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Vibration fatigue is a
mechanical engineering
Mechanical engineering is the study of physical machines that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, an ...
term describing
material fatigue
In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts of ...
, caused by
forced vibration of
random
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual ra ...
nature. An excited structure responds according to its
natural-dynamics modes, which results in a dynamic
stress
Stress may refer to:
Science and medicine
* Stress (biology), an organism's response to a stressor such as an environmental condition
* Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
load in the material points.
The process of
material fatigue
In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts of ...
is thus governed largely by the shape of the excitation profile and the response it produces. As the profiles of excitation and response are preferably analyzed in the
frequency domain
In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a s ...
it is practical to use
fatigue life
In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts of ...
evaluation methods, that can operate on the data in
frequency-domain
In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a si ...
, s
power spectral density (PSD).
A crucial part of a vibration fatigue analysis is the
modal analysis
Modal analysis is the study of the dynamic properties of systems in the frequency domain. Examples would include measuring the vibration of a car's body when it is attached to a shaker, or the noise pattern in a room when excited by a loudspeak ...
, that exposes the natural modes and frequencies of the vibrating structure and enables accurate prediction of the local
stress
Stress may refer to:
Science and medicine
* Stress (biology), an organism's response to a stressor such as an environmental condition
* Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
responses for the given excitation. Only then, when the
stress
Stress may refer to:
Science and medicine
* Stress (biology), an organism's response to a stressor such as an environmental condition
* Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
responses are known, can vibration fatigue be successfully characterized.
The more classical approach of fatigue evaluation consists of cycle counting, using the
rainflow algorithm and summation by means of the
Palmgren-Miner linear damage hypothesis, that appropriately sums the damages of respective cycles. When the time history is not known, because the load is
random
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual ra ...
(''e.g.'' a
car on a rough
road
A road is a linear way for the conveyance of traffic that mostly has an improved surface for use by vehicles (motorized and non-motorized) and pedestrians. Unlike streets, the main function of roads is transportation.
There are many types of ...
or a
wind driven turbine), those cycles can not be counted. Multiple time histories can be simulated for a given
random process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...
, but such procedure is cumbersome and
computationally expensive
In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that re ...
.
Vibration-fatigue methods offer a more effective approach, which estimates
fatigue life
In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts of ...
based on moments of the
PSD PSD may refer to:
Educational bodies
* Pennsylvania School for the Deaf, a Pre-K to 12th grade school for Deaf and Hard of Hearing students, located in the Germantown section of Philadelphia, Pennsylvania
* Philippine School Doha, a Filipino scho ...
. This way, a value is estimated, that would otherwise be calculated with the
time-domain
Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the ca ...
approach. When dealing with many material nodes, experiencing different responses (''e.g.'' a model in a
FEM package), time-histories need not be simulated. It then becomes viable, with the use of vibration-fatigue methods, to calculate
fatigue life
In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts of ...
in many points on the structure and successfully predict where the failure will most probably occur.
Vibration-fatigue-life estimation
Random load description
In a random process, the amplitude can not be described as a function of time, because of its
probabilistic nature. However, certain statistical properties can be extracted from a signal sample, representing a realization of a random process, provided the latter is
ergodic. An important characteristics for the field of vibration fatigue is the amplitude
probability density function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) ca ...
, that describes the statistical distribution of peak amplitudes. Ideally, the probability of cycle amplitudes, describing the load severity, could then be deduced directly. However, as this is not always possible, the sought-after probability is often estimated empirically.
Effects of structural dynamics
Random excitation of the structure produces different responses, depending on the natural dynamics of the structure in question. Different natural modes get excited and each greatly affects the
stress
Stress may refer to:
Science and medicine
* Stress (biology), an organism's response to a stressor such as an environmental condition
* Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
distribution in material. The standard procedure is to calculate
frequency response functions for the analyzed structure and then obtain the
stress
Stress may refer to:
Science and medicine
* Stress (biology), an organism's response to a stressor such as an environmental condition
* Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
responses, based on given loading or excitation.
[ By exciting different modes, the spread of ]vibration
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, su ...
energy over a frequency range directly affects the durability of the structure. Thus the structural dynamics analysis is a key part of vibration-fatigue evaluation.
