Prediction of Separation Performance of Dry High Intensity Magnetic Separator for Processing of Para-Magnetic Minerals Sunil Kumar Tripathy, Veerendra Singh & Nikkam Suresh
Journal of The Institution of Engineers (India): Series D Metallurgical & Materials and Mining Engineering ISSN 2250-2122 Volume 96 Number 2 J. Inst. Eng. India Ser. D (2015) 96:131-142 DOI 10.1007/s40033-015-0064-x
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Author's personal copy J. Inst. Eng. India Ser. D (July–December 2015) 96(2):131–142 DOI 10.1007/s40033-015-0064-x
ORIGINAL CONTRIBUTION
Prediction of Separation Performance of Dry High Intensity Magnetic Separator for Processing of Para-Magnetic Minerals Sunil Kumar Tripathy • Veerendra Singh Nikkam Suresh
•
Received: 3 November 2014 / Accepted: 5 January 2015 / Published online: 3 March 2015 Ó The Institution of Engineers (India) 2015
Abstract High intensity dry magnetic separators are gaining popularity for the separation of para-magnetic minerals due to the cost economic factor. Induced roll magnetic separator is found to be an effective dry separator for the separation of fine particles. Separation efficiency of this separator depends on mineral characteristics and the design features of equipment along with the optimization of process variables. Present investigation focuses on the prediction and validation of separation performance of minerals while treating in induced roll magnetic separator. Prediction of the separation is expressed in terms of separation angle at which a particle leaves the rotor surface by using a modified particle flow model derived by Cakir. The validation of the model is carried by capturing the particle trajectory using an image analyzer. It is found that Cakir’s mathematical model produces reliable results and a new model is proposed to increase the reliability of separation angle prediction by including the particle shape factor. Keywords High Intensity magnetic separator Modeling Image processing Particle flow trajectory Magnetic separation Para-magnetic minerals List of symbols I Spitting current (I) K Volume magnetic susceptibility of ore
S. K. Tripathy (&) V. Singh Ferro Alloys Minerals Research Group, Research and Development Division, Tata Steel Ltd., Burma Mines, Jamshedpur 831 007, JH, India e-mail:
[email protected] N. Suresh Fuel and Mineral Engineering Department, Indian School of Mines, Dhanbad, India
a b r R Ff Fm Fgt Fgr Fc ld ls xp h xr x, y l0 jp B0 K 1, K 2 t Sf Sc Sp Vp qp
Angle of side slope of Franz iso-dynamic magnetic separator Diameter of particle Radius of particle Diameter of roll of magnetic separator Frictional force Magnetic force Tangential component of force of gravity Radial component of force of gravity Centrifugal force Dynamic friction coefficient Static friction coefficient Angular velocity of particle Angle of separation of particle Angular velocity of roll Cartesian coordinate Permeability of free space Particle magnetic susceptibility Magnetic induction Material constants Time Shape factor Area of circle Area of particle Volume of the particle Density of the particle
Introduction The science of dry high intensity magnetic separation has experienced exceptional technological advancements in the last decade. As a consequence, new applications and design concepts in these separators have evolved. Consequent to this, highly effective and efficient separators with a wide
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spectrum of industrial applications are now available in a wide variety of designs. Magnetic separation can now be used as an integral part of the primary process and or as a secondary/scavenging operation to produce mineral concentrates or pre-concentrates. The applications of high intensity dry magnetic separators for para-magnetic minerals are well accepted to selectively concentrate para-magnetic particles such as ilmenite [1, 2] or hematite [3, 4] minerals in mineral concentrators. The technique is also used for removing deleterious magnetic elements to purify non-magnetic elements such as in the manufacturing of ceramics or refractories. Also, for recycling and secondary recovery applications with increasing interest using magnetic separation as an explicit method for recovering mineral/ metal values from various process streams and hazardous constituents from waste streams are very common [5–8]. Numerous technological milestones and key drivers of innovations in magnetic separation have resulted in a wide range of magnetic techniques that are available for application in mineral industry. Dry High Intensity Magnetic Separator Many new types of magnetic separators have been developed for the treatment of para-magnetic particles. The working principle of all these newly invented units is magnetic separation along with different force field environment i.e. two or more forces are involved in the separation along with a magnetic susceptibility. There are different approaches for classification of magnetic separators, but the grouping of these units based on the magnetic field intensity can be described as: (A)
Dry permanent magnetic separator: (a) Dry drum magnetic separator (b) Rare earth drum magnetic separator (c) Rare earth roll magnetic separator
(B)
Dry electro-magnetic separator: (d) Induced roll magnetic separator (e) Lift roll magnetic separator (f) Cross belt magnetic separator (g) Cross disc magnetic separator
(C)
Wet permanent magnetic separator: (h) Wet drum magnetic separator (i) Rare earth wet drum magnetic separator (j) Ferrous wheel magnetic separator
(D)
Wet electro-magnetic separator: (k) Wet high intensity magnetic separator (l) High gradient magnetic separator- Vortex magnetic separator, SLON
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(m) Open/close gradient magnetic separator (n) Roll-type wet magnetic separator (o) Cryofilter superconducting separator Further, to simplify and use it in an application front, another classification on this has been proposed as follows: – – –
Low intensity magnetic separators of magnetic field intensity \0.1 T, Medium intensity magnetic separators of magnetic field intensity in between 0.1 and 0.8 T, High intensity magnetic separator of magnetic field intensity [0.8 T.
