TOPIC 1 UNDAMPED BEAM OSCILLATIONS TOPIC LEARNING OUTCOMES PDF

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TOPIC 1 UNDAMPED BEAM OSCILLATIONS TOPIC LEARNING OUTCOMES At the end of this topic, the students will be able to: 1. Comprehend the concept of undamped beam oscillations (LO4,LO5,LO3) 2. Determine the elastic/deflection coefficient (stiffness) of the spring (LO3, LO4, L05) 3. Measure the natural fr...

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TOPIC 1 UNDAMPED BEAM OSCILLATIONS

TOPIC LEARNING OUTCOMES At the end of this topic, the students will be able to: 1.

Comprehend

the

concept

of

undamped

beam

oscillations

(LO4,LO5,LO3) 2.

Determine the elastic/deflection coefficient (stiffness) of the spring (LO3, LO4, L05)

3.

Measure the natural frequency of the beam using different spring types and positioning (LO3, LO4, L05)

CONTENTS

6.1

INTRODUCTION

Undamped oscillation is an oscillation in which the amplitude remains constant with respect to time. To strengthen the undamped (ζ = 0) situation, the system oscillates at its natural resonant frequency (ωo)

6.2

EXPERIMENTAL THEORY

To determine the deflection coefficient of spring: Force = Kx

(1)

where, K = elastic coefficient of spring and x = spring elongation K =

(m2 − m1)g x2 − x1

Natural frequency angle:

(2)

ϖn =

3Ka 2

mL2 (3)

f =

Natural Frequency:

1 • 2π

[3Ka

2

mL 2

] (4)

Time Interval:

2  t = 2π •  mL  3Ka 2 

(5)

Beam mass = 1.628kg Beam length = 730mm

spring

beam

Figure 1.1 Spri ng Stiff ness

6.3

F igure 1 .2 Na tura l Frequency o f Beam

EXPERI MENTAL EQU IPMENTS

Tab le 1 .1 Appara tus Quantity 3 1 1 1 5 1 1

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Apparatus Spring, type K1, K2, K3 Steel ruler 1m Stop Watch TM150 Universal Vibration System Apparatus 50gm Load Hook Weight set (50g, 150g, 200g) Vernier Caliper

2

6.4

EXPERIMENTAL PROCEDURES

6.4.1 DETERMINE THE SPRING DEFLECTION COEFFICIENT a.

Prepare test apparatus as in Figure 1.1 in the TM150 Universal Vibration Apparatus.

b.

Measure the length of spring K1 without any load.

c.

Attach a 200g load at the spring end and measure the length of spring again.

d.

Add another 200g load to the spring and measure the length of spring.

e.

Add another 200g load to the spring which makes a total of 600g. Measure the length of spring again.

f.

Add another 200g load to the spring which makes a total of 800g. Measure the length of spring again.

g.

Complete the Table 1.2.

h.

Repeat the steps a – e for the springs K2 and K3

6.4.2 DETERMINE THE NATURAL FREQUENCY OF BEAM a.

Prepare the test apparatus as in Figure 1.2 in the TM150 Universal Vibration Apparatus

b.

Attach the end of spring to the lever arm at a distance of 350mm from the lever end.

c.

Level the lever arm with the spring attached. Arrange the grid paper to be at the center of the marker.

d.

Switch on the power.

e.

Pull and release the lever end and at the same time switch on motor to operate the paper grid. Record 10 oscillations.

f.

Repeat the steps a – e by changing the distance of spring position to 650 mm from the lever end.

g.

Repeat the steps a – f by using different types of springs provided. Complete the Tables 1.3 and 1.4. .

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DATAFORTEST1

Table 1.2 Spring Deflection Determination Spring Type

Weight(g)

Load(N)

200 400 K1 600 800 200 400 K2 600 800 200 400 K3 600 800

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Spring Length (mm)

Elongation (mm)

DATAFORTEST2

Table 1.3 Effect of Spring Stiffness on the Natural Frequency of the Beam Sample

Spring Stiffness(N/mm)

Length of Lever ‘a’ (mm)

K1

350 mm

K1

650 mm

K2

350 mm

K2

650 mm

K3

350 mm

K3

650 mm

1 2 3 4 5 6

Natural Frequency (Hz)

Table 1.4 Comparison of Theoretical and Experimental Natural Frequencies of the Beam Sample

Time(s)

Natural Frequency(Hz) (Experimental)

1 2 3 4 5 6

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Time(s)

Natural Frequency Hz (Theoretical)

6.5

ACTIVITIES

6.5.1 ADDITIONAL THEORY (10%) a.

Please describe additional theory according to this topic

6.5.2 RESULTS (15%) a.

Fill in the experimental result in the Table 1.2, 1.3 and 1.4.

6.5.3 OBSERVATIONS (20%) a.

Please make an observations of the experiment that you have conducted

6.5.4 CALCULATIONS (10%) a.

Shows your calculations

6.5.5 DISCUSSIONS (15%) a.

Draw the graph of forces versus elongation and explain briefly the correlation of experimental and theoretical value of the plotted graph (5%)

b.

Explain the effect of spring stiffness on natural frequency of the beam from test 2 (5%)

c.

Explain the factors that affecting the differences of result between experimental value and theoretical value of natural frequency (5%)

6.5.6 QUESTIONS (10%) a.

In an automotive environment, what would be the effect of installing the same coil spring into another cars with a different specifications. Discuss (10%)

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6.5.7 CONCLUSION (15%) Deduce conclusions

from the experiment. Please comment on your

experimental work in terms of achievement, problems faced throughout the experiment and suggest recommendation for improvements.

1.5.8 REFERENCES (5%) a.

Please list down your references according to APA citation standard

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TOPIC 2 BALANCING OF ROTATING MASS

TOPIC LEARNING OUTCOMES At the end of this topic, the students will be able to: 1. Understand the concept of balancing for the single and multiple plane (LO4,LO5,LO3) 2. to study the different balancing of the following body at single plane and multiple-plane (LO3, LO4, L05) 3. to study the different balancing of the following body at static and dynamic state for the multiple plane (LO3, LO4, L05)

CONTENTS

2.1

INTRODUCTION

The high speed of engines and other machines is a common phenomenon now-a-days. It is, therefore, very essential that all the rotating and reciprocating parts should be completely balanced as far as possible. If these parts are not properly balanced, the dynamic forces are set up. These forces not only increase the loads on bearings and stresses in the various members, but also produce unpleasant and even dangerous vibrations. In this experiment we shall discuss the balancing of unbalanced forces caused by rotating masses, in order to minimize the vibration occurred.

2.2

EXPERIMENTAL THEORY

This experiment is to prove on the basic principle of balancing. Before implementing the experiment (2.4.1) and (2.4.2), sector plate B5 and C5

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need to be installed at the internal position of disc by using the short screw (5/8) as shown in Figur e 2. 1.

Figure 2.1 Disc of Balancing of Rotating Masses

2.3

EXPERIMENTAL EQUIPMENTS Table 2.1 Apparatus Quantity 1 1 set 1 set 1

2.4

Apparatus Dynamic balancing apparatus Set of weight Screw/Nut

Label

Refer procedure Refer procedure

Toolbox

EXPERIMENTAL PROCEDURES

2.4.1 BALANCING IN A SINGLE PLANE OF REVOLUTION a. Place

m1 = 30 at , r1 = 60mm where m1 – mass at the single plane r1 – distance m1 from centre of gravity and plane of rotation

Therefore, m1 x r1 = 30 x 60 = 1800 (not zero) OR m1r1 = m1r1

This situation will contribute to the imbalance observe oscillations.

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b. Place

m1

= 30 at , r1

= 60mm and

m2

= 30 at , r2

= 60mm where

m1 – mass at the single plane r1 – distance m1 from centre of gravity and plane of rotation

Therefore, m1r1 + m2r2

= (30 x 60 ) – (30 x 60) = 0 ( zero)

m2r2

OR m1r1 + m2r2 = m1r1

This situation will contribute to the balance observe no oscillations.

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c. Place m1 = 30 at , r1 m2 = 60 at , r2

Therefore, m1r1 + m2r2

= 60mm and = 30mm where

= (30 x 60 ) – (60 x 30) = 0 ( zero)

m2r2

OR m1r1 + m2r2 = m1r1

This situation will contribute to the balance observe no oscillations.

d. Place m1 = 30 at , r1

= 60mm and

m2 = 30 at , r2

= 30mm

m3 = 15 at , r3

= 60mm where

Therefore, m1r1 + m2r2 + m3r3

= (30 x 60 ) – (30 x30) – (15 x 60) =0

m3r3

m2r2

OR m1r1 + m2r2 + m3r3 = m1r1

This situation will contribute to the balance observe no oscillations.

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e. Place m1 = 30 at , r1

= 60mm and

m2 = 30 at , r2

= 60mm

m3 = 30 at , r3

= 60mm where

m1 located at the slot centre and therefore , angle θ1 = 0°, θ2 =12 0°, θ3 = 240°

Therefore,

m1r1 + m2r2 + m3r3 =

This situation will contribute to the balance observe no oscillations.

If m1 located at the end slot, the total of vector as follows;

m1r1 + m2r2 + m3r3 =

This situation will contribute to the imbalance observe no oscillations.

f. Place m1 = 30 at , r1

= 60mm and

m2 = 40 at , r2

= 45mm

m3 = 60 at , r3

= 30mm where

angle θ1 = 0°, θ2 =12 0° and θ3 = 240° Therefore,

m1r1 + m2r2 + m3r3 =

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and

This situation will contribute to the balance observe no oscillations.

2.4.2 BALANCING IN SEPARATE PLANE OF REVOLUTION

a.) Locate the mass, m1 = 30 at r1 = 60mm on plane B m2 = 30 at r2 = 60mm on plane C m3 = 60 at r3 = 60mm on plane D where position m3 is in opposite of the radius m1 and m2

Get the plane A as the reference plane. Therefore, distance L1 =X, L2 = 2X and L3 = 3X The total of, (m1r1 + m2r2 + m3r3) = ( 30 x 60 ) + ( 30 x 60 ) - ( 60 x 60 ) =0

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Vector equation : m1r1 + m2r2 + m3r3 =

This situation will contribute to the balancing plane during static state

But total, m1r1L1 + m2r2L2 + m3r3L3 = ( 30 x 60 x X ) + ( 30 x 60 x 2X ) - ( 60 x 60 x 3X ) = - 5400 X (not zero)

Vector equation : m1r1L1 + m2r2L2 + m3r3L3 =

This situation will contribute to the imbalance plane during dynamic state

b.) Locate the mass, m1 = 30 at r1 = 60mm on plane B m2 = 30 at r2 = 60mm on plane C m3 = 30 at r3 = 60mm on plane D m4 = 30 at r4 = 60mm on plane A where position m3 and m4 is in opposite of the radius m1 and m2

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Get the plane A as the reference plane. Therefore, distance L1 =X, L2 = 2X and L3 = 3X and L4 = 0 The total of, (m1r1 + m2r2 + m3r3 + m4r4) = ( 30 x 60 ) + ( 30 x 60 ) - ( 30 x 60 ) – (30 x 60) =0

Vector equation : m1r1 + m2r2 + m3r3 + m4r4 =

This situation will contribute to the balancing plane during static state But total, m1r1L1 + m2r2L2 + m3r3L3 + m4r4L4 = ( 30 x 60 x X ) + ( 30 x 60 x 2X ) - ( 30 x 60 x 3X ) + 0 = 0 (zero)

Vector equation : m1r1L1 + m2r2L2 + m3r3L3 + m4r4L4 =

This situation will contribute to the balancing plane during dynamic state

c.) Locate the mass, m1 = 60 at r1 = 60mm on plane B m2 = 60 at r2 = 60mm on plane C m3 = 20 at r3 = 60mm on plane D

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m4 = 20 at r4 = 60mm on plane A where position m2 and m4 is in opposite of the radius m1 and m3

Get the plane A as the reference plane. Therefore, distance L1 =X, L2 = 2X and L3 = 3X and L4 = 0 The total of, (m1r1 + m2r2 + m3r3 + m4r4) = ( 60 x 60 ) - ( 60 x 60 ) +( 20 x 60 ) – (20 x 60) =0

Vector equation : m1r1 + m2r2 + m3r3 + m4r4 =

This situation will contribute to the balancing plane during static state

But, total m1r1L1 + m2r2L2 + m3r3L3 + m4r4L4 = ( 60 x 60 x X ) - ( 60 x 60 x 2X ) + ( 20 x 60 x 3X ) - 0 = 0 (zero)

Vector equation : m1r1L1 + m2r2L2 + m3r3L3 + m4r4L4 =

This situation will contribute to the balancing plane during dynamic state

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d.) Locate the mass, m1 = 60 at r1 = 60mm on plane B m2 = 20 at r2 = 60mm on plane D m3 = 40 at r3 = 60mm on plane A where position m2 and m3 is in opposite of the radius m1

Get the plane A as the reference plane. Therefore, distance L1 =X, L2 = 3X and L3 = 0 The total of, (m1r1 + m2r2 + m3r3) = ( 60 x 60 ) - ( 20 x 60 ) - ( 40 x 60 ) =0

Vector equation : m1r1 + m2r2 + m3r3 + =

This situation will contribute to the balancing plane during static state

But total, m1r1L1 + m2r2L2 + m3r3L3 = ( 60 x 60 x X ) - ( 20 x 60 x 3X ) - 0 = 0 (zero)

Vector equation : m1r1L1 + m2r2L2 + m3r3L3 + m4r4L4 =

This situation will contribute to the balancing plane during dynamic state BDA 27401-Edition I/2013

