Abstract:
A vented, multi-staged rotary screw extruder is taught for extruding thermoplastic materials. The screw has a final pumping-section of the screw that includes two or more channel depths which provides exit-pressure and flow stability. The channel-depth of the first segment of the final pumping-section is deeper than the channel depth of the second segment of the final pumping-section. The axial length of the first segment is preferably about two-thirds (⅔) of the final pumping-section length. The deeper first channel-depth acts as a reservoir resulting in smaller fluctuations in axial final fill-length as the input flow to the total pumping-section varies. The second channel-depth in the remaining approximate one-third (⅓) of the total pumping-section is preferably sized so as to optimize pressure development.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention relates generally to polymer extrusion apparatus, and, more particularly, to multi-staged rotary screw extruders for polymer extrusion.  
         BACKGROUND OF THE INVENTION  
         [0002]    A variety of extrusion apparatus for injection molding thermoplastic materials are known in the prior art. Examples of such extrusion apparatus include U.S. Pat. No. 3,023,456 to Palfey, U.S. Pat. No. 4,155,655 to Chiselko et al., U.S. Pat. No. 4,185,060 to Ladney, Jr., and U.S. Pat. No. 5,597,525 to Koda et al. As shown in such patents, a common method for extracting vapors and gases during the extrusion process is to use a vented extruder. Venting is done in an extraction section or sections, and it can be to low pressure or to a vacuum. After the venting, a final pumping-section must develop pressure according to the load at the extruder exit. It must carry the flow rate of the extruder and build the pressure (from vacuum or low pressure) to the required exit pressure (e.g. die pressure required for extrusion).  
           [0003]    In the final extraction section, where vapors are released to vacuum or low pressure, the polymer traveling in the channel must include an unbounded surface so that the gases may escape and travel to a vent port in the extrusion screw or in the barTel. This unbounded surface requires that the screw channel be only partially filled with polymer, and this unbounded surface will continue into the final pumping-section for a distance that is dependent upon the exit pressure of the extruder. At some distance along the length of the screw, the unbounded surface ends and the screw channel(s) are filled such that polymer traveling in the channel is fully bounded. The screw channels in the final pumping-section are completely full of polymer.  
           [0004]    The axial length of the final pumping-section that is completely full of polymer is proportional to the exit pressure being developed. If the exit pressure is low, then the pumping section will have a very short length of fill. As the pressure is increased (greater load on the extruder), the length of the final pumping-section that is completely fall will become longer.  
           [0005]    Theory and practice have shown that the optimum final pumping-section for a two-stage extruder (a final pumping-section that builds the pressure in the shortest length of the extruder) has a channel depth that is greater than that of the metering section (in the first stage of the extruder). For a square pitched screw as shown in U.S. Pat. No. 3,023,456 to Palfey (channel lead length equal to barrel diameter, channel lead length being the axial distance between flights), the pumping section depth must be 50% greater than the metering-section depth of the first stage for optimum pressure development. The so defined optimum channel-depth of the final pumping-section maximizes the pressure capability of the extruder. Subsequent vented extruder designs, such as those mentioned above, have specifically stated and followed the configuration of a single channel-depth final pumping-section as given by Palfey. Further, none of such prior art designs address the issue of pressure stability.  
           [0006]    Pressure stability is addressed for extrusion in U.S. Pat. No. 4,867,927 to Funaki et al. and U.S. Pat. No. 3,712,594 to Schippers et al. In the apparatus taught by Funaki et al. (which does not include venting) a flow restriction is added to the screw to dampen the flow oscillations. A valve mechanism on the axis of the screw in the screw core and controllable from outside the extruder is used by Schippers et al. to dampen the flow oscillations. Screws with metering sections are used for plasticating with features that do not include venting or degassing. Specifically, reference U.S. Pat. No. 3,698,541 to Barr and U.S. Pat. No. 4,049,245 to Tadmor et al.. Both appear to show barrier type screws that include a constant channel-depth final pumping-section. However, neither Barr nor Tadmor et al. utilize the double channel-depth final pumping-section, or address stability of flow or pressure.  
           [0007]    In a non-continuous process (as opposed to a continuous process for which venting here is required) taught in U.S. Pat. No. 4,648,827 to Laimer et al., a screw for injection molding does use a tapered channel-depth in the final pumping-section of the screw. However, Laimer et al. teaches a non-vented design, and the channel depth is not two distinct values. Additionally, since Laimer et al. is a non-continuous injection molding application, flow stability is not a concern.  
