# Studies on the Grinding Kinetics of Limestone Ore using Talcum Powder as an Additive

Forschungsarbeit 2014 71 Seiten

Geowissenschaften / Geographie - Geologie, Mineralogie, Bodenkunde

## Leseprobe

## CONTENTS

Abstract

Nomenclature

List of tables

List of figures

**Chapter-I Introduction**

**Chapter-II Literature Review**

**Chapter-III Experimentation**

**Chapter-IV Results and Discussion**

**Chapter-V Conclusions**

**References**

**Appendix-A Model Calculation**

**Appendix-B Tables**

## ABSTRACT

In mineral processing, most of the operations involve size reduction to the required level to separate the valuable minerals from the ore. The principle operations involved in the size reduction are compression, impact, attrition, grinding and cutting etc. The degree of separation of the valuable mineral from its ore which is indicated by the degree of fineness of the material obtained from the grinding process is related to the cost involved in the process. In mineral beneficiation plants, grinding process is used using different grinding media for separating the valuable mineral from its ore, which should be economically feasible with minimum operational cost. The major of the operational cost is involved the energy consumption during the grinding process to get the desired degree of fineness to separate the valuable minerals from its ore to the maximum possible extent.

Studies on the grinding kinetics of Limestone ore using talcum powder as an additive were under taken in the present work. Effect of various parameters on the performance of a ball mill during the grinding was studied. The parameters studied in the present work are time of grinding, quantity of feed, mill speed, grinding media, quantity of additive and feed size. The present study was mainly emphasized on specific surface area, energy consumption and breakage rate constant. Energy consumption (E) was calculated by varying time of grinding (t, min), quantity of feed (Q, g), mill speed (N, rpm), grinding media (Bs, cm), quantity of additive (QA , g) and feed size (Fs, g). Specific surface area (S) and Breakage rate constant (K) were also calculated for the same parameters.

## NOMENCLATURE

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## LIST OF TABLES

Table A Range of variables

Table 1 Effect of grinding time (feed size -1.125 cm)

Table 2 Effect of grinding time (feed size 0.9 cm)

Table 3 Effect of grinding time (feed size 0.715 cm)

Table 4 Effect of quantity of feed (feed size -1.125 cm)

Table 5 Effect of quantity of feed (feed size -0.9 cm)

Table-6 Effect of quantity of feed (feed size -0.715 cm)

Table 7 Effect of ball mill speed (feed size -1.125 cm)

Table 8 Effect of ball mill speed (feed size -0.9 cm)

Table 9 Effect of ball mill speed (feed size -0.715 cm)

Table 10 Effect of ball size (feed size -1.125 cm)

Table 11 Effect of ball size (feed size -0.9 cm)

Table 12 Effect of ball size (feed size -0.715 cm)

Table 13 Effect of quantity of additive (feed size -1.125 cm)

Table 14 Effect of quantity of additive (feed size -0.9 cm)

Table 15 Effect of quantity of additive (feed size -0.715 cm)

Table 16 Effect of feed size

## LIST OF FIGURES

A Schematic of the experimental Set-up

B Different sizes of Limestone ore

C Different sizes of grinding media (Ball size)

1 Variation of Specific Surface area with Time of grinding

2 Variation of Energy Consumption with Time of grinding

3 Variation of Energy Consumption per Specific Surface area with Time of grinding

4 Variation of Specific breakage rate constant with Time of grinding

5 Variation of Specific Surface area with Quantity of feed

6 Variation of Energy Consumption with Quantity of feed

7 Variation of Energy Consumption per Specific Surface area with Quantity of feed

8 Variation of Specific breakage rate constant with Quantity of feed

9 Variation of Specific Surface area with Mill speed

10 Variation of Energy Consumption with Mill speed

11 Variation of Energy Consumption per Specific Surface area with Mill speed

12 Variation of Specific breakage rate constant with Mill speed

13 Variation of Specific Surface area with Grinding media

14 Variation of of Energy Consumption with Grinding media

15 Variation of Energy Consumption per Specific Surface area with Grinding media

16 Variation of Specific breakage rate constant with Grinding media

17 Variation of Specific surface area with Quantity of additive

18 Variation of of Energy Consumption with Quantity of additive

19 Variation of Energy Consumption per Specific Surface area with Quantity of additive

20 Variation of Specific breakage rate constant with Quantity of additive

21 Variation of specific surface area with feed size

22 Variation of energy consumption with feed size

23 Variation of energy consumption per unit specific surface area with feed size

24 Variation of specific breakage rate constant with feed size

## CHAPTER 1 INTRODUCTION

Ball mill grinding has been widely employed in mineral processing and other industries for more than a century. However, the fundamental mechanism of grinding is not understood fully yet. Comminution is a process of size reduction by using techniques such as crushing, grinding, milling, etc. Many important industrial products can be made by modifying the size of the particles in the material by comminution. For example, sugar can be divided into different grades (granular, castor and icing) based on its particle size ranges and keeping the chemical structure same.

Milling of minerals is an important part in the process of recovery of metals and industrial minerals for many centuries. In general, the mineral of interest needs to be extracted from the gangue mineral. The mineral of interest is separated from the gangue by employing grinding technique. In grinding process, the grain boundary between the desired mineral and the gangue will be broken and thus the mineral of interest is separated from the gangue. Often, grinding is the process used in mining industry for metal ore processing and minerals recovery from its ore.

Ore is a term used to describe an aggregate of minerals from which a valuable metal, can be profitably mined and extracted. Mineral processing involves the preparation and liberation of the valuable minerals from waste minerals (gangue mineral) and the separation of the valuable minerals into two or more products called concentrate.

In the process of comminution, large amounts of energy consumption and the maintenance of the process poses a problem in terms of high operational cost. In comminution, the particle size of the ore is slowly reduced such that the all the valuable minerals present in the ore can be liberated and can be further processed to achieve large surface area per unit mass of material.

In comminution, crushing and grinding processes are operated in a sequence. From the grinding process, ore is obtained in a slurry form and the tailings are required to be separated in further processing. The particle shape and particle size distribution are dependent on the characteristics of the ore and the type of equipment used for the crushing and grinding process.

During the crushing process, liberation of the valuable minerals from the gangue is achieved by compression of the ore against rigid surfaces or by impact against surfaces in a rigidly constrained motion path. In grinding process, the particle size is reduced by impact, abrasion and attrition of the ore by the grinding media.

