Porter Governor Mechanism

7/21/2019 Porter Governor Mechanism

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Sheikh Shahir Porter Governor Mechanism KEM120702

OBJECTIVES

There are two primary objectives in this experiment:

First we are required to determine how the rotational speed of the Porter Governor relates to the

displacement of the load thats being hoisted.

Having done that, we are to compare the results of the experiment with the theoretical values.

ABSTRACT

This experiment allows us to determine how the rotational speed of the Porter Governor relates to thedisplacement of the load thats being hoisted (for a wide variety of loads). After that we compared theexperimental results with the theoretical values. We start of the experiment with no loads being applied tothe Porter Governor. We can adjust the how fast the rotating shaft of the Porter Governor moves by

controlling the amount of power supplied to this machine. Readings of how much the machine isdisplaced is taken at a variety of points from the range of 0 to 5cm. We repeat the experiments in steps by

increasing the load by 5N up until we reach 15N. Its necessary to make sure that the orientation of theloads are different for each of the applied loads. We need to record the value of the displacement of the

load and also the speed at which the Porter Governor rotates. The graph of rotational speed againstdisplacement is plotted based on the data tabulated. And to finish it off, comparisons between theexperimental and the theoretical values were made and conclusions were drawn based upon the results.

INTRODUCTION

A governor can be defined as a device that is capable of controlling the speed of a variety of machines, anengine, or a motor by controlling the fuel supplied or the power available. This supervised and controlledspeed is known as isochronous speed.

Types of Porter Governors:

There are two main types of Porter Governors:- Centrifugal governor (also known as Watt governor)- Inertia governor

Centrifugal govenors are capable, regardless of load or fuel-supply conditions, to maintain control of thespeed of an engine by supervising the amount of fuel or working fluid that is admitted. It makes use of the

proportion control principle.

There are two main types of centrifugal governors:

Dead-weight Governors

It is a governor in which the movement of the governor balls is regulated by the force of gravity. Theradius of the ball path is controlled by lever and weights the latter being usually attached to the sleeve as

in the Watt. The figure below illustrates (a) Porter (b) Proell (c) Governors.


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Figure 1 Dead-weight Governors

Spring-loaded Governors.It is a governor in which the movement of the governor balls is regulated by the spring force.

The balls are controlled by springs acting on them or the sleeve. Three examples are shown in thediagram below

Figure 2 -Spring-loaded Governors.

Whereas, Inertia Governorswork on a different principle. The governor balls are arranged so that theinertia forces caused by angular acceleration or retardation of the governor shaft tend to alter their

positions. The amount of the displacement of the balls is controlled by springs and the governormechanism to alter the supply of energy to the engine. The advantage of this type of Governor is that the

positions of the balls are affected by the rate of change of speed of the governor shaft. Consequently, amore rapid response to a change of load is obtained, since the action of the governor is due to accelerationand not to a finite change of speed. The advantage is offset, however, by the practical difficulty of

arranging for a complete balance of the revolving parts of the governor. For this reason centrifugalgovernors are much more frequently used. (http://www.codecogs.com)
http://www.codecogs.com/http://www.codecogs.com/http://www.codecogs.com/http://www.codecogs.com/


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Figure 3-Intertia governor

There are three major components in a governor:

Frame- structural system that supports others components of a physical construction

Shaft or spindle- A spindle is a rotating axis of the machine, which often has a shaft at its heart. The shaftitself is called a spindle, but also, in shop-floor practice, the word often is used to refer to the entire rotary

unit, including not only the shaft itself, but its bearings and anything attached to it.Motor - Mostly is an electric motor, operates through interacting magnetic fields and current-carryingconductors to generate force, although electrostatic motors use electrostatic forces.

Beside the three main components, there are also some key components: the sleeve, the bearing and ruler.The sleeve valve is a type of valve mechanism for piston engines, distinct from the more common poppetvalve. The bearing is a device to allow constrained relative motion between two or more parts. Bearingsmay be classified broadly according to the motions they allow and according to their principle of

operation as well as by the direction of the applied loads they can handle. Ruler, also known as line gaugeis used to measure the displacement of the loads. (Wheeler, 1947)

Figure 4 Components of Governor


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Before we further discuss more about the porter governor, we will discuss about a much simple governorfirst, Watt governor. Watt governor is named after James Watt who first applied it to his steam engines.

The Watt type Governor can be seen at the below.

