COURSE MATERIAL: MECHANICAL

MEASUREMENT, METROLOGY AND

RELIBILITY

PREPARED BY DR.B.B.CHOUDHURY,

ASSOCIATE PROFESSOR, DEPT. OF

MECHANICAL ENGG., IGIT SRANG

4th Semester , B.Tech in Mechanical Engg.

SUBJECT CODE : PME4I104 20.01.2017

bbchoudhury@igitsarang.ac.in

MODULE-1 Metrology

Metrology is derived from Greek word ‘Metron’, which means to measure. Metrology defined by the international bureau of weight and measure, as the science of measurement embarrassing both experimental and theoretical determination at any level of uncertainty in any field of science and technology.

Metrology is concern with numerous problems theoretical as well as practical related with measurement such as:

(i) Measuring instruments and devices. (ii) Errors of measurements. (iii) Accuracy of measuring instruments. (iv) Design, manufacturing and testing of gauges. (v) Units of measurements and their standards. (vi) Methods of measurements based on agreed units and standards. (vii)

Objectives of Metrology

(i) To determine the process capability. (ii) To provide the required accuracy at least cost. (iii) To determine the capabilities of the measuring instruments for repeatitive

measurements. (iv) To minimize the cost of inspection. (v) Standardization of measuring methods. (vi) Maintenance of accuracies of measurement. (vii) To prepare design for all gauges and special inspection fixtures.

Need for inspection

(i) To ensure the material, parts or components are confirms to the establish standards. (ii) To meet the interchangibility of manufacture. (iii) To provide means of finding problem area. (iv) To produce the parts having acceptable quality with less wastage and reduces scraps. (v) To purchase of good quality raw materilas, tools and equipments. (vi) To measure and reduce rejection percentage for forthcoming production batches. (vii) To judge the possibility of rework of defective parts. (viii) To enhance customer statisfication and ensure that no faulty is reached the customers. (ix) To control the performance of man, machine and process.

Measurement

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.

Methods of Measurements

1. Direct Method:- This is the simplest method of measurement, in which the value of the quantity to be measured is obtained directly without any calculations. it involve contact or non-contact type of inspection. Example- measurements by scale, calipers and micrometers.

2. Indirect Method:- The value of the quantity to be measured is obtained by measuring other quantities, which are related to required value. Example- density calculation by measuring mass and volume.

3. Absolute Method:- It is also called fundamental method. It is based on the measurements of the base quantities used to define a particular quantity.

4. Comparison Method:- The value of the quantity to be measured is compared with a known value of a same or related quantity to it. Example:- dial indicators

5. Substitution Method:- The quantity is measured by direct comparison on an indicating device by replacing the measurable quantity with another which produces the same effect on the indicating device.

6. Coincidence Method:- There is a very small difference between the value of quantity to be measure and the reference. It is also called differential method of measurements.

7. Transposition Method:- In this method the value of the quantity to be measured is first balanced by an initial known value ‘P’ of the same quantity. Then the value the quantity measured is put in place of that known value and balanced again by another initial known value ‘Q’. Finally the value of the quantity to be measured by 푃푄.

8. Deflection Method:- In this method the value of the quantity to be measured is directly indicated by the deflection of a pointer on a calibrated scale.

9. Complementary Method:- The value of the quantity to be measured is combined with a known value of same quantity. Example- determining the volume of solid by liquid displacement.

10. Method of null measurements:- It is a method of differential method. In this method the difference between measured and known value is brought to zero. Example- measurement by potentiometer.

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:- 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. 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

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: - 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. 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 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.

Classifications of the measuring instruments Measuring instruments are classified based on their applications, mode of operation, manner of energy conversation, nature of output signal.

(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.

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 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. 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.

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. 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: 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

(ii) Precision

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). 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.

Where qo and qi 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., 0 - 100°C) or bidirectional (e.g., -10 to 100°C) or it can be expanded type (e.g., 80 - 100°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.

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. 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. 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 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

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)

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

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.

o Principle of operation: Magnetic properties are varied by pressure and stress. o Typical Applications: Measurement of pressure, sound.

Figure: Simple self inductance arrangements

5. Capacitive Transducer

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 m2

d – Distance between two plates in meter ε – Permittivity of the medium in F/m εr – relative permittivity ε0 – the permittivity of free space The schematic diagram of a parallel plate capacitive transducer is shown in the figure below.

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.

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).

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 bandpass 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 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. 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 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 two's complementbinary number that is proportional to the input. An encoder might output a Gray code.

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 768...). 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 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.

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

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. 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.

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. 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.

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:

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.

Steady 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 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 d1 and d2 are the diameters of the pipe line and the orifice opening, then the flow rate can be obtained by measuring the pressure difference (p1-p2).

Figure – Orifice meter

In general, the mass flow rate qm measured in kg/s across an orifice can be described as

where:

Cd= 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

ρ1= 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. 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.

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.

At the point p, the static pressure is Pp and the velocity of fluid is vp. However at the point q, the fluid will be stagnated and its velocity vq = 0 . The pressure at the stagnated point is Pq. So, as per Bernoulli's theorem

................................. ( ii )

If h is the difference in height of mercury column in the manometer,

.................................. ( iii )

From (ii) and (iii),

..................................(iv) Eq. (iv) gives the speed of the air in the pipe.

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 vq=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 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.

Figure- Rotameter

Load cell

• 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 • 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

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

Thermocouples

• 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 • 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.

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.

Figure – Block diagram of pyrometer

Module -2 Line Standard

When the length being measured is expressed as the distance between two lines, this is known as line standard.

A scale is quick and easy to use over a wide range of dimension. Line standards are not as accurate as end standards and cannot be used for close tolerance

measurement. A steel scale can be read to about ± 0.2 mm of true value. The scale graduations are not subject to wear although significance wear on leading end

leads to under sizing. Scales are subjected to parallax error of reading. They may be positive or negative

reading. Errors due to inaccuracy of graduations engraved on the scale are possible. A scale does not provide a “built in” measuring datum.

End Standards

When the length being measured is expressed as the distance between two surfaces or ends, this is known as end standard.

They are time consuming to use and prove only one dimension at a time. End standards are highly accurate and well- suitable to close tolerance measurement. Close dimensional tolerance as small as 0.0005 mm can be obtained. They are subjected to wear on their measuring faces. Also wringing of slip gauges leads

to damage. The parallax error is not associated with such type of measurement because the distance

is measured between two flat surfaces. Such errors are not possible with end standards. They have a “built in” measuring datum as their measuring faces are flat and parallel.

Surface Roughness Measurement

With the more precise demands of modern engineering products, the control of surface texture together with dimensional accuracy has become more important. It has been investigated that the surface texture greatly influences the functioning of the machined parts. The properties such as appearance, corrosion resistance, wear resistance, fatigue resistance, lubrication, initial tolerance, ability 'to hold pressure, ,load carrying capacity, noise reduction in case of gears are influenced by the surface texture.

Factors Affecting Surface Roughness:-

The following factors affect the surface roughness:

Vibrations Material of the workpiece Type of machining. Rigidity of the system consisting of machine tool, fixture cutting tool and work Type, form, material and sharpness of cutting tool Cutting conditions i.e., feed, speed and depth of cut Type of coolant used

Reasons for Controlling Surface Texture:-

To improve the service life of the components To improve the fatigue resistance To reduce initial wear of parