Lab Report On Size Reduction Using Mill And Crusher

SIZE REDUCTION (Crushing of Gravel and Limestone using a Jaw Crusher and a Hammer Mill)

1

1. Introduction Almost all process industries employ size reduction or comminution to produce solid particles of desired shape, size or size ranges, to separate unwanted particles effectively, to improve handling characteristics, and to increase of the surface area of solid materials used especially for chemical reactions or unit operations such as leaching, drying, adsorption and the like. (Swain, Hemlata, & Roy, 2011) Size reduction can be carried out in stages using different types of equipment depending on the characteristics of the feed and the product to be obtained. These equipment vary in their mechanical action to give different kinds of motions and force that would result in the fracturing of the solid particles into smaller sizes. The manner in which the force is applied to the particles may affect their breakage patterns, which are impact, compression, shear, and attrition. Impact refers to the sharp and instantaneous collision of one moving object against another. Compression causes the particles to be disintegrated by two rigid surfaces such as in jaw crushers. (Swain, Hemlata, & Roy, 2011) Shear consists of a cleaving or trimming action while attrition is carried out by the rubbing or scraping of materials against one another or against a rigid surface such as in hammer mills. (Coulson, Richardson, & Backhurst, 2002) Factors that affect size reduction include the properties of the solid, size and amount of material to be handled, lack of feed control, wrong motor size, insufficient crusher discharge area, surface energy of solids, selection of appropriate crushing chamber, and power consumption. (Swain, Hemlata, & Roy, 2011) It is known that the net energy consumption in size reduction is only 0.1 to 2.0% of the total energy consumption. This energy is used for the actual size reduction (i.e. fracturing) of the solids. Although no model has yet been developed that could accurately predict the net energy requirements in size reduction, two well-known empirical laws, the Kick’s and the Rittinger’s Law, have commonly been used to estimate these energy requirements. These Laws are based on the assumption that the energy 𝑑𝐸 required to produce a change in the size 𝑑𝐷 of the material of size D is a power function of 𝑝 (Geankoplis, 2003) as shown in the equation below. dE = −CDp dD

(1)

Kick’s Law is based on the assumption that the energy required to reduce a material in size was directly proportional to the size-reduction ratio regardless of its initial size (Geankoplis, 2003) and therefore, assumes that the power 𝑝 = 1 in Equation 1, giving the following integrated expression for energy consumption, E = K K fc 𝑙𝑛

D1 D2

(2)

where 𝐷1 and 𝐷2 are the mean particle diameters of the feed and the product respectively, 𝑓𝑐 is the crushing strength of the material, and 𝐾𝐾 is Kick’s constant. 2

On the other hand, Rittinger’s Law assumes that the work in crushing is proportional to the new surface created (Geankoplis, 2003), thereby assuming that the power 𝑝 = 2 in Equation 1, such that the integrated expression for energy consumption with Rittinger’s constant 𝐾𝑅 becomes E = K R fc (

1 1 − ) D2 D1

(3)

Thus, Kick's law implies that the energy required to reduce a material of a given mass from 100 mm to 50 mm is the same as is need to reduce the same material with the same mass from 50 mm to 25 mm. In comparison, Rittinger’s Law implies that the energy required to reduce a material with a given mass from 100 mm to 50 mm is the same energy required to produce the same reduction for the material from 5.0 mm to 4.7 mm. (Size Reduction, n.d.). Apart from determining the energy consumption for size reduction, knowing the particle size distribution is also significant because it indicates whether or not the size reduction of a given sample is effective. The particle size distribution is determined by sieve analysis, which is a solids classification scheme wherein a sample of the product is placed in a nested column of sieves mounted on a mechanical shaker for a given period of time. The results of the sieve analysis can then be tabulated or presented graphically through cumulative mass fraction curves and size frequency curves. For a sample retained in a given sieve tray, the mean particle diameter is calculated using Equation 4 where 𝐷1 is the diameter of the screen through which the particles passed and 𝐷2 is the diameter of the screen where the particles are retained. D=

D1 + D2 2

(4)

However, when a collection of the data from a sieve analysis is used, the mean particle diameter can be calculated in several ways, giving various definitions of the mean particle diameter, namely, the volume-surface ̅𝑠 ), the mass mean diameter (𝐷 ̅𝑤 ), and the volume mean diameter (𝐷 ̅𝑣 ), which are mean (Sauter) diameter (𝐷 expressed in the equations below. (McCabe, Smith, & Harriott, 2005) ̅s = D

1

𝑜𝑟

̅ pi ) ∑ni=1(xi /D n

̅v = ( D

1/3

1

∑w w ∑ D

(5)

(6)

̅ w = ∑(xi D ̅ pi ) D i=1

̅s = D

(7)

) ̅ pi 3 ) ∑ni=1 (xi /D

where 𝑥𝑖 is the mass fraction in a given increment (based on sieve openings in the sieve analysis), 𝑛 is the number ̅𝑝𝑖 is the average or mean particle diameter in each increment or sieve. of increments, and 𝐷 3

2. Objectives of the Experiment a) Investigate how the net energy requirement of a jaw crusher varies with the mean particle size of the product. b) Compare the actual relative energy consumption with theoretical relative energy consumption estimated using Kick’s Law and Rittinger’s Law c) Determine how product size distribution varies with respect to the size of the outlet screen of the hammer mill and with respect to the throat opening of the jaw crusher. 3. Methodology 3.1. Methodological Framework Objectives 1 to 3: The feed rate to the jaw crusher and hammer mill are to be kept constant and fast or slow enough so as to allow the equipment to reduce the size of the particles in the feed without overcrushing or undercrushing. The variables adjusted were the throat openings of the jaw crusher and the sieves of the hammer mill with different opening sizes. The type of material being crushed was also varied, with gravel for the jaw crusher samples and limestone for the hammer mill samples. The samples then underwent size reduction and sieve analysis.

