shm-accelerometer by khaja

7/29/2019 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.

shm-accelerometer by khaja

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