COURSE MATERIAL: Mechanical Measurement and Control PREPARED BY DR.B.B.CHOUDHURY, ASSOCIATE PROFESSOR, DEPT. OF MECHANICAL ENGG.

Transcription

1 COURSE MATERIAL: Mechanical Measurement and Control PREPARED BY DR.B.B.CHOUDHURY, ASSOCIATE PROFESSOR, DEPT. OF MECHANICAL ENGG., IGIT SRANG 7th Semester, B.Tech in Mechanical Engg. SUBJECT CODE : PCME bbchoudhury@igitsarang.ac.in

2 Measurement MODULE-I Measurement is the act or the result of a qualitative comparison between predefined standards and unknown magnitude. There are two basic requirements for the measurements such as: (i) The standard which is used for comparison must be accurately defined and commonly accepted. (ii) The procedure and apparatus employed for obtaining comparison must be produce. Functional elements of measuring system A generalized 'Measurement System' consists of the following: 1. Basic Functional Elements, and 2. Auxiliary Functional Elements. Basic Functional Elements are those that form the integral parts of all instruments. They are the following: (a) Transducer Element that senses and converts the desired input to a more convenient and practicable form to be handled by the measurement system. (b) Signal Conditioning or Intermediate Modifying Element for manipulating / processing the output of the transducer in a suitable form. (c) Data Presentation Element for giving the information about the measurand or measured variable in the quantitative form. Auxiliary Functional Elements are those which may be incorporated in a particular system depending on the type of requirement, the nature of measurement technique, etc. They are: (a) Calibration Element to provide a built-in calibration facility. (b) External Power Element to facilitate the working of one or more of the elements like the transducer element, the signal conditioning element, the data processing element or the feedback element. (c) Feedback Element to control the variation of the physical quantity that is being measured. In addition, feedback element is provided in the nullseeking potentiometric or Wheatstone bridge devices to make them automatic or self-balancing. (d) Microprocessor Element to facilitate the manipulation of data for the purpose of simplifying or accelerating the data interpretation. It is always used in 15 conjunctions with analog-to-digital converter which is incorporated in the signal conditioning element. Classifications of the measuring instruments Measuring instruments are classified based on their applications, mode of operation, manner of energy conversation, nature of output signal.

3 (i) Deflection and Null type instruments In a Deflection type system, the quantity to be measured produces an effect either in the form of a voltage or a current. This effect is then utilized to produce a torque that causes a mechanical deflection. With the help of a spring system, this torque is countered by a restoring torque that increases with the increase in deflection. When the torques involved achieves a state of equilibrium, the pointer comes to a standstill. Now by equating the torques involved in a mathematical equation, a relation can be obtained between the cause and the deflection in terms of device constants and thus the Instrument can be calibrated. A prime example of this type of system is the PMMC (Permanent Magnet Moving Coil) Instruments. In a Null type Instrument, the quantity to be measured produces an effect that is compared with an already calibrated effect of another system. It is achieved with the help of a sensitive galvanometer that shows a deflection for any amount of difference between the effect to be measured and the already calibrated effect. By manual or automatic control, the calibrated effect is varied until it becomes equal to the effect produced by the measuring instrument. When such a state is reached, the galvanometer shows no deflection at all and quantity is successfully measured. A prime example of this system is the Wheatstone bridge used for the measurement of electrical resistance. Figure:-A typical spring balance A deflection type weight measuring instrument Advantages of Null Types Instrument The following are the advantages of the null type instruments. 1. The accuracy of the null type instrument is high. This is because the opposing effect is measured with the help of the standards which have a high degree of accuracy. 2. The null type instrument is highly sensitive. In null type instrument, the balanced quantity is measured out. The detector has to cover a small range around the balanced point and hence it is highly sensitive. Also in null type instrument, the detector need not be measured it has only to detect the presence and direction of unbalance and not the magnitude of unbalance.

4 Note: Null type instrument requires many controls before null condition are obtained and hence it is not suitable for dynamic measurement. Because in dynamic measurement the quantity changes rapidly with the time. (ii) Manually operated and Automated type The instrument which requires the services of human operator is a manual instrument. The measurement of temperature by a resistance thermometer incorporating a Wheatstone bridge in its circuit is manual in operation as it needs an operator for obtaining the null position. The instrument becomes automatic when the human operator is replaced by an auxiliary device incorporated in the instrument. For example, the temperature measurements by mercury-in-glass thermometer are automatic as the instrument indicates the temperature without requiring any manual assistance. Automatic instruments are proffered because of their fast dynamic response and low operational cost. (a) Temperature Measurement Using Wheatstone Bridge (iii) Analog And Digital Instruments: - The signals of an analog unit vary in a continuous fashion and can take on infinite number values in a given range. Wrist watch, speedometer of an automobile, fuel gauge, ammeters and voltmeters are examples of analog instruments. Signals varying in discrete steps and taking on a finite number of different values in a given range are digital signals and the corresponding instruments are of digital type. for example, the timers on a scoreboard, the calibrated balance of a platform scale, and odometer of an automobile are digital instruments. The digital instruments convert a measured analog voltage into digital quantity which is displayed numerically, usually by neon indicator tubes. the output may either be a digit for every successive increment of the input or be a coded discrete signal representative of the numerical value of the input. the digital devices have the advantage of high accuracy high speed and the elimination of human operational errors. however, these instruments are unable to indicate the quantity which is a part of the step value of the instrument. the importance of the digital instrumentation is increasing very fast due to the applications of the digital computers for data handling, reduction and in automatic controls. apparently it becomes necessary to have both

5 analog-to-digital converters at input to the computers and digital-to-analog converters at the output of the computers. (iv) Dumb and Intelligent Types A dumb or conventional instrument is that in which the input variable is measured and displayed, but the data is processed by the observer. For example, a Bourdon pressure gauge is termed as a dumb instrument because though it can measure and display a car tyre pressure but the observer has to judge whether the car tyre air inflation pressure is sufficient or not. Currently, the advent of microprocessors has provided the means of incorporating Artificial Intelligence (AI) to a very large number of instruments. Intelligent or smart instruments process the data in conjunction with microprocessor (µp ) or an on-line digital computer to provide assistance in noise reduction, automatic calibration, drift correction, gain adjustments, etc. In addition, they are quite often equipped with diagnostic subroutines with suitable alarm generation in case of any type of malfunctioning. An intelligent or smart instrument may include some or all of the following: The output of the transducer in electrical form. The output of the transducer should be in digital form. Otherwise it has to be converted to the digital form by means of analog-to-digital converter (A-D converter). Interface with the digital computer. Software routines for noise reduction, error estimation, self-calibration, gain adjustment, etc. Software routines for the output driver for suitable digital display or to provide serial ASCII coded output. Measurement Terminologies 1. Accuracy:- The accuracy of a measurement relates to the closeness of agreement between the measured value provided by the measurement system and the true value of the measurand (the dimension being measured). The true value of a measurement parameter (Volts, Amps, Kg, etc) is determined by National Standards laboratories working under international agreement and is disseminated by an unbroken chain of calibration. 2. Resolution:- The smallest distinguishable increment provided by a measurement system whether digital or analogue systems are used. The resolution of a measurement system is by itself no indication of accuracy. 3. Precision:-

6 The precision of a measurement system relates to the closeness of agreement between measurements made of the same dimension. It is possible to have a measurement system, which is precise but not accurate. (a) Precise but not accurate (b) Accurate but not precise (c) Accurate and precise 4. Uncertainty:- This factor comprises two elements, the first being a systematic error; the second being due to random variation. Uncertainty is an indication of the degree to which the variation in values obtained when measuring can be reasonably attributed to the measured itself. Uncertainty is normally expressed ratiometrically (%, db, ppm, etc) or in the relevant engineering units (kn, mm, etc) with a minimum 95% confidence level. All errors affecting measurement uncertainty should be controlled by a documented measurement procedure.

