shm-accelerometer by khaja
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Transcript of shm-accelerometer by khaja
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Data treatment and
preconditioning
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Accelerometers
Laser displacementRaw data
Algorithm to reproduce absolutedisplacement from acceleration patterns
Data treatment andpreconditioning
Data evaluation andverification
Rain flow cycle countingData processing andstatistical analysis
Structural analysis
Stress life approachFatigue analysis andsensitivity analysis
Comparison to prevailing
standards
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Accelerometer
An accelerometer is a device that measures proper accelera
Not exactly rate of change of velocity
Instead, the accelerometer sees the acceleration associatedphenomenon of weight experienced by any test mass at resframe of reference of the accelerometer device
So normally acceleration is shown as 9.81 m/s2
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These accelerometers are used in our study to measure the diindirectly through change in acceleration
There are two types of accelerometers Peizo-electric accelerometer and Force based accelerometer
Now a days force based accelerometers are being used
With these sensors a change acceleration of 5g can be measur
Since the vibrations in the structures are small a accelerometeas low as 2g is sufficient
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Why accelerometers ?
Generally linear variable differential transformers (LVDT) areunder stationary conditions
But most of the load on buildings is dynamics so not a good
Laser displacement sensors are very accurate but they are rcostly so cannot be used in large numbers
Accelerometers are very small and can be easily integrated structure
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Why this algorithm ?
Performing discrete integration on sampled data is a rather task
However, there are a number of problems that need to be awhen performing a double integration
First, there is the problem of unknown initial conditions
There also is the problem of drift in an accelerometer
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Verification and calibration
To determine whether the displacement signal derived fromacceleration signal is accurate, it needs to be compared to tdisplacement
The position from double integration can be compared to a measured position
A laser displacement gauge was used for this purpose
And error should be with in 10%
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Principle
Given a position versus time of an object, x(t), the velocity, v
be found by taking the first derivative and acceleration by a
However while integration we need initial conditions so
However, the only way to get these initial conditions is throug
measurement, which is often impractical or unobtainable
t
t
datvtv
0
0
t
t
dvtxtx
0
0
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Numerical integration methods
Since we cannot use normal methods we use numerical inte Most simple method is rectangular integration method
where x is the integrand, y is the output of the integrator, an
sampling frequency
nxf
nyknxf
nys
n
ks
11
1
0
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As we can see this would a lot error, instead we use trapezoid
From the graph it is clear that this gives better results
0,12
11 nnxnx
f
nynys
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The choice of sampling rate, fs, is also a critical factor in integ
If we chose fs to be high then the resultant curve will be smo
Fs is generally a constant directly proportional to the frequen
So if the sample has higher frequency then the resultant curvsmoother
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More over for position signal we integrate 2 times so it will more smoother
Acceleration has high frequency so position curve is a lot sm
Also, it is 180 degrees out of phase with acceleration, as expEach integration operation shifts the signal by -90 degrees
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Accelerometer Drift
To measure acceleration, accelerometers are used to conveacceleration to an electrical signal
Unfortunately, accelerometers have an unwanted phenomedrift associated with them caused by a small DC bias in the
acceleration signal
Ideally, there should be no DC bias from the accelerometer measurement of a vibration
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A vibration occurs around a fixed point and has a zero mean
The presence of drift can lead to large integration errors
If the acceleration signal from a real accelerometer was intewithout any filtering performed, the output could becomeunbounded over time
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The displacement graph suggests that the object is moving aa fixed point when in fact, the vibration is around a fixed poithe object is not moving over time
To solve the problem of drift, a high-pass filter may be used remove the DC component of the acceleration signal
By filtering before integrating, drift errors are eliminated
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Initial conditions
Though we found a way to integrate without a need for initiconditions , as there are initial readings missing
The graphs will be shifted a little over the axis
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Notice that the middle plot of velocity contains a DC value o11.2540
Had the initial velocity value, v(0), been added in, that samewouldve been subtracted and the plot would be centered azero, as it should
Because the initial value wasnt used and the function was infor the second time, the output increases linearly
One solution to the problem of initial conditions is to use filt
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After the acceleration signal is integrated, it will likely have acomponent
A high pass filter can be used to remove that DC componentsignal
Likewise, after the velocity signal is integrated to get positioposition signal can be high-pass filtered as well
The results show that filtering can be very useful in making tdouble integration process work
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Block diagram
So using filters at appropriate places will eliminate the error a
possible
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FATIGUE
Fatigue is the progressive and localized structural damage twhen a material is subjected to cyclic loading.
