Abstract:
An abrasive tool includes a back plate with a first side and a second side, a plurality of segment mounts disposed in spaced relation along a majority of said first side, a plurality of abrasive segments engaged by the segment mounts, the second side being configured for attachment to a grinding machine. A method of manufacture of an abrasive tool includes providing a backing plate configured to be mounted onto a grinding machine, providing abrasive segments, and mounting the segments onto a majority of the surface of the backing plate.

Description:
RELATED APPLICATIONS 
       [0001]    This application claims the benefit under 35 USC 119(e) of U.S. Provisional Application No. 61/011,473, filed on Jan. 17, 2008, which is incorporated herein by reference in its entirety. 
     
    
     BACKGROUND 
       [0002]    1. Technical Field 
         [0003]    This invention relates to abrasive tools, and more particularly to grinding wheels having customizable grinding faces. 
         [0004]    2. Background Information 
         [0005]    Abrasive tools such as grinding wheels are often customized for particular operations. For example, a grinding wheel may be provided with relatively large abrasive grains for rough grinding, or relatively small abrasive grains for precision grinding. A typical bonded abrasive grinding wheel is manufactured by mixing abrasive particles with a suitable bond matrix material (e.g., in liquid or powder form), which is then compressed in a mold to form a desired shape. This “green” form is then consolidated by sintering at a suitable temperature to form a unitary body having a plurality of abrasive particles dispersed uniformly therethrough. 
         [0006]    Since the abrasive grains are integrated into the tool at an early stage in the production process, neither the tool nor the manufacturing line therefor, can be easily reconfigured for tools of differing sizes or abrasive/bond composition. Moreover, in part because separate tooling (e.g., wheel molds) is required for each wheel size, re-configuring conventional manufacturing lines tends to be labor intensive, often resulting in relatively long lead times. Provisions to increase coolant distribution or swarf removal, such as increasing porosity of the tool, require additional manufacturing steps generally associated with molding/sintering or finishing operations. These aspects typically result in a relatively expensive, multi-step fabrication process, having relatively long lead and process times, for each distinct tool configuration. 
         [0007]    Therefore, a need exists for a tool and fabrication process therefor, which may be easily reconfigured for distinct sizes and abrasive/bond configurations. 
       SUMMARY 
       [0008]    In one aspect of the invention, an abrasive grinding tool is provided with a backing plate, adapted to support abrasive segments in a plurality of positions over a majority of the surface area thereof, the backing plate also being configured to be secured to a grinding machine. 
         [0009]    The abrasive segments and gaps between the segments may form a geometric pattern across all or a portion of the grinding side of the backing plate. The abrasive segments may be threadably secured, secured by adhesive resin (e.g., epoxy), or secured by any other suitable conventional means. The abrasive segments are available in a plurality of shapes and abrasive grain configurations. The sizes of the areas of the grinding surfaces of each of the abrasive segments may optionally be uniform. 
         [0010]    In another aspect of the invention, the abrasive segments are removably secured and interchangeable. This allows the user to remove some segments and to replace them with segments of the desired formulation in the desired geometric pattern on the backing plate. This allows the backing plate to be reused after some abrasive segments have been worn. 
         [0011]    In yet another aspect of this invention, a method of manufacture of an abrasive tool includes providing a backing plate configured to be mounted onto a grinding machine, providing abrasive segments, and mounting the segments onto a majority of the surface of the backing plate. 
         [0012]    The above and other features of the invention including various details of construction and combinations of parts, and other advantages, will now be more particularly described with reference to the accompanying drawings and pointed out in the claims. It will be understood that the particular method and device embodying the invention are shown by way of illustration and not as a limitation of the invention. The principles and features of this invention may be employed in various and numerous embodiments without departing from the scope of the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]    The above and other features and advantages of this invention will be more readily apparent from a reading of the following detailed description of various aspects of the invention taken in conjunction with the accompanying drawings, in which: 
           [0014]      FIG. 1  is a plan view of an embodiment of the claimed invention; 
           [0015]      FIG. 2A  is a perspective, schematic view of the embodiment of  FIG. 1  during a step of fabrication thereof; 
           [0016]      FIG. 2B  is a top plan view of the embodiment of  FIG. 2A  during a step of fabrication thereof; 
           [0017]      FIG. 2C  is a bottom plan view of the embodiment of  FIG. 2A ; 
           [0018]      FIG. 3  is a cross sectional view taken along  3 - 3  of  FIG. 2A ; 
           [0019]      FIG. 4  is a cross sectional view taken along  3 - 3  of  FIG. 2A  of an alternate embodiment of the invention; 