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DATAFORTEST BALANCING IN A SINGLE PLANE OF REVOLUTION Table 2.2 Experiment 1 Results EXPERIMENTS

THEORETICAL

EXPERIMENTAL

CONDITION

CONDITION

a

Imbalance

b

Balance

c

Balance

d

Balance

e

Balance

f

Balance

BALANCING IN SEPARATE PLANE OF REVOLUTION Table 2.3 Experiment 2 Results EXPERIMENTS

2.5

THEORETICAL

EXPERIMENTAL

CONDITION

CONDITION

Static

Dynamic

a

Balance

Imbalance

b

Balance

Balance

c

Balance

Balance

d

Balance

Balance

Static

ACTIVITIES

2.5.1 ADDITIONAL THEORY (10%) a.

Please describe additional theory according to this topic

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Dynamic

2.5.2 RESULTS (15%) a.

Fill in the experimental result in the Table 2.1 and 2.2.

2.5.3 OBSERVATIONS (20%) a.

Please make an observations throughout the experiment especially during static and dynamic state of rotating masses.

2.5.4 CALCULATIONS (10%) a.

Shows your calculations

2.5.5 DISCUSSIONS (10%) a.

Explain the results obtained from the balancing of rotating masses for single plane (5%)

b.

Explain the results obtained from the balancing of rotating

masses

for multiple plane (5%)

2.5.6 QUESTIONS (15%) a.

Give an example on the application of balancing of rotating masses in real time world and describe why balancing of rotating masses is important (15%)

2.5.7 CONCLUSION (15%) Deduce conclusions

from the experiment. Please comment on your

experimental work in terms of achievement, problems faced throughout the experiment and suggest recommendation for improvements.

2.5.8 REFERENCES (5%) a.

Please list down your references according to APA citation standard

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TOPIC 3 COMPUTERIZED GEAR SYSTEM TOPIC LEARNING OUTCOMES At the end of this topic, the students will be able to: 1. Describe the different type of gear system and some of their application (LO4,LO5,LO3) 2. Calculate gear ratios, angular velocity, input and output torque (LO3, LO4, L05) 3. Calculate the efficiency of the gears (LO3, LO4, L05) 4. Understand the concept of gear system, types of gears and its related function and application (LO3, LO4, L05)

CONTENTS 3.1

INTRODUCTION

Gears are a means of changing the rate of rotation of a machinery shaft. They can also change the direction of the axis of rotation and can change rotary motion to linear motion. A gear is a toothed wheel designed to transmit torque to another gear or toothed component. Different size gears are often used in pairs, allowing the torque of the driving gear to produce a large torque in the driven gear at lower speed, or a smaller torque at higher speed. The larger gear is known as wheel and the smaller gear as a pinion

3.2

EXPERIMENTAL THEORY

Consider a simple schematic of a gear box with an input and output shaft as shown in Figure 3.1.

Figure 3.1: Simple Schematic of Gear Box BDA 27401-Edition I/2013

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Gear ratio, G.R = Input Speed / Output Speed ,

= N1 / N2

Gear ratio , G.R = (product of driven teeth )/ (product of driver teeth) Gear ratio, G.R = Input Speed / Output Speed,

= ω1 /ω2

The power transmitted by a torque, T (Nm) applied to the shaft rotating at N (rev/min) is given by: Power,

P = Tω P = [ 2π N T] / 60

In the ideal gearbox, the input and output power are the same so, [ 2π N1 T1] / 60 = [ 2π N2 T2] / 60 In a real gear box, power is lost through friction and the power output is smaller than the power input. The efficiency is defined as; η = Power Output / Power Input η = [ 2πN2T2 x60 ] / [ 2πN1T1x60] η = T2ω2 / T1ω1 Note;-

N - speed in rev/ min

ω - angular velocity ( rad/s )

Table 3.1 Technical Specification of Equipment

0

3 .3

EXPER IMENTAL EQU IPMENTS

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1

2

3

Figure 3.2 Connecting diagram

Figure 3.3 Simple Schematic of Gear Box 3.4

EXPERIMENTAL PROCEDURES

3.4.1 EXPERIMENTS FOR 4 STAGE GEAR WITH SAME SIZE GEAR GEAR SET 1 a.

Make sure gear set 1 is in place. If not, install the gear set 1 into the system according to the following steps:i.

Remove the transparent protective cover of the system.

ii.

Remove the locking bolts of the gear set.

iii.

Remove the gear set by lifting it using the handles.

iv.

Put the removed gear set by lifting on storage table.

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v.

Take the new gear set and put it on the system. Make sure the gear set is completely in place.

vi.

Tighten the locking bolt...