7 5. Traceability The concept of establishing a valid calibration of a measuring instrument or measurement standard, by step-by-step comparison with better standards up to an accepted or specified standard. In general, the concept of traceability implies eventual reference to an appropriate national or international standard. 6. Sensitivity It should be noted that sensitivity is a term associated with the measuring equipment whereas accuracy & precision are association with measuring process. Sensitivity means the ability of a measuring device to detect small differences in a quantity being measured. For instance if a very small change in voltage applied to 2 voltmeters results in a perceptible change in the indication of one instrument and not in the other. Then the former (A0 is send to be more sensitive. Numerically it can be determined in this way for example if on a dial indicator the scale spacing is 1.0 mm and the scale division value is 0.01 mm then sensitivity =100. it is also called amplification factor or gearing ratio. It is possible that the more sensitive instrument may be subjected to drifts due to thermal and other effects so that its indications may be less repeatable than these of the instrument of lower sensitivity. 7. Readability Readability refers to the case with which the readings of a measuring instrument can be read. It is the susceptibility of a measuring device to have its indication converted into more meaningful number. Fine and widely spaced graduation lines ordinarily improve the readability. If the graduation lines are very finely spaced the scale will be more readable by using the microscope however with naked eye the readability will be poor. In order to make micrometer more readable they are provided with vernier scale. It can also be improve by using magnifying devices. 8. Repeatability It is the ability of the measuring instrument to repeat the same results when measurement are carried out By same observer With the same instrument Under the same conditions Without any change in location Without change in the method of measurement And the measurement is carried out in short interval of time. 9. Reproducibility Reproducibility is the consistency of pattern of variation in measurement i.e closeness of the agreement between the results of measurement of the same quantity when individual measurement are carried out By different observer By different methods

8 Using different instruments Under different condition, location and times. It may also be expressed quantitatively in terms of dispersion of the results. 10. Calibration The calibration of any measuring instrument is necessary for the sake of accruing of measurement process. It is the process of framing the scale of the instrument by applying some standard (known) signals calibration is a pre-measurement process generally carried out by manufactures. It is carried out by making adjustment such that the read out device produces zero output for zero measured input similarly it should display output equipment to the known measured input near the full scale input value. If accuracy is to be maintained the instrument must be checked and recalibration if necessary. As far as possible the calibration should be performed under similar environmental condition with the environment of actual measurement 11. Magnification Magnification means increasing the magnitude of output signal of measuring instrument many times to make it more readable. The degree of magnification should bear some relation to the accuracy of measurement desired and should not be larger than necessary. Generally the greater the magnification the smaller is the range of measurement. Errors in Measurement It is never possible to measure the true value of a dimension, there is always some error. The error in measurement is the difference between the measured value and the true value of the measured dimension. Error in measurement =Measured value - True value. The error in measurement may be expressed or evaluated either as an absolute error or as a relative error. Absolute Error True absolute error. It is the algebraic difference between the result of measurement and the conventional true value of the quantity measured. Apparent absolute error. If the series of measurement are made then the algebraic difference between one of the results of measurement and the arithmetical mean is known as apparent absolute error. Relative Error It is the quotient of the absolute error and the value of comparison used for calculation of that absolute error. This value of comparison may be the true value, the conventional true value or the arithmetic mean for series of measurement. The accuracy of measurement, and hence the error depends upon so many factors, such as:

9 - Calibration standard - Work piece - Instrument - Person - Environment etc. as already described. Types of Error During measurement several types of error may arise, these are 1. Static errors which includes - Reading errors - Characteristic errors - Environmental errors. 2. Instrument loading errors. 3. Dynamic errors. Static errors These errors result from the physical nature of the various components of measuring system. There are three basic sources of static errors. The static error divided by the measurement range (difference be the upper and lower limits of measurement) gives the measurement precision. Reading errors Reading errors apply exclusively to the read-out device. These do not have any direct relationship with other types of errors within the measuring system. Reading errors include: Parallax error, Interpolation error. Attempts have been made to reduce or eliminate reading errors by relatively simple techniques. For example, the use of mirror behind the readout pointer or indicator virtually eliminates occurrence of parallax error. Interpolation error. It is the reading error resulting from the inexact evaluation of the position of index with regards to two adjacent graduation marks between which the index is located. How accurately can a scale be read this depends upon the thickness of the graduation marks, the spacing of the scale division and the thickness of the pointer used to give the reading Interpolation error can be tackled by increasing; using magnifier over the scale in the vicinity of pointer or by using a digital read out system. Characteristic Errors It is defined as the deviation of the output of the measuring system from the theoretical predicted performance or from nominal performance specifications. Linearity errors, repeatability, hysteresis and resolution errors are part of characteristic errors if the theoretical output is a straight line. Calibration error is also included in characteristic error.

10 Loading Errors Loading errors results from the change in measurand itself when it is being measured, (i.e., after the measuring system or instrument is connected for measurement). Instrument loading error is the difference between the value of the measurand before and after the measuring system is connected/contacted for measurement. For example, soft or delicate components are subjected to deformation during measurement due to the contact pressure of the instrument and cause a loading error. The effect of instrument loading errors is unavoidable. Therefore, measuring system or instrument should be selected such that this sensing element will minimize instrument loading error in a particular measurement involved. Environmental Errors These errors result from the effect of surrounding such as temperature, pressure, humidity etc. on measuring system. External influences like magnetic or electric fields, nuclear radiations, vibrations or shocks etc. also lead to environmental errors. Environmental errors of each component of the measuring system make a separate contribution to the static error. It can be reduced by controlling the atmosphere according to the specific requirements. Dynamic Errors Dynamic error is the error caused by time variations in the measurand. It results from the inability of the system to respond faithfully to a time varying measurement. It is caused by inertia, damping, friction or other physical constraints in the sensing or readout or display system. For statistical study and the study of accumulation of errors, these errors can be broadly classified into two categories 1. Systematic or controllable errors, and 2. Random errors. Systematic Errors Systematic errors are regularly repetitive in nature. They are of constant and similar form. They result from improper conditions or procedures that are consistent in action. Out of the systematic errors all except the personal error varies from individual to individual depending on the personality of observer. Other systematic errors can be controlled in magnitude as well as in sense. If properly analyzed they can be determined and reduced. Hence, these are also called as controllable errors. Systematic errors include: 1. Calibration Errors. These are caused due to the variation in the calibrated scale from its normal value. The actual length of standards such as slip gauge and engraved scales will vary from the nominal value by a small amount. This will cause an error in measurement of constant magnitude. Sometimes the instrument inertia and hysteresis effect do not allow the instrument to transit the measurement accurately. Drop in voltage along the wires of an electric meter may include an error (called single transmission error) in measurement. 2. Ambient or Atmospheric conditions (Environmental Errors). Variation in atmospheric condition (i.e., temperature, pressure, and moisture content) at the place of measurement from that of internationally agreed standard values (20 temp. and 760 mm of Hg pressure) can give

11 rise to error in the measured size of the component. Instruments are calibrated at these standard conditions; therefore error may creep into the given result if the atmosphere conditions are different at the place of measurement. Out of these temperatures is the most significant factor which causes error in, measurement due to expansion or contraction of component being measured or of the instrument used for measurement. 3. Stylus Pressure. Another common source of error is the pressure with which the work piece is pressed while measuring. Though the pressure involved is generally small but this is sufficient enough to cause appreciable deformation of both the stylus and the work piece. In ideal case, the stylus should have simply touched the work piece. Besides the deformation effect the stylus pressure can bring deflection in the work piece also. Variations in force applied by the anvils of micrometer on the work to be measured results in the difference in its readings. In this case error is caused by the distortion of both micrometer frame and work-piece. 4. Avoidable Errors. These errors may occur due to parallax, non-alignment of work piece centers, improper location of measuring instruments such as placing a thermometer in sunlight while measuring temperature. The error due to misalignment is caused when the centre line of work piece is not normal to the centre line of the measuring instrument. 5. Random Errors. Random errors are non-consistent. They occur randomly and are accidental in nature. Such errors are inherent in the measuring system. It is difficult to eliminate such errors. Their specific cause, magnitudes and source cannot be determined from the knowledge of measuring system or conditions of measurement. The possible sources of such errors are: Small variations in the position of setting standard and work piece. Slight displacement of lever joints of measuring instruments. Operator error in scale reading. Fluctuations in the friction of measuring instrument etc. Characteristics of measurement systems The system characteristics are to be known, to choose an instrument that most suited to a particular measurement application. The performance characteristics may be broadly divided into two groups, namely static and 'dynamic' characteristics. Static characteristics:- The performance criteria for the measurement of quantities that remain constant, or vary only quite slowly. Dynamic characteristics:- The relationship between the system input and output when the measured quantity (measurand) is varying rapidly.

12 Static Performance Parameters (i) Accuracy Accuracy of a measuring system is defined as the closeness of the instrument output to the true value of the measured quantity (as per standards). For example, if a chemical balance reads 1 g with an error of IOˉ²g, the accuracy of the measurement would be specified as 1%. Accuracy of the instrument mainly depends on the inherent limitations of the instrument as well as on the shortcomings in the measurement process. In other words, the accuracy of an instrument depends on the various systematic errors involved in the measurement process. For example, the accuracy of a common laboratory micrometer depends on instrument errors like zero error, errors in the pitch of screw, anvil shape, etc. and in the measurement process errors are caused due to temperature variation effect, applied torque, etc. The accuracy of the instruments (which represents really its inaccuracy) can be specified in either of the following forms: (ii) Precision a) Percentage of true value= (Measured value - True value) 100 True Value b) Percentage of full scale deflection= (Measured value - True value) 100 Maximum scale value Precision is defined as the ability of the instrument to reproduce a certain set of readings within a given accuracy. Precision of an instrument is in fact, dependent on the repeatability. The term repeatability can be defined as the ability of the instrument to reproduce a group of measurements of the same measured quantity, made by the same observer, using the same instrument, under the same conditions. As mentioned before, the extent of random errors of alternatively the precision of a given set of measurements can be quantified by performing the statistical analysis. Accuracy Versus Precision It may be noted that accuracy represents the degree of correctness of the measured value with respect to the true value. On the other hand, precision represents degree of repeat- ability of several independent measurements of the desired input al the same reference conditions. As mentioned before, accuracy and precision involved in a measurement are dependent on the systematic and random errors, respectively.. To illustrate this statement we take the example of a person doing shooting practice on a target. He can hit the target with the following possibilities as shown in Fig. 2.2(b).