           [0020]      FIGS. 5-6F  are views similar to that of  FIG. 1  of an alternate embodiments of the claimed invention; 
           [0021]      FIG. 7A  is a chart of an exemplary manufacturing process in accordance with the claimed invention; 
           [0022]      FIG. 7B  is a chart of a representative manufacturing process of a conventional grinding wheel; 
           [0023]      FIG. 8  is a top plan view of a test wheel of the present invention prior to test grinding operations; 
           [0024]      FIG. 9  is a view similar to that of  FIG. 8 , of a control grinding wheel prior to test grinding operations; 
           [0025]      FIG. 10  is a perspective view of the wheel of  FIG. 8  during test grinding operations; 
           [0026]      FIG. 11  is a perspective view of the control wheel of  FIG. 9  during test grinding operations; 
           [0027]      FIG. 12  is a top plan view of the embodiment of  FIG. 8  after test grinding operations; 
           [0028]      FIG. 13  is a top plan view of the control wheel of  FIG. 9  after test grinding operations; 
           [0029]      FIG. 14  is a graph of surface grinding efficiency versus wheel wear rate for the wheels of  FIGS. 8 and 9 ; 
           [0030]      FIG. 15  is a graph of unit power versus Material Removal Rate for the wheels of  FIGS. 8 and 9 ; 
           [0031]      FIG. 16  is a graph of Wheel Wear Rate versus Material Removal Rate for the wheels of  FIGS. 8 and 9 ; 
           [0032]      FIG. 17  is a graph of Unit Power versus Material Removal Rate for the wheels of  FIGS. 8 and 9 ; 
           [0033]      FIG. 18  is a graph of Wheel Wear Rate versus Material Removal Rate for the wheels of  FIGS. 8 and 9 ; 
           [0034]      FIG. 19  is a graph of Unit Power versus G-Ratio for the wheels of  FIGS. 8 and 9 ; and 
           [0035]      FIG. 20  is a graph of expected Unit Power versus expected Material Removal Rate for embodiments of the present invention. 
           [0036]      FIG. 21  is a graph of Average Power versus G-ratio for several wheels according to embodiments of the invention and for control wheels. 
           [0037]      FIG. 22  is a graph of G-Ratio versus MRR for several wheels according to embodiments of the invention and for control wheels. 
           [0038]      FIG. 23  is a graph of Average Power versus MRR for several wheels according to embodiments of the invention and for control wheels. 
           [0039]      FIG. 24  is a graph of Unit Power versus MRR for several wheels according to embodiments of the invention and for control wheels. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0040]    In the following detailed description, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration, specific embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention, and it is to be understood that other embodiments may be utilized. It is also to be understood that structural, procedural and system changes may be made without departing from the spirit and scope of the present invention. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope of the present invention is defined by the appended claims and their equivalents. For clarity of exposition, like features shown in the accompanying drawings shall be indicated with like reference numerals and similar features as shown in alternate embodiments in the drawings shall be indicated with similar reference numerals. 
         [0041]    Where used in this disclosure, the term “axial” when used in connection with an element described herein, refers to a direction parallel to an axis of rotation of a grinding wheel onto which the element is installed. The term “transverse” refers to a direction substantially orthogonal to the axial direction. 
         [0042]    As discussed above, conventional bonded abrasive grinding wheels are generally manufactured by mixing abrasive grains with a bonding material, molding and sintering the wheel, and attaching the tool onto a tool body or flange for engagement with a grinding machine. The instant invention represents a fundamental departure from such conventional manufacturing processes as it includes a tool which may be manufactured without being molded and sintering as a single unit. Instead, embodiments of the invention may be fabricated by assembling pre-manufactured abrasive segments in nominally any desired pattern on a backing plate to form a collective grinding face customized for any number of grinding applications. Thus, rather than relying on variations in abrasive/bond mixture and wheel diameter, etc., for customization during wheel fabrication, the instant invention enables the wheels to be customized simply by varying the selection (e.g., by grain type, composition), placement, and number of various segments. 
         [0043]    In providing their simplified manufacturing approach, the instant inventors departed from conventional wisdom by increasing, rather than decreasing, the number of discrete components. Despite the increased number of components, relative simplicity was achieved by effectively moving product customization from the conventional abrasive/bond mixture and molding steps, to post-mold operations. In this manner, a wide range of customization may be provided using a relatively small number of discrete segment types, to advantageously simplify and streamline the molding and sintering processes, which processes tend to be relatively labor- and capital-intensive. For example, as described herein, segments of only a single size may be capable of producing grinding wheels having diameters ranging from 125 mm to 1200 mm or more. (Segments of various sizes, e.g., transverse and axial