Aim - PRACTICAL WORK 1: PORTER GOVERNOR (Semester 1, 2019) 1. Aims The aims of this PDF

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PRACTICAL WORK 1: PORTER GOVERNOR (Semester 1, 2019)
1. Aims
The aims of this practical work are:
i. To investigate the variation of the radius of rotation of the fly balls with the vertical movement of the sleeve.
ii. To investigate the variation of the rotational speed...

Description

Table of contents Page

1. Aim, Apparatus

1

2. Theory, Experimental procedure

2

3. Experimental results

3

4. Calculations

4

5. Tabulated results

8

6. Conclusion, References

9

Aim   

To study the variation of the fly balls ' rotation radius r with the sleeve's vertical movement y. To explore the variation of the governor's rotational speed by changing the sleeve's vertical motion y To explore the variation in the governor's rotational speed by changing the governor's height h

Sketch of the apparatus

Figure 1 Porter Governor (Courtesy MTM32AI Lab Guide)

The component with the fly balls, arms, links and the central dead weight is the Porter governor and is the main focus of the experiment as outlined in the aim of the investigation. The mass hanger on the left of the governor serves the purpose of adding load to the governor. The speed adjustment screw allows the operator to change the speed of the electric motor running the governor.

Summary of theory A governor's purpose is to regulate an engine's mean speed when there are variations. When the load increases, the governor's configuration changes and a valve is raised to raise the supply of the working fluid; conversely, when the load lowers the engine velocity rises and the governor lowers the supply of working fluid. The aim of the centrifugal governors is to balance the centrifugal force on the rotating balls by an equal and opposite radial force. As the demand on the engine grows, the centrifugal force on the balls lowers. A governor monitors the velocity of the engine. As it rotates, the weights swing outward, pulling down a spindle that reduces the fuel supply at high velocity. Governors have a variety of applications in industry and these are some of the more common applications: In thermal power generation, governors serve the purpose of opening or closing of the steam control valve in order to reduce or increase the amount of steam going into a turbine, this increases or reduces the speed of rotation of the generating turbine to a pre-set value. Experimental Procedure

1. Add additional weight P1 onto the hanger 2. Start electrical motor of the Porter governor and let the speed gradually increase until the sleeve with the central mass M just begins to lift from its zero position. 3. Record the governor speed for that position. For accurate readings, the speed must be kept constant for at least 10 seconds before the reading is recorded. 4. From 0 to 50 mm, for each increment of 5 mm of the vertical movement of the sleeve, record the governor speed 5. After recording of the speed governor for the sleeve lift of 50 mm from the zero position, switch off the electrical motor of the governor. 6. Add additional weight P2 onto the hanger 7. Repeat steps 2 to 4

Experiment results

Arm length = 125 mm

Dead weigh mass = 25 N

Link length = 125 mm

Fly balls mass = 5 N

Eccentricity = 25 mm

B = 225 mm

Sleeve movement y (mm)

Additional weight P1 (N)

Additional weight P2

Governor rotation speed n (rpm)

Governor rotation speed n (rpm)

0

202

215

5

210

218

10

213

223

15

220

224

20

225

226

25

227

229

30

232

237

35

236

241

40

238

245

45

241

253

50

249

258

(N)

Calculations and graphs Using the sketch below

Figure 2 (Courtesy MTM32AI Lab Guide)

Case 1 Y=0 mm 𝐶𝐷 =

𝑏 − 𝑦 225 − 0 = 112.5 𝑚𝑚 = 2 2

𝐵𝐶 = √𝐴𝐵2 + 𝐴𝐶 2 = √1252 + 112.52 = 54 .486 𝑚𝑚 𝑟 = 𝐵𝐶 + 𝑒 = 54.486 + 25 = 79.486 𝑚𝑚

Σ𝑀𝐼 = 0 (𝐴𝑛𝑡𝑖𝑐𝑙𝑜𝑐𝑘𝑤𝑖𝑠𝑒 +) 𝑚𝑟𝜛 2 (𝐵𝑀) = 𝑊(𝐼𝑀) + (

𝑀𝐺 𝑃 + ) (𝐼𝐷) 2 4

(0.510)(79.486 × 10−3 )𝜔2 (112.5 × 10 −3 ) 25 5 = 5(54.486 × 10−3 ) + ( + ) (108.97 × 10 −3 ) 2 4 ∴ 𝜔 = 19.704 ℎ=