The working range of all the above mentioned separators is given in Fig. 1. There are several separators which fall under high intensity dry category viz. cross belt magnetic separator (CBMS), permanent roll magnetic separator, induced roll magnetic separator (IRMS), lift roll magnetic separator, isodynamic separator, open gradient magnetic separator (OGMS), high gradient magnetic separators (HGMS), vibrating high gradient magnetic separator/filter and super conducting high gradient magnetic separator [5, 9–22]. Among all listed, isodynamic separator is one of the typical units used principally for quantitative analysis of para-magnetic mineral samples. It is also widely used to characterize the mineral sand sample for measuring the magnetic susceptibility and to simulate the grade-yield curve. The other two, OGMS and HGMS are not successful commercially. OGMS was used for a short period but as its magnetic field intensity is not so effective and distribution is not uniform, it did not gain popularity in the market, whereas, dry HGM separators were also not successful on a commercial scale for the same reason. Major application of HGMS was reported for de-shaling and for the removal of pyrite from coals [23–26]. Few studies were also focused on improving the efficiency of the separation by incorporating fluidization phenomenon to the existing system [27–29]. These studies were mostly focused on the removal of pyrite from coal fines at the laboratory scale but found to be inefficient. More research studies are yet to be undertaken in these areas, to have a cost effective and efficient process for the coal preparation like in any other mineral separation. Among these, IRMS is an important unit which is widely used for the separation of para-magnetic minerals and the details about the principle along with working mechanism is narrated in the published literature [3]. Moreover, dry magnetic separators are very useful for the separation of coarser particles where subsequent processing is required in wet method. There are several advantages of the dry separation process when compared to the wet processes. Dry separation has its own advantage over the wet, such as, water consumption, retrieving the water for reuse, tailing pond management etc. [12]. However, easy applicability of technique attracts the researcher to work on the design and optimization perspective
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Fig. 1 Working range of different magnetic separators used in mineral industry
of these separators but the fundamentals of magnetism and modeling aspects are yet to be understood fully. Modeling of High Intensity Magnetic Separator There are a few articles narrating the particle flow modeling in the magnetic based separator. Particle trajectories of the newly-developed two-drum eddy current separators were simulated by the ECSIM software package and it was found that small particles separated by improving the magnetic field intensity and increasing the rotation speed of the magnetic drum assembly [30]. The effect of the gravitational and inertial forces, for various configurations, on the particle capture cross-section was investigated and it was observed that with a decreasing size of a particle, the influence of both forces tends to decrease [31]. Modeling of particle flow in magnetic drum separator for the small particle was analysed and found to be in good agreement with the filed distribution [32]. The particle trajectory of a para magnetic particle between the main belt and cross belt surfaces was calculated by using the flux map. Further, it was found that the ratio between the critical susceptibility for a moving belt and the critical susceptibility for a stationary belt was found to be relatively constant over the normal range of pole air gaps for a given belt speed in a cross belt magnetic separator [33]. It is found that most of the above research work have emphasized on numerical modeling for the particle flow trajectory in magnetic separators. There is a mathematical expression to describe the particle flow in the induced roll magnetic separator. Details about this model was explained by Cakir et al. [30]. Various other attempts also narrate the particle trajectory in roll or drum magnetic separator [9, 31, 34–36].