The nominal maximum stress values are less than the ultimastress limit, and may be below the yield stress limit of the m
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ANALYSIS OF FATIGUE
Stress life approach
Strain life approach
Fracture mechanics approach
In this presentation we shall see about Stress life approach.
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STRESS LIFE APPROACH
This nominal stress (S-N) method was the first approach deto try to understand this failure process
The nominal stress approach is best suited to that area of thprocess known as high-cycle fatigue
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Stress Cycles
Typical Fatigue Stress Cycles,
(a) Fully Reversed (b) Offset, (c) Random
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The S-N Curve
In high-cycle fatigue situations, materials performance is cocharacterized by an S-N curve, also known as a Wohler curve
Most determinations of fatigue properties have been made completely reversed bending (i.e., R =1), by means of the rotating bend test
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The stress level at the surface of the specimen is calculated elastic beam equation,
S= Mc/I
S- the nominal stress acting normal to the cross-section
M- the bending moment
c - the distance of the surface from the neutral axis
I - the moment of inertia
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S-N data are nearly always presented in the form of a log-logalternating stress amplitude versus cycles to failure, with theWhler line representing the mean of the data
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Limits of the S-N Curve
The S-N approach is applicable to situations where cyclic loaessentially elastic
This means that the S-N curve should be confined on the lifenumbers greater than about 10,000 cycles in order to ensursignificant plasticity is occurring.
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The Influence of Mean Stress
Most basic fatigue data are collected in the laboratory by mtesting procedures which employ fully reversed loading
Most realistic service situations involve nonzero mean stres
Fatigue data collected from a series of tests designed to invedifferent combinations of stress amplitude and mean stresscharacterized by Haigh diagram
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HAIGHs diagram
Notice that the influence of mean stress is different for com
and tensile mean stress values for a given number of cycles
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EMPERICAL RELATIONS
Several empirical relationships which relate alternating stresamplitude to mean stress have been developed
Of all the proposed relationships, two have been most wideaccepted
1. Goodman :
2. Gerber :
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Factors Influencing Fatigue Life
Component size
The type of loading
The effect of notches
The effect of surface finish
The effect of surface treatment
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RAINFLOW CYCLE COUNTING
The signal measured, in general, a random stress S(t) is not up of a peak alone between two passages by zero, but also speaks appear, which makes difficult the determination of thof cycles absorbed by the structure
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The counting of peaks makes it possible to constitute a histothe peaks of the random stress which can then be transformstress spectrum giving the number of events for lower than stress value.
The stress spectrum is thus a representation of the statisticadistribution of the characteristic amplitudes of the random
function of time
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Rules of the flow
The origin of the random stress is placed on the axis at the athe largest peak of the random stress
If the fall starts from a peak :
a) The drop will stop if it meets an opposing peak larger thandeparture.
b) it will also stop if it meets the path traversed by another dpreviously determined
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c) The drop can fall on another roof and to continue to slip acrules a and b
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If the fall begins from a valley:
d) the fall will stop if the drop meets a valley deeper than thadeparture
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e) the fall will stop if it crosses the path of a drop coming from
preceding valley
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f) the drop can fall on another roof and continue according to
and e.
The horizontal length of each rainflow defines a range whichregarded as equivalent to a half-cycle of a constant amplitud
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Lets explain it with an example.
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First, the stress S(t) is transformed to a process of peaks and
Then the time axis is rotated so that it points downward.
At both peaks and valleys, water sources are considered. Wdownward according to the rules
Let X denotes range under consideration; Y, previous range ato X; and S starting point in the history
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Details of the cycle counting are as follows:
S=A; Y=|A-B| ; X=|B-C|; X>Y. Y contains S, that is, point A. CB| as one-half cycle and discard point A; S=B
Y=|B-C|; X=|C-D|; X>Y. Y contains S, that is, point B. Count |one half-cycle and discard point B; S=C
Y=|C-D|; X=|D-E|; X
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Y=|E-F|; X=|F-G|; X>Y. Count |E-F| as one cycle anddiscard points E and F.
Y=|C-D|; X=|D-G|; X>Y. Y contains S, that is, point C
Count |C-D| as one-half cycle and discard point C.S=D.
Y=|C-D|; X=|D-G|; X>Y. Y contains S, that is, point C| | h lf l d d d
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Count |C-D| as one-half cycle and discard point C.S=D.
Y=|D-G|; X=|G-H|; X
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Count |D-G| as one-half cycle, |G-H| as one-half cycle, and
one-half cycle
End of counting.