Patent Publication Number: US-2005116077-A1

Title: Mill liner profile

Description:
The present application claims under 35 USC Section 119 priority from co-pending U.S. provisional patent application Ser. Nos. 60/479,671 and 60/508,050, and entitled INTERIOR MILL PROFILE AND LINER, filed on Jun. 18, 2003 and Oct. 2, 2004, respectively, by John A. Herbst and Xiangjun Qiu, the full disclosures of which are hereby incorporated by reference. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIG. 1  is a perspective view of a grinding mill having an interior mill profile according to one exemplary embodiment of the present invention.  
       FIG. 1A  is a fragmentary sectional view of the mill of  FIG. 1  taken along the line  1 A- 1 A.  
       FIG. 2  is a diagram illustrating one embodiment of an interior mill profile of the mill of  FIG. 1  according to an exemplary embodiment.  
       FIG. 3  is a diagram illustrating the first portion of another embodiment of interior profile of the mill of  FIG. 1  according to an exemplary embodiment.  
       FIG. 4  is a diagram illustrating a second portion of the other embodiment of interior profile of the mill of  FIG. 1  according to an exemplary embodiment. 
    
    
     DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS  
       FIG. 1  illustrates mill  10  which has an interior  12  with an inner circumferential profile  16  (schematically shown). In one embodiment, profile  16  is provided by a plurality of individual segments or liners  14  secured to the inner surfaces of cylindrical wall  17 . In alternative embodiments, profile  16  may be provided by other liners supported along the inner circumferential surface of mill  10  or may be integrally formed as part of a single unitary body with wall  17 .  
       FIG. 1A  is a sectional view of mill  10  illustrating profile  16  in greater detail. As shown by  FIG. 1A , profile  16  is formed by liners  14  which are secured to an interior of wall  17  in a side-by-side relationship. In the particular example shown, liners  14  are secured to wall  17  by fasteners  19 , such as bolts formed which pass through wall  17  into corresponding bores  21  intermittently within liners  14 . In the particular example shown, each liner  14  has a high lifter portion  18  and a portion of a speed bump portion  20 . When liners  14  are positioned adjacent to one another along wall  17 , the adjacent portions of speed bumps  20  form a complete speed bump. In other embodiments, liners  14  may be mounted to wall  17  by other fasteners, the junction between liners  14  may be altered and liners  14  may be secured to wall  17  in other fashions.  
       FIG. 2  illustrates one particular embodiment of liner profile  16  in detail.  FIG. 2  is a sectional view along the surface of profile  16 . Profile  16  is generally the contour or boundary surface facing the interior  12  of mill  10 . Profile  16  is defined by the equation: y=A (x/B) p (1-x/B) p , where y is the height of profile  16  from a lowermost point of profile  16 , where x is the distance from the start of profile  16  and where the parameters A, B and p are chosen to optimize performance based on criteria such as mill diameter, filling percent of the mill, character of material being processed and the rotational velocity of the mill. Profile  16  is continuously repeated along the entire inner circumferential surface of the mill  10 . It has been discovered that a profile  16  generally following the above equation has superior performance as compared to other standard profiles. In particular, profile  16  achieves longer liner wear life and/or higher grinding mill throughput.  
      As further shown by  FIG. 2 , profile  16  generally forms a high lifter portion  18  and a speed bump portion  20 . In other embodiments, speed bump  20  may be omitted. When profile  16  is repeated along the entire inner circumferential surface  12  of mill  10 , portions  18  and  20  are interleaved with one another along surface  12 . High lifter portion  18  comprises a raised area of profile  16  having a variable angle. In particular, portion  18  has an edge  22  bounded by tangents T 1 , T 2 , T 3  and T 4 . Tangents T 1 -T 4  extend at varying angles with respect to one another. T 1  has a low angle. T 2  has a larger angle. T 3  has a large angle. T 4  has a lower angle again. This varying angle of edge  22  has been found to achieve longer wear life and/or higher grinding throughput as compared to conventional profiles.  
      As shown by  FIG. 2 , portions  18  and  20  are symmetrical in that their leading and trailing edges are identical. As a result, profile  16  is well suited for use in bidirectional mills. The ratio of the heights of portions  16  and  18  may vary depending upon operating conditions such as those listed above.  
      Although profile  16  is illustrated as being continuous with no breaks or junctions between segments, profile  16  may be provided by multiple segments or sections aligned side-to-side within mill  10 . In alternative embodiments, parts of portions  18  or  20  may be provided by different sections or segments. For example, in lieu of segment junction  24 , profile  16  may be formed by segments having a junction at location  26 . In still another embodiment, profile  16  may be integrally formed as a single unitary segment or may be integrally formed as part of a segment including multiple repeating profiles  16 . In lieu of being formed by liners  14 , profile  16  may be integrally formed with wall  17  of mill  10 .  
       FIG. 2  illustrates one particular application of profile  16  to a particular mill  10 . In the embodiment shown, mill  10  comprises a 34 foot diameter semi-autogenous (SAG) grinding mill having 44 steel liners  14  along its inner circumferential surface. Alternatively, liners  14  may be formed from other materials or combination of materials including rubber, polymers and other metals. The SAG mill has a fill percentage of about 30 percent by volume (10-20 percent fill by balls). The SAG mill processes gold ore and rotates at a speed of between about 9.5 and 11 revolutions per minute. It has been found that the detailed profile  16  shown in  FIG. 2  optimally performs (wear and throughput) in such conditions.  
       FIGS. 3 and 4  illustrate liner profile  116 , an alternative embodiment of liner profile  16 .  FIG. 3  is a sectional view of lifter portion  118  of liner  116 .  FIG. 4  is a sectional view of a speed bump portion  120  of profile  116 . Liner profile  116  extends along an interior  12  of mill  10  shown in  FIG. 1 . Profile  116  of high lifter  118  is generally defined by the following equations: 
 
