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-

Republic of Iraq

Ministry of Higher Education

and Scientific Research

University of Technology-Electromechanical

Department

1435 2014

No. Name of Experiment page. 1 Slider—Crank Mechanism

2 Rope Belt Friction

3 Gear Trains

4 Balancing of Rotating Masses

5 Flywheel

6 The Governor

September 14 2014 Lab. of Engineering Mechanics Electromechanical Eng. Dept.

[2]

Experiment No.1

Slider—Crank Mechanism

Figure (1.1): Slider – Crank Mechanism

1.1 INTRODUCTION

The kinematics of machines is the study of relative motion of machine part (displacement, velocity and acceleration are considered), while the Dynamics of machines treats with the forces acting on the parts of machine and the motions resulting from these forces.

In this experiment the Kinematics of machines is considered. The motion of the machine parts are linear, rotational or general motion (linear and rotational at the same time), and these parts are subjected to the effect of mechanical loading (gas pressure, inertia forces and the thermal forces).

Also, it is necessary to take into consideration the effect of friction between the neighboring surfaces which produces heating that causes damage to these

parts.


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1.2 APPARATUS

The apparatus basically composed of a wooden base plate supporting two steel frames. The first frame holds a 360 circular disk protractor with steps of 10 . The protractor is used to measure the angular displacement of the 8 cm crank. The second frame supports the path the of sliding part with a measuring ruler tying the connected rod of ( 20 cm) length with a piston at the end of the rod as shown in Figure (1.1) .

1.3 OBJECTIVES OF EXPERIMENT

• To obtain the liner displacement ( ) linear velocity ( )

and linear acceleration ( ) of the piston theoretically and experimentally.

• To estimate the angular velocity ( ) and angular acceleration ( )

of connecting rod using theoretical method.

• To compare the values of angular velocity ( ), and angular acceleration ( ) with those obtained from the relative method.

1.4 THEORY

Figure (1.2)

Assuming an angular speed of 1 unit clockwise for the crankshaft, the linear displacement, velocity, and acceleration of the piston '' C'' can be determined analytically in terms of the angular displacement of the crank “ ” as follows: X = ( ) (r ) ..… (1.1)


[4]

From triangles & ( )

sin = sin

sin = ( / ) sin

And =

Since,

Vp = = (Velocity of piston C)

= sin + ..… (1.2)

a = = (Acceleration of piston C)

r (cos + {cos 2 / }) ..… (1.3)

= = (Angular speed of BC) ..... (1.4)

(Angular acceleration of BC) ..… (1.5)

1.5 PROCEDURE

1. Fix the circular disc on " = 0 " (i.e. the piston being at the

TDC Location).

2. Increase the input angle by an increment step of 15° or 30°

clockwise to reach a complete cycle(360°) and measure " "

using the measuring ruler

3. Draw curve relating displacement

'' '' and input crank angle '' '' .

0 180 360

×


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4. To obtain the linear velocity of piston “C", the slope at each

Point on the ( ) curve can be taken and then the curve ( )may be drawn.

B

5. To obtain linear acceleration of piston take the slope of

( ) curve and draw ( ) curve.

0 90 180 360

O d

Velocity diagram

a

C A

B


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6. Draw relative velocity and acceleration diagrams for the mechanism.

1.6 DISCUSSION

Compare between the theoretical and experimental results.

Discuss the effect of changing the crankshaft angle ( ) on

the main parameters of the experiment , , , , . Compare between experimental values of liner

Velocity & acceleration with those obtained from the relative method. Discuss any other related issues of interest.


[7]

Experiment No.2

Rope Belt Friction

Figure (2.1): The Apparatus

2.1 OBJECTIVES

1) To find the ratio of the belt tensions on each side of the flat rimmed pulley for

180° Lap.

2) To determine the coefficients of friction between the rope belt and each pulley.

3) To study the effect of the lap angle and groove angle on the belt tension ratio.

2.2 INTRODUCTION

In factories the power or rotary motion, from one shaft to another, is usually transmitted by means of belts (Flat, V- type belts) or ropes, running over pulleys.


[8]

When using belts normally, moderate amount of power is to be transmitted but power can be increased if V-belt is used. Power transmitted is increased because the contact area between belt and pulley increased. Power transmitted may also be increased by increasing the number of belts.

Belt material may be leather, rubber, cotton, or fabrics.

To investigate belt drives there are two approaches .One is to hold the belt stationary while forcing the pulley to turn , the other ,adopted for this experiment , is to lock the pulley and put the belt round it .

This is a more obvious way of observing the belt tensions at entry to and departure from the pulley groove.

2.3 APPARATUS

It consists of the followings: -

1. Wall mounted plate with jockey pulley.

2. Number of pulleys providing a flat rim and 120° , 90° , and 60° grooves.

3. Continuous rope belt including two load hangers.

The weight set required for this experiment is(4 × 20) , (3 × 10)

(2 × 5) , (4 × 2) , (2 × 1) , and (1 × 0 5) . [ = . / ]

A heavy steel wall mounting plate is fitted with a spigot on which a 150 mm effective diameter pulley can be clamped and a movable Jockey pulley whose fixing points provide a series of belt contact Lap angles in 30° steps from 30° to 120° . Four steel pulley are supplied with various peripheral profiles, namely.

a) Flat rim

b) groove 120°

c) groove 90°

d) groove 60°


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The rope belt comprises two lengths of similar rope belt and two steel load hangers which also act as constant weight of a continuous " belt "

The objective being to provide a constant weight of belt on each side of the fixed pulley.

2.4 PROCEDURE

It is assumed that the wall plate has been mounted about 1.5 m above the ground to the center of the fixed pulley.

Before using the apparatus make sure that the pulleys are clean and free from grease or dust.

Part 1. Belt Tension Ratio

Fit the flat rimmed pulley on the wall plate and hang the rope belt over the pulley thus making an angle of lap of 180°

Let the load hanger on the left hand side be as high as possible, to start with this side tension will be designated Add load to this side until the rope belt given a slight start, Slides very slowly without acceleration.

This load overcomes the self weight of the rope assembly and is to be omitted from the results.

Put a 5 N load on the right hand side hanger which will be the Slack tension ( ) and hold the rope belt to prevent it slipping until the load is added to the left hand hanger.

Then increase The load on the left until the rope given a start slides very slowly over the pulley. Record and in table 1.Repeat the procedure for values of increasing by 5N intervals up to 40 N. By using the tension ratio expression for flat belt to obtain the theoretical values for ( ) for each ( & ) and compare with experimental predicted from graph.

=

LLn µ=slop


[10]

Table (2-1) Flat rimmed pulley with ° lap

Self weight nullifying load N Belt Tension

35 30 25 20 15 10 5 (N) (N)

Part 2. The Determination of Coefficient of Friction

The method here is to keep( ) constant and to measure for a range of lap angles the flat rimmed pulley fix the jockey pulley to give ( 210°) lap and put the rope in place . Add load to the left hand hanger until be the rope given a start, slides very slowly.

Now put (20N) on both load hanger and then increase the left hand load ( ) until the rope will slide very slowly. Record the value of in table 2 ignoring the initial self weight (nullification load).

Repeat the procedure for all the lap angles provided.

Table (2-2) Sliding tension for =20 N

90 120 150 180 210

Lap angle( ° )

Pulley type

Flat

The complete procedure should be repeated for each of the grooved pulleys using table 2 above


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Part 3. Effect of Angle of Lap and Groove Angle

The results for this part are to be derived from the work done in part 2.

2.5 THEORY

The theoretical expression for belt drives on pulleys is

sin

2

1ln eTT

Where:-

= belt tight side tension (departure side)

= belt slack side tension (entry side)

= coefficient of friction between rope and steel surface of pulley

= angle of lap (contact) in radians

= semi- vertex angle of pulley profile

If and are kept constant then is proportional to .

Part -1

Plot the values of against on a graph to verify linear proportionality.


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The gradient of the best fit straight line gives the ratio of / from which a value can be derived since = 90° and = .

Part -2

From table 2 construct table 2A in which the values of log /20 replace the values of plot on one graph the four sets of derived results for / against the lap angle in degrees (simpler than using radians).

Table (2- A) Sliding tension Log for =20 N

90 120 150 180 210

Lap angle( ° )

Pulley type

Flat V- ° V- ° V- °

Then draw the best possible straight lines from the origin through each set of points. The reason for using the origin is that there is no physical meaning for an intercept at zero lap. Use the gradients of the family of lines to derive the coefficients of friction in each case.

Part- 3

Instead of using the experimental reading of part 2 it is better to read off values of / where lap angle ordinates intersect the straight lines.

This does not, of course, compensate for differences in between the pulleys. However, assuming and, are constant then,

sin

ln2

1 KTT

K


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So a graph of / against 1/ ( ) should yield a straight line for each lap angle tested.

Construct Table (2- A) from the graph for part 2 and plot the new graph .It is again possible to use the gradients to derive coefficients of friction which are in some way averages for the set of four pulleys.

As a further exercise use the graph to find a value of , for a pulley with a 70° groove angle and the rope belt at 150° lap.

2.6 DISCUSSION

1. Factors effecting the values of & .

2. Angle of lap effect on the tension ratio.

3. Groove angle effect on tension ratio

4. Coefficient of friction effect on the

tension ratio. slopK

5. Any other effects.

V-60° Flat

V- 120°

V-90°


[14]

Experiment No. 3

Gear Trains


3.1 INTRODUCTION

The gears are mechanisms use with a large manner in mechanical region so that it is used in heavy and light machines and in many other engines and transfer equipment to transmit rotational and translation motion also power from one shaft to another.

3.2 OBJECTIVES

To determine the number of revolution for driven gear with respect to the driver gear as well as to know the direction of rotation of the gear.

Therefore, it is necessary to know the main object of gear which is:-

1- To determine the speed ratio between gears and the value of the gear train speed ratio (train value), in simple compound gear train.

2-To study the epicycle gear train mechanism and determine speed ratios. Thus, from the above review, gears can be classified according to their movement, number of teeth, and types of gears.


[15]

3.3 TYPES OF GEAR TRAIN

1) Simple gear train: - which consists of two or more gears with opposite direction for rotation between one and another as shown in Figures (3.2) (a, b,c)

BA

A B C

Figure (3.2) 2) Compound gear train: - this gear as shown in Figure (3.3) wheels are rigidity connected together to form a compound gear which rotates on independents shaft.

A

b)( (c) a)(

A B


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Figure (3.3)

3) Reverted gear train: - which the center distance must be the same direction as shown in Figure (3.4).

Figure (3.4)

4) Epicycle gear train: - shown in Figure (3.5) which consists of (1) sun wheel and (2) a plant wheel which rotate freely on a pin attached to the arm(3) rotates freely

about axis of sun wheel and (4) the annulus .


[17]

Figure (3.5)

3.4 THEORY

From the velocity ratio applied on the simple gear train show in figure therefore

)

A

Output Input


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= ….. (3.1)

And from the module ( )of the gears which must be the same to hove perfect mesh and constant.

( ) = = ….. (3.2)

=

=

.…. (3.3)

=

Where:

: No. of teeth : Angular velocity (rad/sec)

: Pitch circle diameter of gear (mm) : Module of gear

3.5 CALCULATIONS

1- Calculate output speed

2- number of gears tooth

3- others

3.6 DISCUSSIONS

1. Differences the effect of differences between the theoretical and

experimental values of results.