Energy consumption is a major factor which influence the feasibility of the crushing and grinding processes.

In batch grinding process, the particle size reduction is carried out continuously with respect to time. Grinding studies of each mineral are carried out to study and correlate the effect of various process parameters on the particle size. The present study is focused on the grinding kinetics of Limestone ore.

During the process of achieving the required particle size of the material with required properties, grinding process is considered to be an energy-intensive stage in the overall process. Large amounts of energy consumption is the major problem in grinding in grinding process. Grinding efficiency can be increased with the addition of chemicals as additives during the grinding process. The addiction of additives reduces the energy consumption and further it prevents the formation of the agglomerates of ground particles.

The efficiency of grinding in a ball mill is determined by the size of the grinding media, the mill speed, the size and quantity of feed and the type of circuit used (open or closed circuit). Hence, the present study was carried out to study the effect of various process parameters on the specific surface area generated, the energy consumption per unit surface area produced and the specific breakage rate. The range of process parameters considered in the present study are given in table 1.

**Table 1 Variables studied**

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Their main purpose of using additives in the grinding process is to reduce the energy required to grind the material into a given fineness.

The present work is focused on obtaining improved rate of breakage of particles in the finer stages of grinding, resulting in better grinding performance in the presence of an additive with Limestone ore in a ball mill. In the present study grinding process was carried out by using talcum powder as an additive. An experimental plan has been drafted to study the grinding characteristics of Limestone with Talcum powder as an additive. Talcum powder used in this study is a dry free flowing powder, when mixed with large quantities of Limestone, it reduces the energy consumption considerably in comminution operation. However, it will not affect the quality of the product because of less quantity of additive present in the feed which directly decreases the process cost.

**Composition:**

Limestone is a sedimentary rock and contains around 50 (wt. %) calcium carbonate in the form of calcite along with quartz, feldspar, clay minerals, pyrite, siderite and other minerals. The content of calcium carbonate present in Limestone is used in identifying the rock by determining a property by contacting it with 5% hydrochloric acid.

**Physical properties:**

Physically, Limestone is quite impervious, hard, compact, fine to very fine grained calcareous rocks of sedimentary nature.

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**Typical Applications:**

- Used in the construction industry, paint industry, glass manufacturing industry, plastic industry, water treatment plants, fertilizer industry etc.

- Limestone is used as a flux in steel production and in processing of non-ferrous metals.

- Used in agricultural industry to reduce soil acidity and to absorb water.

- Limestone is used as an additive in plastic and elastomeric applications. It is used to control the crystalline structure of the particles shape such that the polymer attains its required physical properties.

**Health hazards**:

- Pulmonary changes

- Pharyngitis

- Bronchitis and emphysema

## CHAPTER 2 LITERATURE REVIEW

A lot of work has been done on the size reduction and energy utilization of the process for increasing specific surface area and decrease in energy consumption for efficient grinding Process. Deatiled literature review was made on the grinding kinetics and is given below:

**Lingaraju et al** had studied the batch grinding studies of raw coal in a ball mill. Surface area generated was computed from sieve analysis. Effect of grinding time on sample batch was studied. Effect of feed size, ball size, quantity of charge and ball charge were studied for generated surface area and energy consumption per specific surface area. Surface area generated increased upto 6 minutes of grinding time and remained almost static later. Surface area increases with increase in grinding media and decreased with quantity. Energy consumption increased steadily with duration of grinding while consumed energy per specific surface area also exhibited an increasing tendency. Larger size feed required higher energy. Consumption increases steeply with quantity and ball size while the same showed a decreasing tendency with grinding media per specific surface area.

**Yonezawa and Yamagata:** In this study, batch ball mill grinding of limestone was carried out using fly ash as a grinding aid, and investigated the influences of the feed amount and grinding time on the grindability of the mixture or limestone. it was found that fly ash was an effective grinding aid for the fine grinding of limestone, and the optimum feed amount of limestone and fly ash to the grinding mill increased with increase of grinding time. Within the experimental limits, increases in the feed amount of limestone and fly ash mixture enhanced the fine grinding of the mixture or limestone. A correlation between the median particle diameter and the surface area diameter was developed and is correlation is independent of the feed amount and grinding time.

**P.Somasundaran, Colin C.Harris** has **s** tudied the effect of sodium hydroxide, sodium carbonate, sodium oleate, oleic acid and poly (acrylic acid) as an effective additives. The results were evaluated in terms of specific surface area, specific energy and energy efficiency as a function of additive dosage, polymer molecular weight, solid concentration and relevant operating variables. Relevant interfacial properties have been measured and the milling mechanisms involved are explored, particular in terms of the effect of additives on the flow patterns at higher solids concentration. Poly (acrylic) acid (PAA) was found to be the best additive among the tested additives with lowest energy consumption. In this study, optimum concentration of PAA was 0.1% by weight. The optimum molecular weight of PPA was 5000 for the grinding of limestone. For grinding at different solids concentrations, results in the presence of PAA are better for the whole range studied than those with no PAA.

**Rajendran Nair and Paramasivam** has studied the effect of grinding aids on the time-flow characteristics of the ground product from a batch ball mill by estimating the flow characteristics of the ground product. It was found from shear tests results that the presence of calcium stearate as an additive in the mill material charge during fine grinding of calcite in a batch ball mill had increased its bulk density and major consolidation pressure, while reducing the compressibility, internal friction factor, effective angle of friction, unconfined yield strength, shearing cohesion, extrapolated tensile strength and flow ability index. It was concluded that the prime mechanism of the additive is to provide a flow favorable environment for the mill material charge or, in other words, to reduce the degradation in the flow ability of the mill material charge especially during finer stages of grinding.

**D.W. Fuerstenau, A.Z.M. Abouzeid** has investigated the behavior of a coarse material size fraction when dry ground in the presence of a fine fraction of the same mineral in a batch ball mill. Quartz and limestone (99.8% CaCO3) are considered in the present study. The breakage rate function of coarse particles (10×14 mesh) (1.7×1.18 mm), when ground in a mixture of fine particles of the same material, increased as the fraction of fines in the feed increased. When the fine fraction of −100 mesh (−150 μm) is replaced by −48-mesh (−300 μm), the rate of increase in the breakage rate function for the coarse fraction decreased. It was concluded that the average breakage process of the coarse fraction was unchanged even when the ratio of coarse material in the feed was changed. It consumed less energy per unit mass than its proportion in the feed would indicate, with the coarse fraction consuming more than its share of specific energy. But the medium did not interfere with the breakage of the coarse particles in any other way so that their breakage remained first order for the grinding times observed.

