Vibration Durability Testing and Design Validation Based on Narrow Frequency Band

80 Pages·2011·2.07 MB·English

Master's Degree Thesis
ISRN: BTH-AMT-EX--2011/D-01--SE

Vibration Durability Testing

and Design Valid ation Based on

Narrow Frequency Band

Gudeta Berhanu

Department of Mechanical Engineering
Blekinge Institute of Technology
Karlskrona, Sweden
2011

Supervisor: Ansel Berghuvud, Andreas Josefsson, BTH
Holger Dreher, Dan Magnusson, Scania

Vibration Durability Testing
and Design Validation Based on
Narrow Frequency Band

Gudeta Berhanu

Department of Mechanical Engineering
Blekinge Institute of Technology
Karlskrona, Sweden
2011
Thesis submitted for completion of Master of Science in Mechanical
Engineering with emphasis on Structural Mechanics at the Department of
Mechanical Engineering, Blekinge Institute of Technology, Karlskrona,
Sweden.

Abstract

Existing vibration durability testing methods for a component is
conservative in verifying the fatigue strength of a component. They more
of typify the damaging potential of the real world vibration, instead of
the component under test. This thesis proposes a new vibration durability
testing method that works by giving emphasis to the dynamic behaviour
of the component. From several tests carried out at different narrow
frequency bands, it develops a diagram that shows the maximum limit of
a component towards vibration. Design verification will then be made by
comparing the result with the real world vibration. To this aim, a test has
been carried out on a truck alternator at four different frequency regions
and a vibration profile has been extracted by combining them together.
Then, comparing the result with the real world vibration profile, the
design of the alternator has been verified. Accordingly, the alternator
shows less strength at low frequency regions.
Keywords
Vibration testing, Narrow band, Palmgren Miners rule, Rain flow cycle
counting, S-N curve, Fatigue.
Acknowledgement
This thesis work was carried out at Scania RECA in cooperation with the
Department of Mechanical Engineering, Blekinge Institute of Technology
(BTH), karlskrona, Sweden under the supervision of Dr. Ansel Berghuvud
(BTH), Holger Dreher (Scania) and Dan Magnusson (Scania).
I would like to record my sincere gratitude to Dr. Ansel Berghuvud,
program manager of Mechanical Engineering Department, for his valuable
advice, suggestion and guidance throughout my thesis work. I want to
thank Andreas Josefsson, Ph.D student, for his helpful suggestions and
comments.
I express my sincerely appreciation to Dan Magnusson, Senior Engineer,
whom his knowledge and skills helped me seeing the goal of the thesis
clearly. I gratefully acknowledge Holger Dreher, Development Engineer,
for his extensive assistance and encouragement in every step of my
progress. I express my heartfelt thanks again to Holger Dreher and Paula
Oksanen for their hospitality during my stay at Södertälje.
The writer is indebted to Scania for immense test facilities and funding.
Furthermore, I would like to express my thankfulness to all Scania's
employees for providing me a good work environment throughout my
study. The academical and social experience that I got during the time was
really remarkable.
Finally I would like to express my deepest gratitude to all my family that
supported me in everything that I was in need. God bless you all!
Sweden, June 2011
Gudeta Berhanu
2
Contents
1  Notation 5 
2  Introduction 7 
2.1 Background 7 
2.2 Purpose and Aim of the Work 7 
2.3 Methodology 8 
2.4 Organization of the Thesis 9 
3  Historical Background 11 
4  Theoretical Background 13 
4.1 Design Philosophies 13 
4.1.1  Safe-Life approach 13 
4.1.2  Fail-Safe approach 13 
4.1.3  Damage Tolerant approach 14 
4.2 S-N Curve 14 
4.2.1  Effect of Mean Stress on the S-N curve 17 
4.3 Palmgren-Miners Cumulative Damage theory 20 
5  Fatigue Life Estimation 22 
5.1 Time Domain Analysis 22 
5.1.1  Rain-flow Cycle Counting Methods 23 
5.2 Frequency Domain Analysis 26 
5.2.1  Probability Density Function (pdf) from PSD 27 
5.2.2  Narrow Band Solution 29 
6  Standards for vibration durability testing 31 
6.1 nCode International 31 
6.1.1  Shock Response Spectrum (SRS) 32 
6.1.2  Maximum Response Spectrum (ERS) 33 
6.1.3  Fatigue Damage Spectrum 34 
6.1.4  Mission Profiling and Test Synthesis 35 
6.2 Standards for Engine family components 36 
7  A New Vibration Testing Method 38 
7.1 Basic Assumption 38 
7.2 Methodology 39 
7.3 Advantages 41 
7.4 Test Environment 42 
7.5 Application and Limitation 42 
3
8  Case Study on Truck Alternator 44 
8.1 Experimental Set-up: 45 
8.1.1  Experimental set up for modal analysis 45 
8.1.2  Experimental set up for vibration durability testing 46 
8.1.3  Experimental set up for fatigue testing 49 
8.2 Experimental Procedures 50 
8.2.1  Test Procedure for Modal Analysis 50 
8.2.2  Test procedure for vibration durability testing 55 
8.2.3  Test procedure for fatigue testing 57 
9  Result 58 
10 Conclusion and Discussion 72 
References 75 