           [0008]    The flow of polymer in a vented multi-stage extruder has inherent instability, typically in but not limited to, the solids conveying and melting processes therein. As the flow enters the final pumping-section, flow rate variation will cause the inventory of polymer in the final pumping-section to fluctuate. This fluctuation of inventory results in a change in the fill length of the final pumping-section. Since the final pumping-section fill-length is a factor in determining the exit pressure from the extruder, the exit pressure will also vary accordingly. Exit pressure instability in proportion to final fill-length variability of the final pumping-section is the end result. Thus, the prior art fails to teach a vented screw design in which the final pumping-section of the screw includes two or more channel depths in order to provide flow stability in continuous extrusion operations.  
         SUMMARY OF THE INVENTION  
         [0009]    It is therefore an object of the present invention to provide a vented, multi-staged rotary screw extruder for polymer extrusion that allows for flow stability in continuous extrusion operations.  
           [0010]    Another object of the present invention is a vented, multi-staged rotary screw extruder wherein the final pumping-section of the screw includes two or more channel depths in order to provide flow stability in continuous extrusion operations.  
           [0011]    Briefly stated, the foregoing and numerous other features, objects and advantages of the present invention will become readily apparent upon a review of the detailed description, claims and drawings set forth herein. These features, objects and advantages are accomplished by providing a vented, multi-staged rotary screw extruder with a final pumping-section of the screw that includes two or more channel depths. Two or more channel depths in the final pumping-section of a multi-staged vented extruder improves exit-pressure and flow stability. The channel-depth of the first portion of the final pumping-section is deeper than the second portion of the final pumping-section. The axial length of the first portion of the final pumping-section is preferably about two-thirds (⅔) of the final pumping-section length. The deeper first channel-depth acts as a reservoir resulting in smaller fluctuations in axial final fill-length as the input flow to the final pumping-section varies. The second channel-depth in the remaining approximate one-third (⅓) of the total pumping-section is preferably sized so as to optimize pressure development. Therefore, exit-pressure stability is achieved by the depth of the first channel in the final pumping-section, and optimum pressure development is produced by the depth of the second channel in the final pumping-section thereby providing flow stability in continuous extrusion operations. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0012]    [0012]FIG. 1 is a partial cross-sectional view of the vented two-stage extruder of the present invention.  
         [0013]    [0013]FIG. 2 is a pressure profile for the vented two-stage extruder shown in FIG. 1.  
         [0014]    [0014]FIG. 3 is a schematic cross-sectional representation of a prior art extruder screw.  
         [0015]    [0015]FIG. 4 is a schematic cross-sectional representation of a portion of the vented two-stage extruder of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0016]    Turning first to FIG. 1, there is shown the vented two-stage extruder  10  of the present invention. Extruder  10  includes a screw  12  rotatably supported in a barrel  14 . Barrel  14  includes a solids feed hopper  16  and a vent  18  for venting gases and vapors from extruder  10 . A vented screw such as taught in U.S. Pat. No. 6,164,810 could be used as well. A screw with more than one vent (multi-staged vented) would also apply. The screw  12  is shown with a conventional first stage  20  that includes a drive end  21 , a solids conveying section  22 , a melting section  24  and metering section  26 . Solid thermoplastic material  28  (typically in a pelletized form) is delivered to extruder  10  via feed hopper  16 . The solid thermoplastic material  28  becomes a melted polymer  30  in the melting section  24 . The second stage  32  of the screw  12  includes an extraction section  34  with its deep channel  36  to create the unbounded surface  38  for vapor release and transport to the vent  18 . The second stage  32  includes the final pumping-section  40  of the screw  12 . As depicted, final pumping-section  40  includes an initial or reservoir segment  41  having screw channels  48  with a channel-depth  42 . Final pumping-section  40  also includes a second segment  43  having screw channels  49  with a screw channel-depth  44 . Channel-depth  44  is less than the channel-depth  42 .  
         [0017]    Looking next at FIG. 2, there is shown a pressure profile for the extruder  10  shown in FIG. 1. The pressure of the solids conveying section  22  and melting section  24  is shown as building linearly to a pressure P m  Extruder  10  is vented through vent  18  in the extraction section  34  preferably with the aid of a vacuum pump (not shown) to achieve a sub-atmospheric pressure  46 . However, extraction section  34  may also be operated at atmospheric or low pressures (above atmospheric) for some applications. The unbounded surface  38  of the polymer  30  continues into the final pumping-section  40 . In operation, some of the screw channels  48  in the initial or reservoir segment  41  eventually fill with polymer melt  30  at a fill length, L 1 , from the end of the initial or reservoir segment  41 . In operation, the screw channels  49  of the second segment  43  of the final pumping-section  40  are full of polymer. The second segment  43  has a length L 2 . An exit pressure P e  is attained.  
         [0018]    Looking at FIG. 3, in the prior art, the channel depth of the pumping section of an extruder screw, h p , is set as a constant over the entire length, L P , of the pumping section. An optimum depth of this channel for maximum pressure gradient is given by  Processing of Thermoplastic Materials , by Ernest C. Bernhardt from the following ratio:  
                 h     p                 max         h   m       =     1.5   .             Eq   .              1                               
 
