Otto-von-Guericke-University Magdeburg Process Engineering Department Lab exercise: Comminution Content Introduction 2 Fundamentals 2. Comminution energy 2.2 Coarse crushing 2.2. Jaw crusher 2.2.2 Hammer crusher 2.3 Fine grinding 2.3. Vibration ring mill 3 Simulation of grinding based on the generalized size-mass balance model 4 Task formulation 5 Realization of the exercise 6 Discussions about the results 7 Notes for preparation 8 Safety-at-work regulations 9 References Magdeburg 26
2. Introduction Comminution is defined as the mechanical breakdown of solids into smaller particles without changing their state of aggregation. Products that have undergone size reduction surround us daily. Some examples are foods such as flour, sugar, and spices; construction materials such as cement, lime, plaster and sand; and pigment particles in lacquer and paint. Throughputs in industrial size reduction range from a few kilograms to hundreds of tons per hour. The two main objectives of size reduction are:. Production of a specified particle size distribution or a specific surface area. The maximum permitted amount of residual coarse material at the upper particle-size distribution limit or the maximum permitted amount of fines at the lower limit can also be goals. These requirements are always applied if the dispersity properties of the material have a pronounced effect on product quality (e.g. pigment colour intensity, taste of chocolate, cement strength, agglomeration, miscibility, and solubility). 2. Treatment of multi-component materials. In the case of inhomogeneous materials such as ores, the content of a valuable substance in a particle frequently depends on the particle size. As a result, the size must be reduced sufficiently so that the components are obtained as particles of maximum purity which can then be separated. Size-reduction devices have been in use ever since people began to eat cereal crops. The exploitation of water, wind, and steam power led to the development of size-reduction equipment. However, a thorough treatment of size reduction from a scientific and engineering viewpoint began only in the late 95s. The work of Rumpf and co-workers in the Federal Republic of Germany deserves special mention. Additional research groups now exist in Germany, the United States, and Japan. They cover research and progress in the basic understanding and mathematical description of size reduction as well as developments in machinery, processes, and protection against wear. Capacity in tons per hour Power consumption in kwh/t Cost in cents per ton Undersize of µm sieve in %. Fig.. Capacity and cost of grinding operation depending on the particle size. The development of grinding equipment is stimulated because of high energy costs and an increasing number of new products and materials. It was shown that the United States industries use approximately 32* 3 GWh of electrical energy per annum in size-reduction operations. More than half of this energy is consumed in the crushing and grinding of minerals,
3 one-quarter in the production of cement, one-eighth in coal, and one-eighth in agricultural products. The fineness to which a material is ground has a marked effect on its production rate. Fig. is an example showing how the capacity decreases and the specific energy and cost increase as the product is ground finer. 2. Fundamentals 2. Comminution energy In design, operation, and control of communition processes, it is necessary to evaluate correctly the communition energy of solids. In general, the comminution energy (i.e. the size reduction energy) is expressed by a function of particle size. Several models, known as so-called grinding laws, have been proposed to realize a size reduction depending on the energy input to the mill. These models are combined in a general differential equation: de m d( d ) = C () n d where E is the work done, m is the mass of the feed material, d is the particle size, and C and n are constants. For n = the solution corresponds to the Kick s model. This law can be written E m = C K d ln d F P = C K A ln A P F (2) where d F is the feed-particle size, d P is the product size, and d F /d P is the size reduction ratio, A P and A F are the specific surface areas of product and feed, respectively. For n= 2 the solution corresponds to the Rittinger s model E m = CR = CR (A P A F ) d P d (3) F For N=.5, you get the Bond law E 2 2 W = = W C (A / A / i = B P F ) (4) m d8,pr oduct d 8,Feed where W is work input in kilowatt-hours per ton and d 8,Feed and d 8,Product are the particle size in microns at which 8 % of the corresponding feed and product pass through the sieve. W i is generally called Bond Work Index given in kilowatt-hours per ton. The Work Index is an important factor in designing comminution processes and has been widely used. In case of grinding, the task of mechanical process engineering is to find the optimal design and optimal operation conditions for comminution, and to save energy. There are five promis-