In addition to these, a few statistical as well as neural based network models were reported in the literature for predicting the performance of the unit. The effect of rotor speed, feed rate and applied current were varied to understand the separation of the heavy minerals and the results were analyzed statistically [2]. Similarly, another attempt was made to develop the second order quadratic equation for the prediction of grade (in terms of iron and silica content) and recovery in the magnetic product of IRMS while treating low grade hematite fines [3]. Also, an effort was made to derive the optimum levels of magnetic field intensity, rotor speed and feed rate of IRMS for producing maximum grade and recovery. In addition to this, effect of variables on the studied responses is explained by using these equations. This type of modeling methodology helps in identifying the significant and insignificant variables by carrying out limited tests. However, the developed models fail to explain the actual particle separation behavior of IRMS. In 2009, Singh developed a neural based network model for predicting the performance of IRMS while treating low grade ferruginous manganese fines [37]. These models are localized and specific for a particular case study. Also, it is difficult to predict the performance, once the level of the variables deviated from the studied levels which are the main demerit of this type of model. These developed models were found to be effective in predicting the particle separation performance but the separation feature in terms of physics for a given magnetic field was difficult to narrate. It was mentioned that modeling software has been developed for the simulation of magnetic field distribution around a rotor which are used for the selection and design of the separator [18]. There was an effort to model the magnetic field on the surface of
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a magnetic drum separator, but has difficult to replicate for the high intensity separators [22]. In the present investigation, an effort was made to understand the effect of different operating parameters on the particle trajectory in a magnetic field while treating paramagnetic minerals. The particle trajectory by using Cakir model was validated and a new model was proposed to improve the accuracy of results using separation angle as a performance indicator.
Feed Bridge Bar
Coil 1st
Magnetics Primary Pole 2nd Magnetics
Materials and Methods
Primary Pole
Non-magnetics
Fig. 2 Schematic diagram of particle separation in a double stage IRMS
Induced Roll Magnetic Separator Dry high intensity magnetic separator is designed to separate weak magnetic and nonmagnetic materials. It uses a specially designed circuit using variable voltage transformer to produce the magnetic field in between 0 and 16,000 Gauss. The magnetic separation studies were carried out by using Induced Roll Magnetic Separator of laboratory model (Readings of Lismore, Australia) and the rotor speed varied to a maximum of 300 rpm. The separation of particles in the separator mainly depends on particle size, density, magnetic susceptibility, shape along with the machine operating parameters (magnetic field intensity, rotor speed, solid feed rate, etc). Figure 2 shows the schematic particle trajectory of magnetic and nonmagnetic particles in an induced roll magnetic separator with double stage separation. In the present investigation, magnetic separation studies were carried out in an induced roll magnetic separator which is widely used for concentrating paramagnetic minerals. The induced magnetic roll separator consists of a revolving laminated roll formed alternately of magnetic and non-magnetic discs. The roll is placed between specially shaped poles of an electromagnet and the electromagnet induces a magnetic field in the magnetic laminations of a roll forming local regions of high magnetic field gradients. Material to be treated is fed in a controlled thin stream by a vibratory feeder to the top of the roll. As the roll revolves, the material passes through a narrow gap between the pole of the magnet and finally the roll and the non-magnetic particles are discharged from the roll. Para-Magnetic Minerals and Experimental Procedures Experimental studies were carried out with three different types of minerals of manganese, ilmenite and magnetite ores of particle size below 150 lm. The mass magnetic susceptibility of these minerals was measured by Iso-Dynamic Separator (Make: FRANTZ Model LB-1). Spitting
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current (I) was measured and Hess equation was applied to calculate the mass magnetic susceptibility (x) of minerals at an angle of side slope (a). It is defined as [38]: x¼
20 sin a 106 ðcgsÞ I2
ð1Þ
Test balls of size 2–10 mm diameter were made using the mineral fines with 10 % moisture. The details of the magnetic properties of these ores are tabulated in Table 1. These balls were cured at 100 °C for 30 min to improve the strength of the balls. Then, these balls were tested in repetitive experiments to capture the ball trajectory by digital imaging. It was found that 3 mm balls are the most suitable for studies because the imaging system could not perform appropriate operation for other size ranges. A digital video (Canon 350D) was used to capture the quality of images which was further improved by MATLAB software. Modeling studies Modeling studies were carried out for particle separation in IRMS by using numerical methods proposed by Cakir and the validation was carried out by image based modeling. For better understanding of these, a brief description about these two are narrated further. Numerical Modelling A particle of diameter b is moving on the surface of the roll (Diameter of R) of magnetic separator. Particle trajectory for this particle can be classified in three different phases as shown in Fig. 3. In the phase 1, particle accelerates under influence of frictional force (Ff) and tangential component of force of gravity (Fgt). The particle trajectory in this condition can be expressed by Eqs. 2–4 [30]. The first phase ends when particle reaches the roller speed xr i.e. (xp ¼ xr ).