4

Let w1,J

Let

w1,HSA

Weight of Sample 1 Feed to the Jaw Crusher Weight of Sample 2 Feed to the Jaw Crusher Weight of Sample 1 for the Hammer Mill Weight of Sample 2 for the Hammer Mill Weight of Sample 3 for the Hammer Mill Weight of Jaw Crusher Sample 1 Feed to the Sieve Weight of Jaw Crusher Sample 2 Feed for the Sieve Weight of Sample 1 Feed to the Sieve

w2,HSA

Weight of Sample 2 Feed for the Sieve

g

Dj range

Particle Size range of gravel feed

in

DH range

Particle Size range of limestone feed

w2,J w1,H w2,H w3,H

w1,JSA w2,JSA

g

I0

g

V Q

g g g g

g

ϕm

Feed mass flow rate

t tT

Time

s

Di

I

Constants for Crushing with Jaw Crusher w1,J 2500 g w2,J

2500 g

DJ range

(− 3⁄4 + 1⁄2) in.

w1,JSA

500 g

w2,JSA

500 g

wN,i

E0,1

g

in g /s

Total time required to finish crushing each of the jaw crusher samples Mean particle size of Sample i after size reduction Ammeter reading (current) at time t

Wi

E0,2 ET,1 ET,2

s

ENET,1

in

ENET,2

A

Initial Ammeter reading (current) (at t = 0) Voltage reading

A V

Total charge

C

Mass of total product from sample i

g

Mass of particles (product) in each tray of size N, from sample i Experimental initial energy requirement to run jaw crusher alone (based on sample 1) Experimental initial energy requirement to run jaw crusher alone (based on sample 2) Experimental total energy requirement to run jaw crusher with gravel feed sample 1 Experimental total energy requirement to run jaw crusher with gravel feed sample 2 Experimental net energy requirement for jaw crusher sample 1 Experimental net energy requirement for jaw crusher sample 2

g J

J

J

J J J

Constants for Crushing with Hammer Mill w1,H 400 g w2,H

400 g

w3,H

400 g

DH range

(− 1⁄2 + 1⁄4) in.

w1,HSA

400 g

w2,HSA

400 g

5

Objective 1 to 3 INPUT

PROCESS

OUTPUT FINAL OUTPUT

RAW DATA

Independent Variables Jaw crusher opening Outlet screen size (OS)

8 mm for sample 1 4 mm for sample 2 *10 mm. OS for sample 1 *6 mm OS for sample 2 *0.75 mm OS for sample 3

𝐭

 Crushing in Hammer Mill

 Screen Analysis

Calculated values E0,1 & E0,2 ET,1 & ET,2

𝑡

Calculated values Enet,1 & Enet,2

Constant V

Sampl e

Ratios Actu al

Kick’ s Law

Rittinge r’s Law

% Differenc e

1

Calculating net energy requirement ratios using Kick’s and Rittinger’s Law

Variables

Mean Diamet er

2

Wi

Calculated variables

wN,i

Di

% weight per μm

 Crushing in Jaw Crusher

𝐼

SIZE REDUCTION

Variables 𝑄 I0 I V tT

Cumulative % 𝑓𝑖𝑛𝑒𝑟

CONSTANT during crushing for every sample 𝛟𝐦 (FEED RATE)

Particle size, μm

Particle size, μm

6

Objectives 1 and 2: Net energy requirements were determined for the jaw crusher for the 8 mm and 4 mm throat opening settings by subtracting the total energy requirements and the initial energy requirements as shown in Equation 8 below. (8) ENET,i = ET,i − E0,i During the experiment, the voltage reading, which remained constant throughout the

experiment, and the ammeter reading, which varied depending on the feed rate and the size of the gravel being fed, were recorded. The total energy requirement, expressed in Equation 9, was then obtained by multiplying the voltage, and the total charge (𝑄), obtained by taking the area under the curve from the plot of current against time. ET,i = VQ

(9)

Lastly, as shown in Equation 10 below, the initial energy requirement was obtained by multiplying the initial current reading with the voltage and the total time required by the machine to finish crushing the samples. E0,i = I0 VtT

(10) 𝐸

The ratio of the experimental net energy requirements ( 𝐸𝑁𝐸𝑇,1 or simply 𝐸 /𝐸2 ) was 𝑁𝐸𝑇,2

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calculated and compared (using % difference) with the theoretical ratios obtained from Rittinger’s and Kick’s Law Objective 3: The particle distribution of the crushed gravel and milled limestone were analyzed via sieve analysis. The product obtained in each tray of the sieves used in the analysis was weighed and the mean diameter of the particles per tray and of the whole sample were calculated. The former was determined by taking the average of the sieve openings above (𝐷1 ) and below (𝐷2 ) the tray where the particles was retained as shown in the equation below. The latter was obtained by plotting the cumulative frequency of the particles finer than the sieve openings against the particle size (size of sieve openings). Taking the slopes of the curve at set intervals, and plotting the slopes against the particle size would give the size frequency curve of the sample.

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3.2. Materials For this experiment, two 2500-g. samples of gravel with sizes between ½ to ¾ in. were used in the size reduction using the jaw crusher. A quarter of the product (approximately 500 g) after crushing was taken for the sieve analysis. In the size reduction using the hammer mill, three 400-g. samples of limestone with sizes between ¼ to ½ in. were used and all of the product was analyzed by via the sieve analysis. 3.3. Equipment 3.3.1 JAW CRUSHER

Jaw crushers are compressive crushers usually used as a primary crusher, which are heavy-duty machines used to reduce large pieces of solids such as run-of-mine ores into smaller sizes suitable for transport or as feed for secondary crushers. They are run by belt drives driven by an electric motor (1).