4 ing fields: mill design, classification device design, control, additives, and new wear-resistant materials. 2.2 Coarse crushing 2.2. Jaw crusher These crushers may be divided into two main groups (Fig. 2), the Blake, with a movable jaw pivoted at the top, giving greatest movement to the smallest lumps; and the overhead eccentric, which is also hinged at the top, but through an eccentric-driven shaft which imparts an elliptical motion to the jaw. Both types have a removable crushing plate, usually corrugated, fixed in a vertical position at the front end of a hollow rectangular frame. A similar plate is attached to the swinging movable jaw. The Blake jaw is moved through a knuckle action by the rising and falling of a second lever (pitman) carried by an eccentric shaft. The vertical movement is communicated horizontally to the jaw by double toggle plates. Because the jaw is pivoted at the top, the distance between the crushing plates is greater at the discharge, preventing choking. Figure 2. Jaw crushers. 2.2.2 Hammer Crusher Grate bar Pivoted hammer Support for grinding Fig. 3. Hammer crasher. In case of hammer crushers (Fig. 3), impact devices (hammers) are attached to the rotor via pivots so that they are deflected when they hit strong, particularly large particles. In most cases the crushing zone is surrounded by grate bars, so that fragments which are larger than the openings of the grating are retained in the crushing zone. Although hammer crushers wear more quickly than impact crushers, they can process moist materials more efficiently. Impact and hammer crushers operate with peripheral velocities between 2 and 5 m/s, the maximum velocity is around 7 m/s. In principle, only soft to moderately hard materials can be proc-
5 essed because of wear considerations at these high peripheral velocities. However, these crushers are simpler than jaw and cone crushers and units with equivalent throughputs are much smaller in size. Consequently, impact crushers have been developed for the processing of hard rock such as basalt, diabase, and greywacke. The peripheral velocity is then decreased to 25-35 m/s. The fineness of product can be regulated by changing rotor speed, feed rate, or clearance between hammers and grinding plates, as well as by changing the number and type of hammers used and the size of discharge openings. 2.3 Fine grinding 2.3. Vibration ring mill In a typical vibration ring mill, the grinding chamber is a vessel (Fig. 4), which contains a mill ring and a mill cylinder. The grinding chamber is filled with up to 35 5 % of particles to be ground. The vessel, held within a frame and supported by springs, is moved in an almost circular fashion by an unbalance. Owing to the contact with the vessel, the mill ring and the mill cylinder move. vessel mill ring mill cylinder Fig. 4. Schematic of a vibration ring mill. A vibration mill is suitable for grinding of hard and abrasive materials, and can easily be adjusted to different feeds, e.g. by changing the oscillation amplitude or the residence time. The feed particle size is smaller than 5 mm. The grinding time controls principally the fineness of the product. Vibration mills are used to grind fired clay, bauxite, silicon carbide, quartz sand, barium ferrite, and even limestone and talc. Wet grinding is possible but rarely carried out in practice. 3. Simulation of grinding based on the generalized size-mass balance model The most common method of mathematical modelling, the population balance model, describes the change in particle-size distribution with time. To do this, the complete particle-size distribution is divided into fractions i (intervals). A mass balance is set up for each individual fraction i, and the decrease in mass for each fraction is assumed to be proportional to the mass already present in that fraction. In our example of three size fractions, the comminution ve-
6 locities of these three fractions can be described by three differential equations: d µ 3 µ dµ d,, dt dt dt dµ dt dµ dt dµ dt = µ S = µ S + b S 2 = + b2 µ S S + b2 µ (coarsest particles) (5) µ (intermediate particles) (6) (finest particles) (7) The parameter m i is the mass fraction of particle size interval i and S i is the specific rate of breakage. The term b ij is the breakage distribution parameter of the fragments, i.e., the mass fraction of fragments from fraction j that move into size fraction i. In general, the stepwise size reduction process is described by a system of coupled first-order differential equations: dm dt i = S m i i i + j= b S m ij j j i=, 2,n (8) where the class with the coarsest particles is denoted by the index. The first term ( S i m i ) describes the decrease in mass produced by size reduction, and the second describes the increase in mass due to fragments from coarser fractions. If S i and b ij are constant, this system of equations can be solved explicitly. The problem in mathematical modelling is the determination of the size-reduction coefficients S j and b ij. For example, dividing the particle-size distribution into fractions requires 45 coefficients. With this great number of coefficients every experimental date can be to conform to every theoretical model. Sometime the sizereduction coefficients, especially size-reduction rates, are not constant, e.g. are depending on m i. 4. Task formulation. Your task is to study the grinding behaviour of brittle materials, i.e. the influence of the two different stressing modes compression and impact, occurring in a jaw crusher and a hammer mill respectively, on the particle size distribution of the products. What is the difference between the two particle size distributions? 2. The change of particle sizes during grinding in a ring vibration mill is the subject of your next investigation. You have to determine the Bond Index W i of the processed materiel and discuss the influence of moisture on grinding. 5. Realization of the exercise a) Coarse grinding Firstly prepare two identical samples as feed material for both the jaw crusher and the hammer mill. After grinding in the jaw crusher, the crushed material has to be analysed using a sieving machine. Write the particle size distributions obtained in a table and draw its curve. Carry out the same procedure for the hammer mill.