dimensions, may be used to further expand the range of possible wheel configurations. Indeed, embodiments having segments of at least two distinct sizes have been shown to provide a grinding wheel with desired grinding face area and product robustness in some applications.) This may effectively reduce process downtime associated with re-configuration of production lines for various product sizes, types, etc. This also tends to reduce product lead time, since the wheels may be assembled from inventoried segments, i.e., without the need to effect any mixing, molding, sintering, etc., at the time of wheel fabrication. So although the number of components within a specific tool may be relatively high, the number of distinct abrasive/bond combinations molded and sintered may be reduced, with variations in wheel size and composition handled post-mold, simply by varying the number and placement and/or type of segments. 
         [0044]    Turning now to  FIG. 1 , cylindrical abrasive segments  30  are secured to backing plate  20  to effectively form a grinding wheel  10 . The backing plate  20  is a disc which may be made of any material having the requisite structural integrity to secure the segments in position during a particular grinding operation, e.g., during rotation about its central axis at a rotational speed of several hundred rotations per minute (RPM) and surface feet per minute (SFPM) as discussed hereinbelow. Suitable materials may include reinforced polymeric materials such as glass reinforced polyester, and metallic materials such as various steels, cast iron, or various powdered metal constructions. Backing plate  20  may be fabricated in any desired manner, by use of conventional approaches such as molding, casting, machining, powder metallurgy, etc. The backing plate may be fabricated as a single component, or as a multi-component assembly. 
         [0045]    The abrasive segments  30  may contain various types of abrasive grains known to those skilled in the art, such as alumina, alumina zirconia, silicon carbide, cubic boron nitride (CBN), diamond particles, and mixtures thereof. The segments may be fabricated from substantially any abrasive/bond combination known to those skilled in the art of grinding wheels, and/or which may be developed in the future. Examples of suitable abrasive/bond materials and mixtures, and fabrication techniques useful therefor, are disclosed in U.S. Pat. Nos. 5,658,360; 6,015,338; and 6,251,149; and U.S. Ser. No. 10/510,541, assigned to Saint-Gobain Abrasives, Inc., which are fully incorporated herein by reference. 
         [0046]    As shown, the segments each have a grinding face  32  which collectively form a grinding face  22  of the wheel  10 . The grinding faces  32  of the segments may define mutually distinct surface areas, or alternatively, may define areas that are substantially uniform from segment to segment. Moreover, segments  30  may be removable, such as discussed hereinbelow, to be interchangeable with one another for replacement or to reconfigure a wheel for different grinding application. 
         [0047]    Turning now to  FIG. 2A , abrasive segments  30  may be fastened to backing plate  20  in any convenient manner, such as by engagement with suitably sized and shaped mounts  40 , such as in the form of surfaces or cavities disposed along side  24  of backing plate  20  to which segments may be bonded or inserted. Internal threads  60  may be drilled, molded or otherwise disposed in side  26  of plate  20  for securing the wheel  110  to a grinding machine. 
         [0048]    Turning now to  FIG. 2B , segments having nominally any transverse shape may be fastened to backing plate  20 , to provide a wide variety of collective grinding face patterns. As shown, examples of such multi-shaped segments include cylindrical segments  30 , wedge shaped segments  130 , hexagonal segments  230 , diamond shaped segments  330 , and complex segments  430 . The particular segment shape may be chosen based on its suitability for a particular grinding application. For example, cylindrical segments  30  having relatively large size abrasive, may be used for rough grinding, while hexagonal pellets  230  having relatively small size abrasive may be used for fine grinding. The spacing between segments may also be customized for particular operations. Wider spacing, for example, may be desired in some rough grinding applications to facilitate swarf removal. 
         [0049]    In addition to the distinct sizes and shapes shown, abrasive segments  30 ,  130 ,  230 , and  330  may also have distinct abrasive and bond compositions. For example, cylindrical segments  30  may have larger abrasive particulates for rough grinding, and diamond shaped abrasive segments may have smaller abrasive particulates for precision grinding. The segments may be color coded to the various compositions thereof, such as by including a pigment with the abrasive/bond mixture, to enable users to easily distinguish between segments that are otherwise similar in appearance. 
         [0050]    As also shown, the abrasive segments and the gaps formed between them may be arranged to form a collective grinding face  22  having a geometric pattern. The particular geometric pattern may be chosen based on the needs of particular operations. For example, patterns providing for a relatively large network of gaps  42  between segment grinding faces  32 ,  132 ,  232 ,  332 ,  432  may facilitate distribution of coolant and other grinding aids, and the removal of debris such as grinding swarf. These gaps  42  may thus reduce the need for adding porosity to the abrasive/bond mixture to further simplify the molding/sintering operations. 
