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      Grinding media            
      1 Introduction:            
        - The grinding media is a very important factor of the mills internals, not only on a mill's efficiency point of view but also on
           a wear point of view.            
        - Generally, the ball charge consists of grinding balls of several sizes and of different material qualities.    
        - Generally, balls between 125 and 30 mm are used.            
        - The composition of the ball charge depends on various factors, such as:        
          * Mill diameter            
          * Mill length            
          * Ratio L/D
          * Mill speed    
          * Types of linings    
          * Mill circuit    
          * Grindability of the fresh feed    
          * Granulometry of the fresh feed    
          * Hardness of the fresh feed    
          * Product fineness    
        - Concerning the ball quality, it depends of:    
          * Impact forces    
          * Friction forces between the balls and the liners            
          * Abrasiviness of materials            
          * Corrosion especially in wet process            
      2 Ball charges quality:            
        - Three types of balls exist on the market:            
          * Forged balls            
          * Cast Iron balls            
          * High Chromium Cast Iron balls            
        - A small table with the advantages and disadvantages of these balls:          
        - See suppliers websites for composition       
      3 Wear rate:            
        - The wear of grinding media in a mill is a contentious subject and many theories exist regarding the laws governing this process. 
        - The wear of the balls is due to 4 reasons:            
          * Impacts            
          * Friction forces            
          * Abrasivity of the feed components            
          * Corrosion            
        - Depending of these reasons and the grinding medis quality, wear rates can be between 100 and 2000 gr/t.    
      4 Wear rate calculation:            
        - Several theories have made an important contribution to an understanding of the wear process.     
        - Among the models and theories put forward are:            
          * The Bond Wear Model            
          * The Volume theory            
          * The Linear Wear theory            
    Bond wear loss formula:
          For Dry ball mills (with grate discharge):
          For wet ball milling:            
          Where Ai is the abrasion index of material determined from abrasion test.        
          Some figures of abrasion index herebelow:            
        - The volume theory:            
          According to this theory, the rate at which the weight of any ball decreases is proportional to the mass (volume) of a ball.  
          This can be presented mathematically as:            
        - The Linear Wear Theory:            
          The most widely accepted approach to characterize the wear of grinding media in ball mills is known as the Linear Wear Theory.
          Its rate of lost weight is directly proportional to its surface area exposed to impacts, friction forces, abrasion and   
          corrosion phenomenon.             
          According to the surface theory, the size frequency distribution is flat: the same number of balls is found in every interval 
          when the size range is divided into equal widths.            
          It is also called charge in equilibrium.            
          This can be expressed by the following formula:            
          δ = ball consumption in kg/hr            
          m = ball weight in kg after t hours in the mill            
          Cm = surface area of the ball in m2            
          Sb = constant in kg/hr/m2            
          The surface at the equilibrium can be calculated with the following expression:        
          S = surface area of the ball charge in m2            
          Wb = total weight of ball charge in tons            
          Δb = specific gravity of the ball in kg/dm3            
          db = diameter of the ball in mm            
          ds = diameter of the minimum ball permitted in mm (or must be removed or scrap)      
        - Measurement of the filling degree (volume load):            
          Let's take the example of a new ball charge inside the mill.          
          After x hours, we want to know the wear rate of the grinding media.           
          We will measure the filling degree inside the mill.            
          It is better to empty the mill before to realize this operation.          
        - Wear rate in gr/t calculation:            
          Knowing the original filling degree and the one after x hours, we calculate the number of tons consumed.    
        - In order to know the wear rate, we have to divide the number of tons consumed by the production during the x hours period.
        - Example:            
        - Other wear rate unities with an example:            
          * gr/kwh:             
          * mm/100h:            
          * mm/1000tons produced:            
        - Hours required for the smallest ball to reach the minimum ball diameter permitted:      
      5 Cylpebs:            
        - Cylpebs are normally cylindrical grinding media with a ratio length to diameter of 1.      
        - Cylpebs from 45x45 up to 24x24 are normally used in the mining grinding rotary mills.      
        - A picture of cylpebs:            
        - Cylpebs have the following advantages in comparison to balls:          
          * A higher bulk density: 4,9 kg/dm3 against 4,5-4,65 for the balls.          
          * A higher surface area for the same weight:            
          A ball of 14mm diameter has a weight of 11gr and a surface area of 616mm2        
          A cylpebs of 12x12 has a weight of 11gr and a surface area of 679mm2 (+10%)        
          * A contact with an other cylpebs can be a line against only 1 point for the ball.        
        - For these reasons, cylpebs are theorically better than balls for grinding process.         
          A great number of industrial trials or laboratory tests have been carried out in the past and again today but it never been  
          proved that cylpebs are really better than balls.            
        - Other cylpebs type: the boulpebs.            
          Boulpebs are like cylpebs but wit rounded cylinder bases.          
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