         [0019]    where h Pmax  is the depth of the screw channel in the pumping section for maximum pressure development and h m  is the depth of the screw channel in the metering section. This assumes that the lead length of the pumping section, t p , is the same as the lead length of the metering section, t m .  
         [0020]    The results of Bernhardt are extended to include lead length difference between pumping and metering. Based on his one-dimensional isothermal flow equations for flow and pressure gradient in extruder screws, the pressure gradient for a given flow in the pumping section following an extraction section and metering section with the same flow is given as  
                   Δ                 p       Δ                 L       =       6      π                 DN                   μ        [           h   p          (       t   p     -   ne     )              cos   2          (     φ   p     )         -         h   m          (       t   m     -   ne     )              cos   2          (     φ   m     )           ]               h   p   3          (       t   p     -   ne     )            sin        (     φ   p     )            cos        (     φ   p     )             ,           Eq   .              2                               
 
         [0021]    where the helix angles (Φ m , Φ p ) for the metering channel (subscript m) or the pumping channel (subscript p), of different lead lengths, t m  and t p  are given by  
         [0022]    φ i =tan −1 (t i |π|D)   Eq. 3  
         [0023]    where i=m or p.  
         [0024]    Similar to Equation 1, channel depth for maximum pressure gradient is then determined by optimization of Equation 2 to give  
                   (       h   p       h   m       )     max     =       3   2              (       t   m     -   ne     )            cos   2          (     φ   m     )             (       t   p     -   ne     )            cos   2          (     φ   p     )               ,           Eq   .              4                               
 