2 6 9 1

10

Figure 1.. The Retsch Muhle Jaw Crusher

Material is fed into the feed hopper (2) which leads to a set of jaws mounted in a “V” alignment with cheek plates (3) at the sides. One of the jaws is a fixed or anvil jaw (4), which is stationary and is almost vertical in orientation. The other jaw is a movable or swinging jaw (5) which forms an acute angle (20o to 30o) with the anvil, both of which support the crushing plates (wearing parts). This swinging jaw moves elliptically and against the fixed jaw without necessarily having to touch one another. The swinging jaw moves as the eccentric shaft is run by the motor’s when and driven by the flywheel (6). The material is crushed mainly by compressive strength by the motion of the jaws

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and ideally, does not pass through the throat or discharge opening (7) until its size is equal to or smaller than the size of the opening.

5 7

3 4

(a)

(b)

Figure 2. (a) Feed Hopper and Jaws. (b) Discharge opening

An improvised calibration (8) is taped onto one of the levellers (9) so that adjustment of the opening into a desired size is more convenient. The product receiver (10) gathers the product as it falls through the discharge opening.

9 8

(a)

(b)

10

(c)

Figure 3. (a) Levellers (b) Calibration (c) Product receiver

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3.3.2 HAMMER MILL The hammer mill is an impact mill, run by a motor (1) which makes use of a high speed rotating disc where beaters such as hammers, rectangular plates, hanging bars or heavy metal rings, are attached and are swung outwards in a more or less circular motion by centrifugal force. It is suitable for brittle or fibrous materials and may employ screens with cutting edges.

2 6 1 9 8

(a)

(b) Figure 4. (a) The Retsch Muhle Hammer Mill (b) Feed chute

Material is fed via the feed throat or chute (2), which is usually on top or at the center of the mill. Then, the material is thrown out centrifugally and crushed as they are beaten by the hammer bars (3), attached to a shaft (4) which rotates at high speeds, or against the breaker plates (5) fixed around the periphery of the cylindrical casing (6).

10

5 3 4

9 8

7

(a)

(b)

Figure 5. (a) Hammer Mill Interior (b) Product Receiver

The discharge opening (7) is covered by perforated metal screens in order to retain coarse material for further grinding and to allow the properly sized materials to pass through as the finished product into the product receiver (8), which is properly placed in position by locking its side clips (9). The final particle size can be controlled by varying the screen size, shaft speed, and hammer configuration. For this experiment, only the effect of changing the screen size was investigated. 3.3.3 VOLTMETER AND AMMETER Two sets of voltmeters (1) and ammeters (2) are available. The set on the left side (3) is for the jaw crusher while the one on the right is for the hammer mill (4). The round red button (5) is to be pressed in order to display the actual current readings. The rectangular red button (6) is used to stop the voltmeter and ammeter from operating and the rectangular green button (7) is used to start it. 1 5

2 3

4 6 7 Figure 6. Voltmeter and Ammeter

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3.3.4 EXHAUST The exhaust is positioned near the feed hopper of the jaw crusher in order to prevent the crushed fine particles, which escape from the feed hopper, to spread to the air. Dust and fine particles can be considered as hazards that may cause eye and lung irritation.

Figure 7. Exhaust

3.3.5 SIEVE SET AND SIEVE SHAKER The sieve set (1) and sieve shaker (2) are used for the screen analysis of the crushed particles in order to determine their particle size distribution.

1

2

Figure 8. ENDECOTTS Ltd. Sieve set and Intertest Beneflux Sieve shaker

12

Sieves (3) of various opening sizes are nested on top of one another with the receiver (4) at the bottom and the cover (5) on the topmost sieve. 3

5

4

(a)

(b)

Figure 9. (a) Sieve trays (from top right to bottom right)- 180 μm, 250 μm, 450 μm, 850 μm, 3150 μm, 6300 μm (b) Cover and Receiver

The nested sieve (6) is mounted on the sieve shaker, whose settings are adjusted using the controller (7) 7

6

(a)

(b)

Figure 10. (a) Sieve analysis setup (b) Sieve shaker controller

3.4. Procedures 13

As previously mentioned, the two size reduction equipment employed in this experiment were the Jaw Crusher and the Hammer Mill. For the size reduction using the jaw crusher, the two 2500 g-samples of gravel (- ¾” + ½”) were prepared, weighed and labeled as Samples 1 and 2. As for the hammer mill, the three 400-g samples of limestone (- ½” + ¼”) were likewise prepared, weighed and labeled as Samples 1, 2 and 3. The net energy requirement for size reduction employing the jaw crusher was to be determined for both the 8-mm and 4-mm throat openings of the equipment. The jaw of the crusher was adjusted using the levellers to give the said openings. The 2500-g sample labeled as Sample 1 was crushed by operating the jaw crusher with the 8-mm throat opening, while Sample 2 was for the 4-mm opening. Prior to feeding the crusher with the samples, the initial voltage and ammeter readings were taken a few minutes after the equipment was turned on. The product receiver was put in place and the exhaust was angled and positioned a few inches from the jaw crusher feed hopper in such a way that the stray dust or powders from the crushing were properly removed. Afterwards, the crusher was fed with the samples at a uniform and moderate rate such that the feeding was continuous but slow or minimal enough to ensure that no under- or overcrushing occurred and that the crusher would not “choke.” During the run, the ammeter readings were taken every 4 seconds until all of the sample has been crushed by the machine. While feeding the crusher, the experimenters, wearing their dust mask and goggles, were required to stay at an arm’s length from the crusher and care was taken so that the hands used to feed the gravel were never placed inside of the feed hopper. After all of the gravel from a sample was crushed, the collected product was weighed, then quartered to obtain 500 grams for the screen or sieve analysis. Quartering was done by mixing the product thoroughly, piling them into a cone and splitting the cone into two, then once again piling the halved part into another cone and taking half of it. The final half is the quarter, which was weighed prior to being subjected to screen analysis. For the size reduction using the hammer mill, three outlet screens with varying opening sizes— 10-mm, 6-mm, and 0.75-mm—were used. Sample 1 of the limestone was milled using the 10-mm screen opening, sample 2 with the 6-mm opening and sample 3 with the 0.75 opening.

