Abstract:
A screw for a plasticating apparatus has one or more helical flights. A portion of the screw has a plurality of advancing grooves arranged in a noncontinuous helix cut in the screw. The advancing grooves are dimensioned to receive material therein as the material is conveyed through the barrel. The screw has a plurality of noncontinuous cross-cut grooves traversing one or more of the advancing grooves. The cross-cut grooves have a second helix angle greater than the first helix angle and less than ninety degrees; and/or one or more of the cross-cut grooves have a third helix angle of about ninety degrees.

Description:
FIELD 
       [0001]    This invention relates to a plasticating apparatus screw rotatable within a barrel to extrude molten resinous material. More particularly, this invention relates to a longitudinal portion of the screw designed to recirculate material for thorough mixing and melting via grooves of various angles and having various depths and depth tapers. 
       BACKGROUND 
       [0002]    A plasticating apparatus typically receives polymer or thermoplastic resin pellets, granules or powders, from an inlet port, then heats and works the resin to convert it into a melted or molten state. The melt or molten material is delivered under pressure through a restricted outlet or discharge port to make the finished article. It is desirable that the molten material leaving the apparatus be completely melted and homogeneously mixed, resulting in uniform temperature, viscosity, color and composition. 
         [0003]    A typical plasticating apparatus includes an elongated cylindrical barrel, which is usually heated at various locations along its length. An axially supported and rotating screw extends longitudinally through the barrel. The screw is responsible for forwarding, melting, pressurizing and homogenizing the material as it passes from the inlet port to the outlet port. The screw has a core with a helical flight thereon and the flight cooperates with the cylindrical inner surface of the barrel to define a helical channel for forward passage of the resin to the outlet port. 
         [0004]    The typical plasticating screw has a plurality of sections along its longitudinal axis with each section being designed for a particular function. Ordinarily, there is a feed section, a transition section, a metering section and a mixing section in series. 
         [0005]    As disclosed in U.S. Pat. No. 6,498,399 and illustrated in  FIG. 1  a plasticating screw  100  has a main channel defined by a helical flight  113  disposed within and cooperating with an inner-wall of a heated barrel (not shown). As illustrated in  FIG. 1 , the prior art screw  100  has a longitudinal portion with a plurality of staggered rows of noncontinuous advancing grooves  130  arranged in the main channel thereof. The axis of each row of advancing grooves  130  is substantially parallel to the helical axis of the adjacent helical flight  113  of the longitudinal portion to promote flow in the direction indicated by the arrow  140 . A noncontinuous helical channel is formed therein traversing in a reverse direction, compared with the direction of the helical flight  113 , the channel having a plurality of retracting grooves  137 . While the objective of the retracting grooves  137  is to promote mixing of the polymer or thermoplastic resin pellets in the main channel, in some instances mixing is insufficient. 
         [0006]    Based on the foregoing, it is the general object of this invention to provide a screw configured for improved mixing of the polymer or thermoplastic resin pellets. 
       SUMMARY 
       [0007]    The present invention resides in one aspect in a screw for a plasticating apparatus. The plasticating apparatus includes a barrel that has an axial length extending between an inlet port and an outlet port. The barrel has an inner wall. The screw has a longitudinal axis and is rotatably supported in the barrel for rotation about the longitudinal axis. The screw has a core and one or more helical flights extending along a length of the screw. The helical flight defines a helix angle relative to the longitudinal axis and defines a first helical path of a first helix angle less than ninety degrees. The helical flight defines a helical channel. The screw may include a feed section cooperating with the inlet port, an intermediate melt section, and/or a metering section cooperating with said outlet port. A longitudinal portion of the screw (e.g., in the feed section, the intermediate melt section, and/or the metering section) has a plurality of advancing grooves formed therein. Each of the advancing grooves has one or both ends closed. The advancing grooves are arranged in a noncontinuous helix cut in the screw core in the helical channel of the screw. The plurality of advancing grooves are dimensioned to receive material therein as the material is conveyed through the helical channel, to the outlet port. The longitudinal portion further has a plurality of noncontinuous cross-cut grooves traversing one or more of the advancing grooves. One or more of the cross-cut grooves has a second helix angle greater than the first helix angle and less than ninety degrees; and/or one or more of another of the cross-cut grooves has a third helix angle of about ninety degrees. 