         [0025]    Equation 4 becomes the Bernhardt result of Equation 1 for equal leads (and helix angles). These four equations are used to size the two channel-depth pumping-section.  
         [0026]    [0026]FIG. 4, which schematically shows part of the extruder screw  12  shown in FIG. 1 with flights to form a helical path inside in barrel  14  having an inside diameter, D, will be used to describe the sizing of a two-channel depth final pumping section  40 . That portion of the screw  12  shown in FIG. 4 is comprised of several sections  26 ,  34 ,  41 ,  43 , each with its own channel depth, h, and lead length, t. The entire screw  12  contains a solids conveying and melting section (not shown in the FIG. 4). The screw may also contain other sections that are not shown. The elements shown in the FIG. 4 are those pertinent to a two channel-depth final pumping section  40 . The pertinent sections are the metering section  26 , extraction section  34 , and pumping section  40 .  
         [0027]    Determining the proper sizing of the two-channel pumping section  40  of the present invention requires additional calculations. The requirements are that the pumping section  40  must produce a pressure between a minimum pressure, P min , and a maximum pressure, P max , at the extruder design flow rate and at a rotational speed, N. The total length of the pumping section is L p , (see FIG. 4) and the average viscosity of the polymer in the pumping section is μ p . From other considerations, typically flow rate and product melt temperature development, the channel depth and lead length of the metering section  26  and the lead length of the pumping section  40  are previously calculated.  
         [0028]    First, the optimum channel depth for pumping pressure development, h pmax , is obtained from Equation 4. Equation 2 is then used to find the maximum pressure gradient. The length, L 2 , of the second segment  43  of the two-channel depth pumping-section  40  is found by assuming the channels  49  of the second segment  43  to be completely full at minimum pressure. The length is then given as  
               L   2     =         p   min         (     Δ                   p   /   Δ                   L     )         h                 p     =     h                 p                 max           .             Eq   .              5                               
 
         [0029]    The first length of the pumping section is then simply  
         L 1 =L p −L 2 ,   Eq. 6  
         [0030]    where L 1  is the length of the initial segment  41  of the pumping section  40 .  
         [0031]    The maximum pressure will be realized when the total pumping section  40  is completely full. This will require the pressure gradient (ΔP/ΔL) of the initial segment  41  of the pumping section  40  to be given by  
                   (       Δ                 p       Δ                 L       )     1     =       (       p   max     -     p   min       )       L   1         ,           Eq   .              7                               
 
         [0032]    where P max  is the maximum pressure that the extruder will need to produce and P min  is the pressure that will keep the second segment of the pumping section fill of polymer.  
         [0033]    The pressure gradient of Equation 7 must be less than the maximum pressure gradient found previously using Equation 2. Otherwise, the length, L 1 , is insufficient, and a longer total pumping section will be needed. Equation 2 can then be used with the result of Equation 7 to find the depth of screw channel  48  of the initial segment  41  of the pumping section  40 . This is done by computational trial-and-error of Equation 2 with values of h 1  until the result of Equation 7 is obtained. This value of channel depth, h 1 , of the of the initial segment  41  will be greater than the channel depth, h 2 , of the second segment  43  and less than the channel depth, h x , of the extraction section  34 . The depth, h x , of the extraction section  34  is suggested by Bernhardt to be four (4) times the depth, h m , of the metering section  26 . Therefore,  
         2h m ≦h 1 &lt;4h m    Eq. 8  
         [0034]    Also,  
         h 2 =1.5xh m    Eq. 9  
         [0035]    for equal channel lead lengths t m  and t p , or  
                 h   2     =       3   2              (       t   m     -   ne     )            cos   2          (     φ   m     )             (       t   p     -   ne     )            cos   2          (     φ   p     )                xh   m         ,           Eq   .              10                               
 
         [0036]    for unequal lead lengths t m  and t p.    
         [0037]    Since these values are based on one-dimensional isothermal flow theory, the values may be found to be slightly different based on actual operational data.  
       EXAMPLE  
       [0038]    A two-channel pumping section  40  is to be sized. The lengths of the initial segment  41  and the second segment  43  of the pumping section  40  and the channel depths (h 1  and h 2 ) are to be determined. The extruder  10  has the specifications shown in the table.  
                                                                             Nomenclature   Name   Value                                        D   Diameter   200   mm           t m     Metering lead length   200   mm           h m     Metering channel depth   5   mm           n   Number of flights   1           e   Flight width   12   mm           t p     Pumping lead length   250   mm           L p     Pumping section length   1500   mm           N   Screw speed   2   rps           P max     Maximum pressure   20   MPa           P min     Minimum pressure   7   MPa           μ p     Viscosity   100   Pa-s                      
 