𝑟𝑎𝑑𝑠 𝑠

𝑟(𝑏 − 𝑦) 79.486(225 − 0) = 164.119 𝑚𝑚 = 2(𝑟 − 𝑒) 2(79.486 − 25)

Y=5 mm 𝐶𝐷 =

𝑏−𝑦 2

=

225 − 5 = 110 𝑚𝑚 2

𝐵𝐶 = √𝐴𝐵2 + 𝐴𝐶 2 = √1252 + 1102 = 59.372 𝑚𝑚 𝑟 = 𝐵𝐶 + 𝑒 = 59 .375 + 25 = 84.372 𝑚𝑚

Σ𝑀𝐼 = 0 (𝐴𝑛𝑡𝑖𝑐𝑙𝑜𝑐𝑘𝑤𝑖𝑠𝑒 +) 𝑚𝑟𝜛 2 (𝐵𝑀) = 𝑊(𝐼𝑀) + (

𝑀𝐺 𝑃 + ) (𝐼𝐷) 4 2

(0.510)(84.372 × 10−3 )𝜔2 (110 × 10−3 ) 25 5 = 5(59.372 × 10−3 ) + ( + ) (118.744 × 10−3 ) 4 2 ∴ 𝜔 = 20.191 ℎ=

𝑟𝑎𝑑𝑠 𝑠

𝑟(𝑏 − 𝑦) 84.372(225 − 5) = 156.318 𝑚𝑚 = 2(𝑟 − 𝑒) 2(84.372 − 25)

Y=10 mm 𝐶𝐷 =

𝑏 − 𝑦 225 − 10 = 107.5 𝑚𝑚 = 2 2

𝐵𝐶 = √𝐴𝐵2 + 𝐴𝐶 2 = √1252 + 107.52 = 63 .787 𝑚𝑚 𝑟 = 𝐵𝐶 + 𝑒 = 63 .787 + 25 = 88.787 𝑚𝑚

Σ𝑀𝐼 = 0 (𝐴𝑛𝑡𝑖𝑐𝑙𝑜𝑐𝑘𝑤𝑖𝑠𝑒 +) 𝑚𝑟𝜛 2 (𝐵𝑀) = 𝑊(𝐼𝑀) + (

𝑀𝐺 𝑃 + ) (𝐼𝐷) 2 4

(0.510)(88.787 × 10−3 )𝜔2 (107.5 × 10 −3 ) 25 5 = 5(163.787 × 10 −3 ) + ( + ) (127.574 × 10 −3 ) 2 4 ∴ 𝜔 = 20.637 ℎ=

𝑟𝑎𝑑𝑠 𝑠

𝑟(𝑏 − 𝑦) 88.787(225 − 10) = = 149 .632 𝑚𝑚 2(𝑟 − 𝑒) 2(88.787 − 25)

Case 2 Y=0 mm 𝐶𝐷 =

𝑏 − 𝑦 225 − 0 = = 112.5 𝑚𝑚 2 2

𝐵𝐶 = √𝐴𝐵2 + 𝐴𝐶 2 = √1252 + 112.52 = 54 .486 𝑚𝑚

𝑟 = 𝐵𝐶 + 𝑒 = 54 .486 + 25 = 79.486 𝑚𝑚

Σ𝑀𝐼 = 0 (𝐴𝑛𝑡𝑖𝑐𝑙𝑜𝑐𝑘𝑤𝑖𝑠𝑒 +) 𝑚𝑟𝜛 2 (𝐵𝑀) = 𝑊(𝐼𝑀) + (

𝑀𝐺 𝑃 + ) (𝐼𝐷) 4 2

(0.510)(79.486 × 10−3 )𝜔2 (112.5 × 10 −3 ) 25 10 = 5(56.486 × 10−3 ) + ( + ) (108.472 × 10 −3 ) 4 2 ∴ 𝜔 = 20.449 ℎ=

𝑟𝑎𝑑𝑠 𝑠

𝑟(𝑏 − 𝑦) 79.486(225 − 0) = 164.119 𝑚𝑚 = 2(𝑟 − 𝑒) 2(79.486 − 25)

Y=5mm 𝐶𝐷 =

𝑏 − 𝑦 225 − 5 = 110 𝑚𝑚 = 2 2

𝐵𝐶 = √𝐴𝐵2 + 𝐴𝐶 2 = √1252 + 1102 = 59.372 𝑚𝑚 𝑟 = 𝐵𝐶 + 𝑒 = 59 .375 + 25 = 84.372 𝑚𝑚

Σ𝑀𝐼 = 0 (𝐴𝑛𝑡𝑖𝑐𝑙𝑜𝑐𝑘𝑤𝑖𝑠𝑒 +) 𝑚𝑟𝜛 2 (𝐵𝑀) = 𝑊(𝐼𝑀) + (

𝑀𝐺 𝑃 + ) (𝐼𝐷) 2 4

(0.510)(84.372 × 10−3 )𝜔2 (110 × 10−3 ) 25 10 = 5(59.372 × 10−3 ) + ( + ) (118.744 × 10 −3 ) 2 4 ∴ 𝜔 = 20.953 ℎ=

𝑟𝑎𝑑𝑠 𝑠

𝑟(𝑏 − 𝑦) 84.372(225 − 5) = = 156.318 𝑚𝑚 2(𝑟 − 𝑒) 2(84.372 − 25)

Y=10 mm 𝐶𝐷 =

𝑏−𝑦 2

=

225 − 10 = 107.5 𝑚𝑚 2

𝐵𝐶 = √𝐴𝐵2 + 𝐴𝐶 2 = √1252 + 107.52 = 63 .787 𝑚𝑚

𝑟 = 𝐵𝐶 + 𝑒 = 63 .787 + 25 = 88.787 𝑚𝑚

Σ𝑀𝐼 = 0 (𝐴𝑛𝑡𝑖𝑐𝑙𝑜𝑐𝑘𝑤𝑖𝑠𝑒 +) 𝑚𝑟𝜛 2 (𝐵𝑀) = 𝑊(𝐼𝑀) + (

𝑀𝐺 𝑃 + ) (𝐼𝐷) 4 2

(0.510)(88.787 × 10−3 )𝜔2 (107.5 × 10 −3 ) 25 10 = 5(163.787 × 10 −3 ) + ( + ) (127.574 × 10−3 ) 4 2 ∴ 𝜔 = 22.06 ℎ=

𝑟𝑎𝑑𝑠 𝑠

𝑟(𝑏 − 𝑦) 88.787(225 − 10) = 149 .632 𝑚𝑚 = 2(88.787 − 25) 2(𝑟 − 𝑒)

Tabulated results Additional weight P1 (N) Additional weight P2 (N) Sleeve moveme nt y (mm)

Radius of rotatio n

Height (mm)

Rotation speed 𝜔 of the Rotation speed 𝜔 of the governor (rad/s) governor (rad/s) Experiment Theoretic al al

Experiment al

Theoretic al

(mm) 0

79.486

164.11 9

202

19.704

215

20.449

5

84.372

156.31 8

210

20.191

218

20.953

10

88.787

149.63 2

213

20.637

223

22.06

15

92.823

143.70 4

220

21.058

224

21.853

20

96.545

138.31 7

225

21.464

226

22.275

25

100

133.33 3

227

21.862

229

22.687

30

103.22

128.66 1

232

22.255

237

23.095

35

106.24

124.23 4

236

22.648

241

23.503

40

81.24

106.24

238

22.648

245

23.503

45

84.076

109.07 6

241

23.474

253

23.914

50

114.26 8

112.00 5

249

23.853

258

24.33

Conclusion The first set of rotational speed vs fly ball radius graphs reveal a directly proportional relationship which is also right according to the theory summary as the fly ball radius increases with the governor's rising rotational speed. Again in this case, the theoretical and experimental graphs were mostly parallel to each other and this validates the theoretical formulae. The second set of rotational vs. governor height graphs demonstrates that these two variables are inversely proportional. For most of the graph, the theoretical and experimental paths are orthogonal and this confirms that the theoretical theorems are absolutely correct. The error in the experiment may be due to the following factors: 



The sleeve friction that affect the speed readings and the fact that it wasn’t accounted for in the calculations. The measurement of the sleeve movement was done with the naked eye and this is not an accurate tool of measurement.

References Mechanics of Machines (Elementary Theory and Examples), 4th edition, Hannah J and Stephens R C, Edward Arnold, ISBN 0-7131-3471-2.

Theory of Machines, 14th revised edition, R.S Khurmi and J.K. Gupta, S. Chand, ISBN 81-219-2524-X MTM32BI Laboratory Guide, Ms. Olwagen...