International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 6, June 2015)
Modal Analysis and Harmonic Response Analysis of a
Crankshaft
Dr. C. M. Ramesha1, Abhijith K G2, Abhinav Singh3, Abhishek Raj4, Chetan S Naik5
1
Associate Professor, Dept. of Mechanical Engg, M.S.R.I.T, Bangalore, India.
Undergraduate Students, Dept of Mechanical Engg, M.S.R.I.T Bangalore, India
2,3,4,5
Natural frequencies are extracted both for free-free as
well as boundary conditions applied. The geometry
modelling of the crankshaft was done in AUTODESK
INVENTOR 2015.
Abstract— Modal analysis is a very important technique
which helps in determining the natural frequencies as well
as mode shapes of a structure. In this study modal analysis
of a single cylinder engine crankshaft is carried out in
ANSYS Workbench 14.0 and first twelve modes of vibration
are extracted for free-free as well as constrained boundary
conditions. The mode shapes are observed which provide a
comprehensive picture of deformations occurring.
Harmonic response was also studied by subjecting the
component to an exciting frequency range of 0 – 5000 Hz .
The results are provided in a graphical format.
Keywords— Modal Analysis,
Harmonic response, crankshaft
ANSYS
II. LITERATURE REVIEW
Extensive literature survey was done on the procedure
of modal analysis and the past studies done. Finite
Element Method seems to be a better and reliable option
in analyzing modal characteristics as its quick and very
informative
Mr.S.J.Patil [1] in their paper Modal analysis of
compressor crankshaft presents the analytical and FE
modal analysis of a crankshaft. For analytical
calculations, the crankshaft is considered as two rotor
system to calculate the natural frequency.
Quan ke Feng [2] in their study Simple Modeling and
Modal Analysis of Reciprocating Compressor Crankshaft
System proposed to simplify the analysis of the threedimension vibrations of reciprocating compressor
crankshaft system under working conditions, a spatial
finite element model based on 3-node Timoshenko beam.
Jian Meng [3] studied the stress as well as modal
analysis of a 4-cylinder diesel engine by analysis a single
crankthrow.
Momin Muhammad Zia Muhammad Idris et al [4]
discussed the optimization of crankshaft using strength
analysis.The results of modal analysis of modified design
is also done to investigate possibility of resonance.
Farzin H. Montazersadgh and Ali Fatemi [5] presented
that a dynamic simulation was conducted on a crankshaft
from a single cylinder four stroke engine. They have also
studied optimization of the crankshaft.
Amit Solanki et.al [6] explained that the performance of
any automobile largely depends on its size and working
in dynamic conditions.
B.D.N S Murthy et al [7] has been analysed the
Modeling, analysis and optimization of crankshaft. The
analysis is done on two different materials are Annealed
4340 steel, Inconel x750 alloy. The model were created
in catia-v5 and the analysis is to be done in Ansys.
Workbench,
I. INTRODUCTION
Modal analysis is a technique to study the dynamic
characteristics of a structure under vibrational excitation.
Natural frequencies, mode shapes and mode vectors of a
structure can be determined using modal analysis. Modal
analysis allows the design to avoid resonant vibrations or
to vibrate at a specified frequency and gives engineers an
idea of how the design will respond to different types of
dynamic loads. The crankshaft of an engine is one such
structure whose dynamic characteristics can be better
studied by modal analysis.
The objective of this study is to determine the natural
frequencies of a single cylinder engine crankshaft, study
the mode shapes and subject the crankshaft to a harmonic
loading varying in frequency from 0 – 5000 Hz and study
its response in terms of displacement and stress. The
dynamic load analysis has been carried out in MATLAB
and further analysis i.e, modal and harmonic response
has been carried out in Finite Element package ANSYS
Workbench 14.0. Modal analysis proved to be very
helpful in geometry optimization of the crankshaft which
was one of the aims of the complete study. The benefits
of using ANSYS were that mode shapes could be
accurately visualized and simulated. So the deformations
occurring in the crankshaft could be located with
precision. A graphical variation of number of modes vs
the frequency can also be obtained from ANSYS
Workbench.
323
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 6, June 2015)
III. MODAL ANALYSIS
Fig 2 – boundary conditions applied
First twelve modes of vibration were extracted in this
case as well.
FIG 1- SOLID MODEL IN AUTODESK INVENTOR
IV. HARMONIC RESPONSE
Modal analysis was carried out on forged steel
material whose properties are as follows :
A harmonic, or frequency-response, analysis considers
loading at one frequency only. Loads may be out-ofphase with one another, but the excitation is at a known
frequency.
In a harmonic analysis, Young’s Modulus, Poisson’s
Ratio, and Mass Density are required input. All other
material properties can be specified but are not used in a
harmonic analysis
Because of the fact that modal coordinates are used, a
harmonic solution using the Mode Superposition method
will automatically perform a modal analysis first.
Simulation will automatically determine the number of
modes n necessary for an accurate solution
Although a free vibration analysis is performed first,
the harmonic analysis portion is very quick and efficient.
