Mechanica l Measurements & Instrumentat ion

2nd Lecture

Nada Rikabinadarikabi@yahoo.com

29 April 2014

Mechanical Measurement - 3rd year 2

Today’s Lecture

Measurement Participants

Measurement System

Instruments Reading Quality

Uncertainty of Measurement

Basic statistical calculations

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Mechanical Measurement - 3rd year 3

Measurement Participants Measurement: the quantitative comparison between a

predefined standard and a measurand to produce a measured result.

Measurement involves 3 main participants:(i) the measurand(ii) the measurement system(iii) the observer or control unit

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Measurement System The function of measurement system is to provide

information about the physical value of the measurand.

In some cases, the system is made up of only a single component which gives an output signal according to the magnitude of the variable applied to it.

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Measurement System However, in most cases, the measurement system is

made up of several components which can be broadly summarized as:i. Transducersii. Signal conditioning elementsiii. Signal utilization elements

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Measurement System Transducer

A transducer is a device which converts a property difficult to measure into another property more easily measured.

The transducer often comes into contact with the measured and takes a sample of it, which is then converted into another form of output that is a function of the initial value of the input.

It is sometimes referred to as the sensing element. An Example of transducer is: Mercury bulb in

mercury-in-glass thermometers.

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Measurement System Signal Conditioning

Signal Conditioning: This becomes necessary in order to improve the quality of the signal obtained from the transducer and present it in a more convenient form for further processing or transmission.

An example include: Capillary tube in mercury-in-bulb-thermometer

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Measurement System Signal Utilization

Signal Utilization or Data Presentation Element : The final element in a measurement system is utilize either in form of a display, recorder or control system.

In more sophisticated((متطوّر system; the signal conditioning block can be subdivided into a series of blocks, each in its turn modifying the signal.

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Measurement SystemExample

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Measurement System Summary

Detector/Sensorكاشف)): device which detects and responds to measurand

Transducer: converts measurand to an analog more easily measured (force-displacement, resistance-voltage)

Signal Cond.: amplify, filter, integrate, differentiate, convert freq. to voltage, etc.

– Computer: widely used today

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Instruments Reading QualityThe following terms are often employed to describe the quality of an instruments reading.

Range The region between the limits within which a

quantity is measured, received or transmitted, expressed by starting the lower and upper range values.

Example: 0 to 150 ° F, 20 to 200 psi.22 April 2014

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Instruments Reading QualitySpan The algebraic difference between the upper and

lower range values. For example:

a) Range 0 to 150 °F , span 150 ° F.b) Range -20 to 200 ° F, span 220 ° F.c) Range 20 to 150 psi, span 130 psi.

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Instruments Reading QualityMeasured Variable A quantity property or condition that is

measured. Sometimes referred to as the measurand.

Example: Temperature, Pressure, rate of flow.

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Instruments Reading QualityAccuracy The accuracy of an instrument indicates the deviation

of the reading from a known value

Accuracy is typically expressed as:1. Percentage of full scale reading (upper range

value). Example: A 100 kpa pressure gage having an accuracy of ±1% would be accurate of ± 1 kpa over the entire range of the gage.

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Instruments Reading Quality2. Percentage of span.

Example: A pressure gage has span of 200 kpa, Accuracy of ±0.5%.To one reading of 150 kpa is taken, then the true value of measurement will be between

3. Percentage of the actual reading.Thus, for a ± 2% of reading voltmeter, we would have an inaccuracy of ± 0.04 volts for a reading of 2 volts.

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Example 1A temperature transducer has a range of 20 to 250 °C. A measurement results in a value of 55°C for the temperature. Compare the errors if the accuracy is:

a) ± 0.5 % FS.b) ± 0.75 % of span.c) ± 0.8 % of reading.

What is the possible temperature in each case?

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Example 1 - solution

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Uncertainty of Measurement Uncertainty of measurement is the doubt that

exists about the result of any measurement.

Uncertainty is important to make good quality measurements and to understand the results. It is also important in calibration (must be reported on the certificate).

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Basic statistical calculations To increase the amount of information you get

from your measurements take a number of readings and carry out some basic statistical calculations.

The two most important statistical calculations are to find the average or arithmetic mean, and the standard deviation for a set of numbers.

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Standard Deviation The standard deviation of a set of measurements is an

indication of how much the measurements vary from their average value.

To get the standard deviation of a set of numbers, we do the following:1. square all the deviations from the mean, 2. add them together, 3. divide by the number of measurements, and4. take the square root.

The standard deviation is the root mean square of the deviations.

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Example 2Calculate the average (arithmetic mean) and the standard deviation of the following readingsThe readings are: 16, 19, 18, 16, 17, 19, 20, 15,

17 and 13Answer: To find the average, add them together and

divide by the number of values mean

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1710

170

nx

x

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Example 2 Standard deviation:find the difference between each reading and the average;

And square each of them;

Next, find the total and divide by n-1 (n=10 in this case);

The standard deviation, s, is found by taking the square root of the total;

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Example 3 Suppose we measure the temperature of a

metal table five times using a thermometer and get the following results:

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Index Result(°C)

Deviation(°C)

Square ofDeviation(°C2)

1 28.0 +2 42 25.0 -1 13 26.0 0 04 27.0 +1 15 24.0 -2 4Average 26 0.0 2

The mean square deviation is 2 °C2. The standard deviation is the root mean square deviation, which is √2 = 1.4 °C.