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      Ball Charge Sampling                
                               
        1 Introduction:                  
          - It is always interesting to know the ball charge gradation inside a ball mill.        
          - Reasons are:                  
            * to see the difference with the theorical ball charge given by the supplier or somebody else    
            * to adjust the future make-up              
            * to get a good idea of the wear of the balls            
            * to decide if it is time to change completely the ball charge          
            * to check if the classification is good in second chamber          
          - Experienced engineers have a good feeling only having a look during the mill's visit but results of a complete sampling is better
            in order to convince other people.              
          - The problem number one is the difficulty of the job. In fact it is very hard and long work...      
                               
        2 Method used in the mining industry:              
            Let us recall the method often used in wet process.            
        2.1 Tools needed:                  
           
     
       
          - A tube in PVC with a diameter of 300mm and a length of 1000mm (this tube must be resistant, a thickness of 8-10mm is necessary)
          - A piece of wood is necessary between the tube and the hammer due to the impact       
          - A big hammer to knock the tube into the ball charge            
          - A magnet to remove the balls from the ball charge            
          - A cord for lifting the magnet and the balls            
          - A solid bucket to carry the balls in the laboratory            
        2.2 Procedure:                  
          - Take three samples along the mill, the first 1 meter after the mill inlet, the second at the middle of the chamber and the third
            1 meter before the mill outlet. The samples points will be on the mill-axis. See figure below:    
           
     
                 
          - As the sampling campaign of 3 samples take a long time, the procedure can be reduced to a single sample  
            to be taken in the middle the mill              
          - Knock the tube into the ball charge with the help of a piece of wood and the hammer (±20-30cm).    
            After that, remove the balls inside the tube with the magnet linked to the cord.      
            Put the balls inside the bucket.              
            Normally, this operation is repeated 4 or 5 times depending on the facility to enter the tube into the charge.  
            Watch the following drawings:              
           
     
         
          - One sample should weigh between 500 and 600 kg            
          - All this material is sent in a room to be analysed            
        2.3 Comments:                  
          - This method is impossible to implement for the first chamber because the ball charge is too coarse (balls from ø90mm to 60mm).
          - This method could be implemented in the second chamber, especially in the second part where there are not balls of 60, 50mm.
            In any case, it is necessary to empty the mill before to carry out the sampling campaign.      
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        3 Method to be used in the cement mill:            
        3.1 Tools needed:                  
           
     
               
          - A solid bucket to carry the balls in the laboratory            
          - A shovel to take the small balls in chamber 2
               
        3.2 First chamber:                  
          - Take 2 samples in two points as shown on the sketch below:          
           
     
                 
          - For each sample, about ten buckets of 20 kg each are sufficient.          
          - Balls in surface are accepted due to the difficulty to go deeper.          
          - Balls are taken by hand.                
          - All this material is sent in a room to be analysed            
        3.3 Second chamber:                
          - Take 4 samples in four points as shown on the sketch below:          
           
     
             
          - For each sample, about five buckets of 20 kg each are sufficient for samples 1 (1/5) and 2 (2/5).    
          - For each sample, about two buckets of 20 kg each are sufficient for samples 3 (3/5) and 4 (4/5).    
          - For samples 1/5 and 2/5, balls in surface are accepted due to the difficulty to go deeper.      
          - For samples 3/5 and 4/5, take the balls deeper if possible .          
          - Balls are taken by hand if ø60, 50 and 40mm balls.            
          - Balls are taken with a shovel if small balls.            
          - All this material is sent in a room to be analysed            
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        4 Analysis of the samples                
        4.1 All we need:                  
           
     
                 