         [0039]    First, Equation 3 is used to calculate the helix angles (Φ m , Φ p ) for screw  12  as  
         φ m=tan   −1 (200|π|200)−0.308 rad,   Eq. 11  
         [0040]    and  
         φ p   32  tan −1 (250|π|200)=0.379 rad.   Eq. 12  
         [0041]    The ratio of channel depth (h 1 ) of the initial segment  41  of the pumping section  40  to the channel depth (h m ) of the metering section  26  for optimum pressure gradient is then used to find the channel depth (h 2 ) of the second segment  43  of the pumping section  40  from Equation 4 as  
                 h   2       h   m       =         h     p                 max         h   m       =         3   2              (     200.   -   12.     )            cos   2          (   .308   )             (     250   -   12     )            cos   2          (   .379   )             =     1.25   .                 Eq   .              13                               
 
         [0042]    The value of the channel depth (h 2 ) is then  
         h 2 =1.25×5=6.25 mm.   Eq. 14  
         [0043]    Equation 2 then gives the optimum pressure gradient for the channel depth (h 2 ) as  
                       (       Δ                 p       Δ                 L       )     2     =             6        π        (   200   )            (   2   )            (   100   )     [       6.25        (     250   -   12     )            cos   2          (   0.379   )         -                     5        (     200   -   12     )            cos   2          (   .308   )         ]               6.25   3          (     250   -   12     )          sin        (   0.379   )            cos        (   0.379   )                       =     16269                 Pa        /        mm                   Eq   .              15                               
 
         [0044]    The minimum pressure for this example as given above is 7 Mpa. Therefore, Equation 5 gives the length of the second segment  43  as  
               L   2     =         7      e                   10   6       16269     =     430                   mm   .                 Eq   .              16                               
 
         [0045]    The length of the initial segment  41  is then given by Equation  6  as  
         L 1 =1500−430=1070 mm .   Eq. 17  
         [0046]    The length of the initial segment  41  is about twice that of the second segment  43 . This means that the length of the pumping section is adequate to produce the maximum pressure, 20 Mpa, required.  
         [0047]    The pressure gradient for the initial segment  41  then obtained from Equation 7 as  
                 (       Δ                 p       Δ                 L       )     1     =         (       p   max     -     p   min       )       L   1       =         (       20      e                 6     -     7      e                 6       )     1070     =     12152                 Pa        /          mm   .                   Eq   .              18                               
 
         [0048]    Finally, the channel depth (h 1 ) for the initial segment  41  is found by trial-and-error using Equation 2 and the result of Equation 18. The result for a channel depth (h 1 ) of 9.5 mm is  
                       (       Δ                 p       Δ                 L       )     1     =             6        π        (   200   )            (   2   )            (   100   )     [       9.5        (     250   -   12     )          cos   2          (   0.379   )       -                     5        (     200   -   12     )            cos   2          (   .308   )         ]               9.5   3          (     250   -   12     )          sin        (   0.379   )            cos        (   0.379   )                       =     11816                   Pa   /   mm                     Eq   .              19                               
 
