Luo A.C.J. (Ed.) Dynamical Systems: Discontinuity, Stochasticity and Time-Delay

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424 J. Hoelscher et al.

33.2 Technical Approach

The problem can be stated as follows: Develop a technique to monitor the particle

size (through the speciﬁc gravity of the slurry), and then based on that knowledge

control the splitter setting. This problem has the following three components:

1. Find a technique that can monitor the particle size in real time

2. Actuate the splitter

3. Develop a microprocessor based control system that uses the sensor data and

actuates the splitter appropriately

The whole system should be:

1. Economical

2. Reliable

3. Robust

4. Easily retroﬁtted to existing set-ups

5. Zero or very little maintenance

This chapter describes the control system, actuator, and the GUI developed for the

project. For demonstration purposes, the mechanical strain gage system, described

in the chapter, is outlined below. The main idea is to estimate the speciﬁc gravity of

the slurry at multiple lateral positions as it ﬂows of the slide.

Figure33.2 shows a schematic of the concept which includes a sensing system,

a microcontroller, and an actuated splitter. The slurry will ﬂow in to cups whose

volume is known. As these cups ﬁll up to the brim, a strain will be recorded on the

cantilevers which will be monitored by the microprocessor. We are only interested

in the maximum strain, as that indicates the weight of the slurry when it completes

ﬁlling up the cups. This is then used to estimate the speciﬁc gravity of the slurry

on either side of the divider, and an appropriate change can be made to the actuator

Fig. 33.2 Control system concept

33 Automating of Spiral Concentrators in Coal Preparation Plants 425

driven divider. Once reliable readings are taken, then a mechanism could be used to

empty out the cups, or one could use an “off-center center of gravity” that would

topple the cup contents as soon as it is completely ﬁlled. Once the cups are emptied,

the process can start all over again. The greatest advantage of this method is its

simplicity, robustness, and economical nature. The draw back on it is that it relies

on the correlation of speciﬁc gravity to particle size. We do intend to study this

correlation, and if it exists, then this will be the “approach of choice” for us.

The system is implemented using ﬁve subsystems:

1. Metal arms with mounted strain gages to monitor the stress because of weight in

the channels.

2. Wheatstone bridges to create variable voltage outputs based on the weights on

these arms.

3. Differential ampliﬁers which amplify the difference in the values obtained from

the Wheatstone bridges.

4. A PIC microcontroller whose program can monitor the voltages provided by the

ampliﬁers to compute the difference in weight applied to the arms and control

a motor to direct the ﬂow of liquid in attempt to equalize the weight applied to

each arm.

5. A motor which will move an apparatus which will redirect the ﬂow of the coal-

ﬁlled liquid in order to equalize the weight in the channels.

33.2.1 Metal Arms and Wheatstone Bridge

Figure33.3 has shown the laboratory setup for the control system. The arms have

had strain gages mounted on them, which offer approximately 120  Of resistance

Fig. 33.3 Laboratory set up for control system

426 J. Hoelscher et al.

unstrained. When pressure is applied, this value can increase up to approximately

1. The Wheatstone bridges, which are identical, are accomplished by three equal

resistances in addition to the resistance that the gage offers. Each is equivalent to

120 , which is accomplished by 110 and 10  resistances in series.

33.2.2 Differential Ampliﬁers

To amplify the voltages received from the wheatstone bridges, ampliﬁer tlv2464,

which includes four ampliﬁers, two of which are used for the two bridges.

Figure33.4 shows the schematic for the signal conditioning circuiting. The diagram

is given below.

R1 is set at 1 k with R2 at 820 k being used for the gain control. R3 is 1:5 M

and is used to offset the approximately 1.4 V at the output when no stress is on either

arm due to the slightly unbalanced bridge and high gain. R2 will change as different

gain requirements arise.

33.2.3 PIC Microcontroller and Motor

The PIC microcontroller used in this system is the PIC18f4550. It is clocked at 12

MHz, and it continuously monitors the voltages output by both differential ampli-

ﬁers. Based on the difference in these values, with attention paid to which is greater,

it will instruct the motor to move to one of ﬁve degree positions: 30, 15, 0, 15,

30. The voltages read in are translated to hexadecimal numbers between 0 and 255,

and a table is given below to illustrate the logic of the system. The hexadecimal val-

ues given above are subject to immediate change due to further system calibration.

