Instrumentation and Metrology

Whatever exists, exist in some amount. finding this amount is what is called as measurement.

            Measurement is the act or process that consist of obtaining a quantitative comparison between a standard entity and measure entity.  This measured entity is called as measurand.  This act produces a result.

General method of measurement:

            Direct method and indirect method are the two methods of measurement.  In many cases direct  method is not possible, then we use indirect method.

            Measuring system has three stages.  Indirect method makes use of a transducing device coupled to a chain connecting apparatus.  All these are called measuring system.  This chain of devices converts the basic form of input into a analogous form which then processes and presents at the output as a known function of input.  Hence the generalized measuring system can  be divided into three stages.

1. A detector - transducing sensor stage.
2. An intermediate stage - signal conditioning stage and
3. A terminating stage / Read out stage.

Stages in Measurement:

First Stage:

            First stage is to detect and sense the measurand and ideally it should  be insensitive to every other input for example.  If it is a pressure pickup device then it should be insensitive to acceleration, a strain gauge should be insensitive to temperature and frequently one finds there are more than one transduction in the first stage.

Classification of first stage devices:

            First stage may involve number of operation and fences these devices are classified as

1. Those which are used for detection only,
2. Those which are used as detector and single transducer and
3. Those which are used as detector and two stage transducer.

            The first stage instrumentation may be simple consisting of no more than a mechanical spindle or a contacting member to convey the quantity to secondary transducer.  It may also consist of complex assembly of elements.  The sole function of this stag is to selectively sense the quantity of interest and to process the sensed information into a form acceptable to stage two operations.  It does not give any output in an useful form.  Example

• Contracting spindle
• Simple pendulum
• Thermocouple used to convert temperature into voltage
• Variable resistivity
• Photo voltaic cell which converts light to potential and
• Photo emission cell that converts light to current.

            Many of the sensors mentioned above transduces the input displacement into an electrical output.  This is a fortunate situation for realizing practical combination of mechanical sensors acting as a primary transducer and the electrical sensory as secondary transducer.

Second Stage:

            This stage on the system modifies the transduced information so that it is acceptable to the third or termination stage.  It may also include such operations like selective filtering, integration, differentiation or telemetering.  Most common function of the second stage is to increase the power or amplitude of signal or both to the level required to drive the final terminating device.

Third Stage:

            This stage proves the information sort in a form understandable / intelligible to the human beings to a controller either as a relative displacement or in a digital form.

Tyre Gauge (Pressure measurement):

            This is used for measuring the tyre pressure.  It consists of a cylinder and piston.  A spring resisting the piston movements.  As the air pressure pushes the piston the resulting force compresses the spring until the spring force and air force balance.  The calibrated stem shows air pressure.  Piston-cylinder acts as a transducer that produces force and spring converts force to displacement.  Finally the transduced input is transferred without  signal conditioning the scale and inducts the read out.  The pressure is measured in Pascal or atmospheres.

1 Pa = 1 Nm²

1 Torr = 1 mm of mercury = 1.33 x 10² Pascals

1 Atmosphere = 14.696 psi = 101.3 x 10³ Pascal

DISPLACEMENT MEASUREMENT

Sliding contact resistive transducer:

            This converts a mechanical displacement into a electrical output which is either voltage or current.

R = rL / A

Where R is in Ohms, L in mm, A is area in mm2 and r is in Wm.

            The effective length between one end of wire and slider contact is a measure of mechanical displacement.  Devices of this type have  been sued for large displacements.  Potentiometer are called pots.

Electrical Strain gauges - Resistance Strain gauge:

            Lord Kelvin with his experiments demonstrated t hat the resistance of copper or Iron wire change when subjected to strain.  He made use of wheat stones bridge with a galvanometer as indicator.  Unbonded resistance elements are sometimes used as secondary transduces in accelerometer and other component.  

Theory:

           Generally four such separate filaments are connected electrically to wheat stone's bridge.  The general relation between electrical and mechanical properties are derived as follows.