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Table 1 Magnetic susceptibility of materials Material
Angle of side slope (°)
Split Current (Amp.)
Mass magnetic susceptibility(x) (m3/kg)
Volume magnetic susceptibility (k)
Magnetite
25.00
0.03
9.40 9 10-3
47 9 10-3
0.12
4.75 9 10
-4
23 9 10-4
1.55 9 10
-4
7 9 10-4
Ilmenite
20.00
Manganese
20.00
Feed
0.21
d2 h g g sin h ls cos h ¼ dt2 ðR=2Þ þ ðb=2Þ ðR=2Þ þ ðb=2Þ # 2 dh Fm þ dt qp Vp ððR=2Þ þ ðb=2ÞÞ
ωp< ωr Phase -1
ωp = ωr Phase - 2
ωp > ωr
Fc
Ff
ð8Þ
Phase - 3
Initial conditions
θ
Fm
ωr
h ¼ ho1
Fg
dh ¼ xr dt
Roll/Drum
In case of roll magnetic separator the first phase is absent since a particle is deposited on the roll at speed of roll. When the particle leaves the roll, it is being acted upon by the force of gravity and magnetic force. Schematic diagram of situations are shown in Fig. 3. The equations of motion are as follows:
Fig. 3 Particle motion on roll of magnetic separator
Ff ¼ ld Fm þ Fgr Fc
ð2Þ
Fgt ¼ gVp qp Sinh
ð3Þ
2
d h g sin h ¼ dt2 R þ b" # 2 g dh Fm cos h þ ld þ Rþb dt qp Vp ðR þ bÞ
ð4Þ
When the particle achieves the speed of roll, static friction coefficient ls replaces the dynamic friction coefficient. The particle then moves with angular velocity equal to the speed of roll. Particle path in the second phase can be defined by Eqs. 5 and 6. Ff ¼ ls Fm þ Fgr Fc ¼ Fgt ð5Þ 2
d h ¼ 0; dt2
and
dh ¼ xr dt
ð6Þ
When tangential component Fgt, of the force of gravity becomes greater than the force of friction Ff then the particle detaches from the roll. The motion of particle then enters into the third phase. In this phase, the particle begins to accelerate as it slips from the roll surface. The radial component of gravity decreases in this region and the particle leaves the roll surface when centrifugal force exceeds it. Fc ¼ Fm þ Fgr ¼ Vp qp xr ðR=2 þ b=2Þ
ð7Þ
d2 x Fm x pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ dt2 qp Vp x2 þ y2 d2 y Fm y pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ g 2 2 dt qp Vp x þ y2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pðb=2Þ2 n h x2 þ y2 exp 2k2 3 i h pffiffiffiffiffiffiffiffiffiffiffiffiffiffi b=2 R=2 exp 2k2 x2 þ y2 io þb=2 R=2
ð9Þ ð10Þ
Fm ¼ l0 jp B20
ð11Þ
Initial conditions xðt¼0 Þ ¼ ðR=2 þ b=2Þ sin h02 yðt¼0 Þ ¼ ðR=2 þ b=2Þ cos h02 dx ¼ x0 ðR=2 þ b=2Þ cos h02 dt dy ¼ x0 ðR=2 þ b=2Þ sin h02 dt Detailed mathematical analysis for the particle flow in a magnetic field was explained by Cakir et al. [30]. Various other attempts were also made vis-a`-vis the particle trajectory in roll or drum magnetic separator [22, 31–33, 39]. However, in the present case; equations were solved using the computational programming language (C language) and the particle trajectory was plotted using the Gnuplot software.
