Lab Practice 4 - Measurements of Position, Velocity and Acclereration PDF

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lab 4 practice report on measurements of position, velocity and acceleration...

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MECH252 - Week 7 Lab Practice Report Wind Velocity and Motor Speed Measurement Group 38 Mary Edwards 4376481 Milton Stathakis 6063093 Madeline McCarthy 5405518

Aim

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Introduction

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Procedure Test 1 - Wind Measurement Test 2 - Encoder Reading Test 2 - Motor Position, Velocity and Acceleration Measurement

4 4 4 4

Results Test 1 - Wind Measurement Test 2 - Encoder Reading Test 3 - Position, Velocity and Acceleration Readings.

5 5 7 9

Discussion Test 1 - Wind Measurement Test 2 - Encoder Reading Test 3 - Motor Position, Velocity and Acceleration Measurement

11 11 11 12

Conclusion

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References

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1. Aim The aim of this lab practice is to demonstrate the use of instruments to measure the air stream velocity in a wind tunnel. A manometer will measure the distribution of pressure on the surface of an aerofoil. In addition, an incremental encoder will be used to measure the position, velocity and acceleration of a DC motor.

2. Introduction To measure pressure and velocity between two air streams, a device called a manometer can be used. Either a vertical or inclined manometer can be used containing a liquid of known density. As air travels through this tube and pushes the liquid, the difference in height or starting and resting place can be calculated and used in conjunction with an iteration of Bernoulli’s equation below to find the pressure. This is used in conjunction with a pitot tube to find velocity as well.

𝑝

𝑔ℎ =

𝑚

𝑝 𝑎𝑉 2

2

.

When the manometer is on an incline, the corresponding height can be found using trigonometry. There are different types of manometer and in this experiment we will be comparing results between 3 different manometers.

It is a common practice to analyse the position or state of a DC motor in investigations and analyses. To do this, an incremental encoder is used to estimate the position (angle of the shaft) as a degree of revolution. There are many types of encoders with different resolutions or pulses per revolution. For this experiment, the MTL 5400 will be used with a resolution of 5400.

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3. Procedure 3.1.

Test 1 - Wind Measurement

1. Draw a diagram of the wind tunnel set up. 2. Record the current position of the fluid in the manometre while the wind tunnel is off. Ensure the manometer is at the correct angle using the spirit level. Adjust the angle by turning the knob. Record the angle of the manometre. 3. Run the wind tunnel at 5 equispaced speeds and record the following: a. pressure readings of the fixed pitot tube and manometer b. measure the air stream velocity with the handheld pressure sensor and hot wire anemometer. Measure the air stream close to the fixed pitot tube. 4. Turn off the wind tunnel.

3.2.

Test 2 - Encoder Reading

1. Connect the encoder to the DAQ and begin recording at a frequency of 1kHz. 2. Rotate the shaft of the motor manually and plot the number of pulses in x1-mode and x4-mode. 3. Calculate the position of the motor shaft in both radians and degree.

3.3.

Test 2 - Motor Position, Velocity and Acceleration Measurement

1. Run the trajectory tracking control experiment and save the position, velocity and acceleration measurements when the bandwidth of the velocity and acceleration measurements for the following bandwidths: a.

0.1 rad/s

b. 1 rad/s c. 10 rad/s d. 100 rad/s

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4. Results 4.1.

Test 1 - Wind Measurement

Wind Speed

Manometer Pitot (mm)

Digital Pitot (m/s)

Hot Wire (m/s)

0

55

0

0

3

56

0

1.7

6

80

8.9

7.53

9

121

14.1

11.6

12

203

20.9

16.1

14

219

22

16.8

4.1.1 Diagram of Wind Tunnel Setup

Figure 1: WInd Tunnel Setup with Pitot Tube 4.1.2 Table 1: Data given

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To calculate velocity, bernoulli’s equation must be utilised. As

𝑝

Where𝑝

𝑔ℎ =

𝑝 𝑎𝑉 2

𝑚 𝑚

𝑎𝑛𝑑 𝑝

𝑎

2

,

are the densities of the liquid and air respectively.

Velocity can be rearranged as

𝑉 =

2*𝑝

*𝑔*ℎ

𝑚

𝑝

𝑎

For this data series, as the manometer is on an inclined plane, the height is given as sin(h). Also, 55mm is the manometer zero reading therefore the subsequent heights have this value subtracted from their readings in this equation.

Table 2: Manometer velocity m/s

Figure 2: Velocity recorded by digital pitot and hot wire vs manometer readings

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4.2.

Test 2 - Encoder Reading

4.2.1 Time can be calculate given 𝑓 =

1 𝑇

ie. 𝑇 =

1 1000

For radians: (eg. using Single mode) The resolution of this encoder is 5400. If the number of pulses is per revolution, then the following can be calculated using the 2π 5400

* pulse number = position in radians.

Quadruple mode resolution is 4*5400 ppr there denominator is 4*5400. For degrees: There are 360 degrees in one revolution. Therefore following formula can be used. 360 5400

* 𝑝𝑢𝑙𝑠𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 = 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑖𝑛 𝑑𝑒𝑔𝑟𝑒𝑒𝑠.

Angular velocity can be calculated from these positions as below: 𝑝𝑜𝑠𝑖𝑖𝑡𝑖𝑜𝑛 2−𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 1 𝑡𝑖𝑚𝑒 2 − 𝑡𝑖𝑚𝑒 1

.

