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      Types of Tube Mills (second page)            
                             
      3 Tube mills in dry process                
        - Mills presented in this chapter:              
          * Monochamber mills                
          * 2 Compartments compound mills              
          * 3 Compartments compound mills              
          * Central discharge double rotator mills            
          * Airswept mills                
      3.1 Monochamber mills:                
        - Monochamber mills are used:              
          * In the raw meal section to grind the raw meal coming from the homogenization stockpile      
          * In the cement section when the fresh material (clinker + additives) is coming from a pregrinding installation  
          or in the case of 100% slag grinding              
        - A drying chamber can be added before the grinding chamber when the fresh material is very humid.    
        - These mills are operating in closed circuit.            
        - The ratio L/D depends of the case:              
         
     
               
        - The speed of rotation depends of the mill diameter and is usually defined as a percentage of the critical speed (see hereafter).
        - Modern mills have a speed of rotation between 70 and 75% of the critical speed.      
        - All types of steel linings are used depending of the kind of material and the fineness target.    
        - The mill is equipped with an outlet diaphragm (which can be a flow control diaphragm).      
        - Depending of the case, steel balls are from 90mm to 15mm diameter.        
        - The usual filling degree is between 26 and 33%            
        - Sketch of a monochamber mill:              
         
     
         
               
               
               
               
               
               
               
               
               
               
               
               
      3.2 2 Compartments compound mills:              
        - 2 Chambers mills are used:              
          * In the raw meal section to grind the raw meal coming from the homogenization stockpile, but it is quite rare  
          * In the cement section like finishing grinding            
        - These mills can operate in open or closed circuit.            
        - The ratio L/D depends of the case:              
         
     
               
        - The speed of rotation depends of the mill diameter and is usually defined as a percentage of the critical speed (see hereafter).
        - Modern mills have a speed of rotation between 70 and 75% of the critical speed.      
        - The length of the first chamber is defined by the specific energy required.        
          And the specific energy required in chamber 1 is given of the following table:        
         
     
             
        - The usual filling degree is:              
         
     
                 
        - The first compartment is to prepare the material before to go in the second chamber.      
          The target is to have at the end of the chamber: maximum 5% residue on 2,5mm.      
        - The lining of chamber 1 is a lifting effect lining.            
        - Generally, the ball charge is a gradation of balls diameter: 90mm, 80mm, 70mm, 60mm.      
        - The second chamber is the finishing chamber. It means an attrition work in order to produce fineness.    
        - For that reason, the lining of chamber 2 is a classifying lining.          
          The biggest balls are at the beginning of the compartment where the material coming from the first chamber is coarser,
          and the finest balls at the end of the chamber where the material is the finest.      
        - The ball charge will consist in a gradation of balls: 60mm, 50mm, 40mm (dam), 30mm, 25mm, 20mm, 17mm   
          (15mm in open circuit) diameter.              
        - The mill is equipped with an intermediate diaphragm (which can be a flow control diaphragm) and an outlet diaphragm.
        - Sketch of a 2 Compartments compound mill:            
         
     
         
               
               
               
               
               
               
               
               
               
               
               
               
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      3.3 3 Compartments compound mills:              
        - 3 Chambers mills are used in the cement section like finishing grinding.        
        - These mills always operate in open circuit.            
        - The ratio L/D must be higher than 3,5.              
        - The speed of rotation depends of the mill diameter and is usually defined as a percentage of the critical speed (see hereafter).
        - Modern mills have a speed of rotation between 70 and 75% of the critical speed.      
        - The length of the first chamber is defined by the specific energy required, between 8 and 12 kWh/t.    
        - The usual filling degree is:              
         
     
                 
                       
                       
                       
                       
        - The first compartment is to prepare the material before to go in the second chamber.      
          The target is to have at the end of the chamber: maximum 5% residue on 2,5mm.      
        - The lining of chamber 1 is a lifting effect lining.            
        - Generally, the ball charge is a gradation of balls diameter: 90mm, 80mm, 70mm, 60mm.      
        - The second compartment, with a very short length, must crush the last big particles coming from the 1st chamber.  
          It also prepares the material for the 3rd chamber (finishing compartment)        
        - The lining is usually flat or with a smooth lifting effect.          
        - Grinding media can be balls or cylpebs.             
          Gradation of balls recommended: diameters 50, 40 and 30mm          
          Gradation of cylpebs recommended: 45x45, 40x40, 32x32 and 28x28mm        
        - The third chamber is the finishing chamber. It means an attrition work in order to produce fineness.    
        - The lining doesn't need to be classifying due to the presence of the 2nd chamber.      
          A flat lining or a dragpebs lining from FLS is the right solution.          
          In some cases, retaining rings (like Danula rings from FLS) are adopted, but their usefulness has frequently been  
          subject to caution.                
        - The ball charge will consist in a gradation of balls: 25mm, 20mm, 17mm and 15mm diameters.    
        - The mill is equipped with a single intermediate diaphragm between chamber 1 and chamber 2, an other single  
          intermediate diaphragm between chamber 2 and chamber 3 and an outlet diaphragm.      
          All diaphragms are single in order to increase the useful volume.          
        - Sketch of a 3 Compartments compound mill:            
         