**Luis Marcelo Tavares and Raquel D.C.Kallemback** has investigated the size reduction of blends of materials with different grindabilities in a Bond ball mill, as well as in a continuous pilot-scale mill. The accumulation of the harder (tougher) component in the mill charge as grinding progresses was analyzed and a simple empirical model that describes this phenomenon has been proposed. It is found that the accumulation of hard component in the mill increasesdwith the decrease in the ratio of Bond work index values of the individual soft and hard components, and with the increase in the circulating load ratio. It was also concluded that the Bond work index of the mixtures is often higher than the weighed-average value of the individual components in the mixture.

**Rodrigo M. de Carvalho** has studied the simulation of batch mills operating under a range conditions. First-order breakage rates have been estimated using data from these simulations, and used to investigate the effect of operating and design variables in milling. Predictions using the mechanistic model are then compared to those using the scale-up relationships proposed by Austin and collaborators and Herbst and Fuerstenau. The trends predicted using the mechanistic model are in general agreement with the empirical models. Good correlation has also been observed between the simulated specific breakage rates and the specific mill power, which is in agreement with the scale-up method proposed by Herbst and Fuerstenau.

**Yoshiteru Kandea and Naova Kotake:** This chapter highlights comminution energy and evaluation in fine grinding. The purposes for comminution are to liberate minerals for concentration processes, to reduce the size, to increase the surface area, and to free the useful materials from their matrices. Comminution is an old mechanical unit operation for size reduction of solid materials and an important operation in the field of mineral processing, the ceramic industry, and the electronics industry and so on. The energy efficiency of comminution is very low and the energy required for comminution increases with a decrease in feed or produced particle size. Research and development to find energy saving and the energy required in comminution processes have been performed. In design, operation and control of comminution processes, it is necessary to evaluate the comminution energy of solid materials. In general, the comminution energy (i.e., the size reduction energy) is expressed as a function of the particle size of feed and product. In addition, the chapter also presented various Laws of comminution energy including Rittinger's law Kick's law Bond's law, and Holmes's law.

**Bernhard et al** has studied about the mills traditionally used for wet ultra-fine grinding for high-speed stirred ball mills. With increasing solid concentration the energy utilization initially increases up to a maximum, and then it decreases because of the rising viscosity. The used additive acts as dispersing agent it improves the charge of the particles and reduces the apparent viscosity. In the latter case it is possible to produce higher specific surface areas at the same apparent viscosity.

**S amayamutthirian Palaniandy** has studied the ultra-fine grinding of limestone carried out in jet mill using four levels of classifier rotational speed and grinding pressure. The holdup amount was determined during the grinding process, while the feed rate was kept constant at 8 kg/h. The ground product was characterized for its particle size and shape. In addition, the mechano chemical effect on the ground product was characterized through XRD. The particles size of the ground product ranged from 2.21 μm to 7.29 μm, demonstrating various particle shapes such as cubical, angular, and elongated. The degree of crystallinity of the ground product ranged from 54.5% to 93.7%. Afterwards, the ground product was incorporated as filler in polypropylene (PP), and its performance was characterized for mechanical properties. After conducting the test work, we find that the PP filled with ground limestone exhibited excellent thermal and mechanical properties. The composite flexural modulus, impact strength, tensile strength, and elongation at break were 2.1 GPa, 42 kJ/m2, 22.75 MPa, and 21%, respectively, when loaded up to 20%. It likewise exhibited CTE value of 57.2 ppm/°C.

**Francois K. Mullenga and Ngonidzashe Chimwani** has studied the characteristics of a platinum-bearing ore (less than 850 μm in size). The breakage parameters were scaled up to an industrial mill. This enabled the extension of the AR methodology to full-scale milling. However, the analysis was limited to two simple transport models: plug-flow and well-mixed mills without exit classification. Following this, the importance of controlling the residence time of the mill optimally was appreciated. Initial findings showed that milling conditions should be tailored to the desired product size requirements. The lower and upper limits in which the maximum production of fines should lie were also identified. Finally, mill speed was found to be pivotal in controlling the retention time of particles inside the mill.

**A. Sahoo and G. K. Roy** has carried out work involved a meticulous study of the effect of the various parameters on the performance of a ball mill. The parameters studied in this work are particle size, number of balls, time of grinding, particle density, and speed of the ball mill (rpm). An attempt has been made to develop correlation for the performance of the ball mill by correlating these variables with the grindability on the basis of dimensional analysis approach as well as fractional factorial design method. In the present work, an expression correlating the grindability of the ball mill with the various system parameters by means of dimensional analysis and the fractional factorial design methods was developed. It was concluded that the fhe future aspect of this work can be extended to bond index calculation where the power consumption will indicate directly about the cost benefit too.

**Yanmin Wang and Eric Forssberg** has studied the wet ultra-fine grinding of a limestone powder (<100 µm) in a stirred media mill with respect to the effect of slurry rheology. The results were evaluated in terms of energy efficiency and the fineness of a product as functions of various parameters such as molecular weight of a dispersant, solids concentration, additive dosage, addition method and beads load. A polymeric dispersant, Dispersant S40, with a molecular weight of 5500 gave a higher energy efficiency and a smaller product size for wet ultra-fine grinding of the limestone due to its maintenance of a lower viscosity during grinding. At an additive dosage of 0.1 wt.% of Dispersant S40 or more, a smaller additive amount gave a higher energy efficiency and a smaller product size at a given specific energy consumption in a lower level of specific energy input. The excessive additive could cause a cushion layer formed on the surface of the milling beads and thus lowered stress intensities from the collisions of the beads, causing the ineffective grinding operation. This could be avoided by the multi-point addition of the dispersant or by a higher beads load (>83 vol %). The wet ultra-fine grinding operation in the stirred media mill ceased when a discharge slurry from the mill displayed a pseudoplastic flow with an evident extrapolated Bingham yield stress. For a given solids concentration of limestone slurry, the relationships between the specific surface area and the particle size of an FP product and the additive amount of Dispersant S40 were explored, respectively. For a given solids concentration, the particle size and the specific surface area of an FP product were only related to the additive amount of Dispersant S40 regardless of other grinding conditions. Furthermore, a particle size-energy model provided a good fit (R2>0.991) to the grinding results under the experimental conditions studied.

