Abstract:
A plate cylinder includes a cylinder including a longitudinal axis and a centroid located at a geometric center of the cylinder. The cylinder also includes a slot for receiving both ends of a printing plate; the cylinder including a counter balance hole extending axially in the cylinder and being displaced from the longitudinal axis, the counter balance hole balancing the slot; and the cylinder including a mass balance hole extending axially in the cylinder and being displaced from the longitudinal axis, the mass balance hole balancing the plate cylinder. The cylinder further including at least one hole extending axially in the cylinder and being displaced from the longitudinal axis of the cylinder to reduce the variation in products of inertia as the plate cylinder rotates. A cylinder is also provided. A method is also provided.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    The present invention relates to the printing industry and more particularly to cylinders in a printing press susceptible to imbalanced area moment of inertia. 
         [0002]    U.S. Pat. No. 6,131,513 discloses a plate cylinder having a plate slot. The lead edge and tail edge of a plate are situated in the plate slot. An eccentric shaft is disposed within a hole of the plate cylinder, and is preferably disposed near the plate slot. 
         [0003]    U.S. Pat. No. 5,485,784 A1 discloses a printing plate cylinder having an elongate mounting slot with a pair of opposed slot walls. A universal lock-up apparatus is disposed within the elongate mounting slot of the plate cylinder for releasibly holding opposed edges of a printing plate against one of the opposite slot walls of the slot. 
       SUMMARY OF THE INVENTION 
       [0004]    The present invention provides a plate cylinder including: 
         [0005]    a cylinder including a longitudinal axis and a centroid located at a geometric center of the cylinder; 
         [0006]    the cylinder including a slot for receiving both ends of a printing plate; 
         [0007]    the cylinder including a counter balance hole extending axially in the cylinder and being displaced from the longitudinal axis, the counter balance hole balancing the slot; 
         [0008]    the cylinder including a mass balance hole extending axially in the cylinder and being displaced from the longitudinal axis, the mass balance hole balancing the plate cylinder; and 
         [0009]    the cylinder including at least one hole extending axially in the cylinder and being displaced from the longitudinal axis of the cylinder to reduce the variation in products of inertia as the plate cylinder rotates. 
         [0010]    The present invention also provides a method for designing a plate cylinder including the steps of: 
         [0011]    selecting at least one location for at least one axially extending hole displaced from a longitudinal axis of a plate cylinder; 
         [0012]    selecting at least one size for the at least one axially extending hole; and 
         [0013]    the at least one location and at least one size reducing a variation in products of inertia as the plate cylinder rotates, as compared to a plate cylinder without the at least one axially extending hole. 
         [0014]    The present invention further provides a cylinder comprising: 
         [0015]    a cylinder including a longitudinal axis and a centroid located at a geometric center of the cylinder; 
         [0016]    the cylinder including a mass balance hole extending axially in the cylinder and being displaced from the longitudinal axis, the mass balance hole balancing the cylinder; and 
         [0017]    the cylinder including at least one hole extending axially in the cylinder and being displaced from the longitudinal axis of the cylinder to reduce the variation in products of inertia as the cylinder rotates. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]    A preferred embodiment of the present invention will be elucidated with reference to the drawings, in which: 
           [0019]      FIG. 1  illustrates a cross sectional view of a prior art plate cylinder; 
           [0020]      FIG. 2  is a chart depicting variations in cross sectional area moments of inertia variation as the plate cylinder shown in  FIG. 1  rotates; 
           [0021]      FIG. 3  schematically illustrates a process for grinding a plate cylinder; 
           [0022]      FIG. 4  shows a view of a plate cylinder in accordance with an embodiment of the present invention; 
           [0023]      FIG. 5  is a chart comparing variations in cross sectional area products of inertia of the prior art plate cylinder of  FIG. 1  to the variations in products of inertia of the plate cylinder of  FIG. 4  in accordance with the present invention; and 
           [0024]      FIG. 6  shows a view of the plate cylinder shown in  FIG. 4 . 