            Initial length of conductor = L
            Cross sectional area = CD², where C = constant and D = sectional dimension.

            If the section is square then C = 1 and for circle C = p/ 4.  Let us consider the conductor be axially kept under tension there by causing any increase in length and as a consequence the lateral dimension decreases as a function of Poisson's ratio.  Therefore

R = rL / A = rL / CD²

            When strained each quantity in he above equation except C may change.

dR = [ CD² ( -rdL + Ldr) - rL ( 2 CD/dD) ] / C²D⁴

dR / R = dL / L - 2 dD / D + dr / r

Where dL / L = Axial strain and dD / d = Lateral strain.  The ratio of which is the Poisson ratio.  Substituding in the above equation.

Ignoring the third term we have F = 1 + 2g

            The resistivity does not change with strain.  This basic knowledge and the value of g lies between 0.25 and 0.3.  F = 1+2(0.3) = 1.6.  This gauge factor is a function of Poisson ration in the elastic range and should not vary from 1.6.  The gauge factor for metallic gauge is essentially a constant and is in the range  of elastic strain

e_a = DR / RF.  Where DR is the incremental value.  The manufacturers supply the value of F and R.  Hence the DR = F.R.e_a

            In practical applications the value of F and R are supplied by manufacturers and the user determines the value of DR.

Types of strain gauge:

            As the circuit that are used to measure the resistance changes they require a minimum resistance to be measured.  This value depends on the current in the gauge and its length.  Higher the resistance, larger will be the change in DR for a given gauge factor.  It draws lesser current  The smaller the current the dissipation is less.  Normally the resistance chosen is at the order of 60 - 1000 ohms.  Strain gauges are classified as bonded or unbonded strain gauges, according to the method of manufacture.  

            Bonded strain gauge is directly bonded on the surface of the specimen to be measured.  A layer of adhesive cement is used for this purpose.  It serves to transmit the strain from specimen to gauge wires and at the same time serves as an electrical insulator.

            In unbonded strain gauge is one in which there is a free filament sensing element where strain is transferred to the resistance wire directly without any backing.

Semi-conductor gauges:

            They employ piezo resistive property of doped silicon and germanium.  The strain sensitivity is mainly due to resistivity changes in the semi-conductor materials and the change in resistance due to stain is 40 - 100 times more than that of the conventional metal alloys.  The gauge factor F = ( DR/R ) / e = 1 + 2g+m.  Where m = pE, here E is the young's modulus and p is the coefficient of piezo resistance along the axis of the gauge.

Thin film gauges:

            Of late thin film gauges are receiving attention because of certain advantages.  Thin film of metals such as aluminum, gold, nickel, platinum or palladium are formed in desired patterns directly on a substrate by thermal evaporation in vacuum and this substrate is attached to the specimen in the same manner as that used for other gauges.  The thin film gauge resistance is given by

R_f = ( w / l ) x R_g

            Where W is the width of the film, l the length of film Rf the specific sheet resistance.  But R_g = r_f l/A.  Here r_f is the film resistiviy in Ohm-metre and A is the area of cross section.

ERRORS IN MEASUREMENT

            Errors may arise from different sources and are usually classified as follows.

Gross Errors:

            This class of errors mainly covers human mistakes in reading instruments and recording and calculating the results.  The responsibility of the mistake normally lies with the experimenter.  Gross errors can be minimized or avoided.  Care should be taken while recording or reading the data.  Number of readings should be taken and a close agreement between readings assures that no errors has been committed.

Systematic errors:

            These types of errors are classified into three categories.

1. Instrumental errors
2. Environmental errors and
3. Observational errors.

Instrumental errors:

            There are many factors in the design and construction of instruments that limit the accuracy attainable.  Assembly errors (Because of bend or distorted pointers, non uniform division of the scale, or displaced scale that does not coincide with the actual zero position) come under this category of errors.  These types of errors does not alter with time, but it can be easily discovered and corrected.  Examples and causes of this types of errors are as follows.