2. Why is the value of velocity of ( )equal to the velocity of( )

3. Discuss the difference between compound and reverted gear

trains at estimation of the output speed for them. 4. Other observed differences.


[19]

Experiment No.4

Balancing of Rotating Masses


4.1 INTRODUCTION

Balancing is the technique of correcting or eliminating undesirable inertia forces. Many moving parts of machines have either reciprocating motion such as engine piston or rotating motion such as (engine crankshaft, turbine rotor, generator, electric motor). If these parts are not in perfect balance or if the parts have variable motion are subjected to acceleration, inertia forces are setup that tends to produce vibrations in the frame of machine, hence foundation to which the frame is attached. Such vibrations especially if the occur at high speeds may produce excessive noise, causing undue wear and tear on the machinery. The purpose of balancing, therefore, is to neutralize or minimize these unpleasant and dangerous effects as far as may be practicable.


[20]

The modern designs of machines tend to increase speed because of the development occur in the metal improvement and the high technological knowledge as well as the desire to rise the power of these machines or field pressure that worked its or improve their economies. Therefore, whenever machines speed increase whatever was necessary balancing take care of it as much as possible, but if balancing was not enough, the design will be subjected to the following sides:

1) Imbalance causes reciprocating dynamic forces which may lead to the failure

of parts or structure.

2) Imbalance causes discomfort vibrations especially in the machines made for

the human comfort.

3) Imbalance forces may lead to deflections cause inaccuracy of the machine.

4.2 THE OBJECTIVES OF THE EXPERIMENT

1) To study the balancing of machine parts (lumped mass) and identify the

effects due to unbalance.

2) To study the balance of four masses in several different lateral planes

rotating around a single axis.

4.3 THEORY

4.3.1 Static balancing

The body is in equilibrium if its center gravity passes coincides with shaft rotating axis as shown in Figure (4.2a). If the mass is balance (i.e. doesn’t turn when left free) otherwise must be balanced by adding another mass in the opposite direction (i.e. 180 ) so the moment about attached point must be zero, also if the mass is in rotational motion the summation of forces (centrifugal forces) must be equal (i.e = 0)

M1 g r cos = Me re cos

M1 r = Me re or M1 r – Me re = 0

M1 r 2 = Me re 2


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M1 r 2 - Me re 2 = 0

The above theory can be verified using special technique as will be explained in procedure of experiment.

M1: mass to be balanced

Me: equivalent mass

re: equivalent radius

Figure (4.2a): Static balancing

4.3.2 Dynamic Balancing

Figure (4.2b) shows an axis of rotation with mass (M1) and (M2) located in different lateral planes C and D. We observe that the static forces was balanced and also dynamic forces (kinetic) F1 = M1 r1

2 and F2 = M2 r2 2 were equal and

balanced. But each of F1 and F2 generates torque equal (F1 * L) unbalance, which turn generates reaction forces RA and RB at the bearing A and B. The object of balancing anybody has rotational motion or reciprocating must be remove or minimize as much as possible of the forces that transfer to the bearing in order to reduce vibration. So when we balance the rotating system, we must balance not only the forces but also the moment. Therefore the following equations must be varied:

M1 M1

Shaft

M2

M1 g

r

re


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1) The condition of static and dynamic forces must be balance M×r = 0

2) The condition of dynamic couple must be balance M×r×L=0

Figure (4.2b) dynamic balancing

4.4 THE APPARATUS Figure (4. 3) shows a sketch of the apparatus used for the balancing of four different masses (M1-M4) attached in different transverse planes, which placed at distances( 4).

At one side of the steel shaft, there is a metal disk provided with a protractor to measure the angles. Also, an electric motor is connected to the shaft by means of rubber belt to drive the shaft.

There is also in the box a ruler to measure the distance between the masses locations.