         [0008]    In one embodiment, each cross-cut groove passes through the helical flight not more than two times so that the material can back flow and recirculate within said longitudinal portion. 
         [0009]    In one embodiment, one or more of the plurality of advancing grooves includes an advancing groove depth taper; and/or one or more of the plurality of cross-cut grooves having a cross-cut groove depth taper. 
         [0010]    The present invention also resides in another screw for a plasticating apparatus. The plasticating apparatus includes a barrel that has an axial length extending between an inlet port and an outlet port. The barrel has an inner wall. The screw has a longitudinal axis and is rotatably supported in the barrel for rotation about the longitudinal axis. The screw has a core and one or more helical flights extending along a length of the screw. The helical flight defines a helix angle relative to the longitudinal axis and defines a first helical path of a first helix angle less than ninety degrees. The helical flight defines a helical channel. The screw may include a feed section cooperating with the inlet port, an intermediate melt section, and/or a metering section cooperating with said outlet port. A longitudinal portion of the screw (e.g., in the feed section, the intermediate melt section, and/or the metering section) has a plurality of advancing grooves formed therein. Each of the advancing grooves has one or both ends closed. The advancing grooves are arranged in a noncontinuous helix cut in the screw core in the helical channel of the screw. The plurality of advancing grooves are dimensioned to receive material therein as the material is conveyed through the helical channel, to the outlet port. The longitudinal portion further has a plurality of noncontinuous cross-cut grooves traversing several advancing grooves. One or more of the plurality of advancing grooves has an advancing groove depth taper; and/or one or more of the plurality of cross-cut grooves has a cross-cut groove depth taper. 
         [0011]    The present invention also resides in yet another screw for a plasticating apparatus. The plasticating apparatus includes a barrel that has an axial length extending between an inlet port and an outlet port. The barrel has an inner wall. The screw has a longitudinal axis and is rotatably supported in the barrel for rotation about the longitudinal axis. The screw has a core and one or more helical flights extending along a length of the screw. The helical flight defines a helix angle relative to the longitudinal axis and defines a first helical path of a first helix angle less than ninety degrees. The helical flight defines a helical channel. The screw may include a feed section cooperating with the inlet port, an intermediate melt section, and/or a metering section cooperating with said outlet port. A longitudinal portion of the screw (e.g., in the feed section, the intermediate melt section, and/or the metering section) has a plurality of advancing grooves formed therein. Each of the advancing grooves has one or both ends closed. The advancing grooves are arranged in a noncontinuous helix cut in the screw core in the helical channel of the screw. The plurality of advancing grooves are dimensioned to receive material therein as the material is conveyed through the helical channel, to the outlet port. The longitudinal portion further has a plurality of noncontinuous cross-cut grooves traversing one or more of the advancing grooves. The plurality of cross-cut grooves includes one or more first cross cut grooves having a second helix angle and one or more second cross-cut grooves having a third helix angle. The first helix angle, the second helix angle and the third helix angle are different. 
         [0012]    In one embodiment, the plasticating apparatus includes one or more third cross-cut grooves having a fourth helix angle that is different from the first helix angle, the second helix angle and the third helix angle. 
