mm magnetic tracers by

NdFeB rolls of dierent conﬁgurations [F20].

mean particle size of the material to be separated. Thin magnet rings should

be used to separate ﬁne particles, while for larger particles a thicker magnetic

ring oers a larger contact area with the roll, and a longer reach of the magnetic

force, of the order of the radius of the particles.

It transpires from the above discussion that the design of the roll, and specif-

ically the thicknesses of the magnetic and steel rings, is dictated by the magnetic

properties and size distribution of the feed. The roll design must be optimized in

order to maximize the magnetic force and its reach and to match the dimensions

of the particles with the magnet thickness. A speciﬁc conﬁguration expressed as

magnet thickness/steel ring thickness is suitable only for a narrow size fraction

and typical conﬁgurations are summarized in Table 4.7.

The optimum conﬁguration obtained by electromagnetic modelling can be

validated experimentally using magnetic tracers of suitable sizes and accurate

values of magnetic susceptibility. Magnetic partition curves can then be con-

structed, the probable error Hs can be calculated and a conﬁguration with the

lowest Hs can be determined. Hs for a magnetic separator can be deﬁned as

Hs =

 "

(4.58)

where "

and "

are the mass magnetic susceptibilities of particles 75% and

25% of which, respectively, report to the magnetic fraction. Typical partition

curves, for 4 mm particles, are shown in Fig. 4.46. It can be seen that the

partition curve for the roll conﬁguration 4/2.5 is steeper than that for 4/1

4.6. DESIGN OF A MAGNETIC ROLL 297

Table 4.7: Various conﬁgurations of NdFeB magnetic rolls. Conﬁgurations are

expressed as the ratio magnet thickness/steel thickness.

Conﬁguration Size fraction Comment

3/1, 4/1 or 4.1.5 -5+0.1mm Short reach, high ﬁeld

6/1.5, 6/2, 6/3 -10+5mm Longer reach, lower ﬁeld

8/2, 8/3 +10mm For large particles

Figure 4.47: Force index for NdFeB rolls of dierent diameters, as a function

of distance from the roll surface. Roll conﬁguration: 12/7.5. The

data were obtained by computer modelling (adapted from [F18]).

conﬁguration and Hs is correspondingly lower. Conﬁguration 4/2.5 is, therefore,

more selective in separating 4 mm particles of dierent magnetic susceptibilities.

Diameter of magnet rings

In the past, the diameter of a rare-earth magnetic roll was dictated by availabil-

ity of the largest magnetic rings. While the ﬁrst commercial rolls had diameters

of 72 and 76 mm, recent progress in manufacture of rare-earth permanent mag-

net rings and segments allows for the manufacture of rolls with diameter of 100,

220 and 300 mm. The choice is determined by a combination of throughput,

performance and cost considerations. The present advantageous cost situation

favours larger diameter rolls, particularly when large throughputs are required

[A13].

In a simpliﬁed assumption of a constant magnetic force and constant resi-

298 CHAPTER 4. DESIGN OF MAGNETIC SEPARATORS

Figure 4.48: Schematic diagram of a suspended magnet.

dence time, a throughput increase by increasing the roll diameter, follows the

ratio G

,whereG

and G

are the roll diameters, as follows from eq. (5.4).

It is sometimes argued that by increasing the magnet diameter the magnetic

force also increases and an even higher throughput can be expected. It appears,

however, that the increase in the magnet ring diameter above 100 mm brings

only negligible increase in the force index, as is illustrated in Fig. 4.47.

On the other hand, a longer retention time of particles in a larger-diameter

roll, as a result of a longer arc of the magnet ring, to which the particles are

exposed, allows for the increase of speed of rotation of the roll and thus for the

increase of the throughput, while maintaining constant residence time. Experi-

ence indicates that a throughput increase by factor of two to ﬁve, maintaining

the same performance, can be obtained with larger diameter rolls [A23, A13].

4.7 Design of a suspended magnet

Suspended magnets are usually installed over conveyor belts, discharge ends of

feeders or screens and above chutes or launders. Their design is dictated by

the burden depth, the belt speed, the clearance required over the burden and

the size, shape and mass of the tramp iron that is being removed. Strength

and reach of the magnetic ﬁeld and of the magnetic force must, therefore, be

maximized for high e!ciency of the material removal.

A schematic diagram of an electromagnet-based rectangular suspended mag-

net is shown in Fig. 4.48. The magnet consists of an iron yoke and a coil, which

magnetizes the yoke. The magnetic ﬁeld generated at point S ,atdistance}

from the magnet, is the sum of contributions from the magnetized steel and

4.8. DESIGN OF A FERROHYDROSTATIC SEPARATOR 299

Figure 4.49: Pattern of magnetic ﬂux around a suspended magnet.

the coil. Dimensions of individual parts of the yoke determine the distribution

of the magnetic ﬁeld and magnetic force, their value and reach. Using com-

puter modelling, it is possible to investigate the inﬂuence of these dimensions

and to determine the optimum design for a given application. The distribution

of magnetic ﬂux around a suspended magnet is shown in Fig. 4.49, while a

three-dimensional image is presented in Fig. 4.50.

In commercially available suspended magnets, the width 2d

of the magnet

typically ranges from 900 mm to 1400 mm, the depth ranges from 700 mm to

1250 mm and the height K is around 500 mm.

Aluminium is the preferred conductor materials, mainly because of its lower

density. For the same electric power, the mass of the aluminium coil can be

approximately halved, compared with the copper coil [K36]. In addition, the

use of the aluminium foil, rather than of the wire, allows for the increase in

the ﬁlling factor of the winding, by about 40% [K36]. As a result, the number

of ampere-turns can be reduced, or, alternatively, at the constant number of

ampere-turns, a more powerful magnet can be constructed.

4.8 Design of a ferrohydrostatic separator

Commercial and laboratory ferrohydrostatic separators use either an electro-

magnet or permanent magnets to generate the magnetic ﬁeld in the working

space. Of fundamental importance in the operation of separators with magnetic

ﬂuids are the characteristics of the magnetic levitation force, expressed by the

second term on the right-hand side of equation (2.9), namely by M

EuE.These

characteristics are determined by the pattern of the gradient of the magnetic