D M1

M2 F2

F1

M1

B

C

A

F2

L

F1

D


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[24]

Figure (4. 3): Schematic diagram of balancing apparatus

4.5 PROCEDURE

a) Fix one of the masses on the balance shaft firmly so do not slip.

b) Turn the string around the numbered disk which is fixed on one shaft.

c) Add number of small steel balls to one of the containers until the mass. turn 90° and record it's number, which represent weight necessary to balance the attached weight.

d) Register the mass number ( ) by counting the number

of small steel balls which represents( ) .

e) Repeat steps (a-d) for the rest balancing masses to obtain

the values of , and .

0° , L2 = 0 cm .

f) Repeat the table no. (1) . Suppose that 0° , 0 , °

Table (4- 1): balancing of rotating masses

Deg

M*r*L g.

Distance mm

M*r gm.mm

Radius(R) mm

Mass(M) gm

plan

1 2 3 4

g) Draw polygons of forces (M*r) and moments (M*r*L) from which the

magnitudes , , , and then complete the Table (4- 1) .


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h) To examine that the system is balanced, fix the four balanced masses on the steel shaft using the determined positions and angles.

4.6 CALCULATIONS

1) Draw moments and forces polygon and conclude all the unknown

quantities .

2) Check for static and dynamic balance experimentally.

4.7 CONCLUSIONS AND DISCUSSION

1. From the above obtained results, write your own conclusions. 2. Write notes on the suggestions for the development of the apparatus used

3. Draw force and moment polygons for the balancing of only throttling masses. 4. State any possibility of accuracy errors.


[26]

Experiment No.5

Flywheel


5.1 OBJ ECTIVES OF EXPERIMENT

(1) To obtain the value of the mass moment of inertia of Flywheel theoretically and experimentally.

(2) To study the transformations of energy throughout the experiment.

5.2 INTRODUCTION

Most machinery has parts which revolve on their longitudinal axis; for example, wheels, shaft, electric motors, centrifugal pumps, ect. This rotary motion is subject to the same basic laws as linear motion , but all the terms have to be transformed to comply with the motion changes as follows:- Force Mass × Acceleration Couple = Moment of Inertia × Angular Acceleration In symbols


[27]

The couple is also referred to as the torque, being the turning force exerted. The application of this alternative form of the Newton‘s second law is widespread and most important in understanding the performance of rotating machinery. Where it is necessary to start rotating machinery quickly the moment of inertia must be as small as possible to permit fast acceleration with the maximum value of torque. On the other hand, when a reciprocating engine i.e. required to run at a uniform speed regardless of the fluctuation in driving force as each cylinder delivers power it is common practice to increase the overall moment of inertia by adding a flywheel to the engine shaft. A further use of a flywheel is to store rotational energy which is recoverable as it slows down there by making a large couple available for a short period.

Figure (5.2)

5.3 THEORY The work of the falling mass is given by the difference between the potential and kinetic energy at the point of separation from the flywheel. So,

Where is the set number of revolutions

Final velocity of mass

Kinetic energy= )


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Work done on flywheel = . ( )

The flywheel starts from rest and, left to revolve until the falling mass separates, will eventually complete , revolutions and stop. Look at this way, all the work is consumed in bearing friction, which will be assumed constant.

At the point of separation of the falling mass the flywheel will reach its maximum angular velocity and hence its maximum kinetic energy by ( ) .

Let the bearing factional couple be , then equating work consumed in friction:

. 2 ( . ) = . 2 …… (5.1)

The energy balance at the end of revolutions is:

. 2 ( . ) = . 2 + ( ) ..… (5.2)

Hence if , and are measured, can be derived from (5.1) and Substituted in (5.2) to evaluate.

The relation between & is = , When ( ) is time of falling mass to reach maximum .