Figure 3: Position (radians) of single and quadruple mode encoder

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Figure 4: Position of Quadruple Mode Encoder

Figure 5: Velocity of Single and Quadruple Encoders

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4.3.

Test 3 - Position, Velocity and Acceleration Readings.

Figure 6: Positions 1,2 and 3 with references

Figure 7: Velocities 1 with reference

Figure 8: Velocity 2 with reference

Figure 9: Velocity 3 with reference

Figure 10; Velocity 4 with reference

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Figure 11: Acceleration 1 with reference

Figure 13: Acceleration 3 with reference

Figure 12: Acceleration 2 with reference

Figure 14: Acceleration 4 with reference

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5. Discussion 5.1.

Test 1 - Wind Measurement

5.1.1.Describe the operation of the: Pitot tube and manometer; Pitot tube and digital pressure reader; and Hot wire anemometer.

A pitot tube and manometer uses a tube pointed at the airflow. It uses the principles of fluid mechanics and energy conservation to measure the velocity of fluid. A pitot tube with a calibrated digital pressure reader determines the fluid velocity using the relationship between kinetic, potential energy and pressure. A Hotwire anemometer uses an electrically heated wire that is placed in a flowing gas stream. The heat dissipates from the wire as gas flows around it so that the temperature of the wire reduces. This causes a change in the resistance and therefore the mass flow rate is able to be measured. The pressure of the air pushes the fluid inside and obtains a reading. A digital pressure reader is a cylinder with two holes. The pressure difference is measured between the two to obtain a velocity measurement. The hot wire anemometer works by having a hot wire, as the wind flows, the heat is transferred away and this creates a resistance change and therefore a measurement.

5.1.2. Do you get a 1:1 relationship? There exists a linear relationship between the manometre and two other devices. However there are certain deviations and it is not 1:1

5.1.3.Comment on your experience using the various air speed measurement devices. As above the manometer readings are proportional to the hot wire and the digital pitot thereby demonstrating the accuracy of these devices. In future it should not be necessary to utilise manometer calculation except for calibration.

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5.2.

Test 2 - Encoder Reading

5.2.1.Comment on the measurement results when you use different resolutions in your calculations. The quadruple mode encoder (X4) produces more data points therefore will have a more accurate reading when analysed. The resulting plot is smoother, more linear. There appears to be a small error in the nominal vs real value of the encoder. 5400 is the listed resolution for the MTL encoder, however the max data output was 5398. This can suggest either zero drift or human error when completing the revolution.

5.2.2.Explain the working principle of an incremental encoder.

The incremental encoder produces a specified amount of pulses per one rotation to the encoder, a single incremental encoder is a single line of pulses and a quadruple incremental encoder is two lines of pulses. The incremental coder uses a disc with a series of gaps and different levels. The encoder works based on a source of light. The disc’s gaps allow a light source to pass through and be received by a light sensor, giving an output of 1 or 0. The different levels on the disc then allow the encoder to know which direction it is turning by seeing if signal A or B is leading.

5.2.3.How can you determine the resolution of an incremental encoder, if you do not have a data sheet to reference? As resolution of an encoder is also known as pulses per revolution, you can also find this by turning the encoder one revolution and recording how many pulses there are.

5.3.Test 3 - Motor Position, Velocity and Acceleration Measurement 5.3.1.Comment on the measurement results when compared to the reference data. For position: Data points were very similar between reference and readings For velocity: 12

Most of the velocity measurements readings had a much lower amplitude than the reference values. Until bandwidth is increased which is discussed below. For acceleration: Following the trend of velocity, the reading output signal had much lower amplitude and increased as a larger bandwidth was supplied. There were a lot of rough data points for acceleration 4 as can be seen in figure 14 . 5.3.2.How does the bandwidth of the low-pass-filter influence the velocity and acceleration measurement? As bandwidth is the frequency response and shows max deviation of sensitivity, it should affect the velocity and acceleration measurements. As can be seen from figures 5 and above, there is a linear trend whereby as the bandwidth increases, the amplitude of the reading begins increase to match that of the reference.

5.3.3.Explain single, double and quadruple working modes of an encoder. Does working mode change the resolution? As said above, single working mode produces one data output line, either the rising or the falling of channel A. Double mode includes both the rising and the falling, of channel A Quadruple mode includes rising and falling of channel A and channel B. The different working modes have a great effect on the resolution of the of encoder. For example, a single encoder’s resolution might be 5000 (ppr). Producing 5000 pata points. Whereas the quadruple would then be 20000 ppr producing 20000 datapoints greatly affecting accuracy.

5.3.4.How many encoders can be simultaneously connected to Humusoft MF644? 4 independent

6. Conclusion This investigation provided an understanding of manometers and pitots tubes and showed that there are slight differences in readings in between a hot wire, digital pitot and calculated velocity. This experiment also provided a great understanding of implemented encoders function 13

and the difference between single and quadruple modes and outputs. The effects and importance of bandwidth was also discovered through analysis of reference and measured outputs from these encoders of position, velocity and acceleration.

7. References Lab Video Lab Manual Collins, D., 2021. What do X1, X2, and X4 mean for incremental encoders. [online] Motioncontroltips.com. Available at: [Accessed 8 September 2021].

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