         [0051]    As mentioned hereinabove, substantially any geometric pattern formed by abrasive segments and spaces between the segments, may be used. For example, the embodiment of  FIG. 5  includes diamond shaped abrasive segments  330 . Additional exemplary patterns are shown in  FIGS. 6A-6F . The embodiment of  FIG. 6A  includes a pattern formed with cylindrical abrasive segments  30  of uniform size, while the embodiments of  FIGS. 6B and 6F  include cylindrical abrasive segments  30 ,  34 ,  36 ,  38  of varying sizes. As shown in  FIG. 6C , alternate embodiments may include patterns formed by wedge shaped segments  130  of varying sizes, with gaps  142  therebetween. A pattern formed by diamond shaped segments  330  with gaps  342  is shown in  FIG. 6D , while a pattern formed by hexagonal shaped segments  230  and gaps  242  is shown in  FIG. 6E . 
         [0052]    Referring now to  FIG. 2C , backing plate  20  may be provided with an array of threaded fastener portions  60  (e.g., threaded bores, as shown) forming any number of patterns suitable for fastening the wheel  200  to a tool such as a grinding machine. The threaded bores  60  may be provided by any suitable means, such as drilling and tapping, molding into the backing plate, or by molding threaded inserts in-situ within the plate. 
         [0053]    Abrasive segments  30 ,  130 ,  230 , etc., may be fastened to backing plate  20  in any convenient manner. For example, as shown in  FIG. 3 , the segments may be threadably fastened to side  24  of backing plate  20  ( FIG. 2A ) using a threaded mandrel  44 . Any suitable means for fastening mandrel  44  to the abrasive segment  30  may be used. 
         [0054]    As shown, mandrel  44  may be threadably received within a segment backing plate  50 . Alternatively, mandrel  44  may be molded in place within abrasive segment  30  during fabrication thereof, such as in the event segment backing plate  50  is not used. Still further, mandrel  44  may be glued or otherwise secured within a bore in abrasive segment  30 , using an epoxy or other suitable adhesive. 
         [0055]    Turning now to  FIG. 4 , as a further alternative, segment backing plate  50 ′ may include a threaded insert  46  which is molded in-situ within the segment during fabrication thereof. Alternatively, threaded insert  46  may be cemented with epoxy, or otherwise bonded within a suitably sized and shaped recess within abrasive segment  30 . The insert  46  may threadably engage a mandrel  44  such as shown in  FIG. 3 . 
         [0056]    As shown in  FIGS. 7A and 7B , an exemplary manufacturing process ( FIG. 7A ) for embodiments of the present invention includes fewer steps than a typical manufacturing process associated with conventional grinding wheels ( FIG. 7B ). Moreover, various manufacturing steps shown in  FIG. 7A  may be automated for further simplification and associated cost savings. For example, filling of segment molds may be effected automatically using a conventional volumetric automatic press. Assembly of the various segments onto the back plate may also be automated, e.g., using conventional robotic assembly means such as commonly used in automobile assembly plants and the like. Moreover, as discussed hereinabove, because the various segments may be pre-fabricated and stored in inventory, assembly of the segments onto the back plates may be performed on-demand, e.g., to reduce manufacturing assembly/lead time. 
         [0057]    Optional aspects of the exemplary manufacturing process include the reduction or elimination of many finishing steps. For example, any need for discrete segment leveling steps after wheel fabrication may be reduced by arranging the segments with their grinding faces against a planar surface, and then gluing the plate onto the back of the segments. The planar surface would nominally ensure that all of the segment faces are co-planar. Other conventional finishing steps, such as the drilling of holes in the wheel for swarf removal may also be eliminated, due to the existence of gaps  42  between the segments. 
         [0058]    The following illustrative example is intended to demonstrate certain aspects of the present invention. It is to be understood that this example should not be construed as limiting. 
       Example I 
       [0059]    An experimental grinding wheel  10  was fabricated substantially as shown and described hereinabove with respect to  FIG. 8 , including 38 cylindrical segments  30  spaced along a backing plate  20  having a 5 in (12.7 cm) diameter. The abrasive segments  30  were produced using a manual arbor press, having uniform dimensions of approximately ⅝ in (1.59 cm) diameter and approximately ⅝ in (1.59 cm) (axial) depth. The abrasive segments  30  were fastened to the back plate  20  using standard plate mount 2 part epoxy (Epoweld® epoxy 13230 part A &amp; B, from Royal Adhesives and Sealants, LLC, South Bend Ind.). The total contact area of the collective grinding face  22  (i.e., the total contact area of contact between the mosaic wheel and the workpiece) was 15.48 cm2. 
         [0060]    The wheel  10  was tested and compared with a conventional 5 inch (control) grinding wheel  12 , as shown in  FIG. 9 . Both the standard wheel  12  and the abrasive segments  30  of the mosaic wheel  10  were formulated in accordance with the 38A80 (3948) (i.e., semi friable white agglomerated Alundum)/80 grit size—E14 (Porosity/Abrasive vol.) B493 Bond (65% 29-717 phenolic resin and 35% Calcium Fluoride (CaF2) Vortex specification, as shown in the following Table I. The contact area of the standard wheel  12  was 106.45 cm2. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
             
