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MONASH UNIVERSITY
FACULTY OF ENGINEERING
Department of Mechanical & Aerospace Engineering
Subject Name:
Dynamics I
Subject Code:
MEC2401
Subject Coordinator:
Associate Professor Ralph Abrahams
Room 204 - BUILDING 72
Phones: Ex: 51982
Email: [email protected]
1
Syllabus &
Introduction
2
Profile
Associate Professor Ralph Abrahams
•BE(Hons),
PhD(UNSW), Pen Licence
•More
than 340 international journals and conference
publications in Dynamics, Fracture Mechanics and Welding
Technology.
•Main
contribution is in the areas of Aircraft structure,
design of truck lifter, cranes and pressure vessels.
•Also
involve in calculating remaining life of Aircraft
structure and component.
•Development
of a new rail maintenance technology by
using laser cladding
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Manual to Run the Lecture Slides
It is recommended that you run the Powerpoints in slideshow mode. This enables
the embedded links in the lecture.
Things to look out for:
1) Any underlined words contain a link. Click on them in slideshow mode to be
directed to more information about the topic and more examples.
2) The tables on slides 5 – 16 provide information on the topics which will be
discussed each week and the due assessments.
3) The attendance to the weekly 2 hours practical classes/Zoom sessions are
important and the tasks are required to be submitted every week for receiving
feedback. The topics covered are outlined in the slides 5-16 tables.
4) There are five laboratory sessions in this unit. The labs will be running from
Week 7. A written technical lab report is due in week 12.
5) The assessment tasks are outlined in slide 17.
6) The prescribed text book(s) are mentioned in slides 19 and 20.
7) Professor Abrahams’ book will be uploaded on Moodle.
8) The videos are all available in the uploaded zipfiles, and can be viewed by
clicking the icons in the slideshow mode.
4
Lecture
/Tutorial
Week 1
Lecture Description
Introduction to Dynamics.
Revision on Kinematics of
Particles. Rectilinear
Motion. Displacement,
Velocity and Acceleration.
Plane Curvilinear motion,
Rectagular Coordinates,
Normal and Tangential
Coordinates, Polar
Coordinates
Lectures
Tutorial
1
Revision Problems
5
Lecture
/Tutorial
Lectures
Week 2
Tutorial
2
Lecture Description
Dependent Motion of Particles.
Constrained Motion of Connected
Particles
Problems: Constant and Variable
Acceleration.
Curvilinear Motion: Normal and
Tangential
Coordinates
&
Dependent Motion of Two Particles
6
Lecture
/Tutorial
Week 3
Lectures
Tutorial
3
Lecture Description
Kinematics of Planar Mechanism:
Relative Motion. Translation,
Rotation and General Plane
Motion. Absolute Motion. Relative
Velocity.
Problems: Relative Velocity and
Acceleration
7
Revision Class Work will be on Moodle
by Friday of week 3.
Lecture
/Tutorial
Lectures
Week 4
Tutorial
4
Lecture Description
Velocity of a Point on a Link using
Relative Velocity Method (Vector
Analysis and Velocity Diagrams)
Problems: Calculating Velocities
Using Vector Analysis
8
Lecture
/Tutorial
Week 5
Lectures
Tutorial
5
Lecture Description
Acceleration of a Point on a Link
Using Vector Analysis
Problems: Relative Acceleration,
Acceleration Diagram.
9
Lecture
/Tutorial
Week 6
LECTURE
Tutorial
6
Lecture Description
Forces in Mechanisms using
dismemberment
and
D’Alembert’s Principle (Inertia
Forces).
Calculating Forces in Mechanisms
Using Dismemberment (Subgroup and
Links)
Calculating Forces in Mechanisms Using
Dismemberment (Subgroup and Links)
Revision Class Work 1 is due on Friday of week 6.
Revision Class Work 2 will be on10Moodle by Friday of week 6.
Lecture
/Tutorial
Lecture Description
Lectures
Linear and angular
Impulse of free particles.
Week 7
Tutorial
7
Problems: Calculating Forces in
Mechanisms Using
Dismemberment (Subgroup and
Links)
11
Lecture
/Tutorial
Lecture Description
Angular momentum of rigid bodies.
Moment and product of inertia.
Lectures
Week 8
Test – Time will be announced
 Covering Topics up to week 6
 10% of total marks
Tutorial
8
Problems: Impulse, angular Momentum
of free particles.
12
Lecture
/Tutorial
Week 9
Lectures
Tutorial
9
Lecture Description
Balancing of Several Masses
Rotating in the Same Plane and
Different Planes.
Problems:
Calculating the Balancing Masses
13
Week 10
Lecture
/Tutorial
Lecture Description
Lectures
Balancing of Reciprocating Masses
Tutorial
10
Problem:
Calculating the Balancing Masses
for the Reciprocating Mechanism
14
Lecture
/Tutorial
Week 11
Lectures
Tutorial
11
Lecture Description
Free Vibration, Natural Frequency,
Equation of Motion Using