Hence, the Mode Superposition method is usually much
faster overall than the Full method. Since a free vibration
analysis is performed, Simulation will know what the
natural frequencies of the structure are. In a harmonic
analysis, the peak response will correspond with the
natural frequencies of the structure. The analysis settings
used for harmonic response are as follows
Table I –
material properties of forged steel
Young’s modulus
Poisson’s ratio
Bulk modulus
Shear modulus
Yield strength
Ultimate strength
Density
2.21e11 Pa
0.3
1.84e11 Pa
8.50e10 Pa
6.25e08 Pa
8.27e08 Pa
7833 Kg/m3
CONDITION 1 – FREE-FREE
In this analysis no boundary constraints were applied
on the model and modes are extracted. The solver used is
Block Lanczos and settings used in ANSYS are as
follows
Table II –
Ansys settings used
Object Name
Modal (A5)
State
Solved
Physics Type
Structural
Analysis Type
Modal
Solver Target
Mechanical APDL
State
Fully Defined
Environment Temperature
22. °C
Range Minimum
0. Hz
Generate Input Only
No
Range
Maximum
5000. Hz
Solution
Intervals
100
Solution Method
Mode Superposition
Cluster Results
No
Modal
Frequency
Range
Program Controlled
Object Name
Pre-Stress (None)
State
Fully Defined
Pre-Stress Environment
None
Table III
Ansys settings for harmonic response
CONDITION 2 – WITH BOUNDARY CONDITIONS
In this analysis the crankshaft was subjected to
boundary conditions. Ball bearing constraint was applied
for 180 degrees as surface contact on one side and journal
bearing constraint was applied for 180 degrees on the
other side as a line contact.
324
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 6, June 2015)
Frequency and phase response was analyzed for the
crankpin portion of the crankshaft. The load magnitude
considered was 20.894 MPa as this was the maximum
load obtained from dynamic analysis.
Mode shapes
V. RESULTS AND DISCUSSIONS
Natural frequencies for condition 1 free-free are given
as follows
Table IV
frequencies and corresponding modes
Mode
Frequency
[Hz]
Type of mode
1.
0.
Rigid body displacement
2.
0
Rigid body displacement
3.
0
Rigid body displacement
4.
1.7054e-003
Rigid body displacement
5.
3.4265e-003
Rigid body displacement
6.
4.6853e-003
Rigid body displacement
7.
977.46
Bending
8.
1285.1
Bending
9.
2124.7
Bending + Torsion
10.
2126.7
Bending
11.
3131.7
Bending + Torsion
12.
3770
Fig.4- Mode 1(rigid body displacement)
Fig.5 - Mode 2(rigid body displacement)
Bending
Fig.6 – mode 7(bending mode)
Fig.7 – mode 8(combined bending and torsion)
Natural Frequencies for condition 2 –with boundary
conditions
Fig.3- variation of number of modes vs frequency. X-axis contains
number of modes and Y-axis contains frequency
In natural free-frequency the crankshaft should not be
vibrating but some period of time vibrations are occurred
because self-weight of the crankshaft. Of the 12 mode
shapes extracted, some of the mode shapes are shown
here.
325
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 6, June 2015)
TABLE V
FREQUENCIES AND MODES
Mode
1.
2.
3.
4.
5.
6.
7.
8.
9.
Frequency [Hz]
908.55
1023.
1787.9
3660.
3799.3
4143.9
4692.
5026.3
5237.8
10.
5368.7
11.
12.
5623.7
5974.7
Type of Mode
Bending
Bending
Bending
Bending + Torsion
Bending + Torsion
Bending
Bending
Bending + Torsion
Bending + Torsion
Bending + Torsion
Fig.10 – Mode 2 (bending mode)
Bending
Bending
Fig.11 – Mode 4 (combined bending and torsion)
Fig.12 – Mode 5 (combined Bending and Torsion)
Results of Harmonic Response Analysis
FIG 8 – VARIATION OF MODES VS FREQUENCY. X-AXIS CONTAINS
NUMBER OF MODES AND Y-AXIS CONTAINS FREQUENCIES OF MODES
MODE SHAPES
Fig.9 - Mode 1 (bending mode)
Fig.13 – variation of displacement amplitude with different
exciting frequencies
326
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 5, Issue 6, June 2015)
The natural frequencies of two conditions were found
out and analyzed. The variation of number of modes vs
frequency has been plotted graphically. Mode shapes are
observed for careful examination of deformation. The
type of mode with the corresponding frequency has been
tabulated. These characteristics prove to be very helpful
in the design of the crankshaft for dynamic conditions.
Harmonic response of the crankshaft for the excitation
in the range of 0-5000Hz has been studied. Variation of
stress and displacement amplitude (frequency response)
with respect to frequency has been graphically plotted.
Phase response of the crankshaft has also been studied.
These characteristics help in better understanding of
vibration response of a component subjected to dynamic
loading.
REFERENCES
Fig.14 - variation of stress amplitude with different exciting
frequencies
[1]
As can be seen from the graphs the peaks correspond
to the resonance conditions. But the engine operating
frequencies are well below the resonance conditions,
hence resonance conditions are easily avoided.
[2]
[3]
[4]
[5]
Fig.14 – phase response for the forged steel crankshaft for one
complete engine cycle of 720 degrees
[6]
VI. CONCLUSION
[7]
Modal analysis was carried out for a single cylinder
engine crankshaft.
327
Mr.S.J Patil “ Modal analysis of compressor crankshaft”,
International
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Pages:
155-158, July-2013
Yu, Binyan; Yu, Xiaoling; and Feng, Quanke, "Simple Modeling
and Modal Analysis of Reciprocating Compressor Crankshaft
System"
(2010). International Compressor Engineering Conference. Paper
1982.
http://docs.lib.purdue.edu/icec/1982
Finite
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Analysis
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4-Cylinder
Diesel
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Published Online August 2011 in MECS (http://www.mecspress.org/)
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using strength analysis”, International Journal of Engineering
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