13 1. One possibility is that the person hits all the bullets on the target plate on the outer circle and misses the bull's eye (Fig. This is a case of high precision but poor accuracy. 2. Second possibility is that the bullets are placed as shown in Fig. 2.2(b). In this case, the bullet hits are placed symmetrically with respect to the bull's eye but are not spaced closely. Therefore, this is case of good average accuracy but poor precision. 3. A third possibility is that all the bullets hit the bull's eye and are also spaced closely (Fig.2.2(a)]. As is clear from the diagram, this is an ease of high accuracy and high precision. 4. Lastly, if the bullets hit the target plate in a random manner as shown in Fig. 2.2(d), then this is a case of poor precision as well as poor accuracy. Based on the above discussion, it may be stated that in any experiment the accuracy of the observations can be improved beyond the precision of the apparatus. (iii) Resolution It is defined as the smallest increment in the measured value that can be detected with certainty by the instrument. In other words, it is the degree of fineness with which a measurement can be made. The least count of any instrument is taken as the resolution of the instrument. For example, a ruler with a least count of I mm may be used to measure to the nearest 0.5 mm by interpolation. Therefore, its resolution is considered as 0.5 mm. A high resolution instrument is one that can detect smallest possible variation in the input. (iv) Threshold It is a particular case of resolution. It is defined as the minimum value of input below which no output can be detected. It is instructive to note that resolution refers to the smallest measurable input above the zero value. Both threshold and resolution can either be specified as absolute quantities in terms of input units or as percentage of full scale deflection. (v) Static Sensitivity Static sensitivity (also termed as scale factor or gain) of the instrument is determined from the results of static calibration. This static characteristic is defined as the ratio of the magnitude of response (output signal) to the magnitude of the quantity being measured (input signal), i.e.

14 Where q o and q i are the values of the output and input signals respectively. (vi) Linearity A linear indicating scale is one of the most desirable features of any instrument. Therefore, manufacturers of instruments always attempt to design their instruments so that the output is a linear function of the input. However, linearity is never completely achieved and the deviations from the ideal are termed as linearity error. (vii) Range and Span The range of the instrument is specified by the lower and upper limits in which it is designed to operate for measuring, indicating or recording the measured variable. The algebraic difference between the upper and lower range values is termed as the span of the instrument. The range of the instrument can either be unidirectional (e.g., C) or bidirectional (e.g., -10 to 100 C) or it can be expanded type (e.g., C) or zero suppressed (e.g., 5-40 C). (viii) Hysteresis It is defined as the magnitude of error caused in the output for a given value of input, when this value is approached from opposite directions, i.e. from ascending order and then descending order. Whenever, there is solid contact between dry surfaces, stiction (due to Coulomb's friction) comes into play. It is defined as the force or torque necessary to initiate the motion of the instrument. After stiction, dynamic friction comes into play and the output-input characteristics of the instrument takes the shape of a closed curve known as the hysteresis loop shown in [Fig. 2.3(a)]. Further the shape of this loop changes if hydrodynamic or Viscous friction is present in the instrument system. In this case, the magnitude of the frictional force depends on the magnitude of the rate of change of input. In other words, the greater the rate of change of input, greater is the deviations in the friction values in the hysteresis loop [Fig.2.3 (b)]. However, if the rate of change of input goes to zero, the magnitude of the viscous friction also approaches zero, i.e. for steady state inputs, there is no error caused due to viscous friction. However, it causes a lag that needs to be compensated.

15 Fig. 2.3 Typical output-input curves showing hysteresis effect Hysteresis effects are best eliminated by taking the observations both for ascending and descending values of input and then taking the arithmetic mean. For example, in Fig, 2.3(a) and (b), for a value of input qi, the output in ascending order is (qo)1 and in descending order is (qo)2. Then the mean value is: Selection and Specifications of Instruments The selection of any instrument out of those available depends on the performance characteristics of each instrument vis-á-vis its cost. In general, the selection procedure seeks to maximize the 'pay-off ratio' or the 'transfer function' of the investment which is the ratio: Value of useful information Necessary total cost The various considerations involved in the section of the instrument include the following from the 'value viewpoint. Instrument's qualities, value guided 1. Accuracy and precision characteristics including other specifications like sensitivity, linearity, hysteresis, zero and sensitivity drift, dead band, etc. 2. Nature and type of data available, i.e. whether analog, digital, continuous or sampled. 3. Nature and type of read out, i.e. whether indicating or recording type, etc. 4. Nature of further data computations, if required. 5. Signal-to-noise characteristics of the transducer and the system fidelity especially when extensive data transmission or translation is involved. 6. Dynamic response characteristics if input signal is time-dependent. 7. Susceptibility to environmental disturbances.

16 Convenience aspects, value judged 1. Suitability for the given application, i.e. whether for laboratory use, field use or both. 2. Adaptability to different sizes of inputs, i.e. scale expansion, range changes, etc. 3. Ease in calibration, when needed. 4. Simplicity and ease of instrument behavior diagnosis. 5. Material durability and non-fouling design. 6. Fool-proof assembly. 7. Maintenance, repair, local representation and steady delivery. 8. Ready self-indication or check determination in case of instrument malfunction. 9. Safety in use. 10. Proper shape, appealing appearance and necessary protective envelope. Costs, initial and cumulative total 1. Initial cost of instrument procurement, installation including the various attachments and accessories. 2. Maintenance, repair, recalibration, etc. 3. Running cost. 4. Expected life span considering the 'salvage' value of components which may be used in other similar Instruments as interchangeable modules. Dynamic Characteristics of Instruments The static characteristics of measuring instruments are concerned only with the steady-state reading that the instrument settles down to, such as accuracy of the reading. The dynamic characteristics of a measuring instrument describe its behavior between the time a measured quantity changes value and the time when the instrument output attains a steady value in response. In any linear, time-invariant measuring system, the following general relation can be written between input and output for time (t) > 0: Where qi is the measured quantity, qo is the output reading, and ao... an, bo... bm are constants. If we limit consideration to that of step changes in the measured quantity only, then the above equation reduces to: Further simplification can be made by taking certain special cases of Equation (2.2), which collectively apply to nearly all measurement systems.

17 Transducer Elements Normally, a transducer senses the desired input in one physical form and converts it to an output in another physical form. For example, the input variable to the transducer could be pressure, acceleration or temperature and the output of the transducer may be displacement, voltage or resistance change depending on the type of transducer element. Sometimes the dimensional units of the input and output signals may be same. In such cases, the functional element is termed a transformer. Characteristics of transducer element 1 The transducer element should recognize and sense the desired input signal and should be insensitive to other signals present simultaneously in the measurand. For example, a velocity transducer should sense the instantaneous velocity and should be insensitive to the local pressure or temperature. 2 It should not alter the event to be measured. 3 The output should preferably be electrical to obtain the advantages of modern computing and display devices. 4 It should have good accuracy. 5 It should have good reproducibility (i.e. precision). 6 It should have amplitude linearity. 7 It should have adequate frequency response (i.e., good dynamic response). 8 It should not induce phase distortions (i.e. should not induce time lag between the input and output transducer signals). 9 It should be able to withstand hostile environments without damage and should maintain the accuracy within acceptable limits. 10 It should have high signal level and low impedance. 11 It should be easily available, reasonably priced and compact in shape and size (preferably portable). 12 It should have good reliability and ruggedness. In other words, if a transducer gets dropped by chance, it should still be operative. 13 Leads of the transducer should be sturdy and not be easily pulled off. 14 The rating of the transducer should be sufficient and it should not break down. A transducer will have basically two main components. They are a. Sensing Element The physical quantity or its rate of change is sensed and responded to by this part of the transistor. b. Transduction Element The output of the sensing element is passed on to the transduction element. This element is responsible for converting the non-electrical signal into its proportional electrical signal. Classification of Transducers

18 Classification of transducers can be made on the basis of output which may be a continuous function of time or the output may be in discrete steps, so according to it:- 1. Analog transducers:- These transducers produce output that is continuous function of time. The Analog transducer changes the input quantity into a continuous function. The strain gauge, L.V.D.T, thermocouple, and thermistor are the examples of the analogue transducer. Figure- (a) LVDT, (b) Thermister As you can see from the above two examples that the characteristics of the output is analog in nature that's why they are called analog transducers. 2. Digital transducers:- These transducers convert the input quantity into an electrical output which is in the form of pulses. The digital signals work on high or low power. Example= Shaft encoder

