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    Ball Mills Power Formulas              
                           
    1    Introduction:                
        - This paper intends to describe different methods to calculate the power of a ball mill.    
        - Two methods will be presented here:            
          1) Bond formula              
          2) Hogg and Fuerstenau formula            
    2    Bond Formula:              
        - The Bond power formula is the following:          
         
     
         
               
               
          Where:                
          Pb is the power by ton of balls at the shaft in kW/ton,        
          D is the internal mill diameter in m,            
          J is the volume load (filling degree) in % and          
          Vcr is the percentage of the critical speed.          
        - If the mill is in dry process with grate discharge, the formula must be multiplied by 1,08.    
          Like it is the case in the cement industry, we have:          
         
     
         
               
               
        - A correction factor called Ss must be applied for mills with a diameter higher than 3,3m:    
         
     
               
                     
                     
          Where:                
          Ss is the ball size factor in kW/t and            
          dm is the maximum ball diameter in mm.          
          And the formula for these mills is:            
         
     
               
                     
        - To get the absorbed power of the mill at terminals, it is necessary to multiply by the tonnage of balls and to 
          correct with the transmission and motor efficiency factors.        
        - It is obvious that it is necessary to calculate the power for each compartment in the case of a mill larger   
          than 3,3m.                
    3    Hogg and Fuerstenau Formula:            
        - The Hogg and Fuerstenau power formula is the following:        
         
     
       
             
             
          Where:                
          P is the power at the shaft in kW,            
          D is the mill's internal diameter in m.            
          L is the useful length in m,            
          Vcr is the percentage of the critical speed,          
          ρapp is the apparent density of the charge in t/m3,          
          J is the volume load (filling degree) in % and          
          La is the lifting angle of the charge gravity center with the vertical line.      
        - ρapp is given by the following formula:            
         
     
                 
                       
                       
          Where:                
          BC is the tonnage of the ball charge in tons,          
          M is the tonnage of material between the balls (intersticial) and        
          Vch is the volume taken by the ball charge in m3.          
          M is given by the following formula:            
         
     
             
                   
                   
          Where:                
          ρmat is the specific gravity of the material in t/m3          
          J is the volume load (filling degree) in %,          
          D is the mill's internal diameter in m and          
          L is the useful length in m.            
        - To get the absorbed power of the mill at terminals, it is necessary to correct with the transmission  
          and motor efficiency factors.            
    4    Other power formulas:              
        - Cement manufacturers and suppliers adopt generally a formula which contains always Bc (tonnage of the 
          ball charge in tons), D (internal diameter of the mill, v (speed of rotation of the mill) and a power factor  
          often called C.              
        -  This C factor depends of the type of circuit, the filling degree...        
        - The formula is like that:              
         
     
                 
                       
        - We hope to describe some of these formulas in a near future.        
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