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Instrumentation 1

18-12-14 11:33 1.2 Electrical temperature measurement Another way of measuring temperature is to detect the change in electrical resistance caused by change in temperature. A popular transducer used for this method is the Platinum RTD (resistance temperature device). The platinum is sheathed and immersed in a fluid whose temperature is to be measured. The device is then connected as one arm of a “Wheatstone Bridge” circuit.

Engineering Instrumentation What is instrumentation? Instrumentation is the science of measurement and control; it includes making and recording measurements. When we make measurements we can compare them with universal standards to get absolute measurements, or we can compare them with local standards to get relative measurements. We need to identify the needs for each of these measurements. Instrumentation systems in engineering are commonly used for:

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Materials analysis

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Dynamic test rigs (e.g. damper or engine dynamometers)

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“In service” testing (e.g. race car data acquisition systems)

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Real-time process information and control

Thermometer Bulb Transducer

V

Rx 

V

Block Diagrams

1.1 The Mercury/Glass Thermometer One way of measuring temperature is to use a mercury/glass thermometer. Expansion of a quantity of mercury contained in a bulb causes a column of the liquid meal to be forced along a capillary tube. Changes in temperature are thus seen as changes of length of the column. These elements can be represented on a block diagram as below. The mercury in the bulb constitutes a basic measuring component, which converts changes in temperature into small changes in volume. It is called a transducer.

T

R3

R1

Capillary tube Signal conditioner

l

G

R2 R3 at balance R1

RTD

R2

The bridge is used to compare values of resistance. If the ratio of the two resistances in the left hand leg (R2 / R1) is equal to the ratio of the two in the right leg (RTD / R3), then the current through the galvanometer will be zero. However, as the resistance of the RTD changes, the bridge will move out of balance and a current will be shown by the galvanometer. Again we may represent these elements using a block diagram.

Scale Display

T

The capillary tube both magnifies the change in volume of the mercury, and changes it into a more easily detectable form. It is called a signal conditioner. Finally the temperature is displayed by comparing the length of the mercury column with a scale. This is called a display. These three blocks comprise a complete instrumentation system. Block diagrams such as this (although not always as simple) can be used to describe any instrumentation system, but the bare minimum for any system is normally the three block shown above.

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Platinum RTD Transducer

R

Bridge circuit Signal conditioner

I

Galvanometer Display

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Elements in real measuring systems x

2.1 Transducers All transducers make basic measurements by converting one quantity to another. The output signals of transducers are generally mechanical, optical or (ideally) electrical. The energy conversion process that takes place in a transducer is referred to as transduction. The ideal transducer should exhibit the following characteristics.  High fidelity – the transducer output waveform should be a faithful reproduction of the measurand.  There should be minimal interference of the quantity being measured.  The transducer must be capable of being placed exactly where it is needed.  There should be a linear relationship between the measurand and the transduced signal (a linear transfer characteristic).  The transducer should have minimal sensitivity to external effects.

LVDT Transducer

LVDT Signal conditioner

Voltmeter Display

Exercise Draw the circuit diagram for an LVDT circuit

Signals are commonly transmitted electrically, and so it is very common to need to convert a linear motion into an electrical one. One method of doing this is to use a Linear Variable Differential Transformer (LVDT).

2.2 Signal conditioners An amplifier is a device used to magnify a signal. Electrical amplifiers can magnify signals to more than a million times their original size. Magnification can only be achieved by the use of an external power source, and is defined by gain, G, where:

G An EMF is induced across each secondary coil from the primary coil. The magnetic coupling to each secondary is a function of the position of the magnetic core. The secondary coils are connected in series opposition so that the output voltage is the difference between the induced voltages. The coil/core system is designed such that the output is linear, which means that all signal conditioning is internal. The block diagram is shown below.

Vo Vi

Vi

Vo

VE Mechanical amplifiers include levers and gearboxes. Pneumatic and hydraulic intensifiers are also available. If the gain is less than 1 the signal is said to be attenuated, and amplifiers with a gain of less than 1 are called attenuators.

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Many electrical systems are now based on the binary number system. These are referred to as digital systems, since the signals are no longer continuous, but are turned into particular numbers.

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3.1 Accuracy and error Every instrument has an accuracy associated with it. The accuracy is expressed as an error corresponding to the difference between the true value of a measurand and the value indicated by the instrument. For example, a voltmeter may have a possible error of 2 V at 300 V full scale deflection.