 Trailing Side:  
       y   =             H   T     ⁡     (     x     B   T       )         q   T       ⁢       (     2   -     x     B   T         )       q   T       ⁢           ⁢   0     ≤   x   ≤     B   T             
 Leading Side:  
       y   =             H   L     ⁡     (       x   -     B   T     +     B   L         B   L       )         q   L       ⁢       (     2   -       x   -     B   T     +     B   L         B   L         )       q   L         +     H   T     -       H   L     ⁢           ⁢     B     T   ≤   x   ≤       ⁢     B   T       +     B   L             
 where q T &gt;0, q L &gt;0, B T &gt;0, B L &gt;0, H T &gt;0 and H L &gt;0, 
 
 where x is the distance from the start of lifter portion  118 , where y is the height of profile  116  of portion  118 , where B T  is the length of the trailing edge, where B L  is the length of the leading edge  126 , where H T  is the height of the trailing edge, where H L  is the height of the trailing edge  124 . 
 
      As shown by  FIG. 4 , speed bump portion  120  has a trailing edge or side  128  and a leading edge or side  130 . Profile  116  of speed bump portion  120  is defined by the following equations (also found in Exhibit C): 
 
 Trailing Side:  
       y   =               h   T     ⁡     (     x     b   T       )         P   T       ⁢       (     2   -     x     b   T         )       P   T         +     h   L     -       h   T     ⁢           ⁢   0       ≤   x   ≤     b   T           
 
 Leading Side:  
       y   =             h   L     ⁡     (       x   -     b   T     +     b   L         b   L       )         P   L       ⁢       (     2   -       x   -     b   T     +     b   L         b   L         )       P   L       ⁢           ⁢     b   T       ≤   x   ≤       b   T     +     b   L             
 
 where P T &gt;0, P L &gt;0, b T &gt;0, b L &gt;0 and h L &gt;0, 
 
 where x is the distance from the start of speed bump portion  120 , where y is the height of profile  116  of speed bump portion  128 , where b T  is the length of the trailing edge portion  128 , where b L  is the length of the leading edge  128  of portion  128 , where h T  is the height of the trailing edge of portion  128  and where h L  is the height of trailing edge  130  of portion  128 . 
 
      Profile  116  is continuously repeated along the entire inner circumferential surface of mill  10 . In particular, lifter portion  118  and speed bump portion  120  are alternated about the entire inner circumferential surface of mill  10 . It has been discovered that a profile  116  generally following the equations has superior performance in unidirectional milling as compared to other standard profiles. In particular, profile  116  provides for longer life and/or higher grinding mill throughput.  
      In one embodiment, profile  116  is continuous with no breaks or junctions between segments. In another embodiment, profile  116  may be provided by multiple segments or sections aligned side-to-side within mill  10 . For example, in one embodiment, a first section may provide portion  118  while a second section provides portion  120 . In alternative embodiments, parts of portions  118  or  120  may be provided by different sections or segments. In still another embodiment, profile  116  may be integrally formed as a single unitary segment or may be integrally formed as part of a segment including multiple sets of portions  118  and  120 . In lieu of being formed by liners  14 , profile  116  may be integrally formed with wall  18  of mill  10 .  
      In one embodiment, mill  10  comprises a 34 foot diameter semi-autogenous (SAG) grinding mill having 44 steel liners  14  along its inner circumferential surface. Alternatively, liners  14  may be formed from other materials or combinations of materials including rubber, polymers and other metals. The SAG mill has a fill percentage of about 30% by volume (10-20% fill by balls). The SAG mill processes gold ore and rotates at a speed of between 9.5 and 11 revolutions per minute.  
      Profiles  16  and  116  are at least, in part, defined by various parameters chosen to optimize performance based on various criteria such as mill diameter, filling percent of the mill, character of the material being processed and the rotation of velocity of the mill. For example, in one embodiment, the parameters of profiles  16  and  116  are chosen to optimize performance based upon multi-physics modeling. The techniques used in multi-physics modeling include one or more of discrete element modeling (DEM), computational fluid dynamics (CFD), and discrete grain breakage (DGB).  
      DEM simulations focus on discrete “particles” by solving Newton&#39;s Second Law of motion applied to a particle of mass m i  moving with velocity v i  when it is acted upon by a collection of forces f ij  including gravitational forces and particle-particle, particle-fluid and particle boundary interactive forces, i.e.,  
                 D   ⁡     (       m   i     ⁢     v   i       )       Dt     =       ∑             ⁢           ⁢     f   ij               (   1   )             
 
 If particle motion is confined to two directions the simulation is referred to as 2D-DEM; if full three directional movement is allowed the simulation is referred to as 3D-DEM. For mineral processing design applications the “particles” are generally ore particles, grinding media pieces or bubbles. Constitutive equations can be provided for interactive forces, energy dissipation, wear and breakage. 
 