       
    
    
     DETAILED DESCRIPTION 
       [0025]    The manufacturing process for printing plate cylinders is well known in the industry. Typically, the process requires cylinders to be ground within a desired tolerance. With a demand for longer width plate cylinders, for example, plate cylinders in excess of 66 inches in width, manufacturing within an allowable tolerance range has become increasingly difficult. 
         [0026]    Specifically, manufacturers cannot meet an allowable run-out specification of, for example, 0.0002 inches, during the final grind process without having to perform secondary specialty grinding operations. These additional operations add to the cost and time to manufacture the cylinder. Even with specialty grinding operations, a cross sectional radius of the cylinder may vary, for example, by approximately 0.0005 inches, resulting in an elliptical shaped cylinder. The 0.0005-inch variation leads to poor contact between the printing plate and printing blanket, thus resulting in increased plate cylinder vibration and decreasing print quality. Ideally, the plate cylinder has a constant cross sectional radius; the plate cylinder is circular rather than elliptical shaped. 
         [0027]    Non-uniform deflection of the plate cylinder during the grinding process causes variation in the cross sectional radius and the subsequent elliptical-shaped cylinder. Problems associated with non-uniform deflection become increasingly apparent when manufacturing longer width plate cylinders because an increase in length and weight of the plate cylinders results in increased deflection. To offset non-uniform deflection during the manufacturing process, improved inertia balance may be desired so a constant cross sectional radius of a plate cylinder may be achieved when grinding the plate cylinder as well as uniform deflection as measured in a given plane as the cylinder rotates. 
         [0028]      FIG. 1  shows a prior art plate cylinder  10 . Generally,  FIG. 1  shows a plate cylinder  10  cross section with a lock-up bar slot  15 , hole  20  for lock-up bar slot counter balancing and hole  25  for mass balancing of plate cylinder  10 . Also shown is an x-axis  30  normal to the surface of plate cylinder  10  with rotation angle Θ. 
         [0029]    Plate cylinder  10  includes a lock-up bar slot  15 , where a lock-up bar would be added to plate cylinder  10  after the grinding process. The lock-up bar pulls and locks a leading edge and a trailing edge of a printing plate wound around the peripheral surface of plate cylinder  10 . Plate cylinder  10  includes hole  20  to counter balance lock-up bar slot  15 . Without hole  20 , plate cylinder  10  is unbalanced about z-axis  32 . A counter weight bar may be placed inside hole  20  and connected to a lock-up bar in lock-up bar slot  15 . Adding a counter weight bar reduces the centrifugal load component of the lock-up bar which may be very large and unsafe. In addition, hole  20  and the counter weight bar help balance plate cylinder  10  about z-axis  32 . 
         [0030]    Plate cylinder  10  includes an additional hole  25  for counter balancing mass about z-axis  32 . Similar to hole  20 , hole  25  offsets the portion of plate cylinder  10  removed to create lock-up bar slot  15  and hole  20  because the volume of mass removed to create lock-up bar slot  15  and hole  20  shifts a centroid of plate cylinder  10  away from geometric center  12 . When the centroid is in a location different from geometric center  12 , plate cylinder  10  vibrates during rotation. Thus, a properly located hole  25  shifting the centroid to geometric center  12  results in improved dynamic balance. However, this prior art configuration does not improve the inertia balance and bending stiffness of plate cylinder  10  as plate cylinder  10  rotates. As a result, poor inertia balance and non-uniform bending stiffness cause defects in plate cylinder  10  during the grinding process. Such defects may include, for example, variation in cross sectional radius leading to elliptical shaped cylinders. 
         [0031]    Although holes  20  and  25  may improve dynamic balance of plate cylinder  10 , variations in moments of inertia of cylinder  10  still occur.  FIG. 2  shows a chart depicting area moments of inertia versus angular position theta of plate cylinder  10 . More specifically, the chart shows area moments of inertia of plate cylinder  10  about x-axis  30 , as plate cylinder  10  rotates through angle theta. As evident by the sinusoidal nature of the chart, the area moments of inertia vary significantly. 