Vibration-fatigue methods
Calculation of damage intensity is straightforward once the cycle amplitude distribution is known. This distribution can be obtained from a time-history simply by counting cycles. To obtain it from the PSD PSD may refer to:
Educational bodies
* Pennsylvania School for the Deaf, a Pre-K to 12th grade school for Deaf and Hard of Hearing students, located in the Germantown section of Philadelphia, Pennsylvania
* Philippine School Doha, a Filipino scho ...
another approach must be taken.
Various vibration-fatigue methods estimate damage intensity based on moments of the PSD PSD may refer to:
Educational bodies
* Pennsylvania School for the Deaf, a Pre-K to 12th grade school for Deaf and Hard of Hearing students, located in the Germantown section of Philadelphia, Pennsylvania
* Philippine School Doha, a Filipino scho ...
, which characterize the statistical properties of the random process. The formulas for calculating such estimate are empirical (with very few exceptions) and are based on numerous simulations of random processes with known PSD PSD may refer to:
Educational bodies
* Pennsylvania School for the Deaf, a Pre-K to 12th grade school for Deaf and Hard of Hearing students, located in the Germantown section of Philadelphia, Pennsylvania
* Philippine School Doha, a Filipino scho ...
. As a consequence, the accuracy of those methods varies, depending on analyzed response spectra, material parameters and the method itself - some are more accurate than others.
The most commonly used method is the one developed by T. Dirlik in 1985. Recent research on frequency-domain methods of fatigue-life estimation compared well established methods and also recent ones; conclusion showed that the methods by Zhao and Baker, developed in 1992 and by Benasciutti and Tovo, developed in 2004 are also very suitable for vibration-fatigue analysis. For narrow-band approximation of random process analytical expression for damage intensity is given by Miles.[ There are some approaches with adaptation of narrow-band approximation; Wirsching and Light proposed the
empirical correction factor in 1980][ and Benasciutti presented 0.75 in 2004.][ In 2008, Gao and Moan published a spectral method that combines three narrow-band processes.][ Implementation of those method is given in the ]Python
Python may refer to:
Snakes
* Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia
** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia
* Python (mythology), a mythical serpent
Computing
* Python (pro ...
open-source FLife[ package.
]
Applications
Vibration fatigue methods find use wherever the structure experiences loading, that is caused by a random process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...
. These can be the forces that bumps on the road extort on the car chassis, the wind blowing on the wind turbine
A wind turbine is a device that converts the kinetic energy of wind into electrical energy. Hundreds of thousands of large turbines, in installations known as wind farms, now generate over 650 gigawatts of power, with 60 GW added each yea ...
, waves hitting an offshore construction
Offshore construction is the installation of structures and facilities in a marine environment, usually for the production and transmission of electricity, oil, gas and other resources. It is also called maritime engineering.
Construction a ...
or a marine vessel. Such loads are first characterized statistically, by measurement and analysis. The data is then used in the product design process.
The computational effectiveness of vibration-fatigue methods in contrast to the classical approach, enables their use in combination with FEM software packages, to evaluate fatigue after the loading is known and the dynamic analysis has been performed. Use of the vibration-fatigue methods is well-suited, as structural analysis is studied in the frequency-domain
In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a si ...
.
Common practice in the automotive industry
The automotive industry comprises a wide range of companies and organizations involved in the design, development, manufacturing, marketing, and selling of motor vehicles. It is one of the world's largest industries by revenue (from 16 % such ...
is the use of accelerated vibration tests. During the test, a part or a product is exposed to vibration
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, su ...
, that are in correlation with those expected during the service-life of the product. To shorten the testing time, the amplitudes are amplified. The excitation spectra used are broad-band and can be evaluated most effectively using vibration-fatigue methods.
See also
* Fatigue (material)
In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts o ...
* Structural failure
* Vibration
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, su ...
* Structural dynamics
Structural dynamics is a type of structural analysis which covers the behavior of a structure subjected to dynamic (actions having high acceleration) loading. Dynamic loads include people, wind, waves, traffic, earthquakes, and blasts. Any structur ...
* Modal analysis
Modal analysis is the study of the dynamic properties of systems in the frequency domain. Examples would include measuring the vibration of a car's body when it is attached to a shaker, or the noise pattern in a room when excited by a loudspeak ...
* Random vibration
* Rainflow-counting algorithm
The rainflow-counting algorithm is used in calculating the fatigue (material), fatigue life of a component in order to convert a uniaxial loading sequence of varying stress (physics), stress into an equivalent set of constant amplitude stress reve ...