Newton’s Law and Lagrange
Equation
Problems: Vibration
Second Revision Class work is15due on Friday of week 11.
Lecture
/Tutorial
Week 12
Lectures
Tutorial
12
Lecture Description
Equation
of
motion
Lagragian Mechanics +
Revision
using
Solving Previous Exam Papers
16
Assessments:
Examinations
 Final Assessment: 60%
 Mid-semester Test: 10%
 Class Works and Online Quizzes: 20%
 Laboratories and Technical Report: 10%
(The lab report should be submitted in the provided format)
17
Laboratories include three Experiments:
3 Lab experiments run from Week 7 to Week 9.
 Determining the amount and the position of the
unbalanced mass in a dynamic system.
 Balancing of rotating masses in single plane.
 Balancing of rotating masses in different planes.
* Two lab sessions in weeks 10 & 11 focus on verification of the
theoretical calculations prior to submitting the report.
18
Dynamics Book
Dynamics
by Ralph Abrahams
Will be available On Moodle
Please Note:
This book (Dynamics) is covering the whole 12 weeks of Dynamics I
(MEC2401).
19
Prescribed Text:
Author:
Associate Professor Ralph Abrahams
Title:
Dynamics
Publisher:
The book chapters will be uploaded on Moodle, throughout the
semester.
MERIAM, J.L., KRAIGE, L.G.,“Engineering Mechanics”, Vol. 2, Dynamics, ninth
Edition, Wiley, 2019.
Hibbeler, R.C., “Engineering Mechanics”. Dynamics, 11th Edition, Prentice-Hall,
2007
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21
You can view
the video by
clicking on this
image!
Dynamic systems include rotating or
moving mass or masses.
22
Internal Combustion Engine (ICE)
23
Animation for
kinematics of this
mechanism will be
available by pressing the
play button.
24
Animation for
kinematics of this
reciprocating mechanism
will be available by
pressing the play button.
25
Toggle Mechanism
Animation for
kinematics of this toggle
mechanism will be
available by pressing the
play button.
This mechanism is used to
drive three pistons with two
cranks to provide more power .
It is used for applications such
as breaking rocks that requires
high impact.
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When we conduct a dynamics analysis for Industry the following points
have to be considered:
If the mechanical design involves rotating or moving
parts, a dynamic analysis should be carried out to
ensure that the system is dynamically balanced and
there is no rotating/reciprocating unbalanced materials.
By having the system dynamically balanced we will be
able to reduce the noise & vibrations and increase the
life of components, aeroplanes, etc …...
Noise and vibrations can rock the dynamic systems and
cause failures.
By dynamic balancing, we will be able to increase the
productivity and reduce losses caused by vibrations and
noise.
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Caterpillar D7G Gear Box Failure
Investigation performed by me on a gear that
failed as a result of being overloaded.
Future lectures will contain more information on
this analysis, which may be similar to the dynamic
analysis you will perform in the future as
Mechanical and/or Aerospace Engineers.
SEM of Failure Surfaces
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Chevrolet Corvette Cars
Driving shaft
Optimisation of a driving shaft was designed by
me with the aim to reduce the weight of this
component and increase the speed.
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DSA Structural Tube Cross Section
Viewed from the rear looking forward in vehicle
63.5mm arc shown
in red must be
maintained for
shifter linkage
clearance.
Black outline
represent maximum
section envelope for
the extrusion.
Z
127 mm
Y
X
Prop Shaft Center Line
Blue outline
represent minimum
section envelope for
the extrusion.
127 mm
GM Confidential
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Optimised Cross Section of the Driving Shaft
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Dynamic analysis involves kinematics and
kinetics studies of the system.
Dynamic analysis
Kinematics
Geometrical aspects
Of motion
kinetics
2D&3D analysis of
( Displacement,
velocity, acceleration)
2D&3D Analysis of Forces,
Torques, Couples, Power, Balancing of
Rotating Materials, Noise and Vibrations
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Kinematics
Equations of Motion
Constant acceleration
V  V0  at
1
2
S  V0 t  at
2
2
2
V  V0  2as
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Equation of Motion
Variable acceleration
VdV  adS
dS
V 
dt
dV
a 
dt
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CURVILINEAR MOTION
Tangential
acceleration
Total
Acceleration
vt  wr
A
a