A continuous voltage (an analogue signal) may be converted into a digital signal by the use of an AD (Analogue to Digital) converter. The reverse of this operation is carried out using a DA converter, or can even be carried out with cunning use of an operational amplifier (more later). The block diagram for a thermocouple based measuring system with digital readout is shown below:

3.2 Precision, repeatability, and stability An instrument may not always indicate the same value for a given input. This can be a random error (poor instrument design or manufacture), but may depend on whether the value is approached from above or below. The latter effect is known as hysteresis. Instrument specifications will normally give a maximum hysteresis effect.

Temp Thermocouple

Amplifier mV

AD converter

Digital display

V Binary

2.3

Terms and definitions

Output number

Stability reflects changes which may occur over long periods when a constant input is applied. These changes are often associated with environmental effects, particularly temperature.

Displays and recorders 3.3 Noise An instrument may have an error which varies (usually fairly rapidly) with time due to environmental effects, but again sometimes due to poor design. These changes are often due to electromagnetic interference from neighbouring equipment, and are particularly noticeable on small signals.

Displays are generally either digital or analogue, and it is reasonably simple to convert signals from one form to the other if necessary. An indicator gives an instantaneous value for a measurement, while a recorder can be used to register a variable continuously. Recorders nowadays often take the form of cards that can be fitted directly to the PCI bus of a personal computer, or of remote devices connected via serial, parallel or USB ports.

3.4 Calibration – Primary and secondary standards All instruments must be calibrated, and this calibration must be in some way based upon one of the absolute primary standards. These are:

Standalone versions of this system are generally termed data acquisition units, and are very common in race car engineering as well as other disciplines. They can commonly record anywhere between 10 and 64 input channels simultaneously, and have the great advantage that the data can be downloaded directly into a computer so that it can be analysed. These systems always make digital recordings of measurements, and can do so at very high data rates.

metre, kilogram, second, ampere, kelvin, mole, candela, radian, steradian Units for all other quantities are derived from these primaries. Since the primary standards can be difficult to use, there are secondary standards taken from these. In the UK secondary standards (and some primary standards) are held by the National Physical Laboratory. There is a major industry attached to the science of standards and calibration.

Plotters and chart recorders are still used for recording of some measurements, although this is becoming less common.

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3.5 Response times All instruments require a finite time to react to change in input.

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Static performance of instruments

Figure 2 has been used1 to describe the difference between accuracy and precision. It represents a target in which the objective is to hit the centre. Figure 2

measured value

dead band

time Accurate & Precise

Response time may be expressed as a time constant for the system, which is defined as the time taken for the instrument to reach a given percentage of the input value. Electronic systems generally have response times of milliseconds, chemical reactors may have response times of days.

Precise but not Accurate

Accurate but not Precise

The static performance of each element in an instrumentation system can be determined by calibration. The overall performance can then also be determined by calibration and checked with calculation. Assuming that each element has a static sensitivity S1, S2, S3 say then the overall sensitivity is the product of the individual sensitivities i.e.

3.6 Resolution The resolution of an instrument is defined as the smallest signal that can be detected. If a range of 5 volts is displayed on an 8 bit binary device then the maximum signal is the binary number 11111111. In base 10 (decimal) this number is: 20 + 21 + 22 +23 + 24 +25 + 26 + 27 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255. Therefore the resolution of any measurements shown will be limited to 5/255 = 19.6 mV. Resolution of measurement should not be confused with accuracy, as high resolution does not necessarily imply that the calibration is correct or the reading repeatable.

S1 =

Y2 Y Y1 :S = :S = M 2 Y1 3 Y2

giving the Overall Sensitivity S o =

M Input (C)

3.7 Sensitivity The static sensitivity of an instrument is defined as the ratio of the change in output for a given (and known) change in input.

Sensor or Transducer S1 e1

Y1

Y Y Y2 Y1 = S1 .S 2 .S3 = M Y2 Y1 M

Signal Conditioning S2 e2

Y2

Display and/ or Record S3 e3

Y Output (mm)

(mV) (V) The accuracy at a given calibration point can be defined in terms of error or difference between a true or standard value and the output or indicated value for a given parameter. The overall accuracy is simply the sum of the individual accuracies. The error associated with an element is the difference between a 'true' value and an indicated value i.e.

 indicated   true  error       value   value and the %accuracy as the ratio of an error to the particular criteria used i.e.