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE I 
               
               
                   
               
               
                 T361 Grade (Bond) E-14 Abr. rho 3.95&lt; 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Agglom- 
                 Wa 
                 0.974 
                 rho g 
                 Va 
                 0.9579 
                 Aion rho 
               
               
                 erate 
                 Wg 
                 0.026 
                 2.4 
                 Vg 
                 0.0421 
                 4.055 
               
               
                   
                   
                 1.000 
                   
                   
                 1.000 
               
               
                   
               
               
                   
                 Porosity 
                   
                 Abrasive 
               
               
                   
                 (vol.) 
                   
                 (vol.) 
               
               
                   
               
               
                 B 
                 0.50 
                 17 
                 0.30 
                 Va 
                 0.36&lt; 
               
               
                 C 
                 0.48 
                 16 
                 0.32 
                 Vb 
                 0.20 
               
               
                 D 
                 0.46 
                 15 
                 0.34 
                 Vp 
                 0.44&lt; 
               
               
                 E 
                 0.44 
                 14 
                 0.36 
                   
                 1.00 
               
               
                 F 
                 0.42 
                 13 
                 0.38 
               
               
                 G 
                 0.40 
                 12 
                 0.40 
               
             
          
           
               
                 H 
                 0.38 
                 11 
                 0.42 
                 @increase lpr-1 level if mix is dusty 
               
               
                 I 
                 0.36 
                 9 
                 0.46 
                 @go to 76 standard bake if wheels/slugs slump 
               
               
                 J 
                 0.34 
               
               
                 K 
                 0.32 
               
               
                 L 
                 0.30 
                   
                   
                 Slug wt. 9.1 g 
               
               
                 M 
                 0.28 
               
               
                   
               
             
          
           
               
                 resin &gt; 65.00 
                 filler (60/40) 35 
                 bond rho 1.945 
               
               
                   
               
             
          
           
               
                 added bond 
                 Adj 
                   
                 mix 
                   
                   
                   
               
               
                 0.1842 vol 
                 resin 
                 Adj 
                 size 
                 Mix 
               
               
                 fract in 1 cc, 
                 factor 
                 wt % 
                 200 g 
                 weights 
                   
                 Cummulative 
               
               
                   
               
             
          
           
               
                 agg 
                 1.460 
                 0.8030 
                 x1.00 
                 0.803 
                 x200 
                 160.60 
                 3948-80 
                   
                   
               
               
                 resin 
                 0.153 
                 0.0843 
                 x0.23 
                 0.0194 
                 x200 
                 3.88 
                 Lpr-1 
                   
                 164.48 
               
               
                   
                   
                   
                 x0.77 
                 0.0649 
                 x200 
                 12.98 
                 t361 
                  {close oversize brace}  
                 35.52 
               
