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APPENDIX “F” - SCALING FOR RATE & DISPLAY C
The Gemini 5200 offers a simplified method of scaling the rate indicator. The
method does not require time unit conversions. The desired time format (Rate Per
Second, Rate Per Minute, Rate Per Hour) is simply selected as part of the
programming procedure.
Due to the way the rate is calculated, high resolution and accuracy can be
realized at all input rates, slow or fast. It is not necessary to increase the number of
pulses per display unit to obtain higher resolution.
The Rate Minimum Update Time, function code 63, can be increased (from
0.5 Sec. up to 16 Sec.) to provide averaging in applications where the input pulse
spacing is not stable. The Update time selected, however, will not affect the
scaling in any manner.
Scaling the Rate channel simply involves programming the Gemini 5200 so
that pulse units inputted to the unit will be scaled to the desired display units
(revolutions, feet, meters, etc.), in the desired time format (Rate Per Second, Rate
per Minute, Rate Per Hour).
In order to scale the rate, it is only necessary to know the number of pulses per
“Display Unit” or units (feet, revolutions, etc.). For example; if a 48 tooth gear,
which is coupled to a shaft, is being sensed and it is desired to indicate the shaft
speed in revolutions, the “Display Units” would be revolutions. It is obvious that
48 pulses will occur in one revolution.
In order to convert the pulse units to revolutions, it is necessary for the Gemini
5200 to multiply the number of pulses by a scaling factor to convert the pulse
units to revolution units. The Gemini 5200 has two programming codes that serve
to scale pulse units to desired display units. They are: the Scale Factor and the
Scale Multiplier. Both are used to attain the Total Scaling Factor, “K
T
”.
To calculate the Total Scaling Factor, “KT”, for the application, the following
formula is used.
FORMULA #1: K
T
= Display Units/Number of Pulses
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”.
Using the example previously discussed, the display unit would be 1
revolution and the number of pulses per display unit would be 48. Therefore, the
Total Scale Factor would be 0.020833 (K
T
= Display Units/ Number of Pulses = 1
rev/48 pulses per rev = 0.020833). In many applications the Total Scale Factor,
“K
T
”, can be programmed as the Scale Factor, “SF”, and the Scale Multiplier
factory setting, x1, would be used. However, in some applications, such as the
one above, it may be desired to obtain more significant digits in the Scale Factor,
“SF”. These situations occur when the “K
T
” factor does not calculate to a number
that can be entered into the four decimal places available to the Scale Factor. The
following formula can be used to calculate the Scale Factor when a SCM value
other than x1 is needed.
FORMULA #2: SF = K
T
/SCM
In this formula, the Total Scaling Factor, previously calculated, is divided by
the Scale Multiplier Value, “SCM”, to obtain the Scale Factor, “SF”.
The general rule for choosing a SCM value is, when the Total Scale Factor,
“K
T
”, is less than 0.6000, a SCM value of 0.1 or 0.01 can be used to get a Scale
Factor value between 0.6 and 5.9999, or to the point where the maximum number
of significant digits is obtained. If the Total Scaling Factor, “K
T
”, is greater than
5.9999, then a SCM value of 10, 100, or 1000 can be used to obtain a Scale Factor
Value between 0.6 and 5.9999.
In our initial example, the Total Scaling Factor, “K
T
”, was determined to be
0.020833. It is easy to see that this number cannot be programmed into the Scale
Factor, “SF”, without losing significant digits. Using formula #2 and the general
rules stated above, a Scale Multiplier Value of 0.01 is chosen and the Scale Factor
is calculated as shown below. This will provide the maximum amount of
conversion accuracy possible.
SF = K
T
/SCM
SF = 0.020833/SCM
SF = 0.020833/0.01 = 2.0833
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