19 Here you can see that that output is in the form of square pulses, hence it is called a digital transducer. 3. Electrical Transducer An electrical transducer is a device which is capable of converting the physical quantity into a proportional electrical quantity such as voltage or electric current. Hence it converts any quantity to be measured into usable electrical signal. This physical quantity which is to be measured can be pressure, level, temperature, displacement etc. The output which is obtained from the transducer is in the electrical form and is equivalent to the measured quantity. For example, a temperature transducer will convert temperature to an equivalent electrical potential. This output signal can be used to control the physical quantity or display it. Classification of Electrical Transducer: A sharp distinction among the types of transducers is difficult. The transducers may be classified according to their application, method of energy conversion, nature of the output signal and so on. All these classifications generally result in overlapping areas. In one way, the electrical transducers are classified as; (1) Active Transducers (2) Passive Transducers Active Transducers: It is also known as self-generating type transducers. They develop their own voltage or current as the output signal. The energy required for production fo this output signal is obtained from the physical phenomenon being measured. Examples of active transducers: Thermocouple, Piezoelectric transducers, Photovoltaic cell, Moving coil generator, Photoelectric cell. Passive Transducers: It is also called as externally powered transducers. They derive the power required for energy conversion from an external power source. The passive transducers are further classified into Resistive type, Inductive type and capacitive type. (i) Resistance: - Thermistor, Photoconductive cell, Resistance strain gauge (ii) Inductance: - LVDT- Linear Variable Differential Transformer (iii) Capacitance: - Photoemissive cell, Hall effect based devices. Apart from these classifications, some kinds of transducers are known as opto-electronic transducers. They use the principle of converting light energy into electrical energy. Some of the examples of opto-electronic transducers are photoconductive cell, photovoltaic cell, solar cell, photomultiplier tube and photomultiplier. LVDT (Linear Variable Differential Transformer)

20 used to measure linear displacement The LVDT has 3 coils-one primary and two secondary, insulated tube and an armature The armature is basically a ferromagnetic core such as iron An AC voltage is applied to the primary coil The two secondary coils are connected in opposite the output voltage is the difference of the individual voltages of the secondary coils When the core is at the centre both the secondary coils produces equal and opposite voltage Hence the output voltage(vout) is zero When the core moves in left or right direction the output voltage of one secondary coil decreases and the output voltage from the other secondary coil increases The output voltage is proportional to the distance travelled by the armature This output voltage is used to determine the displacement Advantages of LVDT

21 Non-contact-There is no contact between the armature and the primary or secondary coils. Hence there is no friction and wear. Accurate Can be totally sealed and can be made to work in harsh conditions Less sensitive to vibrations Disadvantages of LVDT Internally non-contact but externally has to be connected where the measurement has to be made Not feasible for very long range measurements Some of the applications of LVDT Linear displacement measurement Position sensing 4. Variable inductance transducers Variable inductance transducers use the inductive effect in its operation. Various physical causes like- pressure, displacement, force, sound etc often transform and change the materials self inductance [L] or mutual inductance [M]. Inductance are handy with formula Here µ is permeability, Φ is flux, S is cross section area where flux is established, l is length of concerned part and I is current in coil. They can be briefly categorized into four classes: Magnetic Circuit Transducer. o Principle of operation: L and M of ac excited coil is varied by changes in magnetic circuits [or flux]. o Typical Applications: Measurement of pressure, displacement. Reluctance pick up. o Principle of operation: Reluctance, R is cvaried by changing the position of iron core of coil. o Typical Applications: Measurement of pressure, displacement, vibrations, positions. Differential Transformer [popularly known as LVDT]. o Principle of operation: Differential voltage of two secondary windings is varied by positioning the magnetic core through externally applied force. o Typical Applications: Measurement of pressure, displacement, positions. Magnetostriction gauge.

22 o o Principle of operation: Magnetic properties are varied by pressure and stress. Typical Applications: Measurement of pressure, sound. 5. Capacitive Transducer Figure: Simple self inductance arrangements The capacitive transducer is used for measuring the displacement, pressure and other physical quantities. It is a passive transducer that means it requires external power for operation. The capacitive transducer works on the principle of variable capacitances. The capacitance of the capacitive transducer changes because of many reasons like overlapping of plates, change in distance between the plates and dielectric constant. The capacitive transducer contains two parallel metal plates. These plates are separated by the dielectric medium which is either air, material, gas or liquid. In the normal capacitor the distance between the plates are fixed, but in capacitive transducer the distance between them are varied. The capacitive transducer uses the electrical quantity of capacitance for converting the mechanical movement into an electrical signal. The input quantity causes the change of the capacitance which is directly measured by the capacitive transducer. The capacitors measure both the static and dynamic changes. The displacement is also measured directly by connecting the measurable devices to the movable plate of the capacitor. It works on with both the contacting and non-contacting modes. Principle of Operation The equations below express the capacitance between the plates of a capacitor Where, A overlapping area of plates in m 2 d Distance between two plates in meter ε Permittivity of the medium in F/m ε r relative permittivity ε 0 the permittivity of free space The schematic diagram of a parallel plate capacitive transducer is shown in the figure below.

23 The change in capacitance occurs because of the physicals variables like displacement, force, pressure, etc. The capacitance of the transducer also changes by the variation in their dielectric constant which is usually because of the measurement of liquid or gas level. The capacitance of the transducer is measured with the bridge circuit. The output impedance of transducer is given as Where, C capacitance f Frequency of excitation in Hz. The capacitive transducer is mainly used for measurement of linear displacement. The capacitive transducer uses the following three effects. 1. Variation in capacitance of transducer is because of the overlapping of capacitor plates. 2. The change in capacitance is because of the change in distances between the plates. 3. The capacitance changes because of dielectric constant. Advantage of Capacitive Transducer The following are the major advantages of capacitive transducers. 1. It requires an external force for operation and hence very useful for small systems. 2. The capacitive transducer is very sensitive. 3. It gives good frequency response because of which it is used for the dynamic study. 4. The transducer has high input impedance hence they have a small loading effect. 5. It requires small output power for operation. Disadvantages of capacitive Transducer The main disadvantages of the transducer are as follows. 1. The metallic parts of the transducers require insulation. 2. The frame of the capacitor requires earthing for reducing the effect of the stray magnetic field. 3. Sometimes the transducer shows the nonlinear behaviours because of the edge effect which is controlled by using the guard ring. 4. The cable connecting across the transducer causes an error.

24 Uses of Capacitive Transducer The following are the uses of capacitive transducer. 1. The capacitive transducer uses for measurement of both the linear and angular displacement. It is extremely sensitive and used for the measurement of very small distance. 2. It is used for the measurement of the force and pressures. The force or pressure, which is to be measured is first converted into a displacement, and then the displacement changes the capacitances of the transducer. 3. It is used as a pressure transducer in some cases, where the dielectric constant of the transducer changes with the pressure. 4. The humidity in gases is measured through the capacitive transducer. 5. The transducer uses the mechanical modifier for measuring the volume, density, weight etc. 6. Piezoelectric Effect Basics of Piezoelectric Effect A piezoelectric substance is one that produces an electric charge when a mechanical stress is applied (the substance is squeezed or stretched). Conversely, a mechanical deformation (the substance shrinks or expands) is produced when an electric field is applied. This effect is formed in crystals that have no center of symmetry. To explain this, we have to look at the individual molecules that make up the crystal. Each molecule has a polarization, one end is more negatively charged and the other end is positively charged, and is called a dipole. This is a result of the atoms that make up the molecule and the way the molecules are shaped. The polar axis is an imaginary line that runs through the center of both charges on the molecule. In a monocrystal the polar axes of all of the dipoles lie in one direction. The crystal is said to be symmetrical because if you were to cut the crystal at any point, the resultant polar axes of the two pieces would lie in the same direction as the original. In a polycrystal, there are different regions within the material that have a different polar axis. It is asymmetrical because there is no point at which the crystal could be cut that would leave the two remaining pieces with the same resultant polar axis. Figure 1 illustrates this concept. In order to produce the piezoelectric effect, the polycrystal is heated under the application of a strong electric field. The heat allows the molecules to move more freely and the electric field forces all of the dipoles in the crystal to line up and face in nearly the same direction (Figure 2).

