Appendix "F" - Scaling For Rate - Gemini 4100 Instruction Manual

APPENDIX "F" - SCALING FOR RATE

The Gemini offers a simplified method for 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 (See "General Description" section), high
resolution and accuracy can be realized at all input rates, slow or fast. It is not
necessary to increase the pulse information 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 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).
There are two basic types of rate scaling applications for the Gemini. The first
is when the rate indicator is to display the rate at which the counter is counting
(count and rate using the same sensor). In this case, the rate indicator can be
programmed with the same scaling parameters as the counter. The only other
requirement is that the desired "Rate Conversion Factor", function code 62, be
selected to provide the rate display in the desired time format, i.e., Rate per Second,
Rate per Minute or Rate per Hour. This will automatically scale the rate by x1, x60
or x3600 (1 pulse per second = 60 pulses per minute = 3600 pulses per hour).
Note: If the number of Count Edges for Counter B is 2 or 4, the rate must be
scaled by the same amount using the Rate Scale Factor and Scale Multiplier.
This is due to the fact that the rate indicator only uses 1 edge.
The second basic type of rate application is when the rate indicator and counter
are using two separate sensors. In this case, both the rate and count channels must
be scaled separately.
Scaling for the count channel is discussed in Appendix "E" - Scaling for
Counter.
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.
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In order to convert the pulse units to revolutions, it is necessary for the Gemini
to multiply the number of pulses by a scaling factor to convert the pulse units to
revolution units. The Gemini 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
To calculate the Total Scaling Factor, "K
formula is used.
FORMULA #1: K = Display units/Number of pulses
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".
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
rev/48 pulses per rev = 0.020833). In many applications the Total Scale Factor,
"K ", can be programmed as the Scale Factor, "SF", and the Scale Multiplier,
T
"SCM", 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
number that will be fit into the four decimal places available to the Scale Factor.
The following formula can be used to calculate the Scale Factor when an SCM
value other than x1 is needed.
FORMULA #2: SF = K
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 an SCM value is, when the Total Scale Factor,
"K ", is less than 0.6000, an SCM value of 0.1 or 0.01 can be used to get a Scale
T
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
5.9999, then an 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
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
".
T
", for the application, the following
T
= Display Units/Number of Pulses = 1
T
" factor does not calculate to an even
T
/SCM
T
", is greater than
T
" was determined to be
T