**S. Asahi and Y. Kanda:** In this paper, work was carried out on batch grinding tests of silica glass, limestone and gypsum with a ball mill and investigated the effects of feed size and ball diameter on the grinding rate constant (selection function). The effects of feed size and ball diameter on the grinding rate constant of the materials used when the mass of balls, mass of feed, and the mill’s rotational speed were constant. Variation of the dimensionless grinding rate constant with feed size was roughly analogous, and it was independent of ball diameters and kinds of materials. Equations were obtained for the relationships between the optimum feed size and ball diameter, and between the maximum grinding rate constant and ball diameter for the materials used.

**M. Kimata and M. Yaguchi** ha **s e** xplained the effect and behavior of the dry ultrafine grinding of limestone with the liquid additives, three alcohols (Methanol, Ethanol and 1-Propanol) and two glycols (Ethylene glycol and propylene glycol). The batch experiments were carried out and the change in specific surface area of limestone with grinding time was measured by BET adsorption method. The results showed that the addition of alcohols and glycols promotes the ultrafine grinding of limestone with maximum specific surface area of. It was found that the maximum specific surface area with additives is proportional to the amount of the additive within the experimental range in this work. To increase the initial grinding rate, the stepwise addition method of a small amount of additive was found to be more effective rather than adding the whole amount at once at the start of grinding. The degradation of crystalline structure of limestone can be controlled by the addition of liquid additives. The grinding status can be estimated by monitoring the changes of temperature and pressure in grinding pot during grinding.

**Reynaldo Laborde Brown** has outlined the findings of the evaluation of the grinding process of limonite and serpentine minerals present in oxidized Ni–Co ores, which are contained in the lateritic soils of the north-eastern region of Cuba. The analysis of the grinding behavior of limonite and serpentine mixtures at different contents was carried out determining the breakage function, the specific rate of breakage and the work index at various mixing levels. To carry out this study, samples of mixtures of serpentine and limonite with weight proportions 3:1, 1:1 and 1:3 were prepared. These samples were subject to the following size intervals (in μm): >6300; 6300/5000; 5000/3150; 3150/1600; 1600/400; 400/74; 74/44; 44/0 the same size distribution was prepared in each test, with the aim of avoiding its influence. The results showed that the values obtained in the mixtures were intermediate than in the case of grinding mineral components alone. He concluded that the principle of mineral individual behaviour in multi-component grinding can be applied in the case of the Cuban lateritic nickel ores.

**S. Levent Ergtin & Birol Sonmez** has studied the effects of the ball charge, powder filling, and mill speed and ball size on model parameters of cumulative basis kinetic model of ball mill grinding. The standard Bond mill was used in the experiments. Mogul lead-zinc ore was used as the material. Grinding tests were carried out in a purpose designed laboratory mill which has the same dimensions with the Bond mill (i.e., 30.5x30.5 cm). The mill speed could be adjusted to the range among 25-250 rpm. The material was first crushed to -3.36mm, and then samples were taken from the lot by riffle sampler. The dry grinding tests were carried out for 1, 2, 4 and 8 minute. All the tests were carried out varying one parameter at a time keeping the other parameters fixed at their reference values. The reference values were 44 % ball filling, 87.5 % of critical speed, 18 % powder filling, and 2.54 cm diameter balls. It was found that there exist optimum values for ball size and % ball filling for efficient grinding. The efficiency increased asymptotically with increasing % critical speed and decreased with decreasing % powder filling.

**V. Deniz** has suggested the relationships between bond's Grindability (Gbg) and Breakage Parameters of Grinding Kinetic on Limestone. In this study, the relationship between the Bond's grindability (Ghj.) and breakage parameters (S, a-r, y and ß) were examined. The validity of the obtained relationship parameters of S, a-r, ß and *y* has been confirmed with correlation coefficients of 0.96, 0.92, 0.90 and 0.78, respectively, through a regression analysis of samples of limestone. Result of tests Bond grindability values of limestone samples were appeared 6.14 g/rev, 2.89 g/rev, 2.58 g/rev, 2.48 g/rev, 2.42 g/rev and 1.54 g/rev, respectively. Eight mono-size fractions were prepared and ground batch wise in a laboratory-scale ball mill for determination of the specific rate of breakage. The dry grinding of size intervals of limestone samples showed that these samples followed the first-order breakage law with constant normalized primary breakage distribution function. As a result of comparison for four breakage parameters, a high correlation coefficient is obtained. These four relationships may be used to provide an estimate of Bond's grindability for limestone.

**Rohit Verma and Raj K. Rajamani** has analyzed the dry grinding experimental study performed with limestone. In this study, it was suggested that the breakage rates are dependent on the instantaneous particle size distribution of powder in the mill. Slurry density and the presence of a grinding aid also affect breakage rates substantially. The effect of these variables, which constitute the mill environment, on breakage rates has been quantified with a unique estimation method known as the G-H method. Rajamani and Guo modified the G-H solution to estimate break-age distribution and time-dependent breakage rates the G-H solution scheme proposes an approximate solution to the batch grinding equation. This method enables the estimation of breakage rates of all size intervals by a simple linear graphical scheme. It was concluded that the presence of fines increases the rate of breakage of coarse particles.

**B.R. Yoon and S.S. Kim** has explained the applications of grinding kinetics analysis to fine grinding characteristics of some inorganic materials using a composite grinding media by planetary ball mill. A series of wet grinding experiments using the calcite, pyrophyllite, and talc powder by a vertical type planetary ball mill in which the ball size and distribution of grinding balls were varied with the Gaudin–Schuhmann distribution equation were carried out, and the following were found from the grinding kinetics analysis of particle size distribution of ground products obtained. The regression equation for the grinding rate constant K’ was expressed by an empirical equation involving the mean diameter of composite grinding balls dB (mm), the median diameter of feed xmo(μm), and Bond’s work index Wi (kwh/t) ,Where the values of the empirical constants c1 and c2 were 592, 0.0438, respectively, within the experimental ranges. The value of parameters in grinding rate equation was obtained from the analysis of grinding kinetics. Using the values, the particle size distribution of each test material for a given grinding time was found to be expressed in a type of function as follows: R(x, t) = R (x, 0) exp (-K’xni tv) where the values of constants n’ and v each material are 1.16 and 0.806 for calcite, 1.18 and 0.907 for pyrophyllite, and 0.955 and 1.038 for talc, respectively.

**Kiangi K. Kiangi and Michael H. Moys** has studied the particle filling and size effects on the ball load behaviour and power in a dry pilot mill experimental study The ball load behavior in a pilot mill was studied under conditions of increasing particle filling, for coarse silica feed (0.8–1.8 mm) and fine silica feed (0.075–0.3 mm), at the mill speeds of 63, 78, 88 and 98% of the critical. An inductive probe was used to obtain the ball load behaviour independent of particles present in the mill. The difference in mill power draw obtained from the coarse and fine particle charges are explained via their load behaviour signals. The effect of particle filling and size on the ball load behaviour is quantified through the toe and shoulder angular positions. Increasing the coarse particle filling within the ball load without allowing for a considerable change in the particle size distribution due to grinding, does not cause the particles to have a great influence on the ball load orientation. In this case, the power increases as a result of the additional particle mass within the charge and lift imparted to the ball charge by the particles. No substantial power loss was obtained for high particle fillings. The measurements were obtained using the inductive probes demonstrate its ability to detect various conditions that arise within grinding mills such as cataracting, centrifuging and segregation. This technique of measuring load behaviour holds much promise in becoming a tool to validate computer aided load behaviour models such as the Discrete Element Model (DEM) using experimental data.

**S. Nomura and T. Tanaka** has derived a theoretical energy size reduction relationship based upon the comminution kinetics in which the proportional relationship is applied between the grinding rate constant and the net mill power in the present study. The derived formula is similar to an empirical energy law, dW ∝ dxr/xri ,where W is the specific energy input, xr is the particle size of product and the exponent i is shown to be a variable depending upon the ground material, the type of mill and the method to measure energy. An empirical power law between energy input and size reduced is valid. The exponent of the energy–size reduction relationship i has been related to n and q expressed as i=qn+1, where n is the distribution factor of the Rosin–Rammler equation and q is a variable depending on the type of mill (or the manner of milling) and the method of measuring energy. The Charles finding has been proved to be valid as far as the net energy is concerned (q=1). The derived result has indicated the dependence of the product size on the Bond work index a theoretical background for the correction of the work index has been described. Quantitative confirmation of the theory with experiment is not fully made at present mainly because data associated with material strength properties are scanty. Also, the present analysis is made for batch grinding and plug flow is postulated, whereas size reduction in a continuous grinding is more or less affected by the flow or mixing behaviors of ground material in the mill. Clarifying such phenomena should be made in the near future based on the present treatment towards establishment of a sound theoretical procedure to design mills.

**David Glasser and Diane Hildebrandt** has investigated the effect of ball diameter on milling kinetics using the attainable region methodology. Under a predefined fineness of the grind in the product, attainable region plots were produced and results qualitatively interpreted. By assuming a first-order kinetics law and a normalizable breakage, particle size distributions were generated for the following grinding times: 0.5–1–2–4–10–30–60 min. Several single-sized feed materials ranging from 26,500 μm down to 425 μm together with ball diameters between 10 and 50 mm were considered for simulation. Finally, the obtained data was analyzed with the attainable region technique. The targeted objective was chosen to be the amount of material less than 75 μm produced at each stage of batch milling. A total of 250 kg of coal sample was collected from a selected mill feed. And 150 kg of grinding media was carefully prepared from a regraded mill load. Three ball sizes were considered: 30.6 mm, 38.8 mm, and 49.2 mm; and in each case, 50 kg of media was constituted. After several simulations, AR results suggest a limited effect of ball size for quite large diameters of ball. It was found that that a careful mixture of balls of different diameters might be able to take advantage of both small and large media.

**E.F. Crespo** has developed a kinetic model for ball milling with the primary intention of isolating the influence of the strength of the particles on grinding kinetics. The interaction between the facture energies, which characterize the strength of the particles and the absorbed impact energies, which characterize the motion of the ball charge can be described by the proposed bi-variate grinding kinetics. Thus, the model is prepared to simulate the effect of preferential breakage of the weaker particles in a narrow size interval and the resulting non-first-order breakage. The model was fitted with success to batch grinding data where abnormal breakage was detected. For the larger sizes, it was verified that the breakage rates are essentially controlled by the particle fracture energies and breakage is non-first-order. For the smaller sizes, it was confirmed that the breakage rates are essentially controlled by the size of the particles and breakage is virtually first-order. This fact justifies the success of the classic population balance method when it is applied to systems of particles with sizes inferior to 1 mm. It was also verified that the non-first-order breakage due to a distribution of strengths in a narrow size interval is potentiated by weak impact energy spectra and high particle fracture energies. This result clearly suggests that non-first-order breakage is also limited to the coarser sizes in industrial ball mills of large diameter most part of the size intervals should follow the first-order breakage law.

## CHAPTER 3 EXPERIMENTAL PROCEDURE

In the present study, a ball mill was used for studying the grinding kinetics of limestone ore. It is a cylindrical vessel with dimension of 8"X8" size. One end of the ball mill is open with a provision to close the by using a lid and one side is sealed. The open end is closed with lid and with the help of a gasket around the periphery of the ball mill, to secure the material inside the ball mill during the operation.

The essential dimensions of the mill are given below:

- Inside diameter = 8" and length = 8"

- Thickness of the mill wall = 0.38"

- Theoretical critical speed of the mill = 66 rpm

- Ball size and weight = 2.54 cm (1") & 66.1 g (100 No.)

The ball mill used in the present study was provided with four steps to operate the mill at different speeds 21, 42, 66 & 81 rpm. Based on the requirement of the operation, suitable ball sizes and required ball nos. were chosen. A rotap sieve shaker and a set of BSS sieves with mesh numbers 10, 16, 60, 100, 150, & 200 were alos used in the present study.

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Figure A Schematic of the experimental setup

Initially, the limestone ore was fed to the ball mill to reduce the size of the limestone particles using grinding process in the ball mill. At regular intervals, the product was collected and sieved to study the product size distribution in a rotap sieve shaker and the process was continued till the required particle size fraction was obtained.