         [0013]    The present invention also resides in still another screw for a plasticating apparatus. The plasticating apparatus includes a barrel that has an axial length extending between an inlet port and an outlet port. The barrel has an inner wall. The screw has a longitudinal axis and is rotatably supported in the barrel for rotation about the longitudinal axis. The screw has a core and one or more helical flights extending along a length of the screw. The helical flight defines a helix angle relative to the longitudinal axis and defines a first helical path of a first helix angle less than ninety degrees. The helical flight defines a helical channel. The screw may include a feed section cooperating with the inlet port, an intermediate melt section, and/or a metering section cooperating with said outlet port. A longitudinal portion of the screw (e.g., in the feed section, the intermediate melt section, and/or the metering section) has a plurality of advancing grooves formed therein. Each of the advancing grooves has one or both ends closed. The advancing grooves are arranged in a noncontinuous helix cut in the screw core in the helical channel of the screw. The plurality of advancing grooves are dimensioned to receive material therein as the material is conveyed through the helical channel, to the outlet port. The longitudinal portion further has one or more undercut surfaces located radially inwardly from the flight surface. The undercut surface has a depth that varies in a longitudinal direction parallel to the advancing grooves; and/or in a direction traverse to the longitudinal direction. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]      FIG. 1  is a schematic view of a portion of the surface of a prior art screw for a plasticating apparatus; 
           [0015]      FIG. 2  is a schematic view of a screw for a plasticating apparatus of the present invention, shown in a cut away view of a barrel; 
           [0016]      FIG. 3  is a schematic view of a portion of the surface of a screw for a plasticating apparatus of the present invention illustrating neutrally oriented cross-cut grooves on the screw; 
           [0017]      FIG. 4A  is a schematic view of a portion of the surface of a screw for a plasticating apparatus of the present invention illustrating cross-cut grooves on the screw oriented in a common direction to the flight of the screw and each cross-cut groove cutting through one flight; 
           [0018]      FIG. 4B  is a schematic view of a portion of the surface of a screw for a plasticating apparatus of the present invention illustrating cross-cut grooves on the screw oriented in a common direction to the flight of the screw and each cross-cut groove cutting through two flights; 
           [0019]      FIG. 5  is a schematic view of a portion of the surface of a screw for a plasticating apparatus of the present invention illustrating a combination of neutrally oriented cross-cut grooves and cross-cut grooves oriented in a multiple directions; 
           [0020]      FIG. 6  is a schematic view of a portion of the surface of a screw for a plasticating apparatus of the present invention illustrating advancing grooves having varying depths and depth tapers; 
           [0021]      FIG. 7A  is a cross sectional view of a portion of the surface of the screw of  FIG. 6  taken across line  7 A- 7 A; 
           [0022]      FIG. 7B  is a cross sectional view of another embodiment of a portion of the surface of the screw of  FIG. 6  taken across line  7 B- 7 B; 
           [0023]      FIG. 7C  is a cross sectional view of another embodiment of a portion of the surface of the screw of  FIG. 6  taken across line  7 C- 7 C; 
           [0024]      FIG. 7D  is a cross sectional view of another embodiment of a portion of the surface of the screw of  FIG. 6  taken across line  7 D- 7 D; 
           [0025]      FIG. 7E  is a cross sectional view of another embodiment of a portion of the surface of the screw of  FIG. 6  taken across line  7 E- 7 E; 
           [0026]      FIG. 8A  is a cross sectional view of one of the advancing grooves of  FIG. 6  taken across line  8 A- 8 A showing a decreasing depth taper; 
           [0027]      FIG. 8B  is a cross sectional view of one of the advancing grooves of  FIG. 6  taken across line  8 B- 8 B showing constant depth taper; 
           [0028]      FIG. 8C  is a cross sectional view of one of the advancing grooves of  FIG. 6  taken across line  8 C- 8 C showing an increasing depth taper; 
           [0029]      FIG. 8D  is a cross sectional view of one of the advancing grooves of  FIG. 6  taken across line  8 D- 8 D showing varying depth taper; 
           [0030]      FIG. 8E  is a cross sectional view of one of the advancing grooves of  FIG. 6  taken across line  8 E- 8 E showing another varying depth taper; 
           [0031]      FIG. 8F  is a cross sectional view of one of the advancing grooves of  FIG. 6  taken across line  8 F- 8 F showing another varying depth taper; 
           [0032]      FIG. 9  is a schematic view of a portion of the surface of a screw for a plasticating apparatus of the present invention illustrating cross-cut grooves having varying depths and depth tapers; 
           [0033]      FIG. 10A  is a cross sectional view of a portion of the surface of the screw of  FIG. 9  taken across line  10 A- 10 A 
           [0034]      FIG. 10B  is a cross sectional view of a portion of the surface of the screw of  FIG. 9  taken across line  10 B- 10 B; 
           [0035]      FIG. 10C  is a cross sectional view of a portion of the surface of the screw of  FIG. 9  taken across line  10 C- 10 C; 
           [0036]      FIG. 11A  is a cross sectional view of a portion of the surface of the screw of  FIG. 9  taken across line  11 A- 11 A; 
           [0037]      FIG. 11B  is a cross sectional view of a portion of the surface of the screw of  FIG. 9  taken across line  11 B- 11 B; 
           [0038]      FIG. 11C  is a cross sectional view of a portion of the surface of the screw of  FIG. 9  taken across line  11 C- 11 C; 
           [0039]      FIG. 11D  is a cross sectional view of a portion of the surface of the screw of  FIG. 9  taken across line  11 D- 11 D; and 
           [0040]      FIG. 11F  is a cross sectional view of a portion of the surface of the screw of  FIG. 9  taken across line  11 F- 11 F. 