This also applies to the degree positions as they are more ﬁne-tuned. The high hex-

adecimal values shown for the right arm being greater are due to the differencebeing

less than 0, and the value being “wrapped around.” Avoiding inconclusive logic in

the 50 to B0 value range is accomplished by noting which arm is experiencing the

Fig. 33.4 Circuiting

schematic

33 Automating of Spiral Concentrators in Coal Preparation Plants 427

greater weight. The motor in place is controlled by digital pulses, spaced 20 ms

apart. Based on the length of the pulse (1.25–1.75ms), the motor will position itself

from 0

to 180

, respectively. The motor’s 90

position is taken as our neutral po-

sition, with our positions for the motor being effectively 60, 75, 90, 105, and 120

from left to right. These values are accomplished by applying the proportion of de-

gree movement to total pulse range to obtain the desired pulse length, with 1.5 ms

being 90

, or our neutral. The values for 60, 75, 90, 105, and 120

are 1.417, 1.4583,

1.5, 1.5417, and 1.583ms respectively. Of course, these values are also subject to

further reﬁnement. In addition to this, the current system also includes an RS232

chip which allows us to communicate to the PC through the HyperTerminal pro-

gram. Currently, this program is used to monitor the voltage values in hex, as well

as the current position the motor is at for debug and calibration purposes.

A Graphical User Interface (GUI) has been designed that does the following:

 Sets up communication with the PIC microcontroller

 Sets up the number of sensor channels

 Sets up communication with the motor and displays the position

 Collects data, stores it, and plots it

33.2.4 Demonstration

This section shows a demonstration of the strain gage based mechanical system

as hooked to the motor. One arm (with strain gage 1) was pushed down, and this

causes the motor to move in one direction (eventually this will be controlling the

splitter). An applied force on the other arm causes the motor to move in the opposite

direction. Given below are screen captures of the GUI in the set-up phase as well as

the operation phase (see Fig. 33.5).

In the set-up phase, set the serial port to COM 1 or 2. Set the Baud rate to 9,600.

Then set the number of channels, and pick on online or ofﬂine operation.

In the operation phase, as one arm was pushed down, the strain gages show a

strain, and the motor rotates a predetermined angle; as highlighted in Fig. 33.5.

Fig. 33.5 Computer based

GUI

428 J. Hoelscher et al.

Fig. 33.6 Actual system

assembly

33.2.5 Assembly

Figure33.6 shows how the samples will be taken from the slurry ﬂow. Since the

spiral has a curved proﬁle from the inside to the outside, the blue bars are adjustable

in length and angle to accommodate for any misalignment. The blue bars are held

in place by clamping blocks. Attached to the end of the blue bars will be the cups

that will draw samples from the ﬂow. On the top of the blue bars, strain gages will

be placed as far away from the cups as possible without disrupting the function of

the clamping blocks. Both of the cups will be attached to a central shaft that for

preliminary experiments will be turned by hand and in the ﬁnal stages driven by

a motor.

33.3 Mechanical System Design

A new system has been designed that takes advantage of the different speciﬁc

gravity of the slurry at different points of the cross section of the spiral. Different

speciﬁc gravity implies that the force per unit area of impact will be different at dif-

ferent points of the cross section. Hence, a mechanical ﬁxture has been designed that

has metal ﬁngers in contact with the ﬂoor and are in the normal ﬂow direction of the

slurry. The different ﬁngers form one side of the ﬁxture to the other will experience

different forces and will want to rotate the ﬁxture. The ﬁxture is constrained by a

spring, but the rotation is monitored, and gives an indication of the change in the

speciﬁc gravity of the slurry at the different locations.

The change in the angle of the vertical rod is used as a sensor input to the control

system. This mechanical system needs to be tuned but is expected to be robust,

cheap, and yet effective (see Fig. 33.7). On the metal ﬁngers are replaced by ﬁns in

33 Automating of Spiral Concentrators in Coal Preparation Plants 429

Fig. 33.7 Alternate design for sensing slurry speciﬁc gravity

Fig. 33.8 A more robust

design

the shape of a vertical wing. The principles behind the two systems are the same.

