Random vibration analysis and fatigue life evaluationSIMULIA India
Regional Users Meeting „11 Page 1 of 12
Random vibration analysis and fatigue life evaluation of auxiliary
heater bracket
Arshad Khan, Devashish Sarkar, Reshad Ahmar and Hitenkumar
Patel
Larsen and Toubro Integrated Engineering Services, INDIA
Abstract: CAE has been an important tool in the process of
automotive product development.
Chassis mounted components on the truck are subjected to random
excitations from the road
during their life cycle. While designing the components, it should
be ensured that the component
should sustain the random vibration loads for the life cycle of the
vehicle. These random vibration
loads are also responsible for the fatigue failure of the
component. The object of this study was to
predict the fatigue life cycle of a chassis mounted component, an
Auxiliary Heater Bracket
concept which was, in actual scenario, subjected to random
vibration excitations from the road.
The weld fatigue life was also calculated in this exercise. It was
estimate that the bracket concept
was not able to sustain infinite life in the 1 level of confidence.
A redesign of the Auxiliary
Heater Bracket was suggested to achieve infinite fatigue life.
There is a requirement about the
bracket that it must endure infinite life in 1 and 2 level of
confidence. Infinite life cycle in the
FEA simulation was achieved for the modified bracket. Random
Vibration Analysis was performed
on the bracket model in Abaqus and response was calculated up to
130 Hz. RMS stresses were
used for the fatigue life cycle calculations and the fatigue life
cycle was determined from the
Basquin's relation. Abaqus was very helpful in completing this life
cycle simulation. Python
scripting was used to post process huge amount of data in
generating the RMS stresses.
Keywords: Fatigue, Auxiliary heater bracket, Abaqus, Random
Vibration Fatigue, PSD, Weld
Fatigue, Basquin’s Relation, PYTHON scripting, CAE
1. Introduction
The auxiliary heater bracket mounted on the chassis cross member
along with several other
components on truck is subjected to loads due to the engine
operations and vehicle road
conditions. These loads are typically random in nature. It is very
important to predict the fatigue
life of the components for getting an optimized design for these
components. This application
forms a specialized analysis domain which can be referred as random
vibration fatigue analysis. In
a compressed design cycle, most of the FEA is done on the various
engine and chassis mounted
components using simplified load representations. This is in the
form of applying fixed inertia
loads on the components as per relevant industry standards and
calculating the natural frequencies.
In this paper, we may observe that with the help of Abaqus, the
loads and boundary conditions
were simulated close to the real environment. This was achieved in
a very small time frame, thus
not impacting the design life cycle.
SIMULIA India Regional Users Meeting „11 Page 2 of 12
2. Finite Element Model
The auxiliary heater bracket is mounted on the cross member of the
rail chassis. The components
which were directly attached the bracket are considered in the
simulation. Figure 1shows the
geometry considered for the analysis. We can see the Auxiliary
Heater Bracket mounted on the
cross member.
The finite element model is shown in the Figure 2.
Figure 2 FE Model
SIMULIA India Regional Users Meeting „11 Page 3 of 12
All the sheet metal parts including Auxiliary heater bracket were
assigned steel material. Linear
elastic material properties were considered for the analysis.
Auxiliary heater bracket was meshed
with hexahedral elements (C3D8I), whereas all other sheet metal
components were meshed with
shell elements. Bolted joints have been simulated with rigid and
beam connection.
Density of pump and pipes mounted on auxiliary heater bracket were
adjusted to achieve a total
mass of the assembly.
3.1 Loads and Boundary Condition
The FE model was created in Altair Hypermesh®. The necessary
connections in terms of bolted
joints were modeled.
Loading history was derived from the mission tests in the forms of
accelerations load history in all
the Cartesian directions at certain locations on the chassis. This
load data was converted to the
PSD amplitude data in the form of PSD accelerations vs. frequency
components. One of the
locations for this data acquisition is as shown in Figure 3. The
data collected from the road test
data has to be increased by 1.3 to take into account the pot-hole
effect. This corresponded to 1.69
times increases in the PSD amplitude.
From the loading scenario, it was clear that this was a case of
base excitation. A deck was
prepared in Abaqus for modeling this scenario.
Figure 3 Data acquisition point and Boundary condition
Location
SIMULIA India Regional Users Meeting „11 Page 4 of 12
The PSD data used in the simulation is as shown in the Figure
4.
Figure 4 PSD input for analysis in G2/Hz
The node at PSD application point was connected with chassis cross
member thru rigid elements
and fixed in all degrees of freedom as shown in Figure 3.
3.2 Random response analysis –Existing Bracket
Random Vibration Response analysis was performed using acceleration
spectrum density curve.
Response was obtained up to 130 Hz (First mode of Bracket was 13.59
Hz). Equivalent RMS
Stress was used for the fatigue life calculation. Structural
damping ratio of 2% has been
considered for the analysis.
The first mode for the natural frequency extraction is shown in
Figure 5. We can observe from the
Figure 5 that the bracket is bending in X-directions about
Y-axis.