       
    
    
     DETAILED DESCRIPTION 
       [0041]    Referring to  FIG. 2 , a plasticating apparatus is generally designated by the numeral  200 . The plasticating apparatus includes a cylindrical barrel  2  that defines an inner surface  3 . The barrel  2  includes an inlet port  4  that has a feed hopper  7  connected thereto. The feed hopper  7  and inlet port  4  cooperate to supply one or more solid particulate resinous materials and any additives or agents to the barrel  2 . The barrel  2  includes an outlet port  6  for the discharge of plasticated molten extrudate to a mold or die (not shown). Heating elements  11  are positioned outside of the barrel  2  for applying heat to the barrel  2 . 
         [0042]    As illustrated in  FIG. 2 , a screw  10  is axially supported for rotation in the barrel  2  along a longitudinal axis A 1 . The screw  10  extends from the inlet port  4  to the outlet port  6 . The screw  10  includes a helical flight  13  radially extending from and winding around a core  12  in a first direction (e.g., in a right hand threaded direction). The helical flight  13  includes a radially outermost flight surface  14  (e.g., also referred to as a flight land) which moves in close cooperative association with the inner surface  3  of the barrel  2 . The helical flight  13  defines a helical channel  18  bounded by flight  13 , inner surface  3  of the barrel  2  and the surface of the core  12 . The depth of the helical channel  18  is measured radially from the surface of core  12  to the inner surface  3  of the barrel  2  and is referred to as the root depth RD. With the rotation of the screw  10 , the helical channel  18  forces a forward flow of resinous materials. 
         [0043]    As shown in  FIG. 2 , the screw  10  includes a relatively deep root feed section B for the admission, heating and working of solid resin, a transition section C of reducing root depth to adapt to the reduced volume of resin due to melting and the elimination of air spaces between the solid particles, and a relatively shallow root metering section D wherein the resin is a combination of molten and un-melted material. The metering section D includes a longitudinal portion A. The inlet port  4  is typically at the rear-most part of the upstream feed section B and the outlet port  6  is the forward-most part of the downstream metering section D. 
         [0044]    As shown in  FIG. 3 , the longitudinal portion A of the surface of the core  12  includes a plurality of noncontinuous advancing grooves  30 . The advancing grooves  30  are arranged to make a forward helical pathway in the helical channel  18 . The advancing grooves  30  are cut into the surface of core  12 . There is a plurality of adjacent grooves  30  per channel, preferably three as shown, but not limited to only three. The advancing grooves  30  are generally elliptically tapered. The advancing grooves  30  are parallel to and have the same helical pitch and helix angle H 1  as the forward helical flight  13 . The advancing grooves  30  facilitate the forward flow of the resinous material towards the outlet port  6 . 