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The screen to be used was placed in position and then hammer mill was closed tightly. After, the product receiver was placed in position and locked using its side clips. Then, the hammer mill was switched on and was allowed to run until it reached its full speed. Similar to the size reduction using the jaw crusher, the feed rate was uniform and moderate such that the hammer mill was allowed to run for at least one minute. Also, the same safety procedures were observed by the experimenters while feeding the limestone to the mill. After crushing, the hammer mill was switched off and the product from the receiver was not taken until the hammers in the mill stopped rotating. The collected product was then transferred into a suitable container, labeled and then weighed. After all of the three limestone samples were milled and their products collected, labeled and weighed, they were subjected to the screen analysis. The products of both the jaw crusher and the hammer mill were subjected to screen analysis. As for the jaw crusher, only a quarter (500 grams) of each of the samples were taken for analysis while for the hammer mill, all of the collected product from each of the samples were to be used. The screen analysis was used to determine the particle size distribution of the crushed gravel and limestone in order to determine if the size reduction had been effective. For the screen analysis, six standard sieves, with Nos. 180 μm, 250 μm, 450 μm, 850 μm, 3.15 mm and 6.3 mm were arranged from the bottom to the top with a receiver underneath the 180 μm screen and the cover placed on the topmost screen. The receiver and each of the sieves were weighed prior to arranging and piling them in the order mentioned. The sample to be tested was weighed and then placed on the topmost sieve. Then, the sieve set, which consists of the sieves, the receiver and the cover, were mounted on the sieve shaker. The timer of sieve shaker was set to 5 minutes. Because the sieve shaker made a lot of noise, the experimenters were advised to wear ear plugs. After 5 minutes, when the sieve shaker had stopped vibrating, the sieve set was removed from the shaker and the receiver and each of the sieves containing the crushed products were weighed. The masses of the particles in each sieve and in the receiver were determined by subtracting the mass of the sieve or receiver containing the particles with their masses when they were empty. Compressed air was to be used to clean the hammer mill and screens after milling and after analyzing one sample in order to ensure that the particles left in them after collection would not affect the collected product of the other samples. 15

4. Results and Discussions 4.1 Net Energy Requirement of a Jaw Crusher In the experiment, the initial ammeter and voltage readings were recorded and the ammeter readings were taken every four seconds during the size reduction operation. Fluctuations were observed in the current readings, coupled with the production of noise while the gravel was being fed into the jaw crusher. When bigger or the harder pieces of gravel were fed into the crusher, larger fluctuations in the current readings was observed and more noise was produced by the machine. This is because the larger and harder gravel pieces offered more resistance to the crushing, requiring more energy for them to be able to fracture and break. Some of the crushed particles, especially the finely ground ones, were not collected because they were either stuck in the jaws of the jaw crusher or were released out of the feed hopper and into the exhaust. Keeping the feed rate constant was difficult because the crusher, depending on the pieces of gravel in the feed sample, also varied in its consistency with the amount of time it needed to crush a certain amount of feed. Crushing the sample using the 4-mm throat opening of the jaw crusher took a longer time (656 seconds) than when the 8-mm opening was used (324 seconds). Table 1: Net energy requirements for 8 mm and 4 mm products of the jaw crusher

Average f(xi)

Jaw Crusher Opening

Total time required (s)

Charge, q (C)

Total Energy used by the Jaw crusher (J)

93.29 189.08

8 mm 4 mm

324 656

30,588.84 124,784.32

6,943,666.68 28,700,393.60

Energy of Jaw Crusher needed to operate (J) 85,315.68 165,968

"Net Energy" J

% of total

6,858,351.00 28,534,425.60

98.77 99.42

From Table 1 above, it is evident that the calculated “net energy consumptions” are very large, being 98% to 99% of the total energy consumed by the crusher. This is contrary to the theory that only about 0.1 to 2.0% of the total energy used by the jaw crusher is utilized to actually reduce the size of the particles, particularly by fracturing into smaller pieces, which also causes a change (i.e. increase) in the surface area of a particle. As seen in the table above, the energy required for the operation of the jaw crusher alone is only a very small fraction of the total energy consumed thus, giving very large net energies after being subtracted from the total energy consumed. Generally, the total energy consumption of a size reduction equipment is influenced not only by the energy required to run the machine, but also 16

by the efficiency of motor and transmission, friction between particles, friction between the particles and parts of the machine, windage losses, noise, heat, vibration, hysteresis losses of unfractured material, strain energy of unfractured material, energy of transport of material within the equipment, and the energy of fracture itself. With many of these factors unaccounted for in the calculations for net energy requirements, it comes to no surprise that the net energy requirements determined would indeed be very large. Therefore, in theory, the actual net energy consumption can be determined by calculating the difference between the total energy consumed by the crusher during the run and the energies required for the various operations or processes that take place during crushing (such as heat, friction, noise, etc.). Unfortunately, determining the energy consumed by the friction losses, noise, heat, etc. is beyond the scope of this experiment as it may require the use of additional devices, equipment or even of a different setup altogether. Moreover, with the numerous factors involved, monitoring and determining the energy requirements for such factors may be impractical and very tedious. 4.2 Relative Energy Consumption (Kick’s and Rittinger’s Law) Although no equation or model has yet been developed that could accurately calculate the net energy consumption required for size reduction, theories have been proposed so as to provide a rough estimate of it. Two equations commonly employed for predicting net energy consumptions are from Kick’s and Rittinger’s Law, which are used to calculate the theoretical relative energy consumptions. These are expressed in the following equations, wherein the constants 𝑲𝑹 and 𝑲𝑲, are equal to the relative energy consumption ratios (𝑬𝑬𝟏) as shown below. 𝟐