25 The piezoelectric effect can now be observed in the crystal. Figure 3 illustrates the piezoelectric effect. Figure 3a shows the piezoelectric material without a stress or charge. If the material is compressed, then a voltage of the same polarity as the poling voltage will appear between the electrodes (b). If stretched, a voltage of opposite polarity will appear (c). Conversely, if a voltage is applied the material will deform. A voltage with the opposite polarity as the poling voltage will cause the material to expand, (d), and a voltage with the same polarity will cause the material to compress (e). If an AC signal is applied then the material will vibrate at the same frequency as the signal (f). Using the Piezoelectric Effect The piezoelectric crystal bends in different ways at different frequencies. This bending is called the vibration mode. The crystal can be made into various shapes to achieve different vibration modes. To realize small, cost effective, and high performance products, several modes have been developed to operate over several frequency ranges. These modes allow us to make products working in the low khz range up to the MHz range. Figure 4 shows the vibration modes and the frequencies over which they can work. An important group of piezoelectric materials are ceramics. Murata utilizes these various vibration modes and ceramics to make many useful products, such as ceramic resonators, ceramic band pass filters, ceramic discriminators, ceramic traps, SAW filters, and buzzers. 7. Photoelectric Transducers: A photoelectric transducer converts a light beam into a usable electric signal. As shown in the fig, light strikes the photo emissive cathode and releases electrons, which are attracted towards the anode, thereby producing an electric current in the circuit. The cathode & the anode are

26 enclosed in a glass or quartz envelope, which is either evacuated or filled with an inert gas. The photo electric sensitivity is given by; I=s*f where I=Photoelectric current, s=sensitivity, f= illumination of the cathode. The response of the photoelectric tube to different wavelengths is influenced by (i) The transmission characteristics of the glass tube envelope and (ii) Photo emissive characteristics of the cathode material. Photoelectric tubes are useful for counting purposes through periodic interruption of a light source. Signal Conditioning Element The output of the transducer element is usually too small to operate an indicator or a recorder. Therefore, it is suitably processed and modified in the signal conditioning element so as to obtain the output in the desired form. The transducer signal is fed to the signal conditioning element by mechanical linkages (levers, gears, etc.), electrical cables, fluid transmission through liquids or through pneumatic transmission using air. For remote transmission purposes, special devices like radio links or telemetry systems may be employed. The signal conditioning operations that are carried out on the transduced information may be one or more of the following: Amplification The term amplification means increasing the amplitude of the signal without affecting its waveform. The reverse phenomenon is termed attenuation, i.e. reduction of the signal amplitude while retaining its original waveform. In general, the output of the transducer needs to be amplified in order to operate an indicator or a recorder. Therefore, a suitable amplifying element is incorporated in the signal conditioning element which may be one of the following depending on the type of transducer signal. Mechanical Amplifying Hydraulic/Pneumatic Amplifying Optical Amplifying Electrical Amplifying Mechanical Amplifying Elements such as levers, gears or a combination of the two, designed to have a multiplying effect on the input transducer signal.

27 Hydraulic/Pneumatic Amplifying Elements employing various types of valves or constrictions, such as venturimeter / orificemeter, to get significant variation in pressure with small variation in the input parameters. Optical Amplifying Elements in which lenses, mirrors and combinations of lenses and mirrors or lamp and scale arrangement are employed to convert the small input displacement into an output of sizeable magnitude for a convenient display of the same. Electrical Amplifying Elements employing transistor circuits, integrated circuits, etc. for boosting the amplitude of the transducer signal. In such amplifiers we have either of the following: Signal filtration The term signal filtration means the removal of unwanted noise signals that tend to obscure the transducer signal. The signal filtration element could be any of the following depending on the type of situation, nature of signal, etc. 1. Mechanical Filters that consist of mechanical elements to protect the transducer element from various interfering extraneous signals. For example, the reference junction of a thermocouple is kept in a thermos flask containing ice. This protects the system from the ambient temperature changes. 2. Pneumatic Filters consisting of a small orifice or venturi to filter out fluctuations in a pressure signal. 3. Electrical Filters are employed to get rid of stray pick-ups due to electrical and magnetic fields. They may be simple R-C circuits or any other suitable electrical filters compatible with the transduced signal. Other signal conditioning operators Other signal conditioning operators that can be conveniently employed for electrical signals are 1. Signal Compensation / Signal Linearization. 2. Differentiation / Integration. 3. Analog-to-Digital Conversion. 4. Signal Averaging / Signal Sampling, etc. A-D Conversion An analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into

28 a digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an input analog voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities. Applications Music recording Analog-to-digital converters are integral to 2000s era music reproduction technology and digital audio workstation-based sound recording. People often produce music on computers using an analog recording and therefore need analog-to-digital converters to create the pulse-code modulation (PCM) data streams that go onto compact discs and digital music files. The current crop of analog-to-digital converters utilized in music can sample at rates up to 192 kilohertz. Considerable literature exists on these matters, but commercial considerations often play a significant role. Many recording studios record in 24-bit/96 khz (or higher) pulse-code modulation (PCM) or Direct Stream Digital (DSD) formats, and then downsample or decimate the signal for Compact Disc Digital Audio production (44.1 khz) or to 48 khz for commonly used radio and television broadcast applications. Digital signal processing ADCs are required to process, store, or transport virtually any analog signal in digital form. TV tuner cards, for example, use fast video analog-to-digital converters. Slow on-chip 8, 10, 12, or 16 bit analog-to-digital converters are common in microcontrollers. Digital storage oscilloscopes need very fast analog-to-digital converters, also crucial for software defined radio and their new applications. Scientific instruments Digital imaging systems commonly use analog-to-digital converters in digitizing pixels. Some radar systems commonly use analog-to-digital converters to convert signal strength to digital values for subsequent signal processing. Many other in situ and remote sensing systems commonly use analogous technology. The number of binary bits in the resulting digitized numeric values reflects the resolution, the number of unique discrete levels of quantization (signal processing). The correspondence between the analog signal and the digital signal depends on the quantization error. The quantization process must occur at an adequate speed, a constraint that may limit the resolution of the digital signal. Many sensors in scientific instruments produce an analog signal; temperature, pressure, ph, light intensity etc. All these signals can be amplified and fed to an ADC to produce a digital number proportional to the input signal. Rotary encoder Some non-electronic or only partially electronic devices, such as rotary encoders, can also be considered ADCs. Typically the digital output of an ADC will be a complement binary number that is proportional to the input. An encoder might output a Gray code.

29 D-A converter Digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function. There are several DAC architectures; the suitability of a DAC for a particular application is determined by figures of merit including: resolution, maximum sampling frequency and others. Digital-to-analog conversion can degrade a signal, so a DAC should be specified that has insignificant errors in terms of the application. DACs are commonly used in music players to convert digital data streams into analog audio signals. They are also used in televisions and mobile phones to convert digital video data into analog video signals which connect to the screen drivers to display monochrome or color images. These two applications use DACs at opposite ends of the frequency/resolution trade-off. The audio DAC is a low-frequency, high-resolution type while the video DAC is a high-frequency low- to medium-resolution type. Due to the complexity and the need for precisely matched components, all but the most specialized DACs are implemented as integrated circuits (ICs). Discrete DACs would typically be extremely high speed low resolution power hungry types, as used in military radar systems. Very high speed test equipment, especially sampling oscilloscopes, may also use discrete DACs. Applications Audio Most modern audio signals are stored in digital form (for example MP3s and CDs) and in order to be heard through speakers they must be converted into an analog signal. DACs are therefore found in CD players, digital music players, and PC sound cards. Video Video sampling tends to work on a completely different scale altogether thanks to the highly nonlinear response both of cathode ray tubes (for which the vast majority of digital video foundation work was targeted) and the human eye, using a "gamma curve" to provide an appearance of evenly distributed brightness steps across the display's full dynamic range - hence the need to use RAMDACs in computer video applications with deep enough colour resolution to make engineering a hardcoded value into the DAC for each output level of each channel impractical (e.g. an Atari ST or Sega Genesis would require 24 such values; a 24-bit video card would need ). Given this inherent distortion, it is not unusual for a television or video projector to truthfully claim a linear contrast ratio (difference between darkest and brightest output levels) of 1000:1 or greater, equivalent to 10 bits of audio precision even though it may only accept signals with 8-bit precision and use an LCD panel that only represents 6 or 7 bits per channel. Mechanical A one-bit mechanical actuator assumes two positions: one when on, another when off. The motion of several one-bit actuators can be combined and weighted with a whiffletree mechanism to produce finer steps. The IBM Selectric typewriter uses such as system. When a typewriter key is pressed, it moves a metal bar (interposer) down that has several lugs. The lugs are the information bits. When a key is pressed, its interposer is moved by the motor. If a lug is present

30 at one position, it will move the corresponding selector bail (bar); if the lug is not present, the selector bail stays where it is. The discrete motions of the bails are combined by a whiffle tree, and the output controls the rotation and tilt of the Selectric's typeball. IBM Selectric typewriter uses a mechanical digital-to-analog converter to control its typeball. Simple Current Sensitive Circuits Current sensing devices are often desired in the power supply lines of various circuits, such as battery-powered computers, battery chargers or critical circuits requiring thermal forecasting. Figure 1 shows a simple current sensing circuit that operates over a wide supply range. The circuit uses a micropower LT1494 op amp for its rail-to-rail input and output and ultralow supply current. It requires only 1.5uA supply current, which provides excellent precision for current sensing devices. Circuit operation is straightforward. The current through the sense resistor (RSENSE) creates a voltage across it, which is then imposed across RA by the op amp. The current through RA a flows into the op amp's output and out of the negative supply pin. This acts as a current source through RB, creating VOUT. (VOUT = IL(RB/RA)RS). Rail-to-rail operation is required because the inputs and output operate very near the upper rail when IL is small. The ultra low supply current makes IS very close to zero amps with an output offset of about 1uA. The supply current IS is virtually proportional to the output current. This yields excellent linearity, as shown in Figure 2. The circuit will operate as long as VOUT is below (VS V); that is to say, the output will clip at (VS V). Figure- Simple Current Sensitive Circuits

31 Potentiometer Measure linear and angular position Measure velocity and acceleration Resolution a function of the wire construction Resistive potentiometers are one of the most widely used forms of position sensor Can be angular or linear Consists of a length of resistive material with a sliding contact onto the resistive track When used as a position transducer a potential is placed across the two end terminals, the voltage on the sliding contact is then proportional to its position It is an inexpensive and easy to use sensor Resistance Bridges A resistance bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. The primary benefit of the circuit is its ability to provide extremely accurate measurements (in contrast with something like a simple voltage divider). Its operation is similar to the original potentiometer. The Wheatstone bridge was invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in One of the Wheatstone bridge's initial uses was for the purpose of soils analysis and comparison.