• Improper selecting and poor maintenance of the instrument.
• Faults of construction resulting from finite width of knife edges.
• Mechanical friction and wear, backlash, yielding of supports, pen or pointer drag and hystersis of elastic members due to aging.
• Unavoidable physical phenomenon due to friction, capillary attraction and imperfect rarefaction.

Environmental errors:

            These types of errors are more dangerous as they change with time in an unpredictable manner.  The instrument would have been assembled and calibrated in one environment.  For measurement it would been carried to a different place and because of this change, error occurs.  The change may be due to different temperatures, pressures, humidity and altitude etc.  These errors can be eliminated or reduced by the following precautions mentioned.

• Using the instrument in controlled condition of pressure, temperature, in which it was assembled and calibrated.
• If this is not possible, then the deviations in local conditions from the calibrated value is measured and suitable correction to the instrument readings are applied.
• Automatic compensation using sophisticated devices is possible and is usually applied.
• Make a new calibrations based on the local conditions.

Observational errors:

            Even when the instruments are properly selected, carefully installed and calibrated, short coming in the measurement occur due to certain mistakes on the part of the observer.  These types of errors may be due to

• Parallax apparent displacement when the line of vision is not normal to the scale.
• Inaccurate estimates of average reading, lack of ability to interpolate properly between graduations.
• Non simultaneous observation of independent quantities.
• Personal bias - a tendency to read high or low, or anticipate a signal and read too soon.
• Wrong scale reading, and wrong recording of data.

            Modern instruments use digital systems that eliminate the possibilities of errors due to human observations.  These errors an be eliminated by careful training and by taking independent readings of each item by two or more observers.

Random errors:

            These vary in an unpredictable manners and it is very difficult to list out all the sources of errors since these errors remain even after the consideration of systematic errors these are also called as residual errors.  Following are the most common.

• Friction in the instruments movement.
• Mechanical vibration,
• Finite dimensions between scale and pointer
• Hysterysis in the elastic members
• Backslash in the movement

            The importance of these errors is that they cancel each others effect and ultimately may lead to correct values.  for example vibrations can be avoided by placing on shock absorbing mountings.

            Apart from there errors, there are other types and forms of errors.  A brief outlook of the other types of errors is as follows.  Translation and signal transmission errors caused due to the non capability of the instrument to follow rapid changes in the measured quantity due to inertial and hystersis effect.  The error may also result from unwanted disturbances such as noise, line pick up, hum ripple etc.  These errors are remedied by calibration and by monitoring the signal at one or more points along its transmission path.

            Operational errors are caused due to poor operation techniques.  A few examples are given below.

• A thermometer will not read accurately if the sensitive portion is insufficiently immersed or is radiating heat to colder portion of the installation.
• A pressure gauge will correctly indicate pressure only when it is exposed only to the pressure which is to be measured.
• A steam calorimeter will not give true indication of the dryness fraction of steam unless the sample drawn correctly represents the condition of the steam.

            Systematic errors are caused to the act of measurement.  As it affects the condition of the measurand and thus leading to uncertainties in the measurements, he examples of which are given below.

• Introduction of a thermometer alters the thermal capacity of the system and provides an extra path for heat leakage.
• A ruler pressed against a body results in a differential deformation of the body relative to the ruler.
• A obstruction type flow meter may partially block or disturb the flow condition.  Consequently the flow rate shown by the meter may not be same as before the meter installation.
• Reading shown by a hand tachometer would vary with the pressure with which it is pressed against a shaft.
• A milli-ammeter would introduce additional resistance in the circuit and thereby alter the flow current by a significant amount.

            Systematic errors cannot be determined by direct and repetitive observations of the measurand made each time with the same technique.  The only way to locate there errors is to have repeated measurements under different conditions or with different equipment and if possible by an entirely different method.