* Seismic analysis
Seismic analysis is a subset of structural analysis and is the calculation of the response of a building (or nonbuilding) structure to earthquakes. It is part of the process of structural design, earthquake engineering or structural assessment ...
* Solder Fatigue
Solder fatigue is the mechanical degradation of solder due to deformation under cyclic loading. This can often occur at stress levels below the yield stress of solder as a result of repeated temperature fluctuations, mechanical vibrations, or mec ...
References
{{Reflist,
refs=
[{{cite journal, last=Mršnik, first=Matjaž, author2=Slavič, Janko , author3=Boltežar, Miha , title=Frequency-domain methods for a vibration-fatigue-life estimation - application to real data, journal=International Journal of Fatigue, date=31 July 2012, doi=10.1016/j.ijfatigue.2012.07.005, url=http://lab.fs.uni-lj.si/ladisk/?what=abstract&ID=75, volume=47, pages=8–17]
[{{cite book, last=Nuno Manuel Mendes, first=Maia, title=Theoretical and experimental modal analysis, year=1998, publisher=Research Studies Press, location=Baldock, isbn=0863802087, edition=Reprinted.]
[{{cite book, last=Varoto, first=Kenneth G. McConnell, Paulo S., title=Vibration testing : theory and practice, year=2008, publisher=John Wiley & Sons, location=Hoboken, N.J., isbn=978-0-471-66651-6, edition=2nd]
[{{cite book, last=Sarkani, first=Loren D. Lutes, Shahram, title=Random vibrations analysis of structural and mechanical systems, year=2004, publisher=Elsevier, location=Amsterdam, isbn=9780750677653, edition= nline-Ausg.}]
[{{cite journal, last=Benasciutti, first=D, author2=Tovo, R , title=Spectral methods for lifetime prediction under wide-band stationary random processes, journal=International Journal of Fatigue, date=1 August 2005, volume=27, issue=8, pages=867–877, doi=10.1016/j.ijfatigue.2004.10.007]
[{{cite journal, last=Zhao, first=W, author2=Baker, M , title=On the probability density function of rainflow stress range for stationary Gaussian processes, journal=International Journal of Fatigue, date=1 March 1992, volume=14, issue=2, pages=121–135, doi=10.1016/0142-1123(92)90088-T]
[{{cite thesis , type=Ph.D. , first=Turan , last=Dirlik , title=Application of computers in fatigue analysis , publisher=University of Warwick , year=1985]
[{{cite book, last=Slavič, first=Janko , author2=Boltežar, Miha, author3=Mršnik, Matjaž , author4=Česnik, Martin , author5=Javh, Jaka , title=Vibration Fatigue by Spectral Methods: From Structural Dynamics to Fatigue Damage – Theory and Experiments , year=2020, publisher=Elsevier, location=Amsterdam, Netherlands, isbn=9780128221907, doi=10.1016/C2019-0-04580-3, s2cid=243156155 , edition=1st]
[{{cite journal, last=Miles, first=John W. , title=On structural fatigue under random loading, journal=Journal of the Aeronautical Sciences, date=1954, volume=21, issue=11, pages=753–762, doi=10.2514/8.3199]
[{{cite journal, last=Wirsching, first=Paul H., author2=Light, Mark C., title=Fatigue under wide band random stresses, journal=Journal of the Structural Division, date=1980, volume=106, issue=7, pages=1593–1607, doi=10.1061/JSDEAG.0005477 ]
[{{cite report , last=Benasciutti, first=Denis, author2=Tovo, Roberto , title=Rainflow cycle distribution and fatigue damage in Gaussian random loadings, publisher=Department of Engineering, University of Ferrara, date=2004]
[{{cite journal, last=Gao, first=Zhen, author2=Moan, Torgeir, title=Frequency-domain fatigue analysis of wide-band stationary Gaussian processes using a trimodal spectral formulation, journal=International Journal of Fatigue, date=2008, volume=30, issue=10–11, pages=1944–1955, doi=10.1016/j.ijfatigue.2008.01.008]
[{{cite web , url=https://github.com/ladisk/FLife , title=FLife, website=]GitHub
GitHub, Inc. () is an Internet hosting service for software development and version control using Git. It provides the distributed version control of Git plus access control, bug tracking, software feature requests, task management, continu ...
, accessdate=30 September 2020
Solid mechanics
Mechanical failure modes
Mechanical vibrations
Fracture mechanics
Materials degradation