Figure 5: Watt Governor

As for Watt govener used in engine it is important to note that a change in load on a engine will almostcertainly lead to a change in speed and the Governor is required to alter the supply of energy to the engineto bring the speed back to its original value. This is achieved by connecting the rotating parts of the

governor, through suitable levers, to a sleeve on its axis of rotation. Any change in the speed causes achange in the position of the rotating parts and consequently to the sleeve and this movement actuates thefuel supply valve (this includes compressed air, steam or water) of the particular engine or turbine. Thisfunction is of particular importance in A.C. electric generators since it is important to maintain the correctnumber of cycles per second from the generator whose load may change rapidly and unpredictably.

The porter governor is a modification of a Watts governor; with central load attached to the sleeve. Thisleads to larger centrifugal forces here. High speeds are required to bring the fly balls to the same radius.

Figure 6: Porter Governor


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THEORETICAL BACKGROUND

In this experiment, we will be using the theory below to calculate the theoretical values for the results.

Figure 8: Free body diagram of the Porter Governor

From geometry,

2

22

2

1

xbcra

22222

4

1

4

1

22 bcax

bxrcr (1)

A

ACBBr

2

4 2/12

where:

2222

4

1

4

1

2

2

1

bcaxbx

C

cB

A

Now, consider half of the governorW = the weight of the ballP = lifted loadTake moment at point O,

02

1

2

1 2 crPcrWxbF (2)


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crPW

xb

g

Wr

2

2

r

cr

W

PW

xb

g

22

srad

rcr

WPW

xbg /2

Hence, rotational speed =

2

60RPM

Some of the important terms that we should get to know in understanding governors better are as follows

Controlling Force.The forces that oppose centrifugal force result in the formation of controlling force. It can be considered

to be a one inside force acting radially on the centre of the ball. If the ball is in state of equilibrium

condition, the controlling force can be found to be equal in magnitude to the centrifugal force.

Sensitiveness Of A Governor.

When the governor operates between two different speed limits, those being N1 and N2, then thesensitiveness of the governor can be defined as the ratio of the average of these two speeds to the

difference in value between these two speeds.. Thus,

Isochronous Governor.

An isochronous governor can be defined as one that can be said to be in a steady condition at a particularspeed. This is regardless of the radius of rotation. Isochronous governor also has infinite sensitivity as it

has zero range of speeds

Stability Of Governor.

A stable governor will be displaced from its equilibrium position without any change in speed and willreturn to its equilibrium position without suffering any change to its speed of motion. It will always be in

equilibrium

Hunting Of Governor.

This is a special condition in which a machine whose speed is controlled by the governor varycontinuously from the average speed. This happens in the rare scenario when a governor is considered to

be excessively sensitive. Thus the fuel supplied to the engine is changed by drastic amounts.

Governor Effort.. This is average force in the upward direction that acts on the governor sleeve when the force applied on

the engine decreases. It can be expressed for a percent change in governor speed.


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Governor Power.

. It can be defined as the amount of work thats being done on the sleeve when the sleeve is moved

upward. It is also expressed as one percent change in governor speed.

Height Of Governor.

This simply the measured vertical distance from the centre of the governor ball to the centre of the axis of

the spindle.Equilibrium Speed Of Governor.

The speed at which the governor balls dont undergo any fluctuation and are said to be in a steady state.

Sleeve Lift Of Governor.

When the governor speed changes, the vertical distance travelled by the sleeve is called the sleeve lift of

the governor.

4.0 RESULT

Data of Apparatus.Table 1: Particulars of the porter governor equipment

Symbol Value

Weight of ball W 5NBasic Sleeve Load P 25.56N

Additional Weights w 5N

Total Sleeve Load P+nW 40.56N

a 0.1250m

b 0.2300m

c 0.0250m

BC 0.0795m

A 1

B -0.05

3.142

From the results obtained, four tables are plotted according to load: 0 N, 5N, 10N and 15N respectively.

Table 2: The rotational speed and displacement with respective load variations.

No Load Rotation Speed (RPM) 168 180 186 195 200 211

Displacement (cm) 0 1.0 2.0 3.0 4.0 5.0

5 N Rotation Speed (RPM) 184 197 206 215 222 228

Displacement (cm) 0 1.0 2.0 3.0 4.0 5.0


Displacement (cm) 0 1.0 2.0 3.0 4.0 5.0


Displacement (cm) 0 1.0 2.0 3.0 4.0 5.0

Now that we have obtained the experimental values, we will calculate the theoretical values by makinguse of the formulas provided in the theory that we have discussed above.The following is the sample calculation where there is no additional load

Part 1-Sample Calculation for basic sleeve load:

By taking the third sample to show the calculations doneMeasured Rotational speed = 186 rpm