In the present study, three feed sizes of 11.25 mm, 9 mm and 7.15 mm were considered. Further, experimental work was repeated with the addition of additive (talcum powder) to provide improved grinding efficiency in terms of improved specific surface area and breakage rate constant and to reduce the energy consumption. The effect of various parameters which influence the overall grinding kinetics and energy consumption was studied by considering the following parameters:

- Time of grinding in the mill (t, min)

- Quantity of feed (Q, g)

- Speed of the mill (N, rpm)

- Size of the balls (Bs, cm)

- Quantity of additive (QA, g)

- Feed size (FS, cm)

**Estimation of the specific surface area and energy consumption:**

The specific surface of the product at the end of the experiment is calculated from the sieve analysis data for each run of the mill using the formula,

S= (Ks/ρW)/(åwdP -1)

where, Ks = specific surface factor of the ground particles (6 for spherical particles),

w = weight of the product collected on a Particular sieve, g

W = weight of the total feed taken, g

dP = mean size of the product retained on a sieve under consideration, cm

ρ = density of the material (g/cc).

**Estimation of consumption of energy:**

To estimate and calculate the energy required () for a given size reduction process, a number of theories have been advanced. These theories depend on the basic assumption that energy required to produce a change in a particle of a typical size dimension is a power function of .

Bond postulated that work required to form particle of size from very large feed is proportional to the square root of the surface to volume ratio of the product .

= from which follows that **=**

Kb is a constant that depends on the type of machine and material being crushed. The work index is defined as the gross energy requirement in kilowatt-hour per ton of feed to reduce a very large feed to such a size that 80 percent passes through a 100 microns screen. The above equation leads to a relation between and Wi. If is in mm, P in kilowatts and in tons per hour.

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If 80 percent of the feed passes through a mesh size of mm and 80 percent of the product a mesh of mm it follows from equation

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In Bond's equation, is expressed in centimeters. If other size units are preferred, the equation must be adjusted with the appropriate conversion factor. These equations are used to make comparisons between the power requirements for various degrees of reduction.

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The above equations are dimensional and so, if quoted values are to be used for the various constants, the dimensions must be expressed in appropriate units.

E= consumption of energy, kilowatt hr/ton

P= power in, watts

= work index in, kilowatt hr/ton

average diameter of the feed particle, cm

= average diameter of the product particle, cm

**Time of grinding in the mill (t, min):**

Time of milling was studied at 3, 6, 9 12,15,18 and 21 min with three different feed sizes 1.125, 0.9 and 0.715 cm at ball sizes 2.54, 1.27 and 0.635 cm size, the speed of the mill at 66 rpm and weight of feed 50g and additive as 5g.

**Speed of the mill (N, rpm):**

The effect of mill speed was studied at four different speeds of the mill (21, 42, 66 & 81rpm) provided with the mill, fixing the grinding time 21 minutes and keeping 100 balls of 2.54 cm size as grinding media. The quantity of feed was kept at 50g and additive as 5g

**Feed size (FS, cm):**

The effect of feed size on specific surface area and energy consumption is studied with different feed size 1.125, 0.9 and 0.715 cm as charge material. The other parameters were maintained as 21 min milling time at a mill speed of 66 rpm with 1" steel balls, quantity of feed 50g additive as 5g.

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**Fig B Different sizes of Limestone ore**

(Picture taken in the Mechanical Operation lab)

**Size of the balls ( Bs, cm):**

To evaluate the effect of ball size, balls of same material of 0.63 cm, 1.27 cm and 2.54 cm sizes were used by keeping total ball weight constant at 6610g.

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**Fig C Different sizes of grinding media (Ball size)**

(picture taken in the Mechanical Operation lab)

The effect of ball size was investigated at feed quantity of 50g and additive of 5g, ball mill speed of 66 rpm and a milling time of 21minutes for three different sizes.

**Quantity of additive (** QA, g **):**

The effect of feed quantity of additive was varied from 5 to 20 g in steps of 5 g. The balls used as 1" steel balls. The other parameters that were kept constant are the time of milling is 21min, the speed of mill is 66 rpm and the feed quantity of Limestone ore is 50g.

**Quantity of feed ( Q, g):**

The effect of feed quantity on specific surface area and energy consumption is studied with feed quantities 25, 50, 75 and 100 g as charge material. The other parameters were maintained as 21 min milling time at a mill speed of 66 rpm with 1" steel balls and additive as 5g.

**Estimation of the Specific breakage rate:**

The whole study was conducted on 3 different feed sizes and results were tabulated to estimate the specific breakage rate k (min-1) for each run.

The percentage retained on the selected sieve with time gave the first order rate constant given by the equation:

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## CHAPTER 4 RESULTS AND DISCUSSION

Batch grinding characteristics of Limestone ore were conducted in a ball mill. Grinding performance, in terms of material breakage, specific surface area and energy consumption, was studied with a wide range of operating parameters such as effects of time of grinding, quantity of feed, mill speed, ball sizes and quantity of additive. Grinding media had a significant impact on the performance of ball mill in terms of product size reduction, energy consumption and grinding costs. The efficiency of grinding depends on the surface area of the grinding medium.

The size reduction involves mainly two breakage mechanisms, impact and attrition, and mainly depends on operating parameters like quantity of feed, time of grinding, mill speed, grinding media and feed material characteristics such as size. For breakage to occur, the media must provide sufficient force to the particles to affect breakage. It was also envisaged to find out the specific surface area and energy consumption. The breakage rate is directly proportional to the diameter of the particle under consideration and follows a definite pattern that can be regarded as order kinetics with respect to particle diameter.

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**The impact of energy in a mill**

The energy that is required to break the material in the mill comes from the rotational energy that is supplied by the drive motor. This energy is converted to kinetic and potential energy of the grinding media. The media particles are lifted in the ascending portion of the mill and they fall and tumble over the charge causing impacts that crush the individual particles of the charge. The overall delivery of energy to sustain the breakage process is considered to be made up of a very large number of individual impact or crushing events. Each impact event is considered to deliver a finite amount of energy to the charge which in turn is distributed unequally to each particle that is in the neighborhood of the impacting media particles and which can therefore receive a fraction of the energy that is dissipated in the impact event.

To estimate and calculate the energy required for a given size reduction process, a number of theories have been advanced. These theories depend on the basic assumption that energy required to produce a change in a particle of a typical size dimension is a power function of .

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The above equation is dimensional and so, if quoted values are to be used for the various constants, the dimensions must be expressed in appropriate units. In Bond's equation, is expressed in centimeters. If other size units are preferred, the equation must be adjusted with the appropriate conversion factor. These equations are used to make comparisons between the power requirements for various degrees of reduction.