However, with the probes being shaped like a wing creates less disruption in the

ﬂow. The ﬁns are able to rotate to adjust to the ﬂow. The entire mechanism rotates

because of a change in the ﬂow (see Fig. 33.8).

Before testing the idea on the spiral, a mathematical approach was taken to see

if the mechanism would work as desired. A few assumptions were made and are as

follows: no loss due to friction in the bearings, only drag force acts on the wings,

motion is constrained to the horizontal plane. To further test mathematically, the left

430 J. Hoelscher et al.

ﬁn is placed in section C, while the right ﬁn is placed in section D. Measurements

have been taken for ﬂow rate and pulp density for all six sections. (Measurements

for four different situations are shown in Sect. 33.5.)

If the force acting on the left wing is greater than that on the right wing, a mo-

ment will occur and the spring will deﬂect to counteract the moment. By summing

moments about the center, the equation simpliﬁes and becomes

 F

DF

L; (33.1)

where F

is the drag force acting on the left wing, F

is the drag force acting on

the right wing, and F

is the force being applied by the spring. F

and F

can be

written as

D C



; (33.2)

D C



; (33.3)

where C

and C

are the drag coefﬁcients, 

and 

are the pulp densities for

the left and right, A

are the cross sectional areas of the ﬁn, V

are the ﬂow

velocities for left and right ﬁns respectively. The cross sectional areas for both of

the ﬁns are equal and substitution and simplifying (33.1) becomes



 C



D2

: (33.4)

The coefﬁcient of drag can be found by calculating the Reynolds number and using

Figure 11.6 from Crowe et al. [7]. Figure 11.6 is a graph that gives the coefﬁcient

of drag with respect to the Reynolds number for a ﬁn with the length being four

times that of the width. The ﬁn for the mathematical model has a length of 4 cm

and a width of 1 cm. In calculating the Reynolds number, two more assumptions are

made. The ﬁrst being the height does not change between section C and D and since

the slurry consists of roughly 20–30% solids, the dynamic viscosity of the slurry is

taken to be that of water at 30

C for both sections. The dynamic viscosity of the two

sections of slurry may be higher or lower than that of water; however, the difference

in the viscosity between the two sections should be rather small. Table 33.1 shows

the calculations made.

Table 33.1 Calculations made

Section

Volumetric

ﬂowrate

LPM

Pulp

density

.kg=m

Section

width

(m)

Flow

height

(m)

Area

Velocity

(m/s)

Assumed

viscosity

.Ns=m

Fin

width

(m)

Reynolds

number

C 4.27 1.50 0.0508 0.003 0.0001524 0.467 7.97E04 0.01 8.79E C 00

D 8.8 1.34 0.0698 0.003 0.0002094 0.700 7.97E04 0.01 1.18E C 01

Values taken from Run 1 from previous experiments

Further results can be seen in Sect. 33.5

33 Automating of Spiral Concentrators in Coal Preparation Plants 431

A problem occurs when using the ﬁgure relating the Reynolds number with the

coefﬁcient of drag. The problem occurs because the Reynolds number is around

9–10. The Reynolds number for the given application of the ﬁn ranges from 200 to

. Instead of using the ﬁn design, if a circular cylinder is used, then from Figure

11.6 the coefﬁcient of drag for each of the sections is 2.9 and 2.8 respectively. This

small change limits the ability to notice any small changes present in the ﬂow. Even

if the correct dynamic viscosity for the slurry at different solid percents and pulp

densities are found, the coefﬁcient of drag may be too small to have any affect.

However, if the velocity or volumetric ﬂow rate for a given section is needed to be

measured, this mechanism may be useful.

33.4 The Need for a Model

The need for a model arose out of noticing trends in the data collected on a previous

washability analysis. In the washability analysis, eight runs were made, four on a

rougher coal spiral and four on a rougher cleaner coal spiral. For each set of four,

the volumetric feed rate and solid % were varied as seen in Table 33.2.

For each of the spiral sections (A–F), the volumetric ﬂow rate, solid %, pulp

density, slurry mass ﬂow rate, water mass ﬂow rate, and the ash percentage of prod-

uct/tailings per size fraction were measured or calculated. In looking over the data,

several correlations were seen in the data sets for each of the coal spiral designs.