          - A balance                  
        4.2 Procedure:                  
          - The procedure here below is the one of the website "www.themininggrindingoffice.com" but can be applied here also.
          - The balls are assembled visually by sizes.            
          - The biggest balls (from 90mm to 50mm) are weighed one by one.         
          - For the lower dimensions, we will assemble the balls of the same size by lots in order to save time.    
          - The balls from 50mm to 30mm are assembled by lots of 5. After, each lot of five balls is weighed. In the calculation list which will
            follow, each ball of one lot will have the average weight of the lot (total weight of the lot divided by 5).    
          - The balls from 30mm to 15mm are assembled by lots of 10. After, each lot of ten balls is weighed. In the calculation list which will
            follow, each ball of one lot will have the average weight of the lot (total weight of the lot divided by 10).  
          - The media lower than 15mm are often scraps and will be weighed together. A good approximation of the number of small pieces
            is enough.                  
          - It is also interesting to count the balls which have a defect. This can be achieved with balls having a diameter greater than 40mm.
          - One can see some pictures of the lots by size here below:          
           
     
                     
        4.3 Example:                  
          - The example below is the one of a monochamber ball mill in the mining industry.      
          - In this example, only one sample in the middle of the mill has been taken        
          - Total weight of the sample: 567,9 kg              
          - Number of balls: 480                
          - Here below, the raw list of this sample with the weight of the balls and the balls with defect in red    
           
     
             
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
                     
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          - After the weighing, we must classify the balls by category.           
          - For this, we convert the weight in diameter and we have the following categories (with specific gravity of 7,8kg/dm3):
            categories (with specific gravity of 7,8kg/dm3):            
           
     
                 
          - And we have the following results:              
           
     
               
          - Important notice: In this sample, there were not balls under 40mm and no scraps. The reason was that this mill was always
            working  full of material. The pulp was going out by the door at mill outlet.        
            Normally, a charge at the equilibrium must have a gradation from the top-up size (here 80mm) up to ± 10mm  
            (when the ball becomes a chip and leaves the mill).            
          - This mill was grinding copper ore in Chile.            
          - Ball mills in the mining industry don't have classifying linings.          
        4.4 Analysis of the results and interpretation:            
          - For the first chamber of a cement mill, the most important is to know if:        
            * there is really the right percentage of the biggest balls (often 90mm)         
            * there is a big amount of balls lower than the smallest dimension (often 60mm)      
          - For the second chamber, the most important is to know if:          
            * there is a satisfying classification (segregation) of the balls          
        4.5 Analysis of the results and interpretation of the example here above:        
          - the analysis of a ball mill in the mining industry is realized in order to know if the ball charge has reached its equilibrium.
          - For those who are interested, the analysis of the results and an interpretation of the example here above is the following:
          - In our example, the top size is 80mm and the top up is 100% of 80mm diameter ball.      
          - In order to interpret the sampling results, we have to compare it with the theory.      
          - We take into account sizes with 5mm interval as 80,75,70,65...etc          
          - A theorical charge at the equilibrium is a charge where all the intervals have the same number of balls, except the top size
            which has only one half of interval (80-77,5mm) and the 10mm size (12,5-10mm) because we consider that a 10mm ball will 
            leave the mill                
          - Let's calculate the theoretical equilibrium charge as follows:          
           
     
     
          - We calculate the number of balls as follows:            
           
     
         
            where N = number of balls              
           
     
               
          - All the sizes have 68 balls except 80 and 10mm diameters which have 34 balls        
          - Summary sheet:                
           
     
       
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          - we plot 3 charts in order to compare the reality and the theory and we have:        
           
     
         
          - Comments on the chart here above (Number):            
            We can see than there is a dramatic decrease from 50mm.          
            There are not balls smaller than 40mm.            
            Normally we must find balls up to 10-15mm inside the ball mill.          
           
     
         
          - Comments on the chart here above (Weight):            
            On this graph, we can see the same phenomenon.            
            The surface 2 represents all the smaller balls which don't exist.          
            The surface 1 compensates the surface 2 (there must be equals).          
           
     
         
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            The graph here above is equivalent to the graph "Weight"          
          - Last remark on this sample:  9% of the balls between 80 and 40mm have a defect. This percentage is relatively high and 
            must be investigated              
            Other example:              
           
     
         
           
     
         
          - In the example here above, one can observe that the reality is closer to the theory, especially for the weight chart
                               
        5   Conclusion                  
          - The method presented here is not the only existing.
          - The most important is to collect the necessary information to improve the grinding performance.
                               
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