fourth lecture - static characteristics of measurement systems

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  • 8/11/2019 Fourth Lecture - Static Characteristics of Measurement Systems

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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.

    15

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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

    17

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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

    21

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    Hint:

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    Thank you