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CP Versus DP: Understanding the Differences

Author:  Frank Burgos, FlexoExchange

Have you ever wondered what the designation “CP” or “DP” on a plate cylinder gear means? Most of us are familiar with gear selector charts, but just what is the difference between CP and DP? How are they related to printing repeat length? Here we’ll explore some of the differences and learn how we can liberate ourselves from the charts.

Let’s begin by defining a few terms related to plate cylinders and gear construction:

Printing Circumference:  The measurement of the circle described by a point on a plate’s printing surface while printing. It is equal to the plate cylinder repeat.

Gear Pitch Pitch Circle: The imaginary circle on a plate cylinder gear that corresponds to the printing circumference.

CP: Stands for “Circular Pitch”. It’s the distance from a point on a gear tooth along the pitch circle of the gear to the corresponding point on the next gear tooth. Therefore, it's the difference in repeat between a plate cylinder and the next one in size.

DP: Stands for “Diametral Pitch”. It’s a ratio equal to the number of gear teeth per inch of printing diameter.

Pi: The ratio between the diameter of a circle and its circumference.

          Pi = 3.1416 (to four decimal places)
          Pi x diameter = Circumference
          Circumference / Pi = Diameter

CP Gears:

With CP gears, repeat length calculations are straightforward. If we have 1/8” CP plate cylinder gears, this means that we have a total of 1/8” repeat length for every tooth on the gear; 1/4" CP means that we have a 1/4" repeat per tooth and so on. Therefore, to calculate the total repeat, all we need to do is multiply the number of teeth by the CP.  For example:

    Calculate the total repeat for a 1/8" CP gear with 82 teeth:

    Solution:

    teeth x CP = repeat, so:

    82 X 0.125” (the decimal equivalent of 1/8”) = 10.25" repeat

     

    Calculate the total repeat for a 1/4" CP gear with 66 teeth:

    Solution:

    teeth x CP = repeat, so:

    66 x 0.250” = 16.5" repeat

Conversely, if we want to determine the gear size needed to yield a given repeat length, we divide the repeat length by the CP:

    Calculate gear size to print a 7.5" repeat using 1/8" CP gears:

    Solution:

    repeat / CP = gear size, so:

    7.500” / 0.125” = 60 teeth

     

    Calculate gear size to print a 13.25" repeat using 1/4" CP gears:

    Solution:

    repeat / CP = gear size, so:

    13.25" / 0.25" = 53 teeth

DP Gears:

Calculations involving DP gears differ from those involving CP gears in that the DP number is related to the diameter of the plate cylinder instead of it's circumference. Since printing repeat is directly related to circumference, we need to convert DP to CP first to perform repeat calculations. Once this is done, DP repeat calculations become straightforward CP calculations.

As indicated in our DP definition above, DP is the number of gear teeth on a one inch diameter plate cylinder.

      Since Pi x Diameter = Circumference

      a one inch diameter plate cylinder has a circumference, or repeat, of:

      3.1416 x 1" = 3.1416"
       
      Therefore, dividing 3.1416" by DP yields the circular pitch, or CP.  From here on, repeat calculations are straightforward.

      For example:

      Calculate the repeat of a cylinder with a 32 DP gear that has 70 teeth:

      Solution:

      First, convert DP to CP:

      Remember that Pi / DP = CP, so:

      3.1416" / 32 = 0.0982" CP

      Now, we multiply:

      teeth x CP = repeat, so:

      70 x 0.0982" = 6.874" repeat


      Calculate the repeat of a cylinder with a 10 DP gear that has 51 teeth:

      Solution:

      First, convert DP to CP:

      Remember that Pi / DP = CP, so:

      3.1416" / 10 DP = 0.3142" CP

      Now, we multiply:

      teeth x CP = repeat, so:

      51 x 0.3142" = 16.0242" repeat

Conversely, if we want to determine the gear size needed to print a given repeat length, we divide the total repeat length by the CP equivalent for DP.

      For a 10 DP gear press, calculate the gear size needed to print a 15" repeat:

      Solution:

      First, convert DP to CP:

      Remember that Pi / DP = CP, so:

      3.1416" / 10 DP = 0.3142" CP

      Now, we divide:

      Repeat / CP = gear size, so:
       
      15” / 0.3142 = 47.74 teeth
       
      Because we must have whole number quantities of teeth on a gear, we must either round up or down and then multiply the number of teeth by the CP to determine the actual repeat length that we’ll be able to print:

      47.74 teeth = 48 teeth X 0.3142” per tooth = 15.0816” repeat

Without looking at a gear selector chart, we are not likely to have started with 15.0816" repeat in the problem above.  Therefore, calculations involving DP gears tend to be more involved than those involving CP gears.
 
Here is a small chart which shows some common gear types used on flexo presses and their decimal CP equivalents in inches:
 
------------------------------------------------------------------------------------
Gear type                                Decimal CP Equivalent
------------------------------------------------------------------------------------
1/8” CP                                     0.125” CP
1/4” CP                                     0.250” CP
 
10 mm CP                                 0.3937” CP
 
10 DP                                        0.3142” CP
32 DP                                        0.0982” CP
 
Note that we've only discussed the differences in DP versus CP gears as they relate to repeat calculations.  Another difference is that CP cylinder repeats are in familiar increments (15", 10 1/4", 6 3/8", etc.), while DP cylinder repeats always have decimal remainders (6.874", 16.0242", etc.).  However, while CP gears make for cleaner math, it is argued that DP gearing allows a smaller plate cylinder inventory to satisfy a broader range of repeat lengths by rounding.  There are likely other arguments for one over the other, not excluding personal preference.

Author:  Frank Burgos
E-Mail:  frankb@flexoexchange.com
Web Site: http://www.flexoexchange.com/
 

© 1997-2003 Content of this article is original and may not be copied or reproduced without the express written consent of Frank Burgos, FlexoExchange. Personal, educational, non-commercial use is allowed provided this article appears in its entirety. This copyright notice must appear on all copies made and/or distributed.

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