Modelling and simulation of single rotor system

International Journal of Latest Technology in Engineering, Management & Applied Science (IJLTEMAS)
Volume VI, Issue IV, April 2017 | ISSN 2278-2540
www.ijltemas.in Page 163
Modelling and Simulation of Single Rotor System
Amit. Malgol1
, Yogita. Potdar2
1
M. Tech, Department of Mechanical Engineering, GIT, Belgavi, Karnataka, India.
2
Assistant Professor, Department of Mechanical Engineering, GIT, Belgavi, Karnataka, India
Abstract: - This paper presents study of rotor shaft system for
three different position of the disk, for a simply supported case
and it is important to determine natural frequency, critical
speeds and amplitudes of rotor system. This characteristic are
found by using ANSYS parametric design tool. Modal, harmonic
and transient cases are carried out for the single rotor system.
The results obtained for this analysis are useful for design of
rotor system. The results obtained from analytical method have
close agreement with the results obtained from ANSYS results.
Keywords: - Rotor, natural frequency, critical speeds, amplitudes,
damping.
I. INTRODUCTION
otor dynamics is branch of physics which deals with
study of behaviour of rotating systems under application
of dynamic forces. Rotor is part of system i.e. disks, blades or
couplings mounted on shaft is called as rotor. Rotor is used to
convert one form of energy into another form hence rotational
energy must be maximum, so we must reduce vibrational
energy as much as possible, so they have wide range of
applications in many industries as well as household
applications so we need to analyse the system to prevent
catastrophic failures. Applications such as centrifugal pumps,
generators, motors, compressors, blowers, sewing machine,
steam turbines, gas turbines, aero engines, main and tail rotors
of helicopters. In rotating system flexural vibrations are main
cause as compared to torsional vibration and axial vibration.
Unbalance in rotor gives raise to forces and moments in rotor
this generates flexural vibration in rotor. The vibrations
perpendicular to the axis of rotation such vibrations are known
as flexural vibrations. Whirling is one of the main cause for
failures of rotating systems due unbalance of rotor i.e. due the
manufacturing defects centre of gravity of shaft doesn’t
coincides with axis of rotation, misalignment of rotor shaft
and bearings, due to loose supports or if the machine is
operated at critical speeds may lead to catastrophic failure of
system.
Generally rotors rotate at high speeds, when the natural
frequency of system is equal to the critical speed resonance
occur. Resonance is most common problem in rotating
systems. In rotating system if there is some percentage of
vibration in machine, these vibrations are magnified by
resonance. At these critical speeds the amplitudes of vibration
goes on increasing this cause rotor to bend and twist so this
cause rubs or wear and tear and collide with adjacent parts of
system hence excessive force are developed and hence leads
to failure. So determination natural frequency, critical speeds
and amplitudes of vibrations are very important in rotor
dynamics. As a designer by changing mass, stiffness, position
of disk etc. such design modification to change critical speeds
of system so as to operate in a suitable environment. To
reduce whirling amplitudes, we must avoid rotating at critical
speeds of the system or squeeze film damper is suitable. By
using damper whirling amplitudes are reduced as well as
reduces forces on the supports.
II. METHODOLOGY
2.1 ANSYS
The rotor model consist of shaft and disk modelled in ANSYS
by considering Beam 2D elastic element and two sets of real
constants for shaft and disc are considered, by creating four
key points and drawing straight line, as per shaft and disc real
constants sets are selected for lines created. To create rotor
model table 2.1 and 2.2 data of material properties and
dimensions are considered. Figure 2.3 shows the rotor model.
Table 2.1: Material properties of rotor
S.NO Parameters Value
1 Shaft and disk material Mild steel
2 Young’s modulus (E) 2 ⁄
3 Density ( ) 7800 ⁄
4 Poisson’s ratio ( ) 0.33
Table 2.2: Dimensions of disk and rotor
S.NO Parameters Value
1 Diameter of shaft (d) 0.01
2 Diameter of disk (D) 0.15
3 Thickness of disk (t) 0.01
4 Length of shaft ( ) 0.4
5 Mass of disk ( )
Figure 2.3: Rotor model in ANSYS
R

2.2 Modal analysis of rotor in ANSYS
In modal analysis, three different disk positions are considered
to determine natural frequencies and respective mode shapes
at this natural frequency and critical speeds at this three
different disk position for a simply supported rotor.
2.21 For disk position a = 0.2 and b = 0.2
Figure 2.4: Mode 1 for a = 0.2 and b = 0.2
2.3 Frequency responses of rotor in ANSYS

Figure 2.10: Variation of amplitudes of vibration with operating frequency of
rotor system at damping ratio = 0
rotor system at damping ratio = 0.0073265