32 In the figure, Rx is the unknown resistance to be measured; R 1, R 2 and R 3 are resistors of known resistance and the resistance of R 2 is adjustable. The resistance is adjusted until the bridge is "balanced" and no current flows through the galvanometer Vg. At this point, the voltage between the two midpoints (B and D) will be zero. Therefore the ratio of the two resistances in the known leg (R 2 /R 1 ) is equal to the ratio of the two in the unknown leg (Rx/R 3 ). If the bridge is unbalanced, the direction of the current indicates whether R 2 is too high or too low. At the point of balance, Detecting zero current with a galvanometer can be done to extremely high precision. Therefore, if R 1, R 2 and R 3 are known to high precision, then Rx can be measured to high precision. Very small changes in Rx disrupt the balance and are readily detected. Alternatively, if R 1, R 2 and R 3 are known, but R 2 is not adjustable, the voltage difference across or current flow through the meter can be used to calculate the value of Rx using Kirchhoff's circuit laws. This setup is frequently used in strain gauge and resistance thermometer measurements, as it is usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage. Indicating, Recording and Display Elements Cathode Ray Oscilloscope (CRO) As an indicating element, a CRO is widely used in practice. It is essentially a high input impedance voltage measuring device, capable of indicating voltage signals from the intermediate elements as a function of time. Figure- CRO

33 The figure shows the block diagram of a cathode ray oscilloscope. Electrons are released from the cathode and accelerated towards the screen by the positively charged anode. The position of the spot on the phosphorescent screen is controlled by voltages applied to the vertical and horizontal plates. The impingement of the electron beam on the screen results in emission of light and thus the signal becomes visible. The following are the essential components in a CRO: 1. Display device, viz. the tube, 2. Vertical amplifier, 3. Horizontal amplifier, 4. Time base, 5. Trigger or synchronizing circuit, to start each sweep at a desired time, for display of signal 6. Power supplies and internal circuits. Galvanometric Recorders These are based on the simple principle of rotation of a coil through which current due to the input signal to be recorded, flows while the coil is in a magnetic field, as shown in Figure below. An ink pen attachment to the coil can be used to trace the signal on a paper wrapped around a rotating drum. The system acts like a second order instrument and the frequency response is limited to 200 Hz or so, due to the inertia effects of the pen and the coil.

34 Magnetic Tape Recorders A magnetic tape recorder has been used increasingly for recording data. The magnetic tape is made of a thin plastic material, coated with oxide particles, which become magnetized when the tape passes across a magnetizing head which acts due to an input signal. The signal is recovered from the tape by a reproduce head. There are several types of magnetic recording systems, viz. direct recording, frequency modulated (FM), pulse duration modulation (PDM) and digital recording systems. Figure (a) shows the block diagram of a direct recording system and Fig. (b) a typical magnetic head. Digital Recorder Of Memory Type Figure Magnetic Recording System. Another development in digital recording is to replace the magnetic tape with a large semiconductor memory, as shown in Figure below. Figure -Digital waveform recorder with memory

35 MODULE-II Strain Measurement Strain is the amount of deformation of a body due to an applied force More specifically, strain (e) is defined as the fractional change in length Strain can be positive (tensile) or negative (compressive) While there are several methods of measuring strain but the most common is with a strain gauge It is a device whose electrical resistance varies in proportion to the amount of strain in the device Strain-gauged element It is a device used to measure the strain of an object. The electrical resistance strain gauge consists of Metal wire, Metal foil strip, Strip of semiconductor material. Glue used =Cyano acrylic glue, Epoxy glue The gauge is attached to the object by a suitable adhesive As the object is deformed, the foil is deformed, causing its electrical resistance to change. This resistance change, usually measured using a Wheatstone bridge, is related to the strain by the quantity known as the gauge factor

36 Used for both short term and long term use Preparation of surface of strain gauge is important Utilized mainly in pressure sensors It is Made from silicon, metal film, thick film, and bonded foil It is Attached to flexible elements in the form of Cantilevers, Rings, U-shapes Generally the Flexible element can be bent or deformed Results forces being applied by contact point being displaced Strain gauges strained and so give a resistance change which can be monitored Problems associated with strain gauges Temperature sensitive Semiconductor gauges have much greater temperature sensitivity than metal strain gauges Have a non-linearity error ±1% of full range Pressure Measurement Pressure means force per unit area, exerted by a fluid on the surface of the container. Pressure measurements are one of the most important measurements made in industry especially in continuous process industries such as chemical processing, food and manufacturing. The principles used in measurement of pressure are also applied in the measurement of temperature, flow and liquid level. Pressure is represented as force per unit area. Fluid pressure is on account of exchange of momentum between the molecules of the fluid and a container wall. Static and Dynamic Pressures When a fluid is in equilibrium, the pressure at a point is identical in all directions and is independent of orientation. This is called static pressure. However, when pressure gradients occur within a continuum (field) of pressure, the attempt to restore equilibrium results in fluid flow from regions of higher pressure to regions of lower pressure. In this case the pressures are no longer independent of direction and are called dynamic pressures. Absolute pressure Absolute pressure means the fluid pressure above the reference value of a perfect vacuum or the absolute zero pressure. Gauge pressure It represents the difference between the absolute pressure and the local atmospheric pressure.

37 Vacuum Vacuum on the other hand, represents the amount by which atmospheric pressure exceeds the absolute pressure. Pressure Transducer A pressure transducer is used to convert a certain value of pressure into its corresponding mechanical or electrical output. Measurement if pressure is of considerable importance in process industries. Types The types of pressure sensors are differentiated according to the amount of differential pressure they are able to measure. For low differential pressure measurement Liquid Column Manometers are used. Elastic type pressure gauges are also used for pressure measurement up to 700 MPa. Some of the common elastic/mechanical types are: Bourdon Tubes Diaphragm Piston Type Pressure Transducer Bellows Elastic diaphragms When an elastic transducer (diaphragm is this case) is subjected to a pressure, it deflects. This deflection is proportional to the applied pressure when calibrated. A diaphragm pressure transducer is used for low pressure measurement. They are commercially available in two types metallic and non-metallic. Metallic diaphragms are known to have good spring characteristics and non-metallic types have no elastic characteristics. Thus, non-metallic types are used rarely, and are usually opposed by a calibrated coil spring or any other elastic type gauge. The non-metallic types are also called slack diaphragm. Working The diagram of a diaphragm pressure gauge is shown below. When a force acts against a thin stretched diaphragm, it causes a deflection of the diaphragm with its centre deflecting the most.

38 Since the elastic limit has to be maintained, the deflection of the diaphragm must be kept in a restricted manner. This can be done by cascading many diaphragm capsules as shown in the figure below. A main capsule is designed by joining two diaphragms at the periphery. A pressure inlet line is provided at the central position. When the pressure enters the capsule, the deflection will be the sum of deflections of all the individual capsules. As shown in figure (3), corrugated diaphragms are also used instead of the conventional ones. Applications of Elastic diaphragm gauges: They are used to measure medium pressure. But they can also be used to measure low pressures including vacuum. They are used to measure draft in chimneys of boilers. Advantages of Elastic diaphragm gauges: Best advantage is they cost less They have a linear scale for a wide range They can withstand over pressure and hence they are safe to be used. No permanent zero shift. They can measure both absolute and gauge pressure, that is, differential pressure. Limitations of Elastic diaphragm gauges: Shocks and vibrations affect their performance and hence they are to be protected. When used for high pressure measurement, the diaphragm gets damaged. These gauges are difficult to be repaired. Strain gauge pressure cells Basic Principle: When a closed container is subjected to the appilied pressure, it is strained (that is, its dimension changes). Measurement of this strain with a secondary transducer like a strain gauge ( metallic conductor) becomes a measure of the applied pressure.