         [0045]    As shown in  FIG. 3 , the longitudinal portion A of the surface of the core  12  includes a plurality of staggered rows of noncontinuous cross-cut grooves  37 N cut into the surface of the core  12  and intercept through one flight  13 . The axis of each cross-cut groove  37 N is parallel to the other cross-cut grooves  37 N. The cross-cut grooves  37 N are oriented in a neutral direction parallel to the longitudinal axis A 1 . The cross-cut grooves  37 N facilitate mixing of the resinous material during the transport towards the outlet port  6 . While the cross-cut grooves  37 N are shown and described as intercepting through one flight  13 , the present invention is not limited in this regard as the cross-cut grooves  37 N may intercept more than one flight  13 , for example, two flights  13  (e.g., both leading and trailing flight with respect to the channel  18 ), as shown in  FIG. 4B . 
         [0046]    As shown in  FIG. 4A , the longitudinal portion A of the surface of the core  12  includes has a plurality of staggered rows of noncontinuous cross-cut grooves  37 C cut into the surface of the core  12  and intercept through one flight  13 . The axis of each cross-cut groove  37 C is parallel to the other cross-cut grooves  37 C. While the cross-cut grooves  37 C are shown and described as being parallel to one another, the cross-cut grooves  37 C may be at different angles to one another. The cross-cut grooves  37 C are oriented in the first direction common to that of the helical flight (i.e., a right hand threaded direction). The cross-cut grooves  37 C are oriented at a helix angle H 2  that is different from the helix angle H 1  of the advancing grooves  30  and the helical flight  13 . The helix angle H 2  shown in  FIG. 4B  is greater than the helix angle H 1 , however in one embodiment, the helix angle H 2  may be greater than the helix angle H 1  and less than 90 degrees. The cross-cut grooves  37 C facilitate mixing of the resinous material during the transport towards the outlet port  6 . While the cross-cut grooves  37 C are shown and described as intercepting through one flight  13 , the present invention is not limited in this regard as the cross-cut grooves  37 C may intercept more than one flight  13 , for example, two flights  13  (e.g., both leading and trailing flight with respect to the channel  18 ), as shown in  FIG. 4B . 
         [0047]    As shown in  FIG. 5 , the longitudinal portion A of the surface of the core  12  includes has a plurality of the cross-cut grooves  37 N and a plurality of the cross-cut grooves  37 C cut into the surface of the core  12 . Each of the plurality of cross-cut grooves  37 N and each of the plurality of cross-cut grooves  37 C intersect one or both flights  13 . Each of the plurality of cross-cut grooves  37 N is oriented at helix angle H 2  that is about 90 degrees. Some of the cross-cut grooves  37 C have a helix angle H 2 ′ and some of the cross cut grooves  37 C have a helix angle H 2 ″, wherein the helix angle H 2 ′ is different than the helix angle H 2 ″. The helix angles H 2 ′ and H 2 ″ are greater than the helix angle H 1  of the flight  13 . The cross-cut grooves  37 N and  37 C facilitate mixing of the resinous material during the transport towards the outlet port  6 . 
         [0048]    As illustrated in  FIG. 6 , the advancing grooves  30  have different depths and different depth tapers along a longitudinal axis of the advancing groove in a direction of flow Q 1  in the advancing groove. The depths are measured from the inner surface  3  of the barrel  2  to the radially inner most point of the advancing groove  30 . The different depths and different depth tapers of the advancing grooves  30  facilitate mixing of the resinous material, for example, by changing velocity distributions across the advancing groove  30 . 
         [0049]    For example, as shown in  FIG. 7A  three adjacent advancing grooves  30  have different but uniform depths D 1 , D 2  and D 3 , respectively. In one embodiment, D 1  and D 3  are greater than D 2 , with the advancing groove  30  with the shallow depth D 2  being positioned between two advancing grooves  30  having greater depths D 1  and D 3 . As shown in  FIGS. 7A, 7B and 7C  there is an undercut surface  66  that is formed (e.g., machine cut into) at a depth D 66  which is greater than the land depth LD. Thus, the undercut surface  66  is located radially inwardly from the flight surface  14 . The undercut surface shown in  FIGS. 7A, 7B and 7C  has a constant depth D 66 . 
         [0050]    As shown in  FIG. 7B  three adjacent advancing grooves  30  have different but uniform depths D 4 , D 5  and D 6 , respectively. In one embodiment, D 5  and D 6  are greater than D 4 , with the advancing groove  30  with the shallow depth D 4  being positioned adjacent to the two adjacent advancing grooves  30  having greater depths D 5  and D 6 . 