[29]

5.4 PROCEDURE

Part 1

Figure (5.3) '' Diagram of Mechanism ''

Add 4 to load hanger and wind up the pulling cord to 8 turns. Hold the flywheel in one hand and the stop watch in the other. Release the engraved line and the pointer. The watch must be stopped on the count of eight turns, but the revolutions should be counted till the wheel stops. Repeat the test two or three times.

Part 2

Repeat the whole of part 1 using a different load and /or a different number of turns for the pulling cord. Finally take the dimensions of the flywheel and shaft.

5.5 RESULTS

Tabulate the experimental results and take the average values of ( ) and ( 1)for each part. Calculate ( ) and substitute in expression (1) of the theory to determine the bearing friction couple ( ) . The substitute in expression (2) to obtain the experimental values of ( ) .

Form the dimension of the flywheel and shaft, and using a density for steel of 7850 kg / , calculate the theoretical value of ( ) . Compare this with the

Pointer

engraved


[30]

experimental value. If the result of Experiment ( ) is available include this in the comparison. Also if the results of Experiment ( ) are available compare the friction couple ( ) with the intercept on the graph.

Table (5-1)

No. Weight (N)

Time (Sec)

(Rad/sec)

6.5 DISCUSSION

1. Discuss the time of measurement s (i.e. average of number of try).

2. Discuss the number of revolutions of the flywheel.

3. Compare the experimental and theoretical values.


[31]

Experiment No.6

The Governor


6.1 INTRODUCTION

The governor is a device for co-ordination between the prime mover and external resistance. The function of a governor is to keep the speed of a prime mover constant by adjusting the output of the engine to be equal to the external load on the engine in a given duration. Thus the governor regulates the supply of power to meet the demand. The governor also regulates the speed from cycle to cycle (over a number of cycles of a prime mover the governor mathematically controls change of speed ( N)) .Also the governor regulates the speed by regulating the quantity and quality of working agent, thus it is a device for automate control. A governor being an adjuster of supply with demands is an essential element of every prime mover.


[32]

6.2. OBJECTIVES OF EXPERIMENT

1. Determination of characteristic curves of speed of rotation against sleeve

position and comparison with theory.

2. Derivation of controlling force characteristic curves from the above

characteristic and comparison with theoretical predictions.

3. Investigation of the effect of varying sleeve mass on mass on the porter

governors.

6.3 TYPES OF GOVERNOR

The following chart shows the different types of governors.

Centrifugal governor

Pendulum type loaded type

Watt governor

Dead weight governor spring controller governor

Porter governor proell governor

Hartnell Hartung Wilson Hartnell Pickering

governor governor governor governor

Figure (6.2). Flow chart of type of governor


[33]

6.4 GOVERNOR’S TERMINOLOGY

The following terms are commonly used:-

1- Height of governor: it is the vertical distance from the centre of ball to a

point where the axes of the arms intersect on the spindle axis denoted by

(h).

2- Equilibrium speed: it is the speed at which the governor balls, arms etc., are

in complete equilibrium and the sleeve dose not tend to move upwards or

downwards.

3- Mean equilibrium speed: it is the speed at the mean position of the balls or

the sleeve.

4- Maximum and minimum equilibrium speeds: The speeds at the maximum

and minimum radius of rotations of the balls, without tending to move either

way are known as maximum and minimum equilibrium speeds respectively.

5- Sleeve lift: It is the vertical distance which the sleeve travels due to change in

equilibrium speed.

6.5 THEORY OF PORTER GOVERNOR

In this type a central mass been added to watt governor to increase the speed of revolution required to enable the balls to rise to any pre- determined level.

Using Method of instantaneous centre is to eliminate the effect of the forces (tensions) in the arms of governor.