1 1 −D ) D E1 2 1 8mm = RR = 1 1 E2 ( − ) D2 D1 4mm D ln (D1 ) E1 2 8mm =R = D E2 K ln (D1 ) 2 4mm (

(11)

(12)

where D1 is the initial size of the feed material approximately 0.625 inches or 15.875 mm and D2 is the mean particle diameter of the products obtained via sieve analysis. 17

The ratios of the net energy consumptions of the crushing using the 8-mm opening with respect to the one using the 4-mm opening were calculated using Kick’s and Rittinger’s Law based on the different definitions of mean particle diameter and then compared with the ratios of the calculated experimental net energy requirements as shown in the table below. Table 2. Relative Energy Consumption of a Jaw Crusher

Mean Particle Diameter

Relative Energy Consumption Theoretical

Actual

Rittinger's Law (RR)

% difference

Kick's Law (RK)

% difference

0.31

23.18

0.58

58.67

0.33

27.19

0.45

46.33

0.69

98.96

0.91

99.59

Volume-Surface Mean ̅𝒔 Diameter, 𝑫

8-mm opening 4-mm opening

4.164 1.589

Mass mean diameter,

8-mm opening 4-mm opening

̅𝒘 𝑫

10.201 5.913

0.24

̅𝒗 Volume Mean Diameter, 𝑫

8-mm opening 4-mm opening

0.416 0.289

As mentioned, the mean particle diameter has several definitions and can be expressed in several equations. In the table above, moment means were taken based on definitions set by ISO 9276-2:2014. As observed, the mean particle diameters which gave logical values were the mass and the volume-surface (Sauter) mean diameter. However, since Kick’s and Rittinger’s Law are based on changes in particle dimensions, then the volume-surface mean diameter is assumed to be the most suitable type of mean diameter to be used in the calculations. It has been found out experimentally that Kick's law is more applicable to coarse grinding while Rittinger's Law has some validity in grinding fine powders (Geankoplis, 2003). Generally, coarse grinding refers to grinding in which the ratio of the average diameter of the sample and that of the product is around 8:1 or less, while fine grinding could give ratios up to 100:1. However, the results in Table 2 suggest that Rittinger's Law predicts the theoretical relative energy consumption of the jaw crusher more accurately than Kick's Law, with percent difference values relative to the actual energy consumption ratio of 23.18% and 28.67% respectively, Since 18

the jaw crusher is used in this part of the experiment, coarse grinding of the material is involved, and Kick's Law would have been the appropriate equation to predict the relative energy consumption. For fine grinding such as those operations using the hammer mill, Rittinger's Law equation would be more appropriate to predict the energy requirement. The deviations and the contradiction presented by the experimental data may be due to the limitations in determining the true or actual net energy consumption as explained in the previous section. 4.3 Product Size Distribution The graphs which display percent by weight per μm vs. particle size were obtained by taking the slopes from the cumulative percent finer vs. particle size graph every 500 μm intervals. For the hammer mill with a screen size of 0.75 mm, the slopes were taken at 100 μm intervals in the range from 200 to 1000 μm and then at 1000 μm intervals from 1000 to 6000 μm. These slopes were then plotted as percent by weight per μm in the ordinates of the (b) plots from Figures 12 to 15. The following figures show the size distribution of the gravel and limestone after undergoing size reduction using the jaw crusher and hammer mill respectively.

4.3.1 Jaw Crusher

19

14

Cumulative Percent Finer (%)

12 10 8 6 4

2 0 100

1000

10000

Particle Size (μm)

(a)

Percent by weight per μm (%)

0.0040 0.0035 0.0030 0.0025 0.0020

0.0015 0.0010 0.0005 0.0000 0

1000

2000

3000

4000

5000

6000

7000

Particle size (μm) Mean

Median

Mode

(b) Figure 11. Particle-size-distribution curves using 8 mm throat opening (a) cumulative percent vs particle size (b) percent by weight per μm vs particle size (frequency curve)

20

80

Cumulatize Percent Finer (%)

70 60 50 40

30 20 10 0 100

1000

10000

Particle Size (μm)

(a)

Percent by weight per μm (%)

0.030 0.025

0.020 0.015 0.010 0.005 0.000 0

1000

2000

3000

4000

5000

6000

7000

Particle size (μm) Mean

Median

Mode

(b) Figure 12. Particle-size-distribution curves using 4 mm throat opening (a) cumulative percent vs particle size (b) percent by weight per μm vs particle size (frequency curve)

