A System Approach to Dynamic Characteristics of Hanger Rod in Exhaust System

Abstract

The first and foremost important prerequisite that a designer require to design a part is stiffness information. The dynamic characteristics of auto motives exhaust hanger rods are studied for high frequencies at which the resonance vibration occurs, which is also an important transfer path for vibration to exhaust system. The point is to elaborate an approach which provides guidance towards optimized designs, mainly in early development stages. Theoretical and experimental modal analyses are used to suggest design parameters in terms of natural frequencies, which should be above 150-200Hz from the engine excitation frequency. Case studies are presented to show the methodology and validation of full system hanger rods for stiffness applications. The results acquired in this case study will highlight the potential applications of this approach, as well as the challenges associated with this method.

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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 3 Issue 5,May 2016.
www.ijiset.com
ISSN 2348 – 7968
A System Approach to Dynamic Characteristics of Hanger Rod
in Exhaust System
Mylaudy Dr.S.Rajadurai1, R.Kavin2, Rejinjose3, Prabhakaran4, Rajeshraman5
1Head -Research & Development /Sharda Motor Industries Ltd,
Chennai, State Tamil Nadu, India
2Assistant Manager - Research & Development /Sharda Motor Industries Ltd,
Chennai, State Tamil Nadu, India
3,4,5Senior Engineer- Research & Development /Sharda Motor Industries Ltd,
Chennai, State Tamil Nadu, India
Abstract
The first and foremost important prerequisite that a
designer require to design a part is stiffness information. The
dynamic characteristics of automotives exhaust hanger rods
are studied for high frequencies at which the resonance
vibration occurs, which is also an important transfer path for
vibration to exhaust system. The point is to elaborate an
approach which provides guidance towards optimized designs,
mainly in early development stages. Theoretical and
experimental modal analyses are used to suggest design
parameters in terms of natural frequencies, which should be
above 150 – 200Hz from the engine excitation frequency.
Case studies are presented to show the methodology and
validation of full system hanger rods for stiffness applications.
The results acquired in this case study will highlight the
potential applications of this approach, as well as the
challenges associated with this method.
Keywords: Hanger rod, Modal analysis, Design
parameters, Experimental validation.
1. Introduction
Effective and efficient product development is
critical to corporate success on the increasingly
competitive global market and simulation has proven to
support this in many sectors. This translates in design
’first-time-right’ philosophy, where the use of advanced
numerical and experimental methods that account for the
product environment is essential.
“What if” studies to understand the effects of changing
geometrical parameters or to change a design parameter
to avert failure and improve the product design is
essentially known as design optimization. Design
optimization provides a robust and systematic
methodology by carefully studying the effects of various
design variables and improves the design by varying the
variables. Along with the load - deflection
characteristics to understand the stiffness, the deformed
shape of the component and the resulting stress-strain
distribution can also be predicted.
Noise and vibrations are indiscernible to the
occupants of the car. The main source of vibration
related to exhaust system is engine. There are mainly
two transfer paths namely; structure and airborne
vibrations. The structure borne paths starts from the
engine and transmission line mounts and it transfers to
the exhaust system through the hanger rod. Therefore, it
is of great importance that the hangers are designed so
that their natural frequencies are higher than the
frequencies of the exiting sources acting on the system.
Several papers dealing with the dynamic
behavior of the whole exhaust system have been found
[2-4], but no treatise of the hanger’s dynamic behavior
has been found. The purpose of this paper is to analyze
the design parameters of hangers that have affect on
natural frequencies. Theoretical and experimental modal
analysis will be performed for some existing.

IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 3 Issue 5,May 2016.
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2.Limitations
The main restraint is that all natural frequencies
of the hangers must depend on vehicle applications. The
excitation sources are assumed to vibrate the exhaust
system up to frequency range from 100-250Hz for
passenger car vehicles. The vendors demand includes a
safety margin of 150-200Hz, which should be able to
withstand the loads such as mechanical loads, thermal
loads and corrosion characteristics.
Design parameters are influenced by mass and
geometry. The materials used in all case studies are
stainless steel grades (SS409.S10C). Stiffness depends
on material mechanical properties, geometrical design
and connections between hanger and the exhaust system,
i.e. weld. The geometrical limitation of hanger rod, i.e. it
should be able to fit the standard rubber isolators and
should also meet the packaging conditions of the system.
As a secondary solution, influencing the damping ratio
of the isolator in the structure is possible to decrease the
effects of natural frequencies that cannot be increased
above the desired level. So, damping effects of rubber
isolator will not be discussed in this paper.
3.Modal analysis theory
Modal analysis provides details about mode
shapes, natural frequencies and damping ratios for the
investigated structure. The analyses can be performed
both as theoretical calculations on a FE-model and
experimental tests on the real structures [5-7]. The
damping ratios can only be determined experimentally.
Theory is common for both theoretical and experimental
modal analyses are described briefly below.
3.1.Theoretical modal analysis
 The basic equation for typical un-damped modal
analysis is classic Eigen value problem.
 According to mode theory, the structure will be
typically seen as a system constituted by the mass
point, rigid body, damper and discrete it as finite
number of elastic coupling rigid bodies.
 Therefore, an infinite multi-degree of freedom
system turns into limited multi-degrees of freedom
system.
 When the linear time-invariant system
requirements are met, the system’s general motion
mathematical model can be expressed as:
M + C +Kx = f(t) (1)
Where,
M, C, K: The mass matrix, damping matrix
and stiffness matrix
x: The exhaust pipe vibration displacement
vector
f (t) : The exhaust pipe load vector
 Modal analysis method is to replace the physical
coordinates of modal coordinates that each
principal mode corresponded, so that the
differential equation decoupling to be independent
differential equations in order to obtain the system
modal parameters.
 The vibration of the engine exhaust pipe is a
random vibration, which basically belongs to linear
time-invariant systems. It can be assumed that M is
a constant matrix. The structural damping of
exhaust pipe has little effect on the natural
frequencies and therefore external load and
damping are not considered.
 Thus equation shown above becomes :
K- ω2 MΦ (2)
Where,
M- ∫Ω ρNTNdΩ is the structure overall
quality matrix
 When the order of matrix K and M is n, the ω2 in
formula shown above is the n times real coefficient
equation and the system degree of freedom
vibration characteristics (natural frequencies and
mode shapes) problem is to solve the matrix eigen
value ω.
3.2.Experimental modal analysis
The modal properties are estimated from the
frequency response functions (FRFs) obtained from the
test data. In the FRF, a peak of the magnitude marks
every resonance frequency. Each resonance frequency
can be associated with a certain mode shape that
represents the deflection shape of the structure [8].
There are several methods available for estimation of
the mode shapes, both single and multiple degree of
freedom methods. The estimation techniques, also called
curve-fitting methods, are used to generate an analytical
function that approximates the measured FRFs.
Inertance is the ratio of acceleration like
quantity to a force like quantity, when the arguments of

IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 3 Issue 5,May 2016.
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ISSN 2348 – 7968
the real or imaginary parts of quantities increase linearly
with time (dB reference 1ms-2/N).
Receptance is defined as displacement per unit
harmonic force. (dB reference 1m/N)
Average displacement value of receptance plot
in the range of 200- 600Hz should be considered.
3.3.Correlation
Correlation is a process where data from the
experiment are compared with theoretical results. There
are several methods available, which are more or less
complicated. Two graphical methods are “Graphical
comparison of natural frequencies” and “Graphical
comparison of mode shapes”. They are easy to use, but
they are very time consuming for models with many
nodes. Two numerical methods for comparison of mode
shapes are the “Modal scale factor” and the “Modal
assurance criterion”.
The methods are briefly explained below. For a
more complete discussion the reader is referred to for
example Maia [9].
4.Methodology
This paper includes full exhaust system hanger
rods as subject, which was pre-processed using
Hypermesh software, which was developed with the use
of shell, solid, bush and rigid elements. Exhaust pipes,
hanger rods, sub-resonator, main resonator and tail pipe
are modeled with 4 noded shell elements. Inlet flange
modeled with 8 noded Hexa elements. Flexible bellows
and rubber isolators are modeled with bush elements and
necessary stiffness values are assumed as per available
references. Schematic representation of the system is
shown below in the Figure 3. The natural frequency,
static response and frequency response stress are
determined from Normal modes, Static 1G and
Durability analysis. These are performed using Msc
Nastran and the results are posted using Hyperview. The
results are compared and correlated with experimental
data using NVH and Fatigue lab.
4.1.Analysis simulated for structural validity
 Stiffness analysis - To determine the natural
stiffness of the hanger rods.
 Static 1G loading - System stability, hanger forces
and hanger displacements.
 Resonance frequency analysis - Determining the
mode shape behaviour of the system and checking
for resonance.
 Engine Roll + 4⁰ analyses - To check the bellows
relative displacement, bending moment at the inlet
of the main resonator, inlet and outlet of the sub-
resonator.
Figure 1. System overview
Figure 2. Hanger 1, 2 and 3
4.2.Input details
 No of Cylinders = 3
 Engine Rated Speed = 6000 rpm
 Natural Frequency from engine rated speed =
(6000/60) * (3/2)
= 150Hz
4.2.1.Criteria
From the engine excitation frequency with a
safety margin of 150% which was mentioned above,
criteria was set to 375 Hz for first mode frequency. But
a constraint like diameter of the hanger rod is set by

IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 3 Issue 5,May 2016.
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vendor. So, only the geometrical aspect of the design is
analyzed and validated.
4.2.2.Materials property
Linear material properties in cold condition
like Young’s modulus, density, and Poisson ratio are
considered. Table 1. Material properties
Materials
Young
modulus
N/mm2
Poisson
ratio
Density
Ton/mm3
SS409
2.08e05
0.3
7.7e-09
S10C
2.0e05
0.29
7.84e-09
4.2.3. Analysis process flow
Figure 3. Process flow
4.2.4.Boundary conditions
Table 2.Weld length and hanger type
Hangers
Type
Materials
Weld
length(mm)
Hanger 1
Solid
S10C
60*2
Hanger 2
Hollow
SS409
80*2
Hanger 3
Bracket with
hanger
SS409
60
25
All weld nodes of hanger rod and bracket with
hanger rod are constrained in all degrees of freedom,
which are represented by the Figure 4 shown below
Figure 4. Weld nodes constrained in all d.o.f
4.3.Hanger stiffness analysis- virtual analysis
plots
Figure 5. Hanger 1 min. resonance frequency 400Hz

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Figure 6. Hanger 2 min. resonance frequency 700Hz
Figure 7. Hanger 3 min. resonance frequency 635Hz
4.3.1.Observations
 It has been observed that Hanger rod’s stiffness
is above the targeted natural frequency of 375
Hz.
 It has been concluded that Static analysis,
Modal analysis have to be performed to check
the resonance frequency, hanger forces,
stresses and deformations for validating the
hanger rod design.
4.4.Impact testing
To verify the resonance frequency of the
hanger rod, say for example shown in the Figure 8,
roving hammer impact test has been performed for all 3
hanger rods.
Figure 8. Tri-accelerometer mounted in the hanger 3 for impact
testing
4.4.1.Hanger stiffness analysis-experimental
analysis plots
Figure 9. Hanger-1,frequency-381Hz
1500.000.00 1000.00500.00100.00 200.00 300.00 400.00 600.00 700.00 800.00 900.00 1100.00 1200.00 1300.00
Hz
88.00
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
5.00
15.00
25.00
35.00
45.00
55.00
65.00
75.00
85.00
Amplitude
g/N
688.50
87.72
F FRF Point 1:+Y/Point 2:-Y
Figure 10. Hanger-2,frequency-688Hz

IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 3 Issue 5,May 2016.
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Figure 11. Hanger-3, frequency-663Hz
Table 3. Error calculation
Hanger
rods
Frequency(Hz)
Error (%)
Experimental
Impact test
Hanger 1
400
381
4.75
Hanger 2
700
682
2.57
Hanger 3
635
663
4.4
4.4.2.Observation
It has been concluded that the error results
observed in both the analysis and tests are less than 5%,
and thus the CAE results are validated.
5.Static analysis
5.1.Boundary condition
For rubber isolator– static stiffness has been
defined. Isolator is simulated as spring element –
(cbush) connected to 3 rows of nodes of hanger rod
(modeled with rigid element rbe2)
Figure 12. Bolt holes of manifold connecting to engine are
constrained in all d.o.f (ux, uy, uz, rx, ry, rz= 0)
Figure 13. Top node of isolator is constrained in all d.o.f
5.2.Loading condition
Figure 14. 1G (9810mm/s2) is applied in vertical direction i.e. system
self weight condition