         [0051]    As shown in  FIG. 7C  three adjacent advancing grooves  30  have different but uniform depths D 7 , D 8  and D 9 , respectively. In one embodiment, D 7  and D 8  are greater than D 9 , with the advancing groove  30  with the shallow depth D 9  being positioned adjacent to the two adjacent advancing grooves  30  having greater depths D 7  and D 8 . 
         [0052]    While the undercut surface is shown in  FIGS. 7A, 7B and 7C  as having a constant depth D 66 , the present invention is not limited in this regard. For example, as illustrated in  FIG. 7D  the undercut surfaces have undercut groove depths that vary in a direction traverse to the longitudinal direction along the direction of flow Q 1  including: 1) the undercut surfaces  66  adjacent to the flight  13  each have a depth D 66 ; 2) the undercut surface  66 ′ has a depth D 66 ′ that is less than the depth D 66  and greater than the land depth LD; and 3) the undercut surface  66 ″ has a depth D 66 ″ that is greater than the depth D 66 ′. The traverse change in depths of the undercut surface  66 ,  66 ′ and  66 ″ facilitates mixing of the resinous material, for example, by changing velocity distributions across the advancing groove  30 . 
         [0053]    In one embodiment, as shown in  FIGS. 6 and 7E  the undercut surface has a varying depth in a longitudinal direction along the direction of flow Q 1 , for example: 1) a portion of the undercut surface  66  has a constant depth D 66 ; 2) another portion of the undercut surface  66 D has an increasing depth taper along the longitudinal direction of flow Q 1  in the advancing groove  30  wherein a portion of the increasing taper has a depth D 66 I that is greater than the depth D 66 ; 3) another portion of the undercut surface  66 ″ has a constant depth D 66 ″ that is greater than the depth D 66  and the depth D 66 I; 4) another portion of the undercut surface  66 D has a decreasing depth taper along the longitudinal direction of flow Q 1  in the advancing groove  30  wherein a portion of the decreasing depth taper has a depth of D 66 D that is less than the depth D 66 ″; and 5) another portion of the undercut surface  66 ′ has a depth D 66 ′ that is less than the depth D 66 . 
         [0054]    As shown in  FIG. 8A  the advancing groove  30  has a decreasing depth taper in the first direction (i.e., a longitudinal direction along the advancing groove in a direction of flow though the advancing groove) as indicated by the arrow Q 1 . For example, the decreasing depth taper is defined by a depth D 1   l  that is greater than a depth D 10 . As shown in  FIG. 8B  the advancing groove  30  has a constant depth taper in the first direction as indicated by the arrow Q 1 . For example, the constant depth taper is defined by a uniform depth D 12 . 
         [0055]    As shown in  FIG. 8C  the advancing groove  30  has an increasing depth taper in the first direction as indicated by the arrow Q 1 . For example, the increasing depth taper is defined by a depth D 13  that is less than a depth D 14 . 
         [0056]    As shown in  FIG. 8D  the advancing groove  30  has a varying depth taper in the first direction as indicated by the arrow Q 1 . For example, the varying depth taper is defined by: 1) a section of decreasing depth taper wherein a depth D 15 ′ is less than a depth D 15 ; 2) a section of constant depth D 16 ; 3) and a section of increasing depth taper wherein a depth D 17 ′ is greater than a depth D 17 . 
         [0057]    As shown in  FIG. 8E  the advancing groove  30  has varying depth taper in the first direction as indicated by the arrow Q 1 . For example, the varying depth taper is defined by: 1) a section of constant depth D 18 ; 2) a section of increasing depth taper wherein a depth D 19 ′ is greater than a depth D 19 ; 2) a section of constant depth D 20 ; 4) a section of decreasing depth taper wherein a depth D 21  is less than a depth D 21 ′; and 5) a section of constant depth D 18 . 
         [0058]    As shown in  FIG. 8F  the advancing groove  30  has a continuously varying depth D 22 , D 24  such as a wave or sinusoidal pattern. 