21

The cumulative percent graphs show that for the 8 mm throat opening of the jaw crusher, the product gave particles which were mostly retained in the sieve with 6.3 mm openings and only a few were able to pass through (less than 12%) hence the small percentages of the “cumulative percent finer.” The 4 mm throat opening of the jaw crusher gave a product with more than 70% of the particles smaller than 6.3 mm and less than 30% of the particles smaller than 4 mm. From the shape of the frequency curves and in comparison to the median and the mean (i.e volume-surface mean diameter), it is evident that the particle size distribution is not normal. Instead, both of the curves are skewed to the left, which is to be expected since crushing with the jaw crusher entailed coarse grinding or large particles so majority of the product are expected to have larger particle sizes. Crushing or grinding of large particles may give a bimodal frequency curve, which is observed both in Figures 11. (b) and 12 (b). One of the peaks is characteristic of the equipment and the other one is characteristic of the material. (Coulson, Richardson, & Backhurst, 2002). Since the size reduction using the jaw crusher entailed coarse grinding, which means that the products are expected to still have relatively large particle sizes, it is then safe to assume that the higher of the two peaks is the one that is characteristic of the material and the lower peak, at 1000 μm, is characteristic of the equipment. The highest peak of the frequency curves (percent by weight per μm vs particle size) show the most frequently occurring size (mode) of the particles in the product. Thus, based on the figures above, the products for both the crushing with the 8-mm and the 4-mm throat openings, were mostly composed of particles with a size of 5000 μm. Crushing using the 8-mm (8000 μm) throat opening should have given products close to that size but since the largest sieve opening for the screen analysis was only 6.30 mm (6300 μm), the data in the particle size distribution should have indicated that a large portion of the products should be close to 6300 μm. However, the frequency curve showed otherwise, with majority of the product determined to be around 5000 μm in size, therefore indicating that overcrushing has occurred. On the other hand, the crushing using the 4mm throat opening likewise gave a product which mostly consisted of 5000-μm particles instead of 4000 μm, indicating that undercrushing has occurred.

22

Several factors could have played a role which led to such results including mass loss, manner of quartering, feed sample selection, and feeding rate. However, the primary and most evident factors must have been the feeding rate and the feed sample selection. First of all, despite efforts to choose gravel pieces which more or less had the same sizes for both samples I and II, it was noted that a handful of the gravel pieces in Sample 1 were generally smaller than those in Sample II. Next, the crushing rate of the gravel pieces was not consistent because the nature (i.e. specific type of stone or rock), orientation and size of the particles affect the manner and the time in which the jaw crusher was able to carry out the size reduction. When the feed contained relatively large pieces of gravel, and/ or oriented horizontally as they entered the feed hopper, more noise was produced by the crusher, a higher ammeter reading was observed and more time was required to crush the feed. Continuously feeding the jaw crusher or feeding too much gravel even if the crusher has not yet crushed majority of the sample fed previously, resulted in the crusher being “choked,” which made it unable to crush the gravel properly. Thus, some of the gravel pieces could remain in the crusher far longer than it should and this could result in over crushing or some of the gravel pieces could just pass through the crusher without being crushed properly and thus result in under crushing.

23

4.3.2 Hammer Mill 100

Cumulative Percent Finer (%)

90 80 70 60 50 40 30 20 10 0 100

1000

10000

Particle Size (μm)

(a) 0.06

percent by weight per μm (%)

0.05

0.04

0.03

0.02

0.01

0 0

1000

2000 Mean

3000

4000

Particle size (μm) Median

5000

6000

7000

Mode

(b) Figure 13. Particle-size-distribution curves using 10 mm screen (a) cumulative percent vs particle size (b) percent by weight per μm vs particle size

24

100

Cumulative Percent Finer (%)

90

80 70 60 50 40 30 20 10 0 100

1000

10000

Particle Size (μm)

(a) 0.07

percent by weight, %

0.06 0.05 0.04 0.03 0.02 0.01 0 0

1000

2000

4000

5000

Particle size (μm) Mean Median

3000

Mode

6000

7000

(b) Figure 14. Particle-size-distribution curves using 6 mm screen (a) cumulative percent vs particle size (b) percent by weight per μm vs particle size

25

Cumulative Percent Finer (%)

100

90

80

70

60

50 100

1000

10000

Particle Size (μm)

(a) 1.00 0.90

Percent by weight per μm (%)

0.80 0.70 0.60 0.50 0.40 0.30

0.20 0.10 0.00 0

1000

2000 Mean

3000

4000

5000

6000

7000

Particle size (μm) Median Mode

(b) Figure 15. Particle-size-distribution curves using 0.75 mm screen (a) cumulative percent vs particle size (b) percent by weight vs particle size

26

As observed from the cumulative frequency curves above, most of the product samples passed through the screen with the 6.3 mm opening in the screen analysis after the size reduction of limestone

(- ½” + ¼” in.) using the hammer mill with the three screen openings of 10 mm, 6

mm and 0.75 mm. Size reduction with 10 mm and 6 mm opening gave products wherein 90% and 99-100% (respectively) of the particles are finer than 6300 μm. More than 80% of the product from the size reduction using 6 mm sieve opening were finer than 3150 μm. Size reduction with the 0.75 mm opening gave a product with 100% of the sample finer than 850 μm and almost 60% of it finer than 180 μm. From the frequency curves, it can be observed that the particle size distribution is skewed to the right, indicating that the products mostly contained finer particles. Crushing using the 10-mm and 6-mm screen openings should have given frequency curves which are skewed to the left, which means that more of the larger particles should have been present in the products. Milling using the 10-mm, 6-mm and 0.75-mm throat openings gave products which mostly consisted of particles with sizes of around 800 μm, 1000 μm, and 214.5 μm respectively. The 10mm screen opening should have given products closer to 10,000 μm and so majority of the particles should have been retained in the 6.30-mm sieve during the screen analysis. Likewise, the 6-mm screen opening should have given more or less the same results, with majority of the products expected to be retained in the 3.150 μm or 6.30 μm sieve openings. Lastly, crushing using the 0.75 mm screen opening should have given a product which were mostly retained in the 850 μm or 450 μm sieve but the results indicate that almost 60% of the product passed through the 180 μm sieve. These trends all indicate that the products have been overcrushed. In the first place, limestone, which is the feed material, has an inherent weakness which causes it to easily crumble and disintegrate with minimal impact or mechanical action. Next, as mentioned in the previous section, the rate of feeding and the consistency with the sizes of the feed in each of the samples were difficult to maintain and control. These factors could have led to the overcrushing of the samples.