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5.3.Static plots
Figure 15.Max displacement of 2.87mm in the middle pipe
Table 4.Hanger forces and hanger displacements
Components
Load
(N)
Displacement(mm)
Hanger 1
LH
11.56
1.59
RH
9.27
1.28
Hanger 3
30.05
2.45
Hanger 4
23.67
2.10
5.4.Observations
 For 1G Static loading, maximum displacement
of
2.87mm is observed at the middle of the centre
pipe.
 The stresses obtained are within the stress limit
for all the components when comparing with
their material yield strength.
 Further to this analysis, system natural
frequency has to be verified with engine
excitation frequency to check for resonance, in-
order to proceed with random vibration
analysis.
6.Resonance frequency analysis
6.1.Boundary condition
For rubber isolator and flex bellow – dynamic
stiffness are defined. Boundary condition is same as
above mentioned in the Figure (12-13). Isolator is
simulated as spring element – (cbush) connected to 3
rows of nodes of hanger rod (modeled with rigid
element rbe2.
6.2.Mode shape plots
Figure 16. Mode1-Lateral at 10.33Hz
Figure 17. Mode3-Lateral mode at 15.54Hz
Figure 18. Mode 6-Vertical mode at 24.07Hz
Figure 19. Mode 15-Vertical mode at 159.24Hz

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Figure 20. Mode 16-Twisting mode at 180.30Hz
Table 5. Mode shapes
Modes
Description
Frequency
(Hz)
1st
Lateral of intermediate pipe
10.33
2nd
Lateral mode of sub resonator,
CTR pipe and vertical bending
mode of Main resonator
assembly.
13.78
3rd
Lateral mode of sub resonator,
CTR pipe and Main resonator.
15.54
4th
Vertical Bending mode of
Hanger rods, Sub- resonator
and Main resonator assembly.
17.05
6th
Vertical mode of sub
resonator, CTR pipe and Main
resonator.
24.07
8th
Vertical Bending mode of sub
resonator, Twisting mode of
CTR pipe and Main resonator
37.08
10th
Vertical Bending mode of
Hanger rods, Sub- resonator
and Main resonator assembly.
73.65
12th
Twisting mode of Hanger rods,
Sub- resonator and Main
resonator assembly.
114.35
15th
Vertical bending mode of
Manifold and Converter
assembly.
159.24
16th
Twisting mode of Sub-
resonator, Vertical Bending
mode of CTR Pipe and Main
180.30
resonator assembly.
6.3.Observation
 The natural frequency and mode shapes are
determined from resonance frequency analysis
and compared with excitation frequency.
 The natural frequency values do not match with
excitation frequency(150Hz) values, so
resonance will not occur.
Further to this analysis, dynamic analysis and fatigue
analysis has to be performed on the finalized system
with road load data to validate the design for
optimization.
7.Dynamic analysis
For rubber isolator and flex bellow – dynamic
stiffness are defined. Boundary condition is same as
above mentioned in the Figure (12-13). Isolator is
simulated as spring element – (cbush) connected to 3
rows of nodes of hanger rod (modeled with rigid
element rbe2)
7.1.Loading Conditions
 Dynamic load considered as engine rocking
load of +4⁰ varying with time i.e. (0 - 2sec).
 Deformation and stress plot values are to be
checked for the applied load.
 Bending moment at Front resonator inlet and
outlet and main resonator inlet should meet the
target criteria.
 Stress in the hanger rod should be within the
endurance strength limit.
Figure 21. Applied load as enforced rotational displacement of +/- 4
degree at engine C.G