39 That is, if strain gauges are attached to the container subjected to the applied pressure, the strain guages also will change in dimension depending on the expansion or contraction of the container. The change in dimension of the strain guage will make its resistance to change. This change in resistance of the strain gauge becomes a measure of pressure appilied to the container (elastic container or cell). There are two types of strain gauge pressure cells namely: 1. Flattened tube pressure cell. 2. Cylindrical type pressure cell. Flattened tube pressure cell. The main parts of the arrangement are as follows: An elastic tube which is flat and pinched at its two end as shown in diagram. Two strain gauges are placed on this elastic tube: one is on the top and other is at the bottom of this elastic tube. One end of the elastic tube is open to receive the applied pressure and its other end is closed. Operation: The pressure to be measured is applied to the open of the tube. Due to pressure, the tube tends to round off, that is, the dimension changes (strained). As the strain gauges are mounted on the tube, the dimensions of the strain gauges also change proportional to the change in dimension of the tube, causing a resistance change of the strain gauges. The change in dimension of the tube is proportional to the applied pressure. Hence the measurement of the resistance change of the strain gauges becomes a measure of the applied pressure when calibrated. Cylindrical Type pressure cells: The main parts of this arrangement are as follows: A cylindrical tube with hexagonal step at its centre. This hexagonal step helps fixing this device on to place where the pressure is to be measured. The bottom portion of this cylindrical tube is threaded at its external and is open to receive the pressure to be measured. The top portion of this cylindrical tube is closed and has a cap screwed to it. On the periphery of the top portion of the cylindrical tube are placed two sensing resistance strain gauges. On the cap (unstrained location) are placed two temperature compensating strain gauges. Operation The pressure to be measured is applied to the open end of the cylindrical tube. Due to the pressure, the cylindrical tube is strained, that is its dimension changes. As the strain gauges are mounted on the cylindrical tube, the dimension of the sensing strain gauges also change proportional to the change in dimension of the cylindrical tube, causing a resistance changes of the strain gauges. The change in dimension of the cylindrical tube is proportional to applied pressure. Hence the measurement of the resistance change of the sensing strain gauges becomes a measure of the applied pressure when calibrated.

40 Applications of the strain gauge pressure cells The flattened tube pressure cell is used for low pressure measurement. The cylindrical type pressure cell is used for medium and high pressure measurement. Measurement of Fluid Flow Types of Fluid Flow Fluid flows are classified in several ways as indicated below: Steady Flow i. Steady flow and Unsteady flow. ii. Uniform flow and Non-uniform flow. iii. One-dimensional flow, two dimensional flow and three dimensional flow. iv. Rotational flow and Irrotational flow v. Laminar flow and Turbulent flow. Fluid flow is said to be steady if at any point in the flowing fluid various characteristics such as velocity, pressure, density, temperature etc., which describe the behavior of the fluid in motion, do not change with time. The various characteristics of the fluid in motion are independent of time. Unsteady Flow Fluid flow is said to be unsteady if at any point in the flowing fluid any one or all the characteristics which describe the behavior of the fluid in motion change with time. Thus a flow of fluid is unsteady, if at any point in the flowing fluid. Non-uniform Flow If the velocity of flow of fluid changes from point to point in the flowing fluid at any instant, the flow is said to be non-uniform. In the mathematical form a non-uniform flow may be expressed as: One-dimensional, Two-dimensional and Three-dimensional Flows The various characteristics of flowing fluid such as velocity, pressure, density, temperature etc, are in general the functions of space and time i.e., these may vary with the coordinates of any point x, y and z and time t. Such a flow is known as a three-dimensional flow. If any of these characteristics of flowing fluid does not vary with respect to time, then it will be a steady three dimensional flow. When the various characteristics of flowing fluid are the functions of only any two of the three coordinate directions, and time t, i.e., these may not vary in anyone of the directions, then the flow is known as two-dimensional flow. For example, if the characteristics of flowing fluid do

41 not vary in the coordinate direction Z, then it will be a two-dimensional flow having flow conditions identical in the various planes perpendicular to the Z-axis. When the various characteristics of flowing fluid are the functions of only one of the three coordinate directions and time t, i.e., these may vary only in one direction, then the flow is known as one dimensional flow. Similarly, it will be a steady one dimensional flow if the characteristics of flowing fluid do not vary with respect to time. Rotational Flow A flow is said to be rotational if the fluid particles while moving in the direction of flow rotate about their mass centres. The liquid in the rotating tanks illustrates rotational flow where the velocity of each particle varies directly as the distance from the centre of rotation. Irrotational Flow A flow is said to be irrotational if the fluid particles while moving in the direction of flow do not rotate about their mass centers. Laminar Flow A flow is said to be laminar when the various fluid particles move in layers (or laminae) with one layer of fluid sliding smoothly over an adjacent layer. Turbulent flow A fluid motion is said to be turbulent when the fluid particles move in an entirely haphazard or disorderly manner that results in a rapid and continuous mixing of the fluid leading to momentum transfer as flow occurs. Methods of flow measurement Obstruction type flow meter Obstruction or head type flow meters are of two types: differential pressure type and variable area type. Orifice meter, Venturimeter, Pitot tube fall under the first category, while rotameter is of the second category. In all the cases, an obstruction is created in the flow passage and the pressure drop across the obstruction is related with the flow rate. 1. Orifice meter Depending on the type of obstruction, we can have different types of flow meters. Most common among them is the orifice type flow meter, where an orifice plate is placed in the pipe line, as shown in figure. If d 1 and d 2 are the diameters of the pipe line and the orifice opening, then the flow rate can be obtained by measuring the pressure difference (p 1 -p 2 ).

42 Figure Orifice meter In general, the mass flow rate q m measured in kg/s across an orifice can be described as where: C d = coefficient of discharge, dimensionless, typically between 0.6 and 0.85, depending on the orifice geometry and tappings β= diameter ratio of orifice diameter dto pipe diameter D, dimensionless ϵ= expansibility factor, 1 for incompressible gases and most liquids, and decreasing with pressure ratio across the orifice, dimensionless d= internal orifice diameter under operating conditions, m ρ 1 = fluid density in plane of upstream tapping, kg/m³ = differential pressure measured across the orifice, Pa 2. Venturi Meter Venturi meters are flow measurement instruments which use a converging section of pipe to give an increase in the flow velocity and a corresponding pressure drop from which the flowrate can be deduced. They have been in common use for many years, especially in the water supply industry. Principle of Venturi meter The working of venture meter is based on the principle of Bernoulli s equation.

43 Bernoulli s Statement: It states that in a steady, ideal flow of an incompressible fluid, the total energy at any point of the fluid is constant. The total energy consists of pressure energy, kinetic energy and potential energy or datum energy. Mathematically Here all the energies are taken per unit weight of the fluid. The Bernoulli s equation for the fluid passing through the section 1 and 2 are given by Construction It has three main parts: 1. Short converging part: It is a tapered portion whose radius decreases as we move forward. 2. Throat: It is middle portion of the venturi. Here the velocity of the fluid increases and pressure decreases. It possesses the least cross section area. 3. Diverging part: In this portion the fluid diverges. Working The venturimeter is used to measure the rate of flow of a fluid flowing through the pipes. Lets understand how it does this measurement step by step. Here we have considered two cross section, first at the inlet and the second one is at the throat. The difference in the pressure heads of these two sections is used to calculate the rate of flow through venture meter.

44 As the water enters at the inlet section i.e. in the converging part it converges and reaches to the throat. The throat has the uniform cross section area and least cross section area in the venture meter. As the water enters in the throat its velocity gets increases and due to increase in the velocity the pressure drops to the minimum. Now there is a pressure difference of the fluid at the two sections. At the section 1(i.e. at the inlet) the pressure of the fluid is maximum and the velocity is minimum. And at the section 2 (at the throat) the velocity of the fluid is maximum and the pressure is minimum. The pressure difference at the two section can be seen in the manometer attached at both the section. This pressure difference is used to calculate the rate flow of a fluid flowing through a pipe. 3. Pitot Tube The pitot tube is used to measure the velocity of flow of air or any fluid. Let us consider a horizontal pipe through which air flows. A manometer filled with mercury of density is connected to the pipe as shown in fig. 12. One end of the manometer is connected such that the circular area of cross section 'a' is parallel to the flow of air and the end 'q' is connected such that 'a' is perpendicular to the flow. Figure- Pitot Tube The Bernoulli's theorem for the present problem can be written as, The pressure due to elevation is constant in the horizontal flow of fluid.

45 At the point p, the static pressure is P p and the velocity of fluid is v p. However at the point q, the fluid will be stagnated and its velocity v q = 0. The pressure at the stagnated point is P q. So, as per Bernoulli's theorem If h is the difference in height of mercury column in the manometer,... ( ii ) From (ii) and (iii),... ( iii ) Eq. (iv) gives the speed of the air in the pipe....(iv) For convenience, the pitot tube can also be designed using two concentric tube as shown in the following figure. Air entering through the opening p is connected to p' end of the manometer and it corresponds to static pressure point, where the velocity of fluid is v, Point q is connected to q' end of the manometer and it corresponds to stagnation point where the velocity of the fluid v q =0. Assuming that the vertical height between p' and q' is negligible effect, the velocity of fluid can be determined using eq.(ii). Instead of a manometer, one can also connect a differential pressure gauge between the points p' & q'. 4. Rotameter The rotameter is an industrial flowmeter used to measure the flowrate of liquids and gases. The rotameter consists of a tube and float. The float response to flowrate changes is linear, and a 10- to-1 flow range or turndown is standard. In the case of OMEGA laboratory rotameters, far greater flexability is possible through the use of correlation equations. The rotameter is popular

