SAIF ALDIN ALI MADIN سيف الدين علي ماضي S96aif@gmail.com Torsional oscillation of a single rotor with viscous damping • Effect of including a damper in a system undergo ng torsional oscillation • The amount of damping in the system depends on the extent to which the conical portion of a rotor is exposed to the viscous effects of given oil

1. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
1 | P a g e
[Vibration Laboratory]
University of Baghdad
Name: - Saif Al-din Ali -B-

2. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
2 | P a g e
TABLE OF CONTENTS
ABSTRACT.........................................................................I
OBJECTIVE........................................................................II
INTRODUCTION..............................................................V
THEORY..........................................................................VI
APPARATUS...................................................................VII
Calculations and results................................................VIII
DISCUSSION ...............................................................VIIII

3. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
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Name of Experiment: Torsional Oscillation of a Single
Rotor with Viscous Damping
1. ABSTRACT
 Effect of including a damper in a system undergo ng
torsional oscillation
 The amount of damping in the system depends on the
extent to which the conical portion of a rotor is exposed
to the viscous effects of given oil
2. OBJECTIVE
1. Determining the damping period of oscillation.
2. Determining the logarithmic decrement.
3. Determining the damping coefficient of oil.
4. Determining how damping coefficient depends on the
depth immersion of
the rotor in oil.
3. INTRODUCTION
In This experiment, the effect of including a damper in a system
undergoing torsional oscillations is investigated. The amount of
damping in the system depends on the extent to which the
conical portion of a rotor is exposed to the viscous effects of a
given oil

4. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
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4. THEORY
∑𝑚 = 𝐽𝜃̈
Where:-
𝐽 ∶ 𝑚𝑜𝑚𝑒𝑛𝑡 𝑜𝑓 𝑖𝑛𝑒𝑟𝑡𝑖𝑎
𝑘𝑡 ∶ 𝑡𝑜𝑟𝑠𝑖𝑜𝑛𝑎𝑙 𝑠𝑡𝑖𝑓𝑓𝑛𝑒𝑠𝑠
𝑐 ∶ 𝑑𝑎𝑚𝑝𝑖𝑛𝑔 𝑐𝑜𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
Ө ∶ 𝑑𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
This may be written as:
C Ө`
c
`
ӨKt
Ө
L

5. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
5 | P a g e
5. APPARATUS
Figure shows the apparatus, and
consists of a vertical shaft gripped
at is upper end by a chuck
attached to a bracket (K1) and by
a similar chuck attached to a
heavy rotor (K3) at its lower end
The rotor (K3) suspends over a
transparent cylindrical container,
K4, containing damping oil. The oil
container can be raised or lowered
by means of knobs on its underside,
allowing the contact area between
the oil in the container and the
conical portion of the rotor to vary.
This effectively varies the damped torque on the rotor when
the later oscillates. Record damped oscillation traces on
paper wrapped round the drum mounted above the flywheel.
Unit(K2) consist of a penholder and pen, which adjust to
make proper contact with the paper, the unit undergoes a
controlled descent over the length of the drum by means of
an oil dashpot clamped to the main.
You can use various diameters shafts, but due to the location
and necessary fin adjustment of the oil container the length
is restricted to approximately 0.75 m. Measure the angular
displacement of the flywheel by means of a graduated scale
on the upper rim of the rotor. An etched marking on the
frame serves as a datum for the measurement of angular
displacement.

6. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
6 | P a g e
Fill the cylindrical container K4 with oil to within 10mm of the top. Adjust the knobs
underneath to level the oil surface with one of the upper graduations on the conical
portion of the rotor, K3.A depth, d of 175mm is suggested for maximum damping.
Details of the graduations on the rotor are in Figure
Select and fit a suitable shaft, noting the length of shaft the two inside faces the
chuck, together with the diameter of the shaft. Allow the pen to fall, and measure the
rate of descent of the pen in (mm/second) by timing the descent of the pen over a
fixed length of paper, using a stopwatch.
The system is now ready for recording torsional oscillations. Raise the pen to the top
of the paper on the drum and rotate the rotor to an angle of approximately 40o and
then release. A trace of the oscillations can be obtained by bringing the pen into
contact with the paper using the thumbnut on the support and allowing the pen to
descend.
Record a trace of the amplitude of oscillation showing decay of vibration due to the
damping. The rate of descent of the pen previously carried out will provide suitable
time scale.
From the trace given in Figure measure five successive amplitudes starting with the
initial one (n=0) and tabulate the results in Table below.

7. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
7 | P a g e
6. Calculations and results
A-
𝐼𝑝 =
𝜋𝐷4
32
=
𝜋(4.8 ∗ 10−3
)4
32
= 5.2088 ∗ 10−11
𝑚4
𝑘 𝑡 =
𝐺𝐼 𝑝
𝐿
=
(80 ∗ 109
∗ 5.2088 ∗ 10−11
)
0.88
= 4.73527
𝑤 𝑛 =
2𝜋
(
𝑡20
20)
=
2𝜋
1.24
= 5.0645
𝐽 =
𝑘
𝑤2
=
4.73527
(5.0645)2
= 0.1846
𝑎 =
𝑐
𝐽
N0 n x D(mm) 𝒍𝒏
𝒙 𝟎
𝒙
𝝉 𝒅=d/v
A
1 9 1.5 0 0
2 8 1.5 0.117 0.8241
3 7 1.5 0.1335 0.8241
4 6 1.5 0.1541 0.8241
5 5 1.5 0.1823 0.8241
6 4 1.5 0.223 0.8241
7 3 1.5 0.2876 0.8241
8 2 1.5 0.4054 0.8241
------ -------- -------- ------
∑𝛕 𝐝
= 𝟎. 𝟕𝟐𝟏
B
1 13 2.5 0 0
2 12.5 2.5 0.03922 1.372
3 12 2.5 0.11778 1.372
4 11.5 2.5 0.04255 1.372
5 11 2.5 0.00444 1.372
6 10.5 2.5 0.0465 1.372
7 10 2.5 0.0487 1.372
8 9.5 2.5 0.0512 1.372
------ -------- -------- ------ ∑𝛕 𝐝 = 𝟏. 𝟐

8. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
8 | P a g e
𝑠𝑙𝑜𝑝 =
0.21 − 0.15
5 − 3.39
= 37.26 ∗ 10−3
𝑎
2
𝜏 𝑑 = 37.26 ∗ 10−3
𝑐
0.1846
2
∗ 0.721 = 37.26 ∗ 10−3
𝑐 = 19.07 ∗ 10−3
𝑠𝑙𝑜𝑝 =
0.042 − 0.04
5 − 2.8
= 9.09 ∗ 10−4
𝑎
2
𝜏 𝑑 = 9.09 ∗ 10−4
𝑐
0.1846
2
∗ 0.721 = 9.09 ∗ 10−4
𝑐 = 4.6546
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 1 2 3 4 5 6 7 8 9
𝑙𝑛𝑥./𝑥
n
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 1 2 3 4 5 6 7 8 9
𝑙𝑛𝑥./𝑥
n

9. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
9 | P a g e
The line represents viscosity
0.00E+00
5.00E-01
1.00E+00
1.50E+00
2.00E+00
2.50E+00
3.00E+00
3.50E+00
4.00E+00
4.50E+00
5.00E+00
0.00E+00 2.00E+07 4.00E+07 6.00E+07 8.00E+07 1.00E+08
c
Damping area x effective(mean) radius mm x 10
slop=
2−3
4∗107−6∗107 = 5 ∗ 10−8
r
(mm)
Mean radius
rm( mm)
Area A
(mm)2
A. rm
( mm) 3
Damping
coefficient
12.5 6.25 6.1359 *10^3 3.835*10^4 19.07 ∗ 10−3
25.0 12.50 4.9087*10^4 6.1359*10^5
37.5 18.75 1.6567*10^4 3.1063*10^6
50.0 25.00 3.927*10^5 9.8175*10^6
62.5 31.25 7.6699*10^5 2.3968*10^7
75.0 37.50 1.3254*10^6 4.9701*10^7
87.5 43.75 2.1046*10^6 9.2077*10^7 4.6546

10. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
10 | P a g e
7. DISCUSSION
1. What you conclude from the experiment, is the result of
experiment accurate? How can, increase the accurateness
The experiment is inaccurate and must be calculated for each level
of cone to reach the greatest accuracy possible
Increase the angle of the torsion disk to draw a large wave
possible to handle its measurements and rounding to the lowest
possible value to ensure there is no line
The effect of pen friction on the paper affects the stability of speed
and frequency
Switching this mechanism to a digital device that connects with the
computer to reach a short wave and precise times where motion
sensors and displacement
2. Give some practical example about torsional system, torsional
system with damping or torsional system with viscous dumping,
with take a picture for the system,
 torsional system

11. Saif aldin ali madi
Department of Mechanical Engineering/ College of Engineering/ University of Baghdad
11 | P a g e
torsional system with damping or torsional system with viscous dumping