27

Moreover, errors could have occurred due to the mass losses and even “mass gains” (i.e product of one sample becomes mixed or added into the product of another sample) in the products because only a brush was used to clean the equipment and the screens or sieves after crushing and analysis of one sample instead of the recommended compressed air, which was unavailable during the experimentation. 5. Conclusions The net energy required is the actual energy used to bring about a change in the surface area of the feed material by causing it to fracture into smaller pieces. This net energy was determined to be 6,858,351.00 J and 28,534,425.60 J for the size reduction of gravel samples (- ¾” + ½”) using the jaw crusher with a throat opening of 8-mm and of 4-mm respectively. Instead of the expected 0.1 to 2.0% of the total energy consumption, the values for the net energy calculated in the experiment are larger than expected, being 98.77% of the total energy consumption for the crushing using the 8-mm opening and 99.42% for the 4-mm opening. These calculated values for experimental net energy requirement may not have been truly accurate because other factors which could have also contributed to the energy consumption such as heat and noise production, vibrations, friction, etc. were not taken into account in the calculations due to several limitations in the quantification and collection of data relating to such factors. The actual relative energy consumption determined for the jaw crusher is 0.24. The theoretical relative energy consumptions are 0.58 and 0.31 using Kick's and Rittinger's Law, respectively. The percent differences of the theoretical ratios with the actual were 23.18% for the Rittinger’s Law and 58.67% for the Kick’s Law. Ideally, Kick's law should have given a more accurate estimate of the actual relative energy consumption as it is more applicable to coarse grinding operations such as those in the experiment which involve the jaw crusher. The results of the experiment, however, suggest otherwise and this could be due to the limitations in calculating the true actual net energy consumptions. The size reduction using the jaw crusher with the 8-mm and 4-mm throat openings of the jaw crusher gave results which indicated overcrushing and undercrushing respectively.

The

particle size distribution of the products from the size reduction using the 8-mm and 4-mm openings both gave a frequency curve which were skewed to the left, with a mode of 5000 μm. 28

This indicates that although most of the product contained larger particles, the expected size for majority of the particles in the product were not met. The size reduction using the hammer mill gave products which were overcrushed. For all the screen openings used, at least 90% of their products were finer than 6.3 mm after the size reduction using the hammer mill. Size reduction using the 0.75-mm screen opening gave products in which 100% passed through the 850 μm sieve opening in the screen analysis. The size frequency distribution curves for the three samples were all skewed to the right, indicating that the products mostly consisted of finer particles. Milling using the 10-mm, 6-mm, and 0.75-mm screen openings should gave products which mostly consisted of particles with sizes of 800 μm, 1000 μm, and 214.5 μm respectively. These results, which indicates overcrushing and uncercrushing could have been primarily due to the inconsistencies in the feeding rate and the feed sample selection. As for the size reduction using the hammer mill, the nature of the feed being crushed could have played an important role in giving overcrushed products. The feed was limestone which has a characteristic of being easily disintegrated even with minimal impact or crushing action.

29

References

A Guidebook to Particle Size Analysis. (n.d.). Retrieved February 13, 2016, from Horiba Scientific: https://www.horiba.com/fileadmin/uploads/Scientific/eMag/PSA/Guidebook/pdf/PSA_Guidebo ok.pdf ADC Jaw Crusher Information. (n.d.). Retrieved from Aggregate Designs Corporation: http://www.aggdesigns.com/Jaw-Crusher-info.htm Coulson, J. M., Richardson, J. F., & Backhurst, J. R. (2002). Coulson and Richardson's Chemical Engineering. Oxford: Butterworth-Heinemann. Fellows, P. J. (2000). Food Processing Technology: Principles and practice. Cambridge: CRC Press. Geankoplis, C. J. (2003). Transport Processes and Unit Operations (3rd ed.). United States of America: Prentice-Hall Inc. How Does A Hammer Mill Work? (2014, September 23). Retrieved from SlideShare: http://www.slideshare.net/clkbro/how-does-a-hammer-mill-workslsh LIMESTONE: CHARACTERISTICS, USES AND PROBLEMS. (2012, October 26). Retrieved from GSA: http://www.gsa.gov/portal/content/111930 Malshe, V. C., & Sikchi, M. (2008). Basics of Paint Technology. Mumbai: Antar Prakash Center for Yoga. Mayhar Crusher Co. (n.d.). Retrieved from Jaw Crushers: http://www.mahyarcrusher.com/en/products/bhrs3b/Jaw%20Crushers McCabe, W. L., Smith, J. C., & Harriott, P. (2005). Unit Operations of Chemical Engineering (7th ed.). Singapor: McGraw-Hill . Ortega-Rivas, E. (2012). Unit Operations of Particulate Solids: Theory and Practice. Boca Raton: CRC Press. Size Reduction. (n.d.). Retrieved from The New Zealand Institute of Food Science and Technology Inc: http://www.nzifst.org.nz/unitoperations/sizereduction1.htm Swain, A. K., Hemlata, P., & Roy, G. (2011). Mechanical Operations. New Delhi : Tata McGraw-Hill.