Figure 6 shows the Response of bracket at node number 33939 for PSD
excitation. It can be
observed from the Figure 6 that the bracket response is high at
first natural frequency i.e. 13.59
Hz.
In Abaqus/VIEWER we have a limitation of getting only component
stresses for the PSD stresses.
A python script was used to generate the equivalent stresses from
the component stresses.
The python script used for these calculations can be referred in
the Appendix
SIMULIA India Regional Users Meeting „11 Page 5 of 12
Figure 5 First natural frequency of assembly
Figure 6 Equivalent Stress PSD distribution against frequency
SIMULIA India Regional Users Meeting „11 Page 6 of 12
Figure 7 PSD and RMS Stresses
Figure 7 shows the distribution of 1σ stress against frequency. PSD
Stresses (OR any response) is
taken as a qualitative measure of response due to PSD base
excitation. However Equivalent RMS
Stresses (1 stress) are used for Fatigue Cycle evaluation
corresponding to the PSD excitation.
Square root of area under the PSD Stress (MPa 2 /Hz) curve gives
the RMS Stress (MPa). As the
area under the PSD stress curve increases the RMS value also
increases, as can be observed from
the PSD curve Figure 7. When the PSD Stress response is zero or
negligible, the RMS value
becomes constant as it does not add up to the area.
1 stress plot for the bracket can be seen in the Figure 8.
Figure 8 1σ Stress Plot of the bracket
SIMULIA India Regional Users Meeting „11 Page 7 of 12
3.3 Fatigue Life Calculation –Existing Bracket
Equivalent RMS Stress is used for the fatigue life calculation. By
using Gaussian distribution, 1σ
values occur 68.3% of the time, 2σ values occur 27.1% of the time
in addition to the 1σ time and
3σ values occur 4.33% of the time in addition to the 1σ and 2σ
time.
It has been found in various literatures and forums that basically
random broadband signal with
linear model (Irrespective of distribution) is assumed to have a
Gaussian nature of stresses. Non-
linear model can be a Non-Gaussian phenomenon.
Fatigue Life is determined from the following Basquin's
relation:
Where,
σe = Alternating Stress.
m = Slope of S-N curve.
Weld imperfection effects has been considered in the base material
SN curve (fatigue strength
curve) according to International institute of welding, therefore
the endurance limit has been
reduced to 83.25 MPa.
Random Vibration Analysis on the Auxiliary Heater brackets for the
given acceleration spectrum
density suggests that the bracket experience a very high 1σ stress
(1082.5 MPa), which is much
higher than the endurance limit of material (83.25 MPa), this
suggest that bracket will not endure
infinite life in 1σ level of confidence. Figure 9 shows the SN
curve used for fatigue cycle
calculations.
SIMULIA India Regional Users Meeting „11 Page 8 of 12
3.4 Modified Concept
Figure 10 shows the modified concept to achieve the desired life of
the bracket.
Figure 10: Modified Bracket
3.5 Random response analysis-Modified Bracket
The first natural frequency of the bracket was improved by adding
the rear stiffener as shown in
Figure 11. The first mode of Bracket is 26.5 Hz. Structural damping
ratio of 2% had been
considered for the analysis.
Figure 12 shows the Response of bracket at node number 26278 for
PSD excitation. It can be
observed from Figure 12 the bracket response is high at first
natural frequency i.e. 26.5 Hz.
Figure 13 shows the distribution of 1σ stress against
frequency.
SIMULIA India Regional Users Meeting „11 Page 9 of 12
Figure 11 First natural frequency of assembly
Figure 12 Equivalent Stress PSD distribution against
frequency
SIMULIA India Regional Users Meeting „11 Page 10 of 12
Figure 13 PSD and RMS Stresses
1 stress plot for the bracket can be seen in the Figure 14.
Figure 14 1σ Stress Plot of the bracket
SIMULIA India Regional Users Meeting „11 Page 11 of 12
3.6 Fatigue Life Calculation-Modified Bracket
Random Vibration Analysis on the Auxiliary Heater brackets for the
given acceleration spectrum
density suggests that 1σ stress induced in the bracket is 42.0 MPa,
which is almost half of the
endurance limit of material (83.25 MPa), this suggest that bracket
will endure infinite life in 1σ
and 2σ level of confidence.
4. Conclusion
The original concept of the bracket was not able to sustain
infinite life in the 1level of
confidence. A redesign of the Auxiliary Heater Bracket was
suggested to achieve infinite fatigue
life in 1 and 2 sigma level of confidence. Infinite life cycle in
the FEA simulation was achieved
for the modified bracket. Abaqus proved to be an efficient tool in
modeling the random vibration
environment.
1. “Abaqus Version 6.9 Documentation,” Abaqus 6.9-1.
6. Acknowledgement
We are grateful to our colleagues Dr. PK Roy, Mr. Sridharababu
Inala and Mr. Sohel Ujjaini to
helping us in executing this project and preparing this
paper.
SIMULIA India Regional Users Meeting „11 Page 12 of 12
7. Appendix