4
1 Notation
A Amplitude ratio
b Material constant (Basquin constant)
E[D] Expected fatigue damage
E[P] Expected peaks
E[0] Expected zeros
f Frequency
G Power Spectral Density
G Input Power Spectral Density
(cid:2919)(cid:2924)(cid:2926)(cid:2931)(cid:2930)
G Output Power Spectral Density
(cid:2925)(cid:2931)(cid:2930)(cid:2926)(cid:2931)(cid:2930)
H System transfer function
H Imaginery part of transfer function
imag
H Real part of transfer function
real
K Spring stiffness
m nth moment
(cid:2924)
N Number of i’th stress cycle to failure
(cid:2919)
n Number of cycles of the given i’th stress level
(cid:2919)
p Probability density function
Q Amplification factors
R Stress ratio
r Gamma function
T Equivalent test duration
(cid:2915)(cid:2927)

5
Symbols
σ Stress level
∆σ Stress range
σ Maximum stress level
(cid:2923)(cid:2911)(cid:2934)
σ Minimum stress level
(cid:2923)(cid:2919)(cid:2924)
σ Alternating stress
(cid:2911)
σ Yield stress
(cid:2935)
σ Ultimate stress
(cid:2931)
σ Mean stress
(cid:2923)
σ Effective alternating stress
(cid:2915)
σ Stress at the endurance limit
(cid:2914)
σ Ultimate stress
(cid:2931)
σ i’th stress level
(cid:2919)
σ Fracture stress
(cid:2916)
γ Irregularity factor
(cid:1290) Damping coefficient
* Convolution
Abbreviation
SRS Shock Response Spectrum
ERS Extreme Response Spectrum
FFT Fast Fourier Transform
FRS Fatigue response spectrum
PSD Power Spectral Density
pdf Probability Density Function

6
2 Introduction
2.1 Background
Technological advancement in today’s truck manufacturing has shown a
tremendous change and has resulted in complex component integrity. This
will in turn increase the demand for the durable, efficient and low cost
component which can coincide with the complexity. As a result, a more
sophisticated testing method is highly required to verify if the quality of the
component meets up the requirement.
Every equipment and component are frequently subjected to a mechanical
vibration during their service life. Depending on the magnitude of the
loading and behavior of the structure, the induced dynamic loading would
result in fatigue failure through time. Trucks are exposed for environmental
and operational induced vibration in different events. Following to this
vibration, a cyclic stress loading will be generated at different parts of a
component and equipment, which then leads to the fatigue failure at the
end.
In today's typical durability and performance test, a truck should run for
several hundreds of kilometers on a test track for verification. Depending
on the intensity and extent of the investigation, the test may take several
months to complete its overall procedures. In addition to the considerable
time spent during the test procedure, a big investment is required for fuel,
prototype, labours and other related costs. Thus, the test should be carried
out cautiously to ensure that no structural damage occurs during the
investigation process. However, if the truck is unable to complete its full
test, the procedure should be repeated again on the redesigned product. And
these definitely will double the overall investment cost. Hence, a laboratory
analysis should be implemented on truck components before going for field
test.
2.2 Purpose and Aim of the Work
As mentioned above, today’s vibration testing method, tests and verifies a
component according to a predefined requirement. This test requirement
originates from the field measurement of different events. As an outcome,
7
the result that is obtained at the end of the test will be ‘pass’ or ‘fail’
statements. However, this is a very conservative result as it does not
provide a comprehensive understanding about the component. In other
words, the method devotes more emphasis on characterizing the excitation
signals by owing a little knowledge about the component under test. From
design point of view, this makes the conclusion that is drawn on the
component to be very difficult. Hence, Scania Engineers want to adopt a
new testing method to overcome these shortcomings.
The aim of this thesis is to develop a new vibration durability testing
method for a component at Scania test laboratory. The proposed testing
method is further investigated and verified on a truck alternator. From
series of tests carried out at different narrow frequency bands, the vibration
fatigue limit of the alternator is determined and illustrated in a diagram.
This diagram presumed to show the dynamic behavior of the alternator.
2.3 Methodology
The entire thesis work comprises of a theoretical and experimental work.
The theoretical part of the work will be explained by referring to different
previous works and international standards on the subject matter. As an
outcome, an inclusive knowledge on today’s testing method will be
obtained. In addition to this, it will lay a plateful platform to the newly
developed vibration durability testing method. On the other hand, the
experimental work consists of three different part: modal analysis, fatigue
test and vibration durability test. In fact, the main interest of this
investigation is a vibration durability test. However, as a part of the project,
a modal analysis and a fatigue testing for the alternator is performed by
conducting different test setup. Therefore, during the course of study, the
following tests will be carried out for the achievement of predefined
objective.
• Modal analysis: is required to find the resonance frequencies of the
alternator. This will help to divide the test frequency regions for
vibration durability test in an efficient way. For this, a system
transfer function will be measured at different part of the alternator
using impact hammer; so that the resonance frequencies of the
alternator will be synthesized by using a curve fitting. Furthermore,
a process of extracting the system transfer function from the
8