30

ANNEX 1.80 1.60 1.40

Current, I (A)

1.20 1.00

0.80 0.60 0.40 0.20 0.00 0

50

100

150

200

250

300

350

Time (s) Figure 16. Current reading over time for the size reduction of 2500-g gravel (½” to ¾”) using the jaw crusher operating at 8 mm setting

2.00 1.80 1.60

Current, I (A)

1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 0

100

200

300

400

500

600

700

Time (s) Figure 17. Current reading over time for the size reduction of 2500-g gravel (½” to ¾”) using the jaw crusher operating at 4 mm setting

31

Table 3. Net Energy Requirement for a Jaw Crusher

Jaw Crusher Opening 8 mm 4 mm

Σ f(xi)

Charge, q (C)

93.29 189.08

30588.84 124784.32

Total Energy Used for Crushing (J) 6943666.68 28700393.60

Energy Required in an Idle Jaw Crusher (J) 85315.68 165968

Net Energy Required (J) 6858351.00 28534425.60

Sample Calculations Charge, q: 𝑛−1

𝑏−𝑎 𝑞= [𝑓(𝑥0 ) + 2 ∑ 𝑓(𝑥𝑖 ) + 𝑓(𝑥𝑛 )] 2𝑛 𝑖=1

where 𝑏 = 𝑥𝑛 , 𝑎 = 𝑥0 , 𝑛 (no. of segments) = 1 Total Energy Used for Crushing: 𝐸𝑇 = 𝑉 × 𝑞 𝐸 = 227 𝑉 × 30588.84 𝐶 𝐸 = 6,943,666.68 𝐽 Energy Required in an Idle Jaw Crusher: 𝐸 =𝑉×𝑖 𝐸 = 227 𝑉 × 1.16 𝐴 × 324 𝑠 𝐸 = 85,315.68 𝐽 Net Energy Required: 𝑛𝑒𝑡 𝐸 = 𝐸𝑇 − 𝐸 𝑛𝑒𝑡 𝐸 = 6,943,666.68 𝐽 − 85,315.68 𝐽 𝑛𝑒𝑡 𝐸 = 6,858,351 𝐽

32

Table 4. Particle Diameter and Fictitious Surface Area

Average Particle Diameter per Tray (mm)

Sieve 0 0.18 0.18 0.25 0.25 0.45 0.45 0.85 0.85 3.15 3.15 6.3 6.3 15.875

Fictitious Surface Area at 8 mm at 4 mm

0.09

59.56

175.44

0.22

3.81

16.70

0.35

4.11

19.97

0.65

3.86

17.51

2.00

7.34

35.51

4.73

7.84

57.00

11.09

43.11

14.10

129.63

336.23

Sum

Sample Calculations Fictitious Surface Area 𝑊 𝐴′ 𝑓 = ̅ 𝐷 ̅ = average particle diameter per tray where 𝑊 = mass of particles (g), and 𝐷 5.36 𝑔 𝐴′ 𝑓 = 0.09 𝑚𝑚 𝑔 ′ 𝐴 𝑓 = 59.56 𝑚𝑚

Table 5. Relative Energy Consumption Ratio

Ratio Jaw Crushing Opening

Mean Particle Diameter (mm)

8 mm 4 mm

4.16 1.59

Actual

Rittinger's Law

% error

Kick's Law

% error

0.46

0.31

46.20

0.58

21.33

33

Sample Calculations 1 1 𝐷2 − 𝐷1 )1 𝑅𝑅 = 1 1 ( − ) 𝐷2 𝐷1 2 (

where 𝐷2 = Mean particle diameter, 𝐷1 = 15.875 mm 𝐷1 𝐷2 )1 𝑅𝑅 = 𝐷 (ln 1 ) 𝐷2 2 (ln

where 𝐷2 = Mean particle diameter, 𝐷1 = 15.875 mm Table 6. Cumulative Percent for the Jaw Crusher Sieve (μm) 6300 3150 850 450 250 180 Receiver TOTAL

Mass of particles (g)

Percent Retained (%)

at 8 mm 477.97 37.03 14.68 2.51 1.44 0.82 5.36 539.81

at 8 mm 88.54 6.86 2.72 0.46 0.27 0.15 0.99 100

at 4 mm 156.33 269.31 71.02 11.38 6.99 3.59 15.79 534.41

at 4 mm 29.25 50.39 13.29 2.13 1.31 0.67 2.95 100

Cumulative Retained (%) at 8 mm at 4 mm 88.54 29.25 95.40 79.65 98.12 92.94 98.59 95.07 98.86 96.37 99.01 97.05 100.00 100.00

Cumulative Percent Finer (%) at 8 mm at 4 mm 11.46 70.75 4.60 20.35 1.88 7.06 1.41 4.93 1.14 3.63 0.99 2.95 0.00 0.00

34

Table 7. Cumulative Percent for the Hammer Mil

Sieve 6300

Mass of particles (g) at 10 mm at 6 mm at 0.75 mm 14.94 3.19 0.00

Percent Retained (%) at 10 mm at 6 mm at 0.75 mm 4.01 0.86 0.00

Cumulative Retained (%) at 10 mm at 6 mm at 0.75 mm 4.01 0.86 0.00

Cumulative Percent Finer (%) at 10 mm at 6 mm at 0.75 mm 95.99 99.14 100.00

3150

83.13

66.69

0.01

22.33

17.91

0.00

26.35

18.76

0.00

73.65

81.24

100.00

850

129.67

146.71

0.56

34.84

39.39

0.18

61.19

58.16

0.18

38.81

41.84

99.82

450 250 180 Receiver TOTAL

37.89 27.47 14.17 64.93 372.2

41.17 29.06 15.18 70.43 372.43

45.25 58.95 30.59 180.31 315.67

10.18 7.38 3.81 17.44 100

11.05 7.80 4.08 18.91 100

14.33 18.67 9.69 57.12 100

71.37 78.75 82.56 100.00 200

69.21 77.01 81.09 100.00 200

14.52 33.19 42.88 100.00 200

28.63 21.25 17.44 0.00

30.79 22.99 18.91 0.00

85.48 66.81 57.12 0.00

35