46 because it has a linear scale, a relatively long measurement range, and low pressure drop. It is simple to install and maintain. Principle of Operation The rotameter's operation is based on the variable area principle: fluid flow raises a float in a tapered tube, increasing the area for passage of the fluid. The greater the flow, the higher the float is raised. The height of the float is directly proportional to the flowrate. With liquids, the float is raised by a combination of the buoyancy of the liquid and the velocity head of the fluid. With gases, buoyancy is negligible, and the float responds to the velocity head alone. The float moves up or down in the tube in proportion to the fluid flowrate and the annular area between the float and the tube wall. The float reaches a stable position in the tube when the upward force exerted by the flowing fluid equals the downward gravitational force exerted by the weight of the float. A change in flowrate upsets this balance of forces. The float then moves up or down, changing the annular area until it again reaches a position where the forces are in equilibrium. To satisfy the force equation, the rotameter float assumes a distinct position for every constant flowrate. However, it is important to note that because the float position is gravity dependent, rotameters must be vertically oriented and mounted. Thermocouples Figure- Rotameter A thermocouple consists of two dissimilar conductors in contact, which produce a voltage when heated The voltage produced is dependent on the difference of temperature of the junction to other parts of the circuit. Thermocouples are a widely used type of temperature sensor for measurement and control can also be used to convert a temperature gradient into electricity

47 If two different metals are joined together A potential difference occurs across the junction The potential difference depends on the metal used and temperature of the junction The thermocouple is a complete circuit involving two such junctions If both junctions are at same temperature there is no net e.m.f However, there is a difference in temperature between two junctions, there is an e.m.f The value depends on the two metals concerned and temperature, t of both junctions Usually one junction is held at 0 C and then to a reasonable extend Properties such as resistance to corrosion may also be important when choosing a type of thermocouple Where the measurement point is far from the measuring instrument, the intermediate connection can be made by extension wires which are less costly than the materials used to make the sensor Thermocouples measure the temperature difference between two points, not absolute temperature To measure a single temperature, one of the junctions normally the cold junction is maintained at a known reference temperature the other junction is at the temperature to be sensed The main limitation with thermocouples is accuracy; system errors of less than one degree Celsius ( C) can be difficult to achieve Thermocouples are widely used in science and industry; applications include temperature measurement for kilns, gas turbine exhaust, diesel engines, and other industrial processes. Pyrometer A pyrometer is a type of remote-sensing thermometer used to measure the temperature of a surface. Various forms of pyrometers have historically existed. In the modern usage, it is a device that from a distance determines the temperature of a surface from the spectrum of the thermal radiation it emits, a process known as pyrometry and sometimes radiometry.

48 Design A modern pyrometer has an optical system and a detector. The optical system focuses the thermal radiation onto the detector. The output signal of the detector (temperature T) is related to the thermal radiation or irradiance j * of the target object through the Stefan Boltzmann law, the constant of proportionality σ, called the Stefan-Boltzmann constant and the emissivity ε of the object. This output is used to infer the object's temperature from a distance, with no need for the pyrometer to be in thermal contact with the object; most other thermometers (e.g. thermocouples and resistance temperature detectors (RTDs) are placed in thermal contact with the object, and allowed to reach thermal equilibrium. Pyrometry of gases presents difficulties. These are most commonly overcome by using thin filament pyrometry or soot pyrometry. Both techniques involve small solids in contact with hot gases. Load cell Figure Block diagram of pyrometer A Load cell is a transducer that is used to convert a force into an electrical signal. This conversion is indirect and happens in two stages Through a mechanical arrangement, the force being sensed deforms a strain gauge The strain gauge measures the deformation (strain) as an electrical signal, because the strain changes the effective electrical resistance of the wire Strain gauge load cells are the most common types of load cells There are other types of load cells such as hydraulic (or hydrostatic), Pneumatic Load Cells, Piezoelectric load cells, Capacitive load cells, Piezo resistive load cells...etc. Load cells are used for quick and precise measurements Compared with other sensors, load cells are relatively more affordable and have a longer life span The principle of operation of the Strain Gauge load cell is based on the fact that the resistance of the electrical conductor changes when its length changes due to stress

49 Cu Ni alloy is commonly used in strain gauge construction as the resistance change of the foil is virtually proportional to the applied strain The change in resistance of the strain gauge can be utilized to measure strain accurately when connected to an appropriate measuring circuit A load cell usually consists of four strain gauges in a Wheatstone bridge configuration The electrical signal output is typically very small in the order of a few milli volts It is amplified by an instrumentation amplifier before sending it to the measurement system The output can be Digital or Analog (0-5V) depending on the application Advantages of Load cell:- Rugged and compact construction No moving parts Can be used for static and dynamic loading Highly Accurate Wide range of measurement Can be used for static and dynamic loading

50 Disadvantages of Load cell:- Mounting is difficult Calibration is a tedious procedure How to select a load cell:- Below are some of the important parameters that need to be considered while selecting the load cell Size Accuracy Weight range Operating temperature Duration of measurements Mounting Output type Cost Direction of loading Type of load cell Dynamometer A dynamometer is a brake but in addition it has a device to measure the frictional resistance. Knowing the frictional resistance, we may obtain the torque transmitted and hence the power of the engine. Types of Dynamometers There are the two types of dynamometers, used for measuring the brake power of an engine. 1. Absorption dynamometers, and 2. Transmission dynamometers. In the absorption dynamometers, the entire energy or power produced by the is absorbed by the friction resistances of the brake and is transformed into heat, during the process of measurement. But in the transmission dynamometers, the energy is not wasted in friction but is used for doing work. The energy or power produced by the engine is transmitted through the dynamometer to some other machines where the power developed is suitably measured. Classification of Absorption Dynamometers The following two types of absorption dynamometers are important from the subject point of View: 1. Prony brake dynamometer. 2. Rope brake dynamometer. Prony Brake Dynamometer A simplest form of an absorption type dynamometer is a Prony brake dynamometer, as shown in Fig. It consists of two wooden blocks placed around a pulley fixed to the shaft of an engine whose power is required to be measured. The blocks are clamped by means of two bolts and nuts, as shown in Fig. A helical spring is provided between the nut and the upper block to adjust the pressure on the pulley to control its speed. The upper block has a long lever attached to it and

51 carries a weight W at its outer end. A counter weight is placed at the other end of the lever which balances the brake when unloaded. Two stops S, S are provided to limit the motion of the lever. Rope Brake Dynamometer Figure- Prony Brake Dynamometer It is another form of absorption type dynamometer which is most commonly used for measuring the brake power of the engine. It consists of one, two or more ropes wound around the flywheel or rim of a pulley fixed rigidly to the shaft of an engine. The upper end of the ropes is attached to a spring balance while the lower end of the ropes is kept in position by applying a dead weight as shown in Fig. In order to prevent the slipping of the rope over the flywheel, wooden blocks are placed at intervals around the circumference of the flywheel. In the operation of the brake, the engine is made to run at a constant speed. The frictional torque, due to the rope, must be equal to the torque being transmitted by the engine. Figure-Rope brake dynamometer

52 Tachometer A tachometer (revolution-counter, tach, rev-counter, RPM gauge) is an instrument measuring the rotation speed of a shaftor disk, as in a motor or other machine. The device usually displays the revolutions per minute (RPM) on a calibrated analogue dial, but digital displays are increasingly common. The word comes from Greek ταχος (tachos "speed") and metron ("measure"). Essentially the words tachometer and speedometer have identical meaning: a device that measures speed. It is by arbitrary convention that in the automotive world one is used for engine and the other for vehicle speed. In formal engineering nomenclature, more precise terms are used to distinguish the two. Stroboscope Figure- Tachometer A stroboscope also known as a strobe, is an instrument used to make a cyclically moving object appear to be slow-moving, or stationary. It consists of either a rotating disk with slots or holes or a lamp such as a flashtube which produces brief repetitive flashes of light. Usually the rate of the stroboscope is adjustable to different frequencies. When a rotating or vibrating object is observed with the stroboscope at its vibration frequency (or a submultiple of it), it appears stationary. Thus stroboscopes are also used to measure frequency. The principle is used for the study of rotating, reciprocating, oscillating or vibrating objects. Machine parts and vibrating string are common examples. A stroboscope used to set the ignition timing of internal combustion engines is called a timing light. Vibrometers and accelerometers On the other hand laser vibrometer systems detect relative displacements as opposed to the absolute measures of accelerometers. The accelerations calculated from the laser vibrometer signals and the one directly measured by the accelerometer has been compared.

53 MODULE-III Open Loop System An open-loop control system takes input under the consideration and doesn t react on the feedback to obtain the output. This is why it is also called a non-feedback control system. There are no disturbances or variations in this system and works on fix conditions. Open loop is simple and works on the input. Close Loop System A closed loop system is also referred as a feedback control system. These systems record the output instead of input and modify it according to the need. It generates preferred condition of the output as compared to the original one. It doesn t encounter any external or internal disturbances. Closed loop is complex and works on the output and modifies it. Routh s Stability Criterion Consider a closed-loop transfer function where the ai s and bi s are real constants and m _ n. An alternative to factoring the denominator polynomial, Routh s stability criterion, determines the number of closed loop poles in the righthalf s plane. Algorithm for applying Routh s stability criterion The algorithm described below, like the stability criterion, requires the order of A(s) to be finite.