               
                 filler 
                 0.205 
                 0.1127 
                 x1.00 
                 0.1127 
                 x200 
                 22.54 
                 CaF2 
               
               
                   
                 1.818 
                   
                   
                   
                   
                 200.00 g 
                   
                   
                 200.00 g 
               
               
                   
               
             
          
         
       
     
         [0061]    The experimental and control wheels were tested under the following conditions: 
         [0062]    Machine: Track Grinder Disc Simulation 
         [0063]    Material: 1070 
         [0064]    Work Speed: 3 RPM 
         [0065]    Wheel Speed: 4202 RPM; 5500 SFPM (Surface Feet Per Minute) 
         [0066]    In Feed Rates: 0.002, 0.0027, 0.004 in/rev. 
         [0067]    MRR (Material Removal Rates): 0.67, 0.90, 1.34 in 3 /min./in 2    
         [0068]    To ensure that the segments had the mechanical properties sufficient to withstand the centrifugal forces during the test conditions, the following assumptions and calculations were made: 
         [0069]    centrifugal force acts as a single force at the tip of the segment 
         [0070]    the segment is modeled as a cylindrical cantilever beam 
         [0071]    maximum strength is 80% of the average mechanical strength 
         [0072]    The following equations were used to estimate the stress on a single segment on the OD of the wheel where maximum stress is encountered: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       Force 
                       centrifugal 
                     
                      
                     
                       ( 
                       N 
                       ) 
                     
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               ( 
                               
                                 Mass 
                                  
                                 
                                     
                                 
                                  
                                 of 
                                  
                                 
                                     
                                 
                                  
                                 segment 
                                  
                                 
                                     
                                 
                                  
                                 in 
                                  
                                 
                                     
                                 
                                  
                                 Kg 
                                 * 
                               
                             
                           
                         
                         
                           
                             
                               
                                 ( 
                                 
                                   Velocity 
                                    
                                   
                                       
                                   
                                    
                                   of 
                                    
                                   
                                       
                                   
                                    
                                   segment 
                                    
                                   
                                       
                                   
                                    
                                   in 
                                    
                                   
                                       
                                   
                                    
                                   m 
                                    
                                   
                                     / 
                                   
                                    
                                   s 
                                 
                                 ) 
                               
                               2 
                             
                           
                         
                       
                       ] 
                     
                     
                       ( 
                       
                         radius 
                          
                         
                             
                         
                          
                         of 
                          
                         
                             
                         
                          
                         disc 
                          
                         
                             
                         
                          
                         in 
                          
                         
                             
                         
                          
                         m 
                       
                       ) 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   1 
                 
               
             
             
               
                 
                   
                     
                       Stress 
                        
                       
                           
                       
                       [ 
                       
                         on 
                          
                         
                             
                         
                          
                         segment 
                       
                       ] 
                     
                      
                     
                       ( 
                       MPa 
                       ) 
                     
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     Force 
                                     centrifugal 
                                   
                                    
                                   in 
                                    
                                   
                                       
                                   
                                    
                                   N 
                                 
                                 ) 
                               
                               * 
                             
                           
                         
                         
                           
                             
                               ( 
                               
                                 
                                   L 
                                   [ 
                                   length 
                                   ] 
                                 
                                  
                                 
                                     
                                 
                                  
                                 in 
                                  
                                 
                                     
                                 
                                  
                                 mm 
                               
                               ) 
                             
                           
                         
                       
                       ] 
                     
                     
                       [ 
                       
                         
                           ( 
                           
                             ∏ 
                             
                               / 
                               4 
                             
                           
                           ) 
                         
                         * 
                         
                             
                         
                          
                         
                           
                             ( 
                             
                               radius 
                                
                               
                                   
                               
                                
                               in 
                                
                               
                                   
                               
                                
                               mm 
                             
                             ) 
                           
                           3 
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   2 
                 
               
             
           
         
       
     
         [0073]    The following Table II provides examples of the calculations used to estimate the required sizes of the segments and backing plates for testing. 
         [0000]    
       
         
               
               
               
               
               
             
               
               
               
             
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE II 
               
               
                   
                   
               
             
             
               
                   
                 Sm 
                 Max strength 
                 9.6 
                 MPa 
               
               
                   
                 v 
                 Wheel Speed 
                 48.5 
                 m/s 
               
             
          