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The operating conditions were changed and particle trajectories were simulated and compared with the real particle path found by image based modeling. Image Based Modeling Image processing is one among the emerging research fields mainly due to development of high speed computing facilities over the last few decades. It has already proved its applicability in the area of photography, biology and cinema. There are various ways to use the image based information for research work and a few examples related to particle processing are mentioned in the literature [40– 44]. Image based modeling technique which replicates a system using the data recovered from a real system images and Geometric curve evolution using image processing is well explained by Fre´de´ric [45]. This is a unique application of the concept to model the particle trajectory. The rapid development in the area of information technology enables the scientist to view the process insights very closely and in this case the authors have tried to visualize the real particle path on a roll magnetic separator. Bunches of similar particle sizes were fed at defined process parameters and images were captured at different positions. This method was repeated for different operating conditions and real path of the particle was defined. This concept was applied to modify the existing mathematical models. The numerical and real particle trajectories measured by imaging for three different types of particles are depicted in Figs. 4, 5 and 6.
Results and Discussion Induced roll magnetic separation process primarily depends on magnetic susceptibility of the material/mineral, magnetic field, particle size and roll speed. Studies were carried out to identify the dominating process variables. The existing mathematical models are used to measure the particle trajectory and effect of various process variables on separation efficiency. Particle trajectory is largely controlled by magnetic, centrifugal, and gravitational forces. The increased magnetic force increases the length of phase I and II. The particle covers a longer distance along the roll and it detaches at higher angle of separation. The most reliable mathematical model for particle trajectories was proposed by Cakir et al. This model was validated in the present investigation by particle imaging. Trajectories of different types of magnetic particles were theoretically calculated using Cakir model and these were validated by image based modeling. The mathematical results of the particle trajectories of ilmenite particles are shown in Fig. 7. A particle of 1mm
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diameter reports at 5, 4 and 1 away from the roll center at applied magnetic field strength of 1000 gauss, 5000 gauss and 10,000 gauss respectively. The other parameters such as particle size of radius of 1 mm and speed of the rotor at 100 rpm were kept constant. These parameters helped to position the splitter according to the applied magnetic field. Similarly, a significant difference in magnetic susceptibilities of materials improves the separation efficiency which is shown in Fig. 8. Figure 8 shows that separation of highly magnetic (P1) and feebly magnetic (P3) particles are relatively efficient than the separation of moderately magnetic (P2) and feebly magnetic particles. The other parameters viz. 0.5 mm radius of the particle, magnetic field intensity of 1000 gauss and speed of the rotor was maintained at 150 rpm. Further, three different radii of a feebly magnetic mineral (manganese) were selected to compare the effect of particle size on separation. The other parameters viz. 5000 gauss of magnetic field intensity and rotor speed of 150 rpm were kept constant during the experiment. It shows that when particle size of manganese increases, the centrifugal force starts dominating and particle leaves the roll at lower angle. This shows the importance of narrow size ranges for efficient magnetic separation and shown in Fig. 9. Particle diameter of 3 mm (feebly magnetic material) was rolled over the magnetic separator at four different roll speeds viz: 50, 100, 150, and 200 rpm and flow trajectories are shown in Fig. 10. Particle trajectories in a magnetic rotor are given as P1, P2, P3 and P4 for roll speed 50, 100, 150, and 200 rpm respectively. From Fig. 10, it is observed that at higher rpm, centrifugal force starts dominating on a particle and it can outplay the magnetic force. This effect can reduce the separation efficiency of the