1 See for instance Haslam, Williams and Summers. Engineering Instrumentation and Control. ISBN 0-7131-3431-3. Arnold

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Instrumentation 1

usually %Accuracy = 100 *

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Error

Error

Deflection =

or % Accuracy = 100* Full Scale Value Value as a percentage of scale valueScale and full scale value respectively. It is usual to use the latter as the accuracy as a percentage of scale value usually results in larger coefficients. The overall accuracy is the sum of the individual accuracies i.e. Overall Accuracy (%Full Scale Value)=  Individual Accuracies as % FSV .

(* Many recorders and displays are calibrated in terms of an inverse sensitivity namely the ratio of the change in input to the corresponding change in output i.e. the inverse of the definition that is to be used for sensitivity.)

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(a) Briefly explain what is meant by an instrument calibration chart.

where the modulus of rigidity, G=803

mm and the associated N

error. Which spring parameter would you attempt to control more closely to improve the accuracy of the balance?

A piezo-static force transducer has a static sensitivity of 9 pC/kN and is connected to a charge amplifier with a gain set at 500 mV/pC and to a recorder set to 10 V/cm (*). Determine the overall sensitivity of the system. The system is to be used to indicate forces up to 35 kN. The pen recorder has a maximum travel of 25 cm. Determine the maximum travel of the pen for a change in input of 35 kN and state whether the indicated forces cause the pen to hit the end stops? Given that the overall accuracy is to be within 2.5% and that the force transducer has an accuracy of 0.5% and the display an accuracy of 0.8% determine the allowable tolerance on the charge amplifier.

A pressure transducer has the following specification :Range 0 to 0.5 bar Output 1 to 5 volts d.c. Resolution 0.5% of range Accuracy 2.0% of range Temperature Coefficient -2.0 mV per C Determine the sensitivity of the transducer. Determine the temperature range over which the transducer can be used for an accuracy of 0.015 bar.

* Spring Force

Estimate the average sensitivity of the spring balances in

4.1 Tutorial 1. Identify the three basic elements of a simple mercury in glass thermometer. Determine the effect on the sensitivity of increasing a) the diameter of the capillary tube b) the coefficient of thermal expansion of the glass (i.e. more strain per C), c) the volume of the bulb containing the mercury and d) the thickness of glass.

3.

Gd 4

GPa, the wire diameter, d=2.640.005 mm, the number of coils, n=40 and the mean radius of the spring, R=8.00.05 mm.

Where FSD is used it refers to full scale deflection.

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64nR

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(b) A mass produced spring balance is to be designed using a helical spring made from spring steel. The deflection of a coil spring is given by the formula 5

Instrumentation 1

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An alternative uses the total differential of So  XYZ , namely

4.2 Sensitivity and Accuracy The overall sensitivity of an instrumentation system is the product of the individual

so  dSo 

sensitivities. Consider an instrumentation system with three pieces of equipment having a nominal sensitivities X, Y and Z and values x,y and z as the tolerances. The overall

giving

so = YZ dX + XZ dY + XY dZ

so that

s o YZdX  XZdY  XYdZ x y z    .  So XYZ X Y Z

nominal sensitivity, So,=XYZ has an error, so, say giving So+so=(X+x)(Y+y)(Z+z)=(XY+xY+Xy+xy)(Z+z) So+so=XYZ+xYZ+XyZ+xyZ+XYz+xYz+Xyz+xyz

S o S S dX  o dY  o dZ X Y Z

So+so=XYZ+{xYZ+XyZ+XYz}+{xyZ+xYz+Xyz}+xyz

x y z , and are the individual per unit errors or X Y Z

Imagine that X=Y=Z=1 and that the tolerances are large at say 10% of the nominal values

The results are the same. The

so that x=y=z=0.1. In this case the values will be XYZ=1; {xYZ+XyZ+XYz}=0.3;

accuracies and the sum of the individual errors or accuracies gives the overall accuracy.

{xyZ+xYz+Xyz}=0.03 and xyz=0.001 and it is clear why both {xyZ+xYz+Xyz} and xyz are often assumed small an be assumed small and neglected to give So+so=(X+x)(Y+y)(Z+z)XYZ+{xYZ+XyZ+XYz} so that

S o  s o (X  x)(Y  y)(Z  z) XYZ xYZ  XyZ  XYz    So XYZ XYZ XYZ

giving

so x y z    . So X Y Z

It follows that the overall error or accuracy is the sum of the individual errors or accuracies. ____________________

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