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      Cement ball mill sizing method explanation          
                             
      1    Introduction:                
          - The Bond method is used to size a cement ball mill.        
          - Efficiency correction factors are applied with the Bond equation.      
          - The method is valid both for clinker grinding and for raw materials grinding.      
          - This method only gives a rough and initial idea for sizing a cement ball mill.      
          - To go ahead, a deeper study is necessary with ball mills suppliers or a specialized engineering office.  
          - Two calculators have been developed for sizing monochamber mills and two compartments mills.  
      2    Bond equation and correction factors:          
          - The well-known Bond formula used is the following:        
           
     
             
                     
                     
            With:                
            E = specific energy in kWh/t            
            Wi = work index in kWh/t              
            C = correction factor              
            P80 = sieve which has 80% of passing in the product          
            F80 = sieve which has 80% of passing in the feed          
          - Efficiency correction factors are giving by yhe following equation:      
           
     
               
                       
            With:                
            C1 is a correction for dry grinding,            
            C2 is a correction for open circuit            
            C3 is a correction for mill diameter,            
            C4 is a correction for feed size,            
            C5 is a correction for product fineness.            
            C6 is a correction for high-efficiency separators.          
          - C1 definition:              
           
     
             
                     
          - C2 definition:              
            The graph here below is the basis to get C2:          
           
     
             
                     
                     
                     
                     
                     
                     
                     
                     
                     
          - C3 definition:              
           
     
             
                     
                     
            Where D is the mill diameter in m            
          - C4 definition:              
           
     
       
               
               
               
               
               
          - C5 definition:              
           
     
             
                     
                     
          - C6 definition:              
           
     
         
                 
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      3    Define fresh feed characteristics:            
          - Composition: Percentage of each component, Specific gravity (kg/dm3), Work indes (kWh/t) and F80.  
          - F80 must be a representative average of various sampling campaigns of each component.    
      4    Define target fineness:              
          - Blaine fineness (cm2/gr) and/or a residue on a certain sieve        
          - Specify the P80 of the product. It must be a representative average of various particle size analysis of the product.
      5    Define production target:            
          - Production of the mill in t/h            
      6    Define efficiency factors:              
          - Determine if it is a wet or dry process.            
          - In the cement industry, the dry process is always used except some old installations where the raw mills
            are working in wet process.            
          - Determine if it is a closed or open circuit.          
          - New installations are 99% in closed circuit.          
          - To define C3 which is the correction factor for mill diameter, it is indispensable to choose a temporary diameter
            (which is in fact an unknown) in meters.          
          - An experienced Process Engineer has already a good idea about the future diameter of the mill.    
          - Later, he will have to modify this diameter in function of the result given by the calculation.  
          - It is an iteration.              
          - C4 and C5 factors are automatically calculated with the data of point 4.      
          - Determine if it is a High Efficiency separator or not.          
      7    Define the estimated mill specific energy:          
          - This calculation is carried out with the main Bond formula.        
      8    Define the absorbed power required:          
          - Multiply the estimated energy required E by the target production.       
          - The found value is the absorbed power at the mill shaft, in other words before the transmission.  
          - Determine the type of transmission to add the inefficiency factor.      
          - Recalculate the specific energy with the absorbed power required at terminals.    
      9    Sizing of the ball mill:              
          - Define the right Length/Diameter ratio in function of the circuit.        
          - Usual values can be seen below:            
           
     
             
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
          - Multiply this L/D ratio by the diameter to find the useful mill length.      
          - Define the speed of rotation.            
          - Modern mills have a speed of rotation between 70 and 75% of the critical speed.    
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          - Specify the specific energy required in chamber 1 depending of the following table:    
           
     
           
                   
                   
                   
                   
                   
                   
                   
                   
          - Multiplying the value found here above by the production target will give the required absorbed power 
            for chamber 1.              
          - Specify a working filling degree (volume load) in % for first chamber:      
           
     
             
                     
                     
                     
                     
                     
                     
                     
          - With the power formula, we can now calculate the length of chamber 1.      
          - If a DIN (*) configuration is selected, define a new length closed to the calculated value and verify if the new 
            specific power is OK.              
            (*) distance of 250mm between bolts on the length          
          - A new chamber 1 absorbed power is calculated with the DIN length.      
          - Verify again if the chamber 1 specific power is correct.        
          - Calculate the second chamber length.            
          - If a DIN configuration is selected, define a new length closed to the calculated value.    
          - Specify a working filling degree (volume load) in % for second chamber with the table above.  
          - Calculate the absorbed power of chamber 2.          
          - Calculate the total absorbed power.            
          - Iteration starts here comparing the absorbed power calculated just before with the one found in point 8.
          - A difference of maximum 2% is allowed between both powers.        
          - If the difference is higher, modify the mill diameter, the L/D ratio, the mill speed and the filling degrees
            in order to decrease the difference but keeping in mind that all usual values be respected.  
          - Maybe changing one or two parameters is enough to get the result.      
            Warning: the method is the same for a monochamber mill. It is even easier because there isn't 1st chamber.
      11    Other power correction factors:            
          - If there is 50% or more slag in the fresh feed,          
          - If the clinker is for the production of Alumina cement (ciment fondu in french),    
          - If there are retention rings (similar as Danula rings) in the second chamber,      
          - If there are cylpebs in the second chamber,          
          - If there is a lifting-classifying lining in case of monochamber mill and      
          - If the fresh feed is coal in case of monochamber mill,        
          - Various corrections factors are applied for first chamber and/or second chamber and for monochamber mill
            absorbed power.              
      11    Ball mill final dimensions:            
          - Specify the width internals: feed end liners, intermediate diaphragm and outlet diaphragm to know the full
            length of the mill.              
          - Calculate the tonnage of balls in function of the volume loads defined before.    
      12    If necessary, drying chamber (for raw mill):          
          - Specify the maximum moisture of the fresh feed components.        
          - The required drying chamber volume is automatically calculated.      
          - Define the diameter which usually is the same than the grinding part of the mill but can also be a bit lower.
          - The required length is automatically calculated by dividing the volume by the area.    
          - If a DIN configuration is selected, define a new length closed to the calculated value.    
          - The drying chamber absorbed power is calculated.          
          - The total mill absorbed power is calculated.          
      13    Required installed power:            
          - We take into consideration a factor of 1,1 to calculate the installed power of the mill but the mill's supplier has to
            recommend for that (possibility of filling degree increase).        
            See the example of calculation here: Infographic      
            Go to the calculators here:   Calculators      
                             
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