     
         
               
               
               
               
               
               
               
               
               
               
               
               
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      3.4 Central discharge double rotator mills:              
        - These kinds of mills are used in the raw meal section of a cement plant.        
        - Limestone is prepared in order to produce the clinker in the kiln.          
        - The fineness requested is generally between 10 and 20%R90m and 1-2%R210m.      
        - These mills always operate in closed circuit with a static and a dynamic separator.      
        - The ratio L/D must be around 3.              
        - The speed of rotation depends of the mill diameter and is usually defined as a percentage of the critical speed (see hereafter).
        - Modern mills have a speed of rotation between 70 and 75% of the critical speed.      
        - The usual filling degree is:              
         
     
                 
        - In practically all cases, the double rotator mill has a drying chamber before the 1st chamber      
        - The length of the first chamber is corresponding to 40-45% of the total useful length.      
        - The first compartment is to prepare the material before to go in the second chamber.      
        - The lining of chamber 1 is a lifting effect lining.            
        - Generally, the ball charge is a gradation of balls diameter: 90mm, 80mm, 70mm, 60mm and 50mm.    
        - The second chamber is the finishing chamber.            
        - For that reason, the lining of chamber 2 is a classifying lining.          
        - The ball charge will consist in a gradation of balls: 50mm, 40mm, 30mm and 25mm diameter.    
        - The double rotator mill is also composed of:            
          * A transfer diaphragm between the drying and the 1st chamber which allows important ventilation.    
          * A peripheral discharge diaphragm.              
        - Sketch of a central discharge double rotator mill:            
         
     
         
               
               
               
               
               
               
               
               
               
               
               
               
      3.5 Airswept mills:                  
        - These kinds of mills are used in the raw meal section of a cement plant and in a coal grinding section.    
        - These mills always operate in closed circuit with a static or dynamic 3rd generation separator.    
        - The material is swept out of the mill by a pneumatic system (buckets elevators are not required).    
        - A big amount of air is then essential.              
        - This type of mill has only one grinding chamber with or without drying chamber.      
        - The ratio L/D is around 2 and less.              
        - The speed of rotation depends of the mill diameter and is usually defined as a percentage of the critical speed (see hereafter).
        - Modern mills have a speed of rotation between 70 and 75% of the critical speed.      
        - The usual filling degree is between 22 and 28% in order to insure a large passage for the hot gas.    
        - The internals configuration is the following:            
          * 40% of the length with a lifting lining              
          * 60% of the rest with a classifying lining            
          In the past, a lifting-classifying lining was also a solution for this monochamber mill      
          * From time to time, it is interesting to add a retaining ring between both linings.      
        - The ball charge will consist in a gradation of balls: 90mm, 80mm, 70mm, 60mm, 50mm, 40mm and 30mm diameter.  
        - There isn't outlet diaphragm.              
        - Sketch of an airswept mill:              
         
     
         
               
               
               
               
               
               
               
               
               
               
               
               
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      4 Mill's critical speed:                
        - The speed of rotation is often expressed as a percentage of the critical speed.        
        - We will see here below how to calculate the mill's critical speed.          
        - In two words, the critical speed is defined as the rotational speed where centrifugal forces equal gravitational forces  
          at the mill shell's wall.                
          At this point, balls will not fall away from the mill's shell.          
      4.1 Calculation:                  
        - General sketch:                
         
     
             
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
                   
        - The grinding ball is subjected to two forces            
          * Centrifugal force: Fc                
          * Gravitational force: Fg                
        - The centrifugal force is given by the following formula:          
         
     
                   
          Where:                  
          m is the mass of the ball,                
          ω is the angular speed and              
          Di is the mill's internal diameter              
        - The gravitational force is given by the following formula:          
         
     
                   
          Where:                  
          m is the mass of the ball,                
          g is the standard gravity (9,81 m/s²)              
        - The ball will remain against the wall if these two forces are in balance, it means:      
         
     
                   
          Where:                  
          The angle θ is shown on the sketch above            
        - At the top of the mill, θ is equal 0, then cosθ = 1, then:          
         
     
                     
          Which gives:                  
         
     
                   
          And:                  
         
     
                   
                         
                         
                         
        - The critical speed is usually expressed in terms of the number of revolutions per second:      
         
     
               
                     
                     
                     
        - An this gives in revolutions per minute:            
         
     
                   
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