2.4 Transient response
In transient vibration, the amplitudes of vibration goes on
decreasing. Transient response of rotor system in ANSYS for
disk position a = 0.066, b = 0.334 is carried out. A time
dependent force for is considered, a force of 100N is applied
on the disk for 1ms hence time history post processor in
ANSYS is used to plot displacement versus time for rotor
system is plotted. Figure 2.20 shows the variation of
displacement with time of rotor system under a case of time
dependent load.
Figure 2.20: Variation of displacement with time of rotor system
III. NUMERICAL METHOD
Let us consider a single rotor shaft system, the equation of
motion and natural frequency of vibration can be derived
using newton’s method, energy method or Rayleigh’s method.
The equation of motion of undamped free vibration is given
Where is stiffness and is mass of the disk. Natural
frequency of free vibration is given
√
Equivalent mass for simply supported beam carrying disk of
mass at middle where, is mass of shaft and is mass of
disk.
Equivalent stiffness for simply supported rotor with disk at
middle where is young’s modulus of rotor material, is
moment of inertia and is length of shaft
Stiffness for disk offset position is given by
For case damped forced vibration,
( )

On solving equation (3) we get the amplitudes of vibration
√( ) ( )
Where is Natural frequency of the system, is force
applied on the disk, is forcing frequency, is the damping
ratio and is the amplitudes of vibration.
Deflection of simply supported rotor with disk offset position
is given by
Natural frequency for simply supported rotor with disk offset
√
According to dunkerley’s method, Natural frequency of free
transverse vibration
√
According to Rayleigh’s method lowest natural frequency
given by
√
∑
∑
Where : total static deflection
Where : influence co-efficient
IV. RESULT
Table 4.1: Comparison of analytical results and ANSYS
results
SI.No Disk position Critical speeds
( rpm )
Natural frequencies
( Hz )
a
( )
b
( )
Analytical
method
ANSYS Analytical
method
ANSYS
1 0.2 0.2 2208 2201.64 36.80 36.694
2 0.133 0.267 2487 2431.08 41.45 40.518
3 0.066 0.334 3345.6 3383.04 55.76 56.348
Table 4.2: ANSYS Results
SI.No Disk position Amplitudes of vibration ( )
a
( )
b
( )
=0 =0.1748
1 0.2 0.2 0.92 8.8977 8.85034 5.6236 3.34862 3.13305
0.94 0.0139523 0.0137719 6.41135 3.5963 3.144
2 0.133 0.267 0.92 5.963 5.94 4.53092 2.77307 2.43602
0.94 8.22429 8.164 5.0349 2.82603 2.47163
3 0.066 0.3
44
0.92 2.70538 2.69096 1.80246 1.08735 4.07223
0.94 3.53928 3.50708 1.93959 1.09244 0.955360
Table 4.3: Analytical Results
SI.No
Disk position Amplitudes of vibration ( )
a
( )
b
( )
=0 =0.1748
1
0.2 0.2
0.92
8.8420 8.8079 5.9686 3.8103 3.40572
0.94 0.01167
0.011586
6.5517 3.8955 3.45041
2 0.133 0.267
0.92
6.9687 6.9334 4.7024 2.77307 2.43602
0.94
9.1924 9.1287 5.1618 3.0691 2.7184
3
0.066
0.3
44
0.92
2.68541
2.6767 1.81309 1.15735 4.01206
0.94 3.54364 3.5194 1.98996 1.18324 1.04796

V. CONCLUSION
The academic finite element software ANSYS is a good tool
to understand the dynamics of rotor system. It is observed that
all the verification of analysis that of numerical results for a
single rotor system is very good agreement with ANSYS
results. Modal analysis of rotor system, for three cases of disk
position helps us to understand the variation of rotor dynamic
parameters such as natural frequency, critical speed and
amplitudes for different damping ratios. The natural frequency
and critical speeds of the simply supported rotor system
increases as the disk position distance decreases form the
support. The resonance effect can be easily understood by
plotting modes shapes of the rotor system. The frequency
response curves helps us to understand the amplitudes of
vibration for three cases of disk position. As the disk position
near to the support the stiffness increases so as the amplitudes
of vibration decreases. It is also shown in case of transient
vibration, the amplitudes gradually goes on decreasing on an
application of a time dependent load.
This parameters are helpful in design of rotor dynamic system
and finally conclude that the natural frequency, critical speeds
and amplitudes of vibration depends on the effect of disk
position, material properties and dimensions of rotor system
and also this analysis of rotor system helps in safe and stable
operation of the rotor system. Further this analysis can be
carried out for a different materials for disk and shaft and also
for two or more disk rotor system.
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