Mechanics of Machines & Vibrations
Dr Farid Khan
Dr. Farid Khan
Assistant Professor in UET Peshawar since 1997
B.Sc Mechanical Engineering 1997
M.Sc Mechanical Engineering Design 2005
PhD MicroElectroMechanical Systems (MEMS) 2011
sfaridkhan@gmail.co
Mechanics of Machines & Vibrations
Lecture: 17
Dr Farid Khan
MDOF systems
2
MDOF systems
3
MDOF systems
4
MDOF systems
5
MDOF systems
6
MDOF systems
7
MDOF systems
8
MDOF systems
9
MDOF systems
10
MDOF systems
11
MDOF systems
12
MDOF systems
13
MDOF syste
Mechanics of Machines & Vibrations
Lecture: 18
Dr Farid Khan
MDOF systems
2
MDOF systems
3
MDOF systems
4
MDOF systems
5
MDOF systems
6
MDOF systems
7
MDOF systems
8
MDOF systems
9
MDOF systems
10
MDOF systems
11
MDOF systems
12
MDOF systems
13
MDOF syste
Mechanics of Machines & Vibrations
Lecture: 19
Dr Farid Khan
MDOF systems
2
MDOF systems
3
MDOF systems
4
MDOF systems
5
MDOF systems
6
MDOF systems
7
MDOF systems
8
Example: Compute the force transmitted to a machine
through base motion at resonance
9
Ex
Mechanics of Machines & Vibrations
Lecture: 21
Dr Farid Khan
Gear type
Worm gears:
A worm gear is a gear set in which a worm resembles a screw, while
the other is like a normal spur/helical wheel
Transmit power between out of plan perpendicular shafts
Can
Mechanics of Machines & Vibrations
Lecture: 20
Dr Farid Khan
Gear
?
2
Gear
A circular disc/wheel with a specially designed teeth
Used to transmit power (Power transmission element)
Gears are toothed, cylindrical wheels used for transmitting
motion and
Mechanics of Machines & Vibrations
Lecture: 22
Dr Farid Khan
Gear train
2
Gear train
3
Internal gear train
Speed of driver gear t eeth on driven gear
GR
Speed of driven gear t eeth on driver gear
4
Epicyclical Gear train
Arm
5
Epicyclical Gear train
last
Mechanics of Machines & Vibrations
Lecture: 23
Dr Farid Khan
Cam
?
2
Cam
A Cam is a machine component that either rotates or moves back
and forth (reciprocates) to create a prescribed motion in a
contacting element known as a follower
3
Cam-Follower
The
Mechanics of Machines & Vibrations
Lecture: 14
Dr Farid Khan
SDOF forced vibrations
2
SDOF forced vibrations
Base excitation
3
Base excitation
4
Base excitation
5
Base excitation
6
Base excitation
7
Base excitation
8
Base excitation
9
Base excitation
10
B
Mechanics of Machines & Vibrations
Lecture: 12
Dr Farid Khan
SDOF forced vibrations
Force of excitation is always acting on the system during vibrations
The system will vibrate at the frequency of excitation
The response of the system depends on the na
Mechanics of Machines & Vibrations
Dr Farid Khan
Review slide
2
Review slide
Classification of vibration
3
Review slide
4
Classification of vibration
5
Classification of vibration
6
Classification of vibration
7
Degree of freedom of a system
8
Single DOF
Mechanics of Machines & Vibrations
Dr Farid Khan
Vibration analysis procedure
2
Free/Natural vibrations
Natural frequency
Or
Undamped natural frequency
n
k
m
3
Free/Natural vibrations
How ?
n
k
m
4
Free/Natural vibrations
Equation of motion
m kx 0
x
Res
Mechanics of Machines & Vibrations
Lecture: 6
Dr Farid Khan
Harmonic motion
Newtons law
m kx 0
x
Other forms of solutions
k
m
x
2
Harmonic motion
Newtons law
m kx 0
x
3
Some useful quantities
4
Peak values
5
Rayleighs method
Used to find the natural freq
Mechanics of Machines & Vibrations
Dr Farid Khan
Equation of motion
Newtons law
m
x
F
k
m
m kx
x
m kx 0
x
x
n
k
m
x(0) x0
x(0) v0
2
Equation of motion
Newtons law
m
x
k
F
m
m kx
x
x
m kx 0
x
x(0) x0
x(0) v0
n
k
m
Initial conditions
3
Equation of motio
Mechanics of Machines & Vibrations
Lecture: 7
Dr Farid Khan
Damped free vibration
Damped natural vibration
Considerable energy losses due to:
- Dry friction = Coulomb damping
- Resistance to air/fluid = Fluid damping
- Material interlayer friction = Mat
Mechanics of Machines & Vibrations
Lecture: 9
Dr Farid Khan
Problem
2
Problem
3
Problem
4
Problem
T I
5
Problem
6
Problem
7
Problem
8
Problem
9
Assignment
10
Mini projects
1. Demonstration model of Spring-mass-damper vibration
system (Portable)
2. Piezoel
Mechanics of Machines & Vibrations
Lecture: 10
Dr Farid Khan
Problem 1
Solution:
2
Problem 1
. 1
. 2
. 3
rad/s
<1
3
Problem 1
4
Problem 2
5
Problem 2
Solution:
I
T
( above the pivot)
I bz l kzl
mbarl 2
I
3
( above the pivot)
6
Problem 2
Solution:
mbarl
Mechanics of Machines & Vibrations
Lecture: 11
Dr Farid Khan
Damping ratios, examples
2
Logarithmic decrement
A method to experimentally measure damping ratio in underdamped systems
X
3
Logarithmic decrement
4
Logarithmic decrement
5
Logarithmic decremen
Mechanics of Machines & Vibrations
Lecture: 24
Dr Farid Khan
Water wheel rotor balancing
?
2
Pump impeller balancing
3
Gas turbine rotor balancing
4
Train wheel balancing
5
Compressor rotor balancing
6
Water wheel balancing
7
Car tyre balancing
8
Car tyre