         [0032]    The moment of inertia relates to lateral deflection. Generally, the inertia and lateral deflection of the plate cylinder may be calculated using conventional mathematical modeling techniques. Specifically, the lateral deflection of the plate cylinder with respect to the plate cylinder&#39;s axis of rotation can be expressed as a second derivative as shown in the following Equations (1) and (2): 
         [0000]    
       
         
           
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         [0033]    wherein 
         [0034]    w=Lateral deflection in the x direction; 
         [0035]    v=Lateral deflection in the y direction; 
         [0036]    M x =Bending moment in the x axis; 
         [0037]    M y =Bending moment in the y axis; 
         [0038]    I xy =Mixed Product of inertia; 
         [0039]    I xx =Product of inertia in the x direction; 
         [0040]    I yy =Product of inertia in the y direction; and 
         [0041]    E=Modulus of elasticity of material. 
         [0042]    Equations (1) and (2) show the relationship between area moment of inertia, lateral deflection in the x and y axes, and the applied moments. Referring to  FIG. 3 , during plate cylinder manufacturing, a force due to gravity  315  is imposed in the y-axis  34  on plate cylinder  310  and a force along the x-axis  30  is imposed on plate cylinder  310  from grinding wheel  300 . The principal moments of inertia are the maximum and minimum values obtained as the axis of interest is rotated. The axes where the principal moments occur are known as principal axes. Ideally, the product of inertia I xy  (also referred to as mixed inertia) is zero about the principal axes. When considering lateral deflection of the cylinder during the grinding process, the displacement in the y direction (shown in  FIG. 3  and denoted as v in Equation (2)) and displacement in the x direction (denoted as w in Equation (1)) indicate the cylinder deflects relative to the gravity and the grinding wheel, respectively. The displacement is caused by the force of gravity and/or the force of the grinding wheel acting on the plate cylinder as well as the variation in the relevant area moments of inertia. 
         [0043]    Theoretically, a balanced and rigid cylinder rotates without inertial or bending stiffness imbalances and has a constant cross sectional radius, the plate cylinder being circular. When the mass of plate cylinder  10  is asymmetrical, for example, when cylinder  10  includes a lock-up slot  15 , the centroid shifts and causes imbalances. Holes  20 ,  25  are added to plate cylinder  10  to offset the cut in cylinder  10 , however, holes  20 ,  25  only improve dynamic balance. The holes  20 ,  25  do not improve variations in area moments of inertia of plate cylinder  10 , as shown in  FIG. 2 . Further, as shown above, variations in area moments of inertia are related to non-uniform deflection in plate cylinder  10  as the cylinder rotates, resulting in manufacturing defects in the plate cylinder  10 . 
         [0044]    As shown in  FIG. 3 , during manufacturing of plate cylinder  310 , a grinding wheel  300  is placed against a surface of plate cylinder  310  and moved relative to plate cylinder  310  in the longitudinal direction, defined by z-axis  32 , to carry out the grinding of plate cylinder  310 . As plate cylinder  310  rotates, grinding wheel  300  moves along z-axis  32  to grind plate cylinder  310  to the desired diameter or tolerance. A force due to gravity  315  acts downward on cylinder  310  along vertical y-axis  34  and imparts a bending moment about horizontal x-axis  30 , creating a cross section with a non zero product of inertia (I xy , I xx , I yy ) and resulting in lateral deflection of plate cylinder  310 . When lateral deflection occurs during this process, the desired tolerance may not be met and the cylinder may be manufactured elliptical shaped. 
         [0045]    The above-mentioned prior art modifications and adjustments, for example, holes  20  and  25 , do not improve the inertia balance or the bending stiffness of plate cylinder  10 . As a result, the plate cylinder deflects non-uniformly during the grinding process and results in defects, including an elliptical shaped cylinder. In accordance with an embodiment of the present invention, a plate cylinder may have less variation in products of inertia as the plate cylinder rotates, improved bending stiffness, reduced vibration during rotation and subsequently less lateral displacement. Thus, the manufactured plate cylinders may be ground to a more desirable run-out tolerance and have less rotational disturbances during printing. 
