fourth lecture - static characteristics of measurement systems
TRANSCRIPT
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Fourth Lecture
Static Characteristics of Measurement
Systems (continued)
Instrumentation and Product Testing
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Repeatability
Repeatability is used for expressing the precision of an instrument.
BS 5233 defines repeatability as follows:
the ability of a measuring instrument to give identical indications,
or responses, for repeated applications of the same value of the
measured quantity under the same conditions of use.
The quantitative definition of repeatability may be defined as:
the half range random uncertainty of a typical measurement underspecific conditions of use and at a defined level of confidence.
Repeatability (R) is then numerically equal to the half range
random uncertainty (Ur) of the measurement.
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For normal distribution (n), at 95% confidence level
xmean,population
-1.96 +1.96
Repeatability,R=Z=1.96
z
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For normal distribution (n), at % confidence level
-Z +Z
Repeatability,R=Z
z
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Quite often, the repeatability of an instrument varies from
time to time by a considerable amount. This does not
necessarily indicate that the instrument is faulty but rather
that repeatability is a somewhat variable quantity.
Some authorities advocate that three repeatability tests be
carried out on three similar but not identical specimens in
quick succession. If the ratio between the highest and
lowest value is not greater than 2:1, then the root mean
square value of the three results should be regarded as the
repeatability of the instrument.
If the ratio obtained is greater than 2, then the instrument
should be examined for faults, and on rectification further
tests should be made.
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Example. Three repeatability tests were carried out on the
balance introduced in last example. The results obtained
were as follows:
R1= 22g,R2= 24g, andR3= 28g
Find the repeatability of the balance.
Solution:
R3/R1= 28/22 = 1.27 < 2
79.243
282422
3
2222
3
2
2
2
11
2
...
RRR
n
R
R
n
i
i
smr
Rounding up, the repeatability,Rr.m.s.= 25
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Sensitivity
This is the relationship between a change in the output
reading for a given change of the input. (This
relationship may be linear or non-linear.)
Sensitivity is often known as scale factor or instrument
magnification and an instrument with a large
sensitivity (scale factor) will indicate a large
movement of the indicator for a small input change.
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Load Cell
Force,F
Output, Vo
Output, Vo(V)
Input,Fi(kN)
Slope = 5 V/kN
K
Input,F(kN) Output, Vo(V)
Sensitivity,K= 5 V/kN
Block Diagram:
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Linearity
Most instruments are specified to function over aparticular range and the instruments can be said to be
linear when incremental changes in the input and
output are constant over the specified range.
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Resolution
This is defined as the smallest input increment changethat gives some small but definite numerical change in
the output.
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Threshold
If the instrument input is very gradually increasedfrom zero there will be a minimum value required
to give a detectable output change. This minimum
value defines the threshold of the instrument.
input
Output
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Readability
This is defined as the ease with which readings may
be taken with an instrument. Readability difficulties
may often occur due to parallax errors when an
observer is noting the position of a pointer on a
calibrated scale.
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Range
The scale range is defined as the difference between the
nominal values of the measured quantities correspondingto the terminal scale marks. This is normally expressed
in the form A to B where A is the minimum scale
value and B the maximum scale value.
The instrument rangeis the total range of values which
an instrument is capable of measuring. In a single range
instrument this corresponds to the scale range. In amulti-range instrument the difference is taken between
the maximum scale value for the scale of highest values
and the minimum scale value for the scale of lowest
values, provided that adjacent ranges overlap.
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Hysteresis
This is the algebraic difference between the averageerrors at corresponding points of measurement when
approached from opposite directions, i.e. increasing as
opposed to decreasing values of the input.
Actual/ Input
Value
Measured
Value IdealHysteresis is
caused by
energystorage/
dissipation in
the system.
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Drift
Zero driftis variation in the output of an
instrument which is not caused by any change in
the input; it is commonly caused by internal
temperature changes and component instability.
Sensitivity driftdefines the amount by which
instruments sensitivity varies as ambient
conditions change.
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input
Output
zero
drift
input
Output
sensitivity
drift
input
Output sensitivity
drift
zero
drift
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Zero stability
This is a measure of the ability of the instrument to
return to zero reading after the measurand has returned
to zero and other variations such as temperature,
pressure, vibration, etc. have been removed.
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Dead band
This is the range of different input values over whichthere is no change in output value. This is produced
by friction, backlash or hysteresis in the instrument.
(Please use this definition to replace the one in your
notes.)
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Worked Example
What is sensitivity?
Plotting output (y) against input (x)
Part (a)
What is sensitivity drift?
Plotting the new output (y) against input (x)
Part (b)
Please do the Classwork at home using MS Excel and a calculator.
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Assignment One List twenty websites related to this subject by non-repeating the those
provided.
Visiting the web-sites provided and then searching for more relevant
information by yourself (new web-sites, books, and
national/international standards) to summarize the units and the
standards of length, mass, time, temperature, and electrical.
Each subgroup should write a short report of no more than six pages.
Submission deadline: Tuesday 22 October 2013; Class
representatives please help me to collect all the submissions
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Hint:
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Thank you