In Table 33.3, one can see how the volumetric ﬂowrate and solid % affects the pulp

density. As the volumetric ﬂowrate increases from 75 to 150 LPM and the solid

% remains roughly constant at 33%, the pulp density of 1:34 kg=m

shifts roughly

one trough section from C to D. Likewise with a lower solid %, the pulp density of

1:34 kg=m

shifts from B to C. (The highlighted box may be considered an error

during the sampling.)

Table 33.2 Volumetric feed

rate and solid %

Four sets of data of primary interest

Rougher coal

spiral

Volumetric feed rate

LPM Solid %

Run 1 150 33.78

Run 2 75 33.44

Run 3 90 20.34

Run 4 150 20.03

Table 33.3 The volumetric ﬂow rate and solid % affects the pulp density

Pulp density per trough section

Flow rate LPM Solid % A B C D E F

150 33.78 1.59 1.58 1.50 1.34 1.20 1.19

75 33.44 1.54 1.49 1.36 1.21 1.21 1.17

150 20.03 1.48 1.68 1.33 1.20 1.25 1.10

90 20.34 1.77 1.34 1.23 1.17 1.17 1.09

432 J. Hoelscher et al.

Fig. 33.9 Pulp density variation in a spiral cross section

Figure33.9 is a graphical representation of the above table for the six locations

on the last part of the spiral cross-section (1–6) going from the inside to the out-

side. A splitter is superimposed to illustrate how a comprehensive model would be

beneﬁcial for developing a way to control the splitter’s position.

Some observations:

1. There is a considerable density change in the middle, but not as much at the inner

or the outer sides.

2. For the same LPM, i.e., LPM 150, there is a shift of density from 1.3 to 1.5 at

location 3 and 1.2 to 1.35 at location 4 as the solid % changes from 20 to 30%.

This is the location where the splitter position can make a difference.

3. For the same solid %, i.e., 20%, there is a smaller change in density due to the

LPM. The change is 1.24–1.32 at location 3 when the ﬂow changes from 90 to

150, and 1.18 to 1.25 at location 4 for the same change in ﬂow.

4. Overall, for different ﬂows and solid %, the change in density could be anywhere

from 1.2 to 1.5 at location 3 and 1.15 to 1.35 at location 4. This is signiﬁcant and

a strong proponent for a control system for the splitter.

However, the pulp density is not an accurate measurement for the amount of ash

in each section. In comparing the pulp density measurements of sections D and E

from the 90 LPM 20.34% Solids and the product ash percentage for those same

sections, a pulp density measurement of 1:17 kg=m

correlates to a 8.75 or 7.09%

ash content.

33 Automating of Spiral Concentrators in Coal Preparation Plants 433

Fig. 33.10 Product ash % vs. spiral trough section

Table 33.4 Product ash % vs. spiral trough section

Initial conditions Trough section

LPM Solid % 1 2 3



150 33.78 Product ash % 26.21 21.44 18.56 13.89 12.03

75 33.44 23.65 16.96 13.79 11.38 9.08

90 20.34 21.46 13.92 11.17 8.75 7.09

150 20.03 26.54 16.25 13.61 11.20 9.08



C100 Mesh

In Fig. 33.10, the data presented is the product ash % vs. spiral trough section.

In the chart, the 150 LPM 20.03% Solid line corresponds with the 75 LPM 33.44%

solid line from section 3 to 5 (Table 33.4).

Since two different ﬂow rates at different solid % behave almost identically,

it may be practical to measure these two variables plus the solid material density

(if needed) in order to control the splitter position. The solid material density may

need to be measured depending on the affect of higher ash content (higher solid

density) on the spiral.

The data collected thus far on the spiral is inconclusive. The ﬁrst question raised

is on how the spiral changes with time even though the slurry remains relatively

unchanged. Since each sample measurement was taken only once, how does one

distinguish the difference between an accurate measurement and a measurement

taken in error? Currently, there are only four sets of data for a rougher coal spiral

with only one sample measurement for each variable being taken per section. In the

test spiral, the ash content remains relatively unchanged. One can speculate that if