OPTICAL ENCODER AND VELOCITY CALCUATION
Finding Relationship Between The Frequency Response and Radius
In this document, we are going to take a look at two optical encoders in order to determine a
general calculation of the velocity of an encoder with respect to the anemometer cups.
Figure 1: EC202A075A-27D
Figure 2: QD787-05/05-2048-01-010-S1
Based on the datasheet of the rotary encoder in Figure 1, it has a resolution of 75 pulses per
revolution (PPR) and a maximum frequency response of 500Hz. The frequency response is a
system’s response to an input signal at varying frequencies. So given the square wave
below(Figure 3), the frequency response is F = 1/T Hz. T is the amount of time the encoder takes
to generate another clock pulse after one full period. Therefore, ‘F’ symbolizes the frequency of
one waveform at T periods.
Figure 3
Analyzing this data,
- The encoder has 75 PPR = 75pulse/Revolution
- 1 Revolution = (2*pi*r) , where r = radius of the rotary encoder
Assuming it takes 1 second to complete on full resolution (1 revolution per second), knowing
that 1 revolution is (2*pi*r), then
- (2*pi*r) = (2*pi*F) = w, where w is the angular frequency. Essentially, r equals F
-
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If we decide to plot the angular frequency against the frequency in relation to the pulses, we
would have a linear relationship.
Angular Frequency (w, 2*pi increment)
Angular Frequency Versus Pulse/Revolution Graph
40
35
30
25
20
Series1
15
10
5
0
75
Series1 6.2832
150
13
225
18.85
300
375
450
25.133 31.416 37.699
Frequency(Pulse)
Figure 5
The formula for this graph comes out to be
Now, Analyzing the Wind cups,
Figure 6
Notice that in Figure 6, the radius of the circle is denoted as r.
Circumference of a circle ( C ) = 2*pi*r = w
- C = v*t, where v = velocity (meter/seconds), and t = time or period (seconds)
- 2*pi*r = v*t
- t = (2*pi*r)/v
- w = (2*pi)/t
2
if w = (2*pi)/t and t = (2*pi*r)/v, then
w = v/r
Recall, w also equals (2*pi*F)/75, therefore
(2*pi*F)/75 = v/r
Letting v = V,
The radius, r is given to be exactly 0.053 meters, and the maximum frequency response is
500Hz. Therefore, the velocity of the anemometer without any resistance is equal to
2.220058809 meter/second. If 1meter/second = 2.23693629 miles/hour, then the maximum
speed the anemometer can go without damaging the optical encoder is equal to 4.966130115
miles/hour.
Analyzing the QD787-05/05-2048-01-010-S1 optical Encoder (Figure 2),
Based on the datasheet, the encoder has a frequency response of 200kHz and a maximum shaft
speed of 8000RPM; which is 133.333 Revolution per second.
if 2*pi*F = v/r, then 837.758041 = v/r. We also know that r = 0.053meters, so
v = 44.40117617meters/second = V2, which results to
V2 = 99.326023 miles/hour; the maximum velocity the anemometer can rotate
without damaging the optical encoder.
Clearly this shows that the second optical encoder is better than the first. Another advantage of
the second encoder over the first in this project is that, the lead connected to the encoder’s shaft
has a diameter of 0.1247 inches for the second encoder compare to the first which has a diameter
of 0.2000 inches. Since this lead would be connected to opening that the center of the wind cups
attachment (view Figure 6 at center, M) which is 0.1 inches wide, the second encoder is better.
The only advantage of the EC202A075A-27D encoder other the QD787-05/05-2048-01-010-S1
in this project is that, it requires a maximum input current of 30mA, while the QD787-05/052048-01-010-S1 encoder requires a maximum input current of 100mA.
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Finding Relationship between the Actual Wind Speed and Encoder’s frequency response
In the real world, there is no such thing as a perfect shaft encoder; therefore the encoder’s lead
would always have some resistance. So we have to find a relationship between the wind speed
and the frequency response of the encoder. Figure 7 and Figure 8 basically explains what needs
to be done.
Figure 7.
Figure 8
The use of a wind tunnel is to study the effect of air moving around a solid object. The wind
coming through a wind tunnel would be calibrated to different wind speed. The wind would
come through the tunnel then blow on the anemometer. As the anemometer rotates it produces
different frequencies based on the calibration of the wind speed. These frequencies could be
stored in the PIC. The data would then be plotted against the varying speed.
QUESTION: WHERE CAN WE GET WIND TUNNEL?
A WIND TUNNEL IS LOCATED IN THE MECHANICAL ENGINEERING
DEPARTMENT IN THE FLUIDS LABORATORY OF THE UNIVERSITY OF
LOUISIANA.
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