           
               
                 plug density 
                 1.85 
                 g/cc 
               
               
                   
               
             
          
           
               
                   
                 Rw 
                 radius, wheel 
                 m 
               
               
                   
                 Rp 
                 radius, plug 
                 mm 
               
               
                   
                 L 
                 length, plug 
                 mm 
               
               
                   
                 m 
                 mass 
                 kg 
               
               
                   
                   
               
             
          
           
               
                   
                 radius, 
                   
                   
                   
                   
                   
                   
               
               
                   
                 wheel 
                 Rp 
                 L 
                 Mass 
                 Fcent 
                 Stress 
               
               
                 in 
                 m 
                 mm 
                 mm 
                 kg 
                 (N) 
                 (MPa) 
                 Failure ? 
               
               
                   
               
               
                 6 
                 0.1524 
                 7.9 
                 25.4 
                 0.0093 
                 143.2 
                 9.3 
                 No 
               
               
                 6 
                 0.1524 
                 7.9 
                 20.3 
                 0.0074 
                 114.6 
                 5.9 
                 No 
               
               
                 6 
                 0.1524 
                 7.9 
                 17.0 
                 0.0062 
                 95.9 
                 4.2 
                 No 
               
               
                 6 
                 0.1524 
                 7.9 
                 12.7 
                 0.0046 
                 71.6 
                 2.3 
                 No 
               
               
                 30 
                 0.762 
                 7.9 
                 76.2 
                 0.0279 
                 85.9 
                 16.7 
                 Yes 
               
               
                 30 
                 0.762 
                 19.1 
                 101.6 
                 0.2142 
                 659.8 
                 12.4 
                 Yes 
               
               
                 30 
                 0.762 
                 25.4 
                 101.6 
                 0.3808 
                 1173.0 
                 9.3 
                 Yes 
               
               
                 6 
                 0.1524 
                 12.7 
                 25.4 
                 0.0238 
                 366.6 
                 5.8 
                 No 
               
               
                   
               
             
          
         
       
     
         [0074]    Advantages of the empty gaps between the abrasive segments became apparent during and after testing. During the grinding test it was observed that the two wheels distribute coolant differently. As shown in  FIG. 10 , the mosaic wheel  10  distributed coolant more evenly than the standard wheel  12  shown in  FIG. 11 . After the grinding operation, the standard wheel  12  had swarf in the grinding area ( FIG. 13 ). The mosaic wheel  10  had grinding swarf trapped in the gaps between the segments, and a small amount of swarf on the grinding contact area ( FIG. 12 ). 
         [0075]    A graph was developed ( FIG. 14 ) comparing Wheel Wear Rate and Surface Grinding Efficiency. This graph does not take into account that the mosaic wheel  10  is drawing less power, cutting at a lower material removal rate, and has 30% less workpiece contact area than the standard  12 . Notwithstanding these qualifications, the graph of  FIG. 14  shows that the mosaic wheel  10  has a slightly better cutting efficiency and is somewhat more durable than the standard wheel  10 . 
         [0076]    When comparing unit power plotted against the material removal rate (MRR), the performances of the mosaic wheel and the standard wheel were approximately equal. ( FIG. 15 ). The performances of the mosaic wheel and the standard wheel were also approximately equal when Wheel Wear Rate (WWR) was plotted against the MRR. ( FIG. 16 ). At a particular MRR, the mosaic wheel has higher wheel wear and shorter life, likely due to the lower abrasive volume of the wheel relative to the control wheel. ( FIGS. 17 ,  18 ). 
         [0077]    As seen in the graph of  FIG. 19 , the mosaic wheel appears to operate as efficiently as the standard wheel, except at higher MRRs, where the exemplary wheel exhibits a slightly lower G—ratio (the ratio of work material to wheel material removed during grinding), and draws more power than the control wheel. As seen in the graph of  FIG. 20 , performance of the mosaic wheel may be improved as the proportion of resin content is increased. Increased resin content may also advantageously improve mechanical strength, as can be seen in Table III. It is also expected that the use of various conventional fillers may be desired in some applications to improve MMR and reduce power consumption. 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE III 
               
             
             
               
                   
                   
               
               
                   
                 Mosaic wheel 
                 Mechanical Properties 
                   
               
             
          
           
               
                   
                 content 
                 Dry (MPa) 
                 Wet (MPa) 
               
               
                   
                   
               
             
          
           
               