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Displacement, x = 0.02m

C = - +

- a2+ c2+

= - + - 0.1252+ 0.0252+

= -0.0040

r =A

ACBB

2

42

=)1(2

)-0.0040)(1(4)05.0()05.0( 2

= 0.0930m

=r

cr

W

PW

xb

g )()(

)(

2

= 0.0930 )025.0(0.09305 )56.255()02.0230.0( )81.9(2

= 20.4336rad/s

Rotational speed =

2

60

=)142.3(2

)20.4336(60

= 195.1265rpm

The percentage difference can be calculated using this formula: Percentage of difference (%)

=|[(Measured speed -Calculated speed)/Calculated speed]| x100%Hence by taking the above sample values for the sample calculation whereby the calculated speed,

N=195.1265rpm and the measured speed will be 188rpm

Percentage of difference (%) = |[(186-195.1265)/ 195.1265] |x100%

= 4.67%Similar theoretical calculations which were shown in the sample calculations above were carried out andtabulated in the table below:

Table 3: Theoretical results of the no load

Measuredspeed(rpm)

Measureddisplacement

x (m)

C r (m) (rad/s) Calculatedspeed, N

(rpm)

Percentage

of

difference

(%)


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168 0.0 -0.0023 0.0795 19.1146 182.5310 4.67

180 0.01 -0.0031 0.0860 19.7528 188.6253 4.04

186 0.02 -0.0040 0.0930 20.4336 195.1265 4.67

195 0.03 -0.0046 0.0973 20.8996 199.5765 3.30

200 0.04 -0.0052 0.1013 21.3583 203.9567 3.41

211 0.05 -0.0066 0.1100 22.5024 214.8821 3.20

Using the data from the table the graph of rotational speed against displacement were plotted as shownbelow

Graph 1: Basic sleeve load

Part 2: Sample calculations for additional load of 5NConsider the second sample:Measured Speed = 197 RPMMeasured Displacement, x = 0.01m

From formula,

160

170

180

190

200

210

220

230

240

250

0 0.01 0.02 0.03 0.04 0.05

RotationalSpeed(rpm)

Displacement, x (m)

A Graph of Rotational Speed versus Displacement

Experimental result

Theoretical result


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Rotational Speed

To calculate the percentage of difference the formula used is as follows:-Percentage of difference(%)=|[(Measured speed -Calculated speed)/Calculated speed]| x100%

Hence by taking the above sample values for the sample calculation whereby the calculated speed,N=198.1183rpm and the measured speed will be 194rpm

Percentage of difference(%) = |[(197 -207.312)/ 197] |x100%= 5.23%

Similar theoretical calculations which were shown in the sample calculations above were carried out andtabulated as shown in the table below:

Table 4: Theoretical results of the 5N load

Measuredspeed

(rpm)

Measureddisplacement,

x (m)


(rpm)

Percentage

of

difference

(%)

184 0.00 -0.0020 0.0762 20.2785 193.6454 5.23


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197 0.01 -0.0025 0.0809 20.7469 198.1183 2.08

206 0.02 -0.0041 0.0937 22.1249 211.2772 2.50

215 0.03 -0.0047 0.0980 22.6280 216.0815 2.81

222 0.04 -0.0057 0.1045 23.4527 223.9568 1.77

228 0.05 -0.0068 0.1112 24.4460 233.4421 2.44

Next the graph of rotational speed against displacement were plotted as shown below

Graph 2: Additional weight of 5N

Part 3- Sample Calculation for additional weight of 10N:

Consider the first sample:

Measured Speed = 197 RPMMeasured Displacement, x = 0.0 m

From formula,

180

190

200

210

220

230

240

0 0.01 0.02 0.03 0.04 0.05 0.06

RotationalSpeed

(rpm)

Displacement, x (m)


Theoretical result

Experimental result


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Rotational Speed

=Percengtage difference is calculated using the formula below:

Percentage of difference(%)=|[(Measured speed -Calculated speed)/Calculated speed]| x100%

Hence by taking the above sample values for the sample calculation whereby the calculated speed,

N=210.0406rpm and the measured speed will be 205 rpm

Percentage of difference(%) = |[(197-201.050)/ 201.050] |x100%= 2.01%



Measured

speed(rpm)

Measured

displacement,x (m)

C r (m) (rad/s) Calculated

speed, N(rpm)

Percentage

of

difference

(%)197 0.005 -0.0023 0.0791 21.9954 210.0406 2.01

212 0.012 -0.0031 0.0860 22.7563 217.3067 1.06

219 0.021 -0.0041 0.0937 23.6292 225.6422 1.61

228 0.030 -0.0050 0.1000 24.4303 233.2922 2.27

235 0.040 -0.0060 0.1064 25.3150 241.7404 1.55

248 0.047 -0.0066 0.1100 25.9239 247.5550 1.84

After the table was tabulated, the graph of rotational speed against displacement were plotted as shownbelow the table

Graph 3: 2 additional weight of 10N


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Part 4- Sample Calculation for additional weight of 15N:

Consider the first sample:Measured Speed = 212 RPMMeasured Displacement, x = 0.0 m

From formula,

200

205

210

215

220

225

230

235

240

245

250

0 0.01 0.02 0.03 0.04 0.05


Displacement, x (m)


Theoretical result

Experimental result


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Rotational Speed To calculate the percentage of difference the formula used is as follows:-

Percentage of difference(%)=|[(Measured speed -Calculated speed)/Calculated speed]| x100%

Hence by taking the above sample values for the sample calculation whereby the calculated speed,N=226.3527rpm and the measured speed will be 222rpmPercentage of difference(%) = |[(212-212.9836)/ 212.9836] |x100%

= 0.46%



Measuredspeed(rpm)

Measureddisplacement,

x (m)


(rpm)

Percentageof

difference

(%)

212 0.000 -0.0027 0.0827 23.7036 226.3527 0.46

224 0.01 -0.0033 0.0876 24.2978 232.0269 0.87

237 0.02 -0.0044 0.0959 25.3301 241.8846 0.78

243 0.03 -0.0055 0.1033 26.3615 251.7338 1.48

255 0.04 -0.0061 0.1070 26.9241 257.1062 0.82

259 0.05 -0.0067 0.1106 27.5727 263.2999 0.87

After this step the graph of rotational speed against displacement were plotted as shown below


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Graph 4: 3 additional weight on sleeve load P= 40.56N

DISCUSSIONS

From the results we can see that the rotational speed can be said to be proportional to the displacement

incurred vertically for the variety of loadings. The explanation is simply that we need stronger centrifugalforces to balance out the bigger loads. Also from calculations it can be seen that theoretical value is

higher than the practical value. However the deviation is very small. A maximum of 5.23% only. We can

reason that this is because of friction which we assume to be zero. But in reality friction cannot beignored. Friction exists in the system as both external and internal friction and the effect it has on the

result has to be taken into account. Some of the rotational force therefore are wasted to overcome thisfriction.

Difference in theoretical and experimental values can be accounted for the following reasons:1)

Energy dissipated because of friction.2) The generalized and over-used parallax error that we attribute to almost every experiment in

which a ruler is involved. The observers eyes might not be parallel to the reading on the ruler.3) The system is not static and the porter governor doesnt stay still at one position . Therefore some

errors creep in because of this.4) If the additional loads arent given proper orientation the experiment will be erroneous. Since we

dont have the necessary tool to calculate the angle its not possible to ensure 100% that the loads

were given proper orientation.

We can take certain steps to get more accurate results and for general safety:a)

Make sure that the casing of the governor is always closedb) The apparatus is very sensitive so great care must be taken while adjusting the speed.

215

220

225

230

235

240

245

250

255

260

265

270

0 0.01 0.02 0.03 0.04 0.05 0.06


Dispalcement, x (m)


Experimental result

Theoretical result


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c) When the load is lifted to the steady position, the readings of the rotational speed should berecorded after some short period of time so that the displacement obtained will be the most

accurate one.d) We should try to avoid parallax error by keeping our eye level with the ruler.e) We should use a protractor while putting the loads to make sure that they have proper orientation.

We can also avoid any unnecessary friction between surfaces and vibrations effect can be reduced

and possibly eradicated

CONCLUSION

We can conclude that the rotational speed of the Porter Governor varies linearly with the verticaldisplacement of the loads being lifted. We can also conclude that theoretical values are slightly higher

than the experimental values.

REFERENCES

1. Wikipedia2. Benson H. Tongue, (1996). Principle of Vibration. Oxford University Press.

3.

Porter Govener : Retrieved 27 October 2012 fromhttp://www.codecogs.com/reference/engineering/theory_of_machines/engine_governors.php

4.

Goveners : Retrieved 27 October 2012 fromhttp://ptumech.loremate.com/tom1/node/7

5. Laboratory worksheet6. http://nes.dilutionbarberryplangent.com/7. http://www.engineersedge.com/mechanics_machines/porter-governor.htm
http://www.codecogs.com/reference/engineering/theory_of_machines/engine_governors.phphttp://www.codecogs.com/reference/engineering/theory_of_machines/engine_governors.phphttp://ptumech.loremate.com/tom1/node/7http://ptumech.loremate.com/tom1/node/7http://ptumech.loremate.com/tom1/node/7http://ptumech.loremate.com/tom1/node/7http://www.codecogs.com/reference/engineering/theory_of_machines/engine_governors.php

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