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**Effect of time of grinding**

The effect of time of grinding in a ball mill was studied covering a range of 3 to 21 minutes. 50 g of feed with different feed sizes of 1.125, 0.9 and 0.715 cm were fed to the mill and the mill was run at the constant speed of 66 rpm. The number of balls of one inch size was kept as constant at 100 and additive of 5g. The procedure was attained until the 80% passage of feed through selected screen of 150 mesh so, that the optimum time taken as 21 minutes in this experiment for time of grinding. The specific surface area per each run is calculated. Figure 1, 2 and 3 shows the effect of specific surface, energy consumption and E/S ratio with grinding time respectively. From figure 1 and 2, it was observed that specific surface area and energy consumption were increased with an increase in grinding time. From figure 3, it was observed that E/S ratio was decreased with an increasing in time of grinding.

Figure 4 shows that the effect of Specific breakage rate with time of grinding. The Specific breakage rate was observed to be decreased with an increase in time of grinding.

The reasons for increasing specific area and energy consumption in the initial periods are due to the fact that coarse particles are being introduced in to the mill are easily grounded, but after attaining a certain degree of fineness, further division become a slower process due to the cushioning action of the fines formed. Also the small particles may agglomerate to form bigger particles with prolonged grinding. Similar observations were made by Rohit verma and Raj K. Rajamani [1].

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Figure 1 Effect of time of grinding on specific surface area

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Fig 2 Effect of time of grinding on energy consumption

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Fig 3 Effect of time of grinding on energy consumption per unit specific surface area

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Figure 4 Effect of time of grinding on specific breakage rate constant

**Effect of the quantity of feed (Q)**

To study the effect of quantity of feed on the performance of the mill was measured in terms of the specific surface area and the energy consumption for four samples of 25, 50, 75, & 100 g of feed samples. In all these systems, the feed was grounded for a grinding time of 21 minutes at a mill speed of 66 rpm using 1" steel balls and additive of 5g.

Figure 5 shows the effect of quantity of feed on the specific surface area. From figure 5, it was observed that the specific surface area was decreased with an increase in feed quantity.

This is attributed to the choking of the mill with the increased feed quantity. At larger feed quantities, the chances of balls coming closer are meager; as a result of comminution by attrition and impact is greatly reduced.

Figure 6 shows the effect of quantity of fed on the energy consumption. The energy consumption was found to be decreased with an increase in feed quantity. At this stage, the formation of new surface area of product particle get decreases so that energy consumption is also decreases. Similar observation is made by Lingaraju [2].

Figure 7 shows the effect of quantity of feed on the energy consumed per unit surface area (E/S) produced. The E/S values were increased linearly with an increase in feed quantity from 25 g to 100 g.

Figure 8 shows the effect of quantity of feed with specific breakage rate (k). The specific breakage rate was decreased with an increase in feed quantity.

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Figure 5 Effect of feed quantity on specific surface area

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Fig 6 Effect of feed quantity on energy consumption

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Fig 7 Effect of feed quantity on energy consumption per unit specific surface area (E/S)

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Fig 8 Effect of feed quantity on specific breakage rate constant with quantity of feed

**Effect of the mill speed (N)**

The effect of mill speed on the specific surface area was studied at four different specified speeds 21, 42, 66 & 81 rpm while other variables were kept constant. The values of grinding time, feed quantity, ball size and additive quantity were maintained at 21 min, 50g, 100 and 5 g respectively.

A plot was drawn (Figure 9) between the specific surface area generated and the mill speed. From the figure, it was evident that the specific surface area generated was increased with an increase in mill speed from 21 rpm to 66 rpm and then decreased with further increase in mill speed from 66 to 81 rpm. The maximum specific surface area was obtained at a mill speed of 66 rpm. The increase in specific surface area up to 66 rpm could be explained as follows.

Action of the balls at low mill speed is cascading, i.e. impact rather than attrition. As speed increases the impact increases resulting in an increase of specific surface area but at very high speed reaching critical speed afterwards decreases in specific surface area. This may be due to the peripheral speed of the mill is very high, it begins to act like a centrifuge and the balls do not fall back, but stay on the perimeter of the mill and that speed is called as "Critical Speed”. Hence the specific surface area decreases even after increasing the mill speed.

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Fig 9 Effect of mill speed on specific surface area

Figure 10 shows the effect of mill speed on the energy consumption. From the figure, it was observed that the energy consumption was increased with an increase of mill speed from 21 rpm to 66 rpm and then decreased with further increase in mill speed from 66 to 81 rpm. Mill rotational speed is believed to be one of the most important factors in fine grinding, which is directly related to the stress intensity of individual grinding ball. Similar observation made by Kiangi K. Kiangi and Michael H. Moys [3].

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Fig 10 Effect of energy consumption with mill speed

Figure 11 shows the effect of mill speed on energy consumption per unit specific surface area (E/S). The E/S values were decreased to a minimum at 66 rpm and then increased with the mill speed up to 81 rpm.

Fig. 12 shows the Effect of Specific breakage rate (k) with mill speed and the breakage rate is increased with an increase in mill speed from 21 rpm to 66 rpm, and there after it is decreased with further increase in mill speed upto 81 rpm. It is observed that larger particles undergo impact breakage when impacted by balls with sufficient kinetic energy. As particles get smaller they become difficult to break by impact hence breakage rates decreases with decreasing particle size and attrition becomes the dominant mode of breakage for finer particle sizes.

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Fig 11 Effect of mill speed on energy consumption per unit specific surface area (E/S)

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Fig 12 Effect of mill speed on specific breakage rate constant with mill speed

**Effect of ball size (Bs)**

To study the effect of ball size on the mill performance measured in terms of the specific surface generated and energy consumed, three sizes of ball viz., 0.63 cm (1/4״), 1.27 cm (1/2״) and 2.54 cm (1״) were chosen. The effect of ball size was studied for a feed quantity of 50 g and keeping the time of grinding at 21 minutes, speed of the mill at 66rpm and additive of 5g. Even though the size of the balls were changed, the total weight of the balls is kept constant at 6610 g.

A graph was drawn to show the effect of ball size on specific surface and shown in Figure 13. From the figure, it was concluded that the specific surface area is directly proportional to the ball size.