[34]

Triangle of Forces for the Link

Mg21

Mg

W

F C

h

r

T2

T 2

1/2Mgtan

Forces Acting on the ball

Mg

r

Mg21

h

1/2Mgtan

CF

T1

o

Figure (6.4) Force analysis

Figure (6.3) porter governor


[35]

Where:- w = mg = weight of each ball. W = Mg = weight of central load (sleeve) r = radius of rotations

= angular speed of the balls = centrifugal force acting on the ball

h = height of governor , = Inclination of upper and lower arm to the vertical

Taking moment about I :

× = × + × ..… (6.1)

= × + × ….. (6.2)

= an + × .…. (6.3)

F = + × ( + ) ….. (6.4)

= + ( + ) ..… (6.5)

= + + ….. (6.6)

= , divide eq. (6) by ( )

= +2

+2

Let = , if = ,q=1 , =

= + + = + (1 + ) ….. (6.7)

=( )

…… (6.8) ÷

= 1 + (1 + ) × ….. (6.9)


[36]

= 1 +2

(1 + ) ×

Or =( )

…..(6.10)

If q=1

= = / ..… (6.11)

This is the relationship between rotating speed and height of governor.

If the effect of friction between sleeve and spindle is considered must be added in eq. (6.8) ± (friction force), this depend on direction of the movement upward or downward.

= + (1 + ) ± ..… (6.12)

6.6 EXPERIMENTAL PROCEDURE

The porter governor-basic characteristics

1. Remove the Perspex dome and screw the governor to the turntable. check

that the screws are screwed down fully and that the drive belt is correctly

located in the grooves replace dome.

2. Construct A table of shaft speed (rev/min) against sleeve between zero and

24 mm, in steps of 4mm.

Allow two columns for speed readings – one headed "Sleeve raising" the other "Sleeve falling".

3. Set the E64 MKII range selector to 300. Start the motor by turning the speed

control and slowly increase the speed until the sleeve just begins to lift .Note

the tachometer reading.

4. Slowly increase the motor speed until the sieve rises to the first mark on the

shaft. This is 4mm from the base. Note the tachometer reading (see note,

below).


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5. Repeat step 4 for each successive mark on the shaft. Alter the E64MKII

range if the reading goes off the scale.

6. When the sleeve is at its highest position, decrease the motor speed until the

sleeve just begins to fall. Note the tachometer reading (sleeve falling).

7. Slow down the motor until the sleeve reaches the next highest mark and note

the tachometer reading. If you should overshoot the mark, increase the speed

until the sleeve rises above the mark then approach the mark again from

above .

8. Repeat step 7 until the sleeve has reached the base.

9. Plot a graph of shaft speed against sleeve movement. Draw arrows on the

curves to show which correspond to the sleeve rising or falling.

6.7 RESULTS & CALCULATIONS

1. Construct a table of results as shown :

Sleeve lift (mm)

0

4

8

12

16

20

24

Ball radius (mm)

Governor speed (rad/sec)

Controlling force (N)

2. With the sleeve in its lowest position, measure the distance between the ball

centers. Halve this to obtain the ball radius.

3. Repeat paragraph 2 for each sleeve position.

4. From the experimental results previously obtained, read off the governor

speed corresponding to each sleeve height. Calculate the experimental

controlling force from Equation 2.5.Note that the units of speed must be

converted to radius per second before insertion into the equation.


[38]

6.8 THEORETICAL RESULTS of Speed and Controlling Force in PORTER GOVERNOR

The theoretical speed and controlling force curves are obtained by a tabulation technique. 1. Choose a range of values of r, say from 50 to 70 mm in steps of 5mm (or

10 mm if time is limited).

2. Calculate and from the geometry of the governor arms and links (see

figure 3) :-

= , = 3. Calculate h from h= .

4. Calculate values of sleeve lift =138 85 65 (see Figure3)

5. Calculate from Equation 4.

6. Calculate F from Equation 3.

7. Plot curves of the theoretical speed and controlling force on the same axes

as your experimental curves.

8. Compare the theoretical and experimental curves, and explain any

differences between them.

6.9 DISCUSSION

1. Compare results.

2. Discuss the effect of increasing speed on , ,


[39]

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