      CFD simulations focus on continuous flow behavior of fluids and slurries modeled as pseudo-fluids by solving a modified form of the full Navier Stokes Equation, i.e.,  
               ρ   ⁢     Dv   Dt       =       -     ∇   P       +     η   ⁢           ⁢       ∇   2     ⁢   v       +     ρ   ⁢           ⁢   g     +       (     1     1   -   ɛ       )     ⁢     f   i                 (   2   )             
 
 at any point in the continuous phase x, y, z. The last term is a fluid-particle interaction term which accounts for losses resulting from mutual interactions. DGB simulations focus on discrete particles in the same way that DEM does except in this case each physical particle is made up of discrete grains into which strain energy can be stored/released and cracks can propagate along their boundaries governed by the energy conservation equation which governs crack extension force, G, i.e.,  
             G   =       -     1     2   ⁢   t         ⁢       δ   ⁢           ⁢   u       δ   ⁢           ⁢   a                 (   3   )             
 
 where u is the stored strain energy around the crack, a is the crack length and t is the crack width. 
 
      These techniques are used to model the charge motion within the mill. One direct output from this modeling is a complete history of all impact events in the mill and their magnitude. This history of the magnitude, direction and duration of the impact events dissipated inside the mill (energy spectra) are used to determine the wear rate of a liner profile, and in combination with the breakage characteristics of the ore being treated, the throughput capacity of the mill. As the liners wear, the liner profile changes, and therefore also the energy spectra, during the life cycle of the liners. A relationship is developed between the mill throughput capacity and the condition of the liner profile over the life of the liner. This throughput capacity/liner life relationship, together with the liner wear data, are combined with economic data from the mill being optimized and are used to generate a Nett Present Value (NPV) model for the mill. Such an NPV model clearly defines the financial benefit of one liner profile over the other. This NPV data, or alternatively a more simplified criteria of maximum liner life or maximum mill throughput capacity, are used to generate the parameter values that are used in the liner profiles  16  and  116 .  
      In the particular applications described above, it has been found that selection or identification of the parameters for the equations forming profiles  16  and  116  may be limited to the following ranges: 
      H L , H T , h L  and h T : &gt;5 mm     P, q L , q T , P L , and P T : 0.00001-20.0, 2.7-12.8, 13.8-50.8, and &gt;52.8     B, B L , B T , b T , and b L : &gt;5 mm    

      Profiles  16  and  116  have overall characteristics that have been found to optimize throughput of the mill and/or life of the liner. Although profiles  16  and  116  are generally defined by the above described equations, inconsequential or insubstantial changes may be made to such profiles which may result in portions of the profile not precisely meeting the described equations, but which may still achieve the through put and/or prolonged life. For example, a profile which does not exactly follow the above defined equations may still achieve the noted benefits if the alternative profile meets the following criteria.  
      Given two liner profiles, for the leading or trailing part of each of the two liner lifters, or for the leading or trailing part of each of the two liner speed bumps: 
          i) Calculate the equal-weighted root-mean-square (RMS) of the difference between the height (y co-ordinates) of the two liner profiles along the entire length (x co-ordinates) of the leading or trailing edge, and     ii) calculate the equal-weighted mean value of the height of the lifter or the speed bump, measured with respect to the base of the lifters or speed bump, and     iii) divide the calculated value of the difference in the lifter height (RMS) by the calculated mean value of height of the lifter or speed bump and define the quotient as the error.        

      If the error as defined above is less than 5%, then the liner profile would be considered similar to that described.  
      Although profiles  16  and  116  are illustrated and described and utilized in an SAG mill, inner profiles  16  and  116  may alternatively be utilized by other grinding applications. For example, profiles  16  and  116  may alternatively be utilized in cylindrical, rod and pebble mills, conical ball and pebble mills batch mills, vibrating ball mills, stirred media mills and other mills.  
      Although the present invention has been described with reference to example embodiments, workers skilled in the art will recognize that changes may be made in form and detail without departing from the spirit and scope of the invention. For example, although different embodiments may have been described as including one or more features providing one or more benefits, it is contemplated that the described features may be interchanged with one another or alternatively be combined with one another in the described example embodiment or in other alternative embodiments. Because the technology of the present invention is relatively complex, not all changes in the technology are foreseeable. The present invention described with reference to the example embodiment and set forth in the above definitions is manifestly intended to be as broad as possible. For example, unless specifically otherwise noted, the definitions reciting a single particular element also encompass a plurality of such particular elements.