Appendix "E" - Scaling For Counting - Gemini 4100 Instruction Manual

APPENDIX "E" - SCALING FOR COUNTING

The Gemini is factory set to provide 1 count on the display for each pulse that
is input to the unit. In many applications, there will not be a one to one
correspondence between input pulses and display units. In these applications it
will be necessary for the Gemini to scale or multiply the input pulses by a scaling
factor to achieve the proper display units (feet, meters, gallons, widgets, etc.).
There are three different function codes that are used in scaling the input pulses to
the desired reading. They are: the "Counter Scale Factor", the "Counter Scale
Multiplier", and the "Counter Number of Count Edges". All three are factored
together to provide the Total Scaling that is necessary.
This section applies to Counter A (if Dual Counter personality) and Counter B.
There are separate Scale Factors and Scale Multipliers associated with each counter.
The "Number of Count Edges", function code 44 or code 43 (Quad x4), will
apply to both counters. In other words, if one counter requires that 2 count edges
be used per input pulse, programming that mode will cause both counters to use
both count edges. In the Quadrature x4, Inputs 1 & 2 Response mode, both the
rising and falling edges of both Inputs, 1 & 2, are counted. In this mode the
"Number of Count Edges" is 4.
The first step in scaling the counter requires that the "Number of Pulses" per
"Display Unit" or "Display Units" be obtained. This may require a small amount
of deductive reasoning. For example: A 48 tooth gear is mounted to a 2 ft
circumference feed roll in a paper processing plant. It is desired to totalize the
total footage of paper processed. In this example the units of display will be in
feet. A sensor sensing the gear teeth will provide 48 pulses for each revolution of
the feed roll. Each revolution will equate to a linear distance of 2 feet. The
number of "Display Units" will be 2. The "Number of Pulses" per "Display
Units" (2 feet) would naturally be 48.
Once the number of "Display Units" and the "Number of Pulses" have been
obtained, the Total Scaling Factor can be calculated.
The "Total Scaling Factor", denoted as "K
scaling required. It is obtained by dividing the "Display Units" by the "Number
of Pulses" as shown in Formula #1 below.
FORMULA #1: K = Display Units/Number of Pulses
T
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", is simply the total amount of
T
WHERE:
DISPLAY UNITS - The number of units (revolutions, feet, 10ths of feet, meters,
etc.) that would be acquired after the "Number of Pulses" has occurred.
NUMBER OF PULSES - The Number of pulses required to achieve the number
of "Display Units".
For the preceding example, the Total Scaling Factor, "K
plugging in 2 and 48 in the formula. K
= 0.041667.
As previously stated, the Total Scaling Factor, "K
Scale Factor, Scale Multiplier, and Number of Count edges. In many applications the
Total Scale Factor, "K ", can be programmed directly into the Scale Factor, the
T
Scale Multiplier and Number of Count Edges factory settings, of x1, would be used.
In some applications, more display resolution may be required. Whenever the
Total Scaling Factor is greater than 1.0000 and when utilizing only one edge per
count pulse, there may not be enough display resolution. For example; with a
Total Scaling Factor of 2.000, when an input pulse is generated, the display will
increment by 2. If the display units is in feet, when 3 feet has gone by, the display
will still only read 2. It will not increment again until 4 feet has been
accumulated. With this amount of display resolution it would be impossible to set
the Preset and have the output respond at odd feet intervals (1, 3, 5, etc.). To
increase resolution, the Number of Count edges will have to be increased. This
can be achieved by programming Function code 44 to mode 2, 2 edges, or
Function code 43 to mode 6, Quad x4, if quadrature counting is being used.
If enough resolution still has not been attained, more input pulses will need to
be generated per display unit.
The amount of resolution required will vary depending on the particular
application. In cut-to-length applications, a high amount of resolution is often
necessary. However, in totalizing applications, display resolution may not be
important. It should be noted that whenever the number of count edges is
increased to 2 or 4 (Quad x4), the maximum count frequency will decrease. (See
Appendix "B" for maximum count frequency specification.)
Note: When using 2 or 4 edge counting for length sensor, on/off duty cycle must
be 50% to maintain max. accuracy (mag. pickup will not work).
", is calculated by
T
= Display Units/Number of Pulses = 2/48
T
", is the combination of the
T