Radial
acceleration
a  at  an
ρ = Radius of curvature
dVt
at 
dt
2
Vt
an 

a
a a
2
2
t
n
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Angular Velocity and Acceleration
Displacements
s  qr
q  Angular displacement
r = radius of the circle or
curvature of path
Speeds
v  wr
w  Angular Velocity
Accelerations
aar
a  angular acceleration
• Every point on the rotating object has the same angular
motion
• Every point on the rotating object does not have the
same linear motion
e.g. pulley
N=RPM ( Revolutions per minute)
w = N x 2π/60 = rad/sec
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Normal and Tangential Components
an 
v2

v  wr
dv
dwr
at 

 ar
dt
dt
dw
 a  Angular Accelerati on
dt
•Tangential component of acceleration
reflects change of speed and normal
component reflects change of direction.
• Tangential component may be positive
or negative. Normal component always
points toward centre of path curvature.
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Dependent motion
The motion of one particle depends entirely on
the motion of the other
39
Cable
1
B=
4Kg
Cable
2
A=
6KG
40
Relative Velocity of Two particles
Moving in Straight Lines
v A  vB  v AB
41
v A  vB  v AB
A
B
o
VA
VA
VB
a
VAB
b
VB
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Relative Velocity of Rigid Bodies
The general plane motion of a rigid body can be described as a combination
of translation and rotation. To view these “component” motions separately
we will use a relative-motion analysis involving two sets of coordinate axes.
The position vector rA specifies the
location of the “base point” A, and the
relative-position vector rB/A locates
point B with respect to point A. By
vector addition, the position of B is then
rB =rA + rB/A
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drB =drA + drB/A
drB drA drB / A


dt
dt
dt
VB =VA + VB/A
differentiate with respect to time
aB = aA+ aB/A
44
Velocity in mechanism
This year we will study the velocity in mechanism by
applying the relative velocity method using the
relative velocity equation:
vA = vB + vA/B
1-Vector Analysis
2- Velocity Diagram
45
Studying the velocity,
acceleration,
displacement of the
planar mechanism we
can design the cutting
stroke and the returning
stroke.
By inspecting, the cutting
stroke takes more time
than the return stroke.
46
Shaper Mechanism
Animation for
kinematics of this Shaper
mechanism will be
available by pressing the
play button.
47
Animation for
kinematics of this Toggle
mechanism will be
available by pressing the
play button.
Toggle Mechanism
48
Animation for
kinematics of this Toggle
mechanism will be
available by pressing the
play button.
Toggle Mechanism
49
Forces In Mechanisms
Forces, torques, and
NA
powers transmitted from
link to link need to be
calculated to design the
dimensions and the
materials of the links and
joints. Also we need to
check that the system is
dynamically balanced to
avoid forced vibration and
noise.
A
3
300
2
W3
G2
W2
F
Fi2
T2
NB
4
Fi4
B
W4
50
Linear motion
D’Alambert’s Principle
SF = ma -- For Dynamic equilibrium
SF =0 ---- For Static equilibrium
SFx=max
SFy=may
Rotational motion
T  T  
i
Ia
Τ = Torque
I = Moment of Inertia
α = Angular acceleration
51
Dynamic equilibrium
The equation ΣF=ma can be
written as
ΣF-ma=0
This is the most important equation in
Dynamics analysis (D’ Alambert’s Equation)
Free Body Diagram (F.B.D.)
Free Body Diagrams are always required
for the Kinetics analysis
The excavator’s arm ABC is considered as a single rigid body. Its mass is
1200 kg and the moment of inertia about its centre of mass is IG=3600 kg-m2.
if point A is stationary, the angular velocity of the arm is zero, and the angular
acceleration is 1.0 rad/s2 counter clockwise, what force does the vertical
hydraulic cylinder exert on the arm at B?
The distance from A to the centre of mass is =
(3.4)  (3)  4.53 m  rG / A
2
2
at  a  r   1 4.53  4.53m / s 2
 
an  w 2 r  0 since ω  0
ω=0
α
Ti
at
G
an
54
ω=0
Taking moment about A
MA  0
Static Case
α
Ti
at
G
an
1.7FB  3.4mg  TA
TA  I Aa
Dynamic Case
Fit  mat  ma  r   1200(1 4.53)  5436 N
 
Fi n  man  m  w 2 r  0 since ω  0
1.7 FB  3.4 1200  9.81  3600  a  mr 2a
Ti
Fin
 3600 1  1200  4.53 1
2
solving
FB  40146 N  40.146 kN
Fit
mg
FB
55
Balancing of
Rotating Masses
56
57
Rolling Contact Fatigue & Wear as a result of Dynamic
Unbalanced Load
58
In Balancing of Rotating Masses
We will be studying the following:
Balancing of a single rotating mass by a
single mass rotating in the same plane.
 Balancing of different masses rotating in a
single plane.
 Balancing of different masses rotating in
different planes.
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Balancing of a single rotating mass by a
single mass rotating in the same plane.
m1
Disturbing
mass
r1
r1
Axis of
Rotation
r2
r2
m2
Balancing mass
Centrifugal force due to mass
FC  m .w 2 .r
60
Balancing of Several Masses Rotating in the Same Plane
c
FC3
FC2
FC2
m2
d
FC4
FC1
r2
b
θ2
FC1
e
r1
θ1
θ3
a
r3
m4
FC4
m3
FC3
61
Balancing of different masses rotating in
Different planes.
62
Crankshaft balancer
Crankshaft Balancing
Video is available by
pressing the play button.
63
Balancing of Reciprocating Masses
to eliminate the shaking
force and a shaking couple,
Hammer Blow
Reciprocating Mechanism
64
65
66
Natural Frequency of Free and Longitudinal
Vibrations Using Newton Law and Lagrange
Mechanics
67
Final EXAMINATION (60%)
 The
exam will cover major classworks,
weekly classwork problems, and lecture
examples.
 The uploaded Dynamics Text Book should
be enough to revise for your exam.
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