         [0059]    While the advancing grooves  30  are shown and described as having different depths and different depth tapers, the present invention is not limited in this regard as the cross-cut grooves may also or in the alternative have different depths and different depth tapers. For example, as shown in  FIGS. 9, 10A, 10B, 10C, 11A, 11B, 11C, 11D, 11E, and 11F , the cross-cut grooves  37 N and  37 C have different depths and different depth tapers along a longitudinal axis of the cross-cut groove in a direction of flow Q 3  in the cross-cut grooves  37 C and in the direction of flow Q 2  in the cross-cut grooves  37 N. The depths are measured from the inner surface  3  of the barrel  2  to the radially inner most point of the cross-cut groove  37 N or  37 C. The different depths and different depth tapers of the cross-cut grooves  37 N and  37 C facilitates mixing of the resinous material, for example, by changing velocity distributions across the cross-cut grooves  37 N and  37 C. 
         [0060]    As shown in  FIGS. 9, 10A and 11A  the cross-cut groove  37 C has a constant depth D 30  along the longitudinal axis of the cross-cut groove in a direction of flow Q 3 . As shown in  FIGS. 9, 10B and 11B  the cross-cut groove  37 C has a constant depth D 32  along the longitudinal axis of the cross-cut  37 C groove in a direction of flow Q 3 . As shown in  FIGS. 9, 10C and 11C  the cross-cut groove  37 N has a constant depth D 33  along the longitudinal axis of the cross-cut groove in a direction of flow Q 3 . The depth D 30  is greater than the depth D 32  and the depth D 32  is greater than the depth D 33 . Thus, the cross-cut grooves  37 C and the cross-cut grooves  37 N have different depths relative to other ones of the cross-cut grooves  37 C and the cross-cut grooves  37 N. While, the cross-cut grooves  37 C and the cross-cut grooves  37 N are shown and described as having different depths, the present invention is not limited in this regard as the cross-cut grooves  37 C and the cross-cut grooves  37 N may have equal depths or some of the cross-cut grooves  37 C and the cross-cut grooves  37 N may have equal depths and other of the cross-cut grooves  37  and the cross-cut grooves  37 N may have different depths. 
         [0061]    As shown in  FIGS. 9, 11D, 11E and 11F , the cross-cut grooves  37 C and the cross-cut grooves  37 N have different depth tapers. As shown in  FIGS. 9 and 11D , the cross-cut groove  37 C has an increasing depth taper along the longitudinal axis of the cross-cut groove  37 C in a direction of flow Q 3  (e.g., the cross-cut groove  37 C has a depth D 40  proximate one end thereof and a depth D 41  proximate another end thereof, wherein the depth D 41  is greater than the depth D 40 ). As shown in  FIGS. 9 and 11E , the cross-cut groove  37 C has a decreasing depth taper along the longitudinal axis of the cross-cut groove  37 C in a direction of flow Q 3  (e.g., the cross-cut groove  37 C has a depth D 44  proximate one end thereof and a depth D 43  proximate another end thereof, wherein the depth D 44  is greater than the depth D 43 ). As shown in  FIGS. 9 and 11F , the cross-cut groove  37 N has a varying depth taper along the longitudinal axis of the cross-cut groove  37 C in a direction of flow Q 3 . For example: 1) the cross-cut groove  37 N has a depth D 50  proximate one end thereof and a depth D 53  adjacent thereto, wherein the depth D 53  is greater than the depth D 50  thereby defining an increasing depth taper; 2) the cross-cut groove  37 N has a constant depth D 55  along a central section thereof, wherein the depth D 55  is greater than the depth D 53 ; 3) the cross-cut groove  37 N has a depth D 52  proximate another end thereof and a depth D 53  adjacent thereto, wherein the depth D 53  is greater than the depth D 52  thereby defining an decreasing depth taper. 
         [0062]    Although the invention has been described with reference to particular embodiments thereof, it will be understood by one of ordinary skill in the art, upon a reading and understanding of the foregoing disclosure that numerous variations and alterations to the disclosed embodiments will fall within the scope of this invention and of the appended claims.