                   
                 100% resin 
                 24 
                 20 
               
               
                   
                 80/20 resin/filler 
                 18.3 
                 13 
               
               
                   
                 60/40 resin/filler 
                 11.1 
                 8.2 
               
               
                   
                   
               
             
          
         
       
     
         [0078]    It is estimated that the experimental wheel may be manufactured at a material cost savings of approximately 12 percent, a labor cost reduction of about 70 percent, a process time reduction of about 80 percent, and a lead time reduction of about 75 percent relative to the control wheel. 
       Example II 
       [0079]    Experimental grinding wheels, otherwise similar to those of Example I, were fabricated with the segment pattern shown in  FIG. 6B , to provide a collective grinding face of relatively increased surface area. As shown, these wheels each included twenty one cylindrical segments  30 ,  34  spaced along a backing plate  20  of 5 in (12.7 cm) diameter. Each wheel was provided with segments of the following quantity and dimensions. 
         [0000]    
       
         
               
               
               
             
               
               
               
             
           
               
                   
               
               
                 No. of segments 
                 Diameter 
                 Axial Depth 
               
               
                 per wheel 
                 in. (cm) 
                 in. (cm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 14 
                    1 (2.54) 
                 0.750 (1.9) 
               
               
                 7 
                 0.750 (1.9) 
                 0.750 (1.9) 
               
               
                   
               
             
          
         
       
     
         [0080]    The segments were formulated substantially as described in Example I, using phenolic and epoxy resins (Durez Varcum® phenolic resin 29-717, Durez Corporation, Dallas Tex., and Araldite® epoxy resin, Huntsman Advanced Materials Americas Inc., Brewster, N.Y.). The segments were fabricated in the following structure and grade series (Table I) and resin/filler amounts. 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Structure 
                 Grades 
                 Resin/Filler 
               
               
                   
                   
               
             
             
               
                   
                 14 (36% 
                 H-I-J 
                 Phenolic (29-717) 65/35 CaF2 
               
               
                   
                 abrasive) 
               
               
                   
                 14 
                 G-H-I 
                 Phenolic (29-717) 80/20 CaF2 
               
               
                   
                 14 
                 E-F 
                 Epoxy (Araldite 6004) 70/30 CaF2 
               
               
                   
                   
               
             
          
         
       
     
         [0081]    The segments were molded in a multi cavity mold capable of producing 12 segments, (6 of each size). Epoxy segments were baked in the mold: oven preheated to 75° C.; Soak for 1 hour; Ramp to 100° C. and soak for 2 hours. 
         [0082]    The wheels were tested and compared with conventional 5 inch vortex (control) grinding wheels  12 , as used in Example I, and with a similar control wheel fabricated as a conventional L9 (i.e., 30% porosity, 46 wt. % abrasive, Table I) B18 Bond (Saint-Gobain Abrasives, Inc., Worcester, Mass.). 
         [0083]    Test results are shown in  FIGS. 21 to 24 . Referring to  FIG. 21 , the inventive 80/20 phenolic wheels and the epoxy wheels exhibited higher G—Ratios at higher power consumption than both control wheels. The 65/35 phenolic wheels reached nominal parity with the vortex control wheel at I grade, with comparable power consumption and a small increase in MRR. As shown in  FIG. 22 , the epoxy mosaic wheel exhibited a significant increase in G—ratio over the vortex control wheel. As shown in  FIGS. 23 and 24 , both phenolic wheels and the epoxy wheel nominally met or exceeded the MRR of vortex control wheels in many instances. 
         [0084]    The inventive wheels of Example II have therefore been shown to be suitable for many disc grinding applications, particularly those requiring a relatively high MRR. 
         [0085]    The foregoing demonstrates that the grinding wheels of the invention perform comparably, if not better, than conventional grinding wheels, while providing the advantages of a streamlined, less expensive manufacturing process with the capability of relatively simple wheel customization and production line changeover for significantly reduced lead time and manufacturing time. Moreover, in many embodiments, the backing plate may be re-used by simply replacing worn segments with new ones. 
         [0086]    In the preceding specification, the invention has been described with reference to specific exemplary embodiments thereof. It will be evident that various modifications and changes may be made thereunto without departing from the broader spirit and scope of the invention as set forth in the claims that follow. The specification and drawings are accordingly to be regarded in an illustrative rather than restrictive sense. 
         [0087]    While this invention has been particularly shown and described with references to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.