7 The operation sequence is identical for the jaw crusher and the hammer mill: Clean the mill Switch on the motor of the mill Fill in the feed material Switch off the motor of the mill Take out the grinding product b) Grinding kinetics Use the ring vibration mill to determine the kinetics of grinding. Before starting prepare two samples of sand, each with a mass of 2 g, by means of quartz sand sieving. The Operation sequence of the experiment. Clean the mill 2. Fill in the feed material 3. Switch on the motor of the mill 4. Start the timer 5. After 5 s switch off the mill 6. Take out the ground material and carry out the particle size analysis The second, third and fourth steps are the same but the grinding times are, 2, 4, 8 s. Put the results of measurement into following table: Table. Particle size distribution vs. time, Time interval t= s t=5 s t= s t=2 s t=4 s t=8 s Grinding time t= s t=5 s t=5 s t=35 s t=75 s t=55 s 63 µm<d<8 µm 2 4 µm <d<63 µm 2 µm <d<4 µm d<2 µm Sum of 2 c) Study the influence of moisture on the grinding behaviour Clean the mill Fill in the feed material and add ml water to it Switch on the motor of the mill Start the timer After s switch off the mill Take out the ground material and carry out the particle size analysis using water flow
8 Table 2. Particle size distribution resulting from wet grinding. Particle size d in µm 8<d< 63<d<8 4<d<63 2<d<4 <d<2 <d< t= s 6. Discussions about the results Task Find the grinding rate constant S for the coarsest fraction m (63 µm <d<8 µm). Use Eq. 5, compute ln(m (t=5s, 5s, 35s...)/m (t=)), and draw these figures against the grinding time t in an x-y plot. The slope of the approximated straight line is S. Task 2 Check whether your experimental data fit the Bond law by calculating the constant W i (Eq. 4). First draw the particle size distributions corresponding to the grinding times t=5 s, 5 s... and read d 8 from their graphs. Then compute term T for each grinding time. T = d 8 in µm d8,pr odukt d8,feed The energy consumption E of the vibration mill is the product of the electric power of the mill P=65 W and the grinding time t=5 s, 5 s, 35 s... Draw E/m=(P*t)/m, m=2 g) against the term T in an x-y plot. The slope of the approximated straight line is W i. Task 3 Explain why wet grinding in our vibration ring mill is more effective than dry grinding. 7. Notes for preparation A careful preparation for the lab exercise is essential. Please, use the lecture and seminars on Mechanical Process Engineering and the books. You can test your knowledge by explaining following keywords: Particle size distribution Q 3 (d), screen analysis, Bond law, grinding kinetics, population balance model.
9 8. Safety-at-work regulations Pay much attention to the action of closing the grinding chamber of the vibration mill. There is danger of squashing your hands. Only start the vibration mill when it is closed, i.e. the grinding chamber is lidded and the mill cover is closed. Pay attention to sieving. Be careful about avoiding getting any sand into your eyes. You find the electric emergency stop switch near the entrance on the right side (red-yellow colour) and the fire extinguisher on the gangway. The telephone is fixed on the left side of the entrance. The university emergency number is 5. Further, you have to wear robust shoes and not easily damaged clothing. Wearing jewellery such as necklaces is forbidden. Smoking, making fire, eating and drinking are not allowed in the laboratory. Be careful not to have any residual alcohol. In case of injuring yourself or somebody else or damaging any experimental equipment during the experiments, inform your tutor. 9. References. Lecture on Mechanical Process Engineering 2. Crushing and grinding, in Powder Technology Handbook, New York, 997, edited by Keishi Gotoh, pp. 527-63. 3. K. Schönert, Size reduction (fundamentals), Ullmann s Encyclopedia of Industrial Chemistry, Vol. B2, VCH-Verlagsgesellschaft, Weinheim, Germany, 988, pp.5.-5.4 4. Perry s Chemical engineering Handbook, 999, pp. 2, -2, 24.