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Figure 22. Stress plots
7.3.Observation
 Maximum Von-mises stresses of 85MPa
observed in the bend region of the intermediate
pipe. And von misses stress of 60MPa near the
weld regions of hanger 1.
 It has been concluded that the system satisfies
the durability requirements under engine roll
loading condition.
 Dynamic stresses are compared with the
acceptable limit of the materials. Since the
Power-train translation and the engine vibration
loading have a high number of cycles, the Von-
mises stresses were judged against endurance
limit of the material at the respective temperature
for expected life. Empirical formulas were used
to convert the ultimate strength to endurance
limit. Number of cycles to failures observed in
testing (life of the system) justifies the stress level
predicted in the analysis.
8.Validation
The exhaust system models were validated by
comparing the natural frequencies and modes of the FE
model to the experimentally measured values. To
calculate the natural frequencies, modal analysis was
performed with the preloading effect to capture accurate
behavior of system. The modal strain energy distribution
was used to identify the critical locations. These critical
locations were refined in the model to meet stress
convergence criteria before full dynamic analysis. Table
3 shows theoretical and experimental modal analysis
results for the exhaust system. It shows good agreement
with the testing and CAE evaluation.
8.1.Durability test
 Maximum load that may act on the exhaust
system during its service life may be derived
from RLDA.
 RLDA input can be used for accelerated
validation of exhaust system durability by
component wise.
 RLDA is very important to derive whether the
system will meet the end usage durability target
or not.
 Usually, the load is acquired for Hanger rod is
in the vertical direction (Fz).
8.2.Analysis and test setup
 To carry out the test, hanger rods are fixed in
the same direction as it is mounted in the
chassis.
 To interpret the same position, hanger rods was
fixed as shown in the Figure (26-28) below.
From damage comparison, the drive file
generated by Belgian block was considered.
Drive file was applied to vehicle’s vertical (Z)
direction.
 Uni-axial actuator is connected to the hanger
rod in which the force Fz is applied.
Figure 23. Fz applied-hanger 1
Figure 24. Fz applied-hanger 2

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Figure 25. Fz applied-hanger 3
8.3.Test result
The test profile was repeated to pre-defined
cycles to simulate the durability target. After the test, the
hanger rods showed no defects.
Figure 26. Test setup-hanger 1
Figure 27. Test setup-hanger 2
Figure 28. Test setup-hanger 3
Figure 29. Drive file-hanger 1
Figure 30. Drive file-hanger 2
Figure 31. Drive file-hanger 3
9.Design improvement
In order to make the design optimization in the
hanger rods 2 & 3, parameters like diameter, thickness
and types can be altered. Stress results should be
compared for initial design and modified design in same
locations. Need to evaluate the dynamic analysis of
initial design and improved design to predict the
induced stresses which should be within acceptable
limits of the material.
10.Conclusion
The detailed analysis approach developed in
this study will help the engineers to predict the stiffness
and durability performance of the exhaust system and
develop a better exhaust system with quick turnaround
time. Application of measured excitations, assembly
loads and effects of manufacturing inaccuracies in
dynamic analysis has shown enhancement in predicting

IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 3 Issue 5,May 2016.
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ISSN 2348 – 7968
the performance of exhaust system. Material properties
change significantly with temperature; material stiffness
is reduced by the increased temperature and has effect
on the vibration characteristics.
It is possible to identify the failure locations
and find out solution for the problem. The results
obtained assure the structural integrity of the modified
exhaust system when implemented on the vehicle. This
methodology also contributes to a better understanding
of system behavior and its structural strength, for future
project applications. The same approach can also be
extended to analysis of exhaust system resonator shell,
baffles, end cap, heat shield and mounting brackets.
Acknowledgement
The authors wish to thank Sharda Motor
Industries Ltd - R&D Centre for offering and supporting
the opportunity to document and present this paper.
References
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[2] Helms.H, 1989. “Investigation of Vibration, oscillation
and Noise in the Car Test”. International Journal. of
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[3] Belingardi G. and Leonti S, 1987. “Modal Analysis in the
Design of An Automotive Exhaust Pipe”. International
Journal. of Vehicle Design, Vol. 8, no. 4/5/6, UK.
[4] Shih-Fu Ling, Tso-Chein Pan, Geok- Hian Lim and
Ching-Huan Tseng,1994. “Vibration Isolation of Exhaust
Pipe Under Vehicle Chassis”. International Journal. of
Vehicle Design, Vol. 15, nos.1/2, UK.
[5] Eriksson.L.J and Thawani.P.T,1985. “Theory and Practice
in Exhaust System Design”. SAE 850989.
[6]Masters thesis,Kadam.V.V,2000. “Modal Analysis and
Hanger Design Optimization of Exhaust System for Utility
Vehicle by using Finite Element Method”. SGGS College
of Engineering, Ann-University-Nanded, India.
[7] Nastran “Theory of Real Eigen value Analysis” on page
101
[8] LMS “LMS test lab, Rev 13A Service Level 1-Manual”.
See also URL www.lmsintl.com
[9] Maia N. N. M., Silva J. M. M., He J., Lieven N. A. J., Lin
R. M., Skingle G. W., To W. M., Urgueria A. P. V.,1997.
“Theoretical and Experimental Modal Analyst’. Research
Studies Press Ltd, Somerset.
Dr.S.Rajadurai,Ph.D. born in Mylaudy, Kanyakumari District, Tamil
Nadu, India, received his Ph.D. in Chemistry from IIT Chennai in
1979. He has devoted nearly 35 years to scientific innovation,
pioneering theory and application through the 20th century, and
expanding strides of advancement into the 21st century. By authoring
hundreds of published papers and reports and creating several patents,
his research on solid oxide solutions, free radicals, catalyst structure
sensitivity, and catalytic converter and exhaust system design has
revolutionized the field of chemistry and automobile industry.Dr.
Rajadurai had various leadership position such has the Director of
Research at Cummins Engine Company, Director of Advanced
Development at Tenneco Automotive, Director of Emissions at
ArvinMeritor, Vice-President of ACS Industries and since 2009 he is
the Head of R&D Sharda Motor Industries Ltd. He was a panelist of
the Scientists and Technologists of Indian Origin, New Delhi 2004.
He is a Fellow of the Society of Automotive Engineers. He was the
UNESCO representative of India on low-cost analytical studies
(1983-85). He is a Life Member of the North American Catalysis
Society, North American Photo Chemical Society, Catalysis Society
of India, Instrumental Society of India, Bangladesh Chemical Society
and Indian Chemical Society.
Second Author: Kavin R, Assistant Manager - Structural Analysis
at Sharda Motor Industries Limited, R&D centre, Chennai, for the
past 4 years. Mr. Kavin holds a bachelor degree from Anna
University, Tirunelveli.
During his career, Mr. Kavin has been involved in FE model
building and assembly, solver input deck preparation and CAE
structural analysis such as Modal, Static, and Dynamic & Thermal
stress simulations for exhaust system hot end, cold end and full
system. Team Lead for Structural analysis team. He published 5 SAE
technical papers and also more than international 6 journals. He won
3rd prize in 2013 - Altair technology conference, Pune for paper titled
on” Passenger car Exhaust system Muffler Bead Optimization and
Comparative study using OptiStruct”.
Area of interest includes Engine and power train, Project/product
management,Techno-commercial activities, Product design, structural
analysis, fatigue /durability analysis, experimental/operational modal
analysis. Future plans include develop my experience and expertise in
dynamic analysis (modal and transient frequency response), fatigue or
durability analysis on Exhaust system and acoustic simulation of
muffler. The objective of concentration is to move towards

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experimental testing such as tensile, compression, component fatigue,
Full exhaust system fatigue, experimental modal analysis, NVH
analysis and correlation with FEA simulation
Third Author: Rejin Jose.J, Senior Engineer - Structural analysis
Department at Sharda Motor Industries Limited, R&D centre,
Chennai, holds a Bachelor degree in Mechanical Engineering from
Anna University, Chennai and completed Bachelor’s thesis about
exhaust system joints of automobiles.
During his career Mr. Rejin Jose. J, has been involved in validation of
exhaust system joints, coordinating material testing, advanced
development works like hanger rod weld life prediction and mutually
coordinated the developing Road Load Data Acquisition (RLDA) and
Road Load Reproduction Test procedure to validate the exhaust
systems. He has been involved in performing finite element modeling
and analysis including Modal, Static, Dynamic, Fatigue, and Thermal.
Mainly, He concentrates in Fatigue Analysis by utilizing
commercially available FEA tools. Also he focused in development of
new CAE capabilities, methodologies and expertise by staying aware
to trends in the computational technology fields. He is also published
research papers in technical conferences and international journals.