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Fig 13 Effect of specific surface area with ball size

The media must provide sufficient force to the particles to effect breakage; thus a charge composed of smaller balls will not effectively break large particles in the feed. On the other hand, larger media minimizes the specific surface area available for contact with particles. With smaller size feed material and less mass, grinding efficiency decreases because particles become difficult to break, and abrasion becomes the dominating mode of breakage while, for larger particle sizes, particles can be easily broken down because of high impactive forces imparted by falling balls.

Figure 14 shows the effect of ball size on the energy consumption. The energy consumption was increased with an increase in ball size.

Figure 15 shows the effect of ball size on the E/S. E/S ratio was decreased with an increase in ball size.

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Figure 14 Effect of energy consumption with ball size

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Fig 15 Effect of ball size on energy consumption per unit specific surface area (E/S)

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Figure 16 Effect of ball size on specific breakage rate constant

To study the effect of ball size on the breakage rate function, graphs were drawn between k (the specific breakage rate) against ball size and shown in Figure 16. From the figure, it was concluded that with an increase in ball size the grinding rate was increased and also there was a relative increase in grinding rate in the presence of an additive. Similar observation made by Michael H. Moys [3].

**Effect of Quantity of additive on grinding (QA)**

The effect of an additive is to increase or decrease the strength of the solids. As far as the process of comminution is concerned, the effect sought is the weakening of the solids and a decrease in the energy necessary to break them to the sizes required. Since the process of comminution includes the creation of new surface and therefore the creation of surface energy, the possibility suggests itself that if the amount of this surface energy is decreased, less energy would be required to create the new surface. Hence an attempt was made to grind the Limestone ore with an additive (Talcum powder).

The quantity of additive used was marginal ranging from 1 to 5 % of the feed, i.e., 5 to 20 g and the other parameters chosen were quantity of feed 50 g, speed of the mill at 66 rpm and grinding media of 100 no’s of 1" steel balls. Talcum powder as an additive has shown good results in the reduction of energy consumption. The Effect of additive on specific surface produced with the quantity of additive is shown figure 17, which indicated that the specific surface area was increased with an increase in the quantity of additive. The explanation for the effect of these so-called additives is that they are able to enter the micro-cracks of the solids and hence increased specific surface area is obtained.

The additive fills the cracks during stress relief and preventing them from sealing up during the comminution process. The effect of favorable additives is further to reduce the grinding time to reach a certain degree of subdivision and thus the decrease in energy. These additives have to prevent agglomeration of the finest particles.

From Figure 18, it was observed that the energy consumption was decreased with an increase in quantity of additive. Similar observation was made by P. Somasundaran [4]. From Figure 9, E/S ratio was decreased with an increase in the quantity of additive. As the ore loses its strength by the effect of additive, less energy is consumed for grinding.

Figure 20 shows the effect of additive on specific breakage rate constant (k). Specific breakage rate was increased with an increase in quantity of additive, as the additive is added to the feed, the hardness of the feed particles decreases and the particles will be grounded very easily. Hence the specific breakage rate increases.

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Fig 17 Effect of specific surface area with quantity of additive

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Fig 18 Effect of quantity of additive on energy consumption

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Fig 19 Effect of quantity of on energy consumption per unit specific surface area (E/S)

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Fig 20 Effect of quantity of on specific breakage rate constant

**Effect of feed size (FS)**

To study the effect of feed size on the performance of the mill measured in terms of the specific surface area generated and the energy consumption, three samples of sizes 1.125 cm, 0.9 cm and 0.715 cm were taken. In all these systems the feed was grounded for a grinding time of 21 minutes, at a mill speed of 66 rpm using 1" steel balls and additive of 5 g.

A graph was drawn between the feed size and the specific surface area and shown in Figure 21. From the figure 21, it was observed that the specific surface area was decreased with an increase in feed size. Figure 22 shows the effect of feed size on energy consumption. The energy consumption was decreased with an increase in feed size. From this, it can be concluded that for effective size reduction the ball size must be proportional to feed size. Otherwise there will not be nipping of the particles resulting in the particles remaining uncrushed.

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Fig 21 Effect of feed size on specific surface area

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Fig 22 Effect of feed size on energy consumption

Figure 23 shows the effect of feed size on energy consumption per unit specific surface area. Gradual increase in the energy consumption was observed.

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Fig 23 Effect of feed size on energy consumption per unit specific surface area (E/S)

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Fig 24 Effect of feed size on specific breakage rate constant

Figure 24 show the effect of feed size specific breakage rate constant (k). It was observed that specific breakage rate was gradually decreased with the increase in the feed size. Similar observation was made by S. Samanli, D. Cuhadaroglu [5].

## CHAPTER 5 CONCLUSIONS

- As the grinding time increased, specific surface area was increased and energy consumption was also increased with decreased energy consumption per unit specific surface. Specific breakage rate was decreased with an increase in the time of grinding.

- With an increase in the quantity of feed, specific surface area and energy consumption were decreased, while energy consumption per unit specific surface was increased. Specific breakage rate was decreased with an increase in the time of grinding.

- With the increase in speed of the mill, the specific surface area and energy consumption were increased up to 66 rpm and then decreased because 66 rpm is the critical speed. Hence it is worthless to run the mill at higher speeds of rotation beyond 66 rpm.

- Ratio of energy consumption to specific surface area was decreased up to 66rpm and gradually increased with further increase of the speed of the mill.

- Breakage rate constant was increased as mill speed increases up to 66rpm after that it was decreased.

- With an increase in size of the grinding media specific surface area and energy consumption were increased.

- Ratio of energy consumption to specific surface area was decreased with an increase of grinding media. Breakage rate constant was also increased with an increase of size of the grinding media.

- With an increase of quantity of additive, specific surface area was increased while energy consumption was decreased.

- With the increase in quantity of additive, ratio of energy consumption to specific surface area and breakage rate constant were decreased.

- With an increase of feed size, specific surface area energy consumption were decreased.

- With the increase in feed size, ratio of energy consumption to specific surface area was increased while breakage rate constant was decreased.

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**MODEL CALCULATION**

The Specific surface area was calculated in the following manner:

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Therefore, specific surface are of the product, according to the formula

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**TABLE-1**

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**TABLE-2**

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**TABLE-3**

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**TABLE-4**

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**TABLE-5**

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**TABLE-6**

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**TABLE-7**

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**TABLE-8**

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**TABLE-9**

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**TABLE-10**

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**TABLE-11**

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**TABLE-12**

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**TABLE-13**

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**TABLE-14**

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**TABLE-15**

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**TABLE-16**

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