magnetic separation process. Therefore, a higher rpm is desired for finer sizes and lower rpm can produce better results with coarser particles. However, optimization of the rotor speed is necessary based on the characteristics of the treating minerals. Image Based Modeling The particle trajectory was identified by collating the information retrieved from different images at different particle locations during the particle motion in different operating conditions. The particle trajectory calculated by the mathematical model has been compared with the actual particle trajectory identified using image based system. This concept can be used to modify the existing mathematical models by using the curve fitting techniques. (a)
Ferruginous manganese ores contain Mn of 40 % with Fe of 16 % (having density 4.5 g/cc). Volume
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(a)
(c) Fig. 4 Image-based modeling for ferruginous manganese ore samples. a IL1 (b 3 mm, Rpm 200, Bo 5,000 gauss, k 7 9 10-4 (SI)), b IL2 (b 3 mm, Rpm 200, Bo 7,000 gauss, k 7 9 10-4 (SI)), c IL3 (b
(b)
(d) 3 mm, Rpm 220, Bo 7,000 gauss, k 7 9 10 -4 (SI)), d IL4 (b 3 mm, Rpm 250, Bo 10,000 gauss, k 7 9 10-4 (SI))
(a)
(b)
(c)
(d)
Fig. 5 Image-based modeling for ilmenite ore samples. a M1 (b 3 mm, Rpm 100, Bo 2,500 gauss, k 23 9 10-4 (SI)), b M2 (b 3 mm, Rpm 100, Bo 3,000 gauss, k 23 9 10-4 (SI)), c M3 (b 3 mm, Rpm
170, Bo 3,000 gauss, k 23 9 10-4 (SI)), d M4 (b 3 mm, Rpm 170, Bo 4,000 gauss, k 23 9 10-4 (SI))
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(a)
(b)
(c)
(d)
Fig. 6 Image-based modeling for magnetite ore samples. a FM1 (b 3 mm, Rpm 250, Bo 1,000 gauss, k 47 9 10-3 (SI)), b FM2 (b 3 mm, Rpm 250, Bo 1,200 gauss, k 47 9 10-3 (SI)), c FM3 (b 3 mm, Rpm
Fig. 7 Effect of magnetic field strength on magnetic separation of ilmenite particle at constant particle size, roll speed and magnetic field intensity
magnetic susceptibility of ores was measured by IsoDynamic separator and was reported to be 7 9 10-4 (SI). The fines of these ores were grounded to pass 150 lm and converted to 3mm diameter balls. These balls were then used for experimentation. The detachment of the ball and magnetic roll was
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300, Bo 1,200 gauss, k 47 9 10-3 (SI)), d FM4 (b 3 mm, Rpm 300, Bo 1,500 gauss, k 47 9 10-3 (SI))
Fig. 8 Effect of magnetic susceptibility of particle on magnetic separation at constant roll speed and magnetic field intensity
measured and the angle was compared with the theoretical value calculated by Cakir model. The comparative particle trajectory shown in Fig. 11 reveals that there is significant difference in separation angle in lower magnetic field intensity but there is an acceptable resemblance for rest of the values. (b) 3 mm diameter balls of ilmenite (having density 4.8 g/cc) were made and the trajectories of these balls
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139 120.00
Separation Angle -Theoretical (Degree) Separation Angle-Measured(Degree)
100.00
%, Error
80.00 60.00 40.00 20.00 0.00 -20.00
Rpm : 200, B0 : 5000, r : 3mm
Rpm :200, B0 : 7000, r : 3mm
Rpm :250, B0 : 7000, r : 3mm
Rpm :250, B0 : 10000, r : 3mm
Fig. 11 Comparative analysis of measured and theoretical separation angle for manganese particle separation Fig. 9 Effect of particle size on magnetic separation at constant magnetic susceptibility, roll speed and magnetic field intensity Separation Angle -Theoretical (Degree)
135
Separation Angle-Measured(Degree) %, Error
115 95 75 55 35 15 -5 -25
Rpm :100,B0 : 2000,Rpm :100,B0 : 3000,Rpm :170,B0 : 3000,Rpm :170,B0 : 5000, r: 3mm r: 3mm r: 3mm r: 3mm
Fig. 12 Comparative analysis of measured and theoretical separation angle for ilmenite particle separation
Fig. 10 Effect of rotor speed on magnetic separation at constant magnetic susceptibility, particle size and magnetic field intensity
140 120
(c)
were monitored for four different conditions. The comparative analysis is shown in Fig. 12. It shows that model and experimental results differ for higher magnetic intensity at higher rpm values. Magnetite sand samples (having density 5.0 g/cc) were taken as highly magnetic material and volume magnetic susceptibility of these samples were found to be 47 9 10-3 SI. Balling of these samples was found to be difficult and particle adherence to the roll was observed at lower rpm. It was difficult to measure the angle of separation of particle and high rpm was required. Results are shown in Fig. 13. The results have lower experimental values for higher magnetic field and rpm.