         [0049]    This pressure gradient is close to the desired value of Equation 18. Therefore, the channel depth (h 1 ) of the initial segment  41  is 9.5 mm. It is approximately twice the depth (h m ) of the channel (5 mm) in the metering section  26  as required by Equation 8. The result is that the pumping section  40  will have an initial segment  41  having a length (L 1  ) of 1070 mm and a channel depth (h 1 ) of 9.5 mm. The second segment  43  of the pumping section  40  will have a channel depth (h 2  ) of 6.25 mm and a length (L 2 ) of 430 mm. The length of the initial segment  41  will be foreshortened to accommodate a tapered transition section  60  (which may be, for example, frusto-conical in shape) of about 50 mm for the change in channel depth from 9.5 mm to 6.25 mm. Therefore, the total pumping section  40  is made up of a 1020 mm long part at a depth of 9.25 mm, a 50 mm long transition, and a 430 mm long part at a channel depth of 6.25 mm.  
         [0050]    The vented multi-stage extruder of the present invention creates a more stable flow rate and exit pressure. Used in conjunction with a feedback control system, this translates into a more constant operating speed for the screw as well as a more constant operating pressure. Product uniformity is enhanced by constant exit pressure. Any auxiliary metering system used to dampen the output of any vented extruder with this dual-channel depth pumping design of this invention (screw or melt pump) will more easily dampen pressure fluctuations because such fluctuations will be smaller.  
         [0051]    The improved stability will provide an increased rate. A screw speed (which is under feedback control) will have less variation if the pressure is inherently more constant. This means that the practical maximum speed will be closer to the maximum speed of the screw drive because excess speed will not be needed to keep the exit pressure constant. A higher rate of rotation is then possible for a particular screw having a maximum drive speed.  
         [0052]    If an existing auxiliary metering extruder is used to further dampen the pressure, the maximum capacity of the existing auxiliary metering extruder will be increased. The reason is that the channel depth for an existing auxiliary metering extruder screw must be minimized to dampen pressure surges from the plasticator. Therefore, minimum metering-screw channel-depth (for acceptable thickness uniformity) limits flow rate. The improved pressure stability of the dual channel-depth screw design of plasticator permits use of a metering screw with a deeper channel-depth, hence a greater rate for a given size of the metering extruder.  
         [0053]    Although the present invention may be practiced by building a new extruder apparatus as described herein, those skilled in the art will recognize that the present invention is also applicable to existing extruder apparatus. Many existing extruder apparatus can be fitted with a new screw designed in accordance with the present invention and thereby achieve the benefits described herein. This will not be universally true in that some existing extruder apparatus may have insufficient barrel length, diameter, or rotational speed to receive a screw designed to practice the present invention.  
         [0054]    As noted above, the length of the initial segment  41  preferably should be about two times the length of second segment  43 . However, for purposes of practicing the present invention it is believed that the length of the initial segment  41  can be from about 1.5 to about 2.5 times the length of second segment  43 . Also as noted above, the channel depth h 1  of channels  48  preferably should be about two times the channel depth h 2  of channels  49 . However, for purposes of practicing the present invention it is believed that the channel depth h 1  of channels  48  can be from about 1.5 to about 2.5 times the channel depth h 2  of channels  49 .  
         [0055]    Although the preferred embodiment as discussed herein has a pumping section  40  with an initial segment  41  and a second segment  43 , those skilled in the art will recognize that pumping section  40  can be modified to include more than two segments. In other words, for example, the pumping section may be designed to include three segments, with each succeeding segment having a channel depth that is shallower than the channel depth of the preceding segment. Further, instead of three (3) or multiple steps in the channel depth, the initial segment  41  could also be made to have its channel depth continuously decrease from entrance to exit to provide a change in channel depth according to a prescribed (and probably linear) tapering function.  
         [0056]    From the foregoing, it will be seen that this invention is one well adapted to obtain all of the ends and objects hereinabove set forth together with other advantages which are apparent and which are inherent to the apparatus.  
         [0057]    It will be understood that certain features and subcombinations are of utility and may be employed with reference to other features and subcombinations. This is contemplated by and is within the scope of the claims.  
         [0058]    As many possible embodiments may be made of the invention without departing from the scope thereof, it is to be understood that all matter herein set forth and shown in the accompanying drawings is to be interpreted as illustrative and not in an illuminating sense.  
                                             PARTS LIST                                    10   vented two-stage extruder           12   screw           14   barrel           16   solids feed hopper           18   vent           20   first stage           21   drive end           22   solids conveying section           24   melting section           26   metering section           28   solid thermoplastic material           30   melted polymer           32   second stage           34   extraction section           36   deep channel           38   unbounded surface           40   final pumping section           41   initial reservoir segment           42   channel depth           43   second segment           44   channel depth           46   sub-atmospheric pressure           48   screw channels           49   screw channels           60   frusto-conical transition section