         [0046]      FIG. 4  shows a cross sectional view of plate cylinder  410 . Cylinder  410  includes inertia balancing holes  440  and  445 , in accordance with an embodiment of the present invention. Similar to  FIG. 1 ,  FIG. 4  illustrates a lock up bar slot  415 , hole  420  for lock-up bar slot counter balancing, hole  425  mass balancing plate cylinder  410 , an x-axis  430  normal to the surface of plate cylinder  410  and a rotation angle Θ. 
         [0047]    Plate cylinder  410  includes lock-up bar slot  415  for pulling and locking the leading edge and trailing edge of a printing plate wound around the peripheral surface of plate cylinder  410 . Plate cylinder  410  includes holes  420 ,  425  counter balancing lock-up bar slot  415  and shifting a centroid of cylinder  410  back to geometric center  412  similar to  FIG. 1 . 
         [0048]    Plate cylinder  410  includes additional inertia balance holes  440 ,  445 . Equations (1) and (2) can be used along with conventional mathematical modeling techniques to determine the placement and size of additional holes  440 ,  445  added to plate cylinder  410  to improve inertia balance and bending stiffness. The location and size of inertia balance holes  440 ,  445  are related to the plate cylinder cross sectional area products of inertia. Using modeling techniques and equations (1) and (2), hole sizes and positions in plate cylinder  410  can be selected. In a preferred embodiment, holes  440 ,  445  extend axially through plate cylinder  410  as shown in  FIG. 6 . Thus, holes  440 ,  445  are displaced from the longitudinal axis, (z-axis in  FIG. 6 ), of plate cylinder  410  and varied in size and location until products of inertia are measured within a desirable criterion, as shown in  FIG. 5 , at chart  505 . 
         [0049]    Holes  440  and  445  minimize variations in product of inertia of plate cylinder  410  and improve bending stiffness of plate cylinder  410  during rotation. By reducing variation in the products of inertia, the displacement variations during the grinding phase of cylinder  410  are reduced similarly, as shown by Equations (1) and (2). 
         [0050]    In a preferred embodiment shown in  FIG. 6 , holes  440 ,  440 ′ and  445 ,  445 ′ may be drilled from ends  450 ,  452  respectively of plate cylinder  410  axially inward. As shown in  FIG. 6 , it may be desirable to not drill holes  440 ,  440 ′ and  445 ,  445 ′ entirely through cylinder  40 . Thus, holes  440  and  440 ′ may or may not connect. For example, holes  440  and  440 ′ may be spaced by a width preferably between 0.25 and 0.50 inches, for example, to accommodate manufacturing limitations. 
         [0051]      FIG. 5  shows the variation in products of inertia as the angle of rotation Θ changes. A prior art plate cylinder chart  510  shows a large variation in products of inertia. In accordance with the present invention, a plate cylinder chart  505  shows a small variation in products of inertia when plate cylinder  410  includes two inertia balance holes  440  and  445  ( FIG. 4 ). As shown in chart  505 , the products of inertia over 360 degrees of rotation are significantly improved for plate cylinder  410  including two inertia balance holes  440 ,  445  ( FIG. 4 ). As variations in products of inertia decrease, the bending stiffness uniformity improves resulting in more uniform lateral deflection. The inclusion of additional inertia balance holes  440 ,  445  in plate cylinder  410 , as shown in  FIG. 4 , reduces variation in products of inertia during rotation while maintaining primary mass balance. Thus, manufacturing cylinders within tighter tolerances may be achieved. 
         [0052]    The foregoing merely illustrates the principles of the invention. It will thus be appreciated that those skilled in the art will be able to devise numerous other arrangements which embody the principles of the invention and are thus within its sprit and scope. 
         [0053]    For example, based on the above disclosure, it is apparent that the principles of the invention can readily accommodate various cylinder types and is not limited to print cylinders to achieve the benefits of the invention. 
         [0054]    In addition, based on the disclosure, it is apparent that the principles of the invention is not limited to two inertia balancing holes and can readily accommodate more or less holes depending on the configuration of the cylinder.