Separation Angle -Theoretical (Degree) Separation Angle-Measured(Degree) %, Error
100 80 60 40 20 0 -20
Rpm :250,B0 : 1000, r 3mm
Rpm :250,B0 : 1200, r 3mm
Rpm :300,B0 : 1200, r 3mm
Rpm :300,B0 : 1500, r 3mm
Fig. 13 Comparative analysis of measured and theoretical separation angle for magnetite particle separation
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Fig. 14 Surface plot of predicted and measured separation angle along with process variables
Proposed Modified Model The Cakir model produces significantly reliable results. Separation angle measured by the model and experimental results were compared and it shown R2 value more than 0.70. However, accuracy was low for moderately applied magnetic field and lower roll speed. It was observed that comparison of particle trajectory was not possible by the existing image acquisition system. A high-speed digital camera to capture the particle path for fraction of second and comparison of frames were needed. However, an attempt was made by comparing the separation angles which mainly decide the particle trajectory. The error found in theoretical and measured separation angles showed a significant (p value = 0.00001, R = 0.50) correlation with roll speed. Cakir suggested that phase 1 and 2 would be absent from the induced roll magnetic separator but in the current study it was found that when the particle leaves the roll surface in first quadrant it shows a positive error. The measured separation angle is less than that calculated by Cakir model. The main cause is that particles do not roll with the roll speed and its angular velocity is lower than that calculated. The particle shape and size are also two important factors, which decide the angular velocity of a particle. A spherical particle will achieve the roll speed after rolling for a while. The magnetic intensity of applied field also plays an important role since at high intensity, a high intensity particle stick to the roll, and achieves the roll rpm. A shape factor has been added to modify the particle angular velocity and it depends on the particle size and shape. Magnetite ore balls are less spherical than the ilmenite and ferruginous manganese ores. Comparative analysis of proposed model and Cakir model is given in Fig. 13. It shows that the surface plot for the measured and that proposed by the new model follow
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the same trend, whereas Cakir model produces slightly higher values. The correlation coefficient between the measured and new model is 0.87 and same was 0.70 for Cakir model and the measured. Figure 14 shows the sensitivity of separation angle with the other process variables for all the three cases. It also indicate that separation angle measured by Cakir model is more sensitive to roll speed (rpm), whereas measured and proposed models do not show the same trend. Angular velocity of particle is modified and it is multiplied with a shape factor (Sf). The shape factor was decided by analyzing the shapes of the ore pellets used for the experimental studied. The modified model of Eqs. 5 and 6 is given in Eq. (12). pffiffiffiffiffiffiffiffiffiffiffiffiffiffi i pb2 n h Fm ¼ l0 jB20 exp 2k2 x2 þ y2 b=2 R=2 h 3 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi io exp 2k2 x2 þ y2 þ b=2 R=2 ð12Þ Initial conditions xðt ¼ 0Þ ¼ ðR=2 þ b=2Þ sin h02 yðt ¼ 0Þ ¼ ðR=2 þ b=2Þ cos h02 dx ¼ Sf x0 ðR=2 þ b=2Þ cos h02 dt dy ¼ Sf x0 ðR=2 þ b=2Þ sin h02 dt Sc Sf ¼ ¼ (Area of particle / circle) Sp Conclusion Efficiency of Induced roll magnetic separator depends on particle size, roll speed, applied magnetic flux and
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magnetic susceptibility of materials. In the image-based modeling, it was found that Cakir model produces acceptable results and the regression coefficient between measured and calculated was 0.70. The particle shape plays an important role in the real system and it does not achieve the roll speed instantly as Cakir model considered. Analysis of images revealed that particles do not move instantly with roll speed in roll magnetic separation as suggested by Cakir Model. But in a real time process, the particles flow in a magnetic field also depends on the particle shape. The non-spherical particles slip over long distances and leave the roll without achieving the roll speed for higher roll speeds, small particle size and low applied magnetic flux. This problem was modified by multiplying the particle angular velocity with the shape factor. The regression coefficient was improved to 0.87 while predicting the separation angles by using the proposed model. The proposed model can be utilized to optimise the magnetic separation process while treating paramagnetic minerals. High speed imaging with a magnification system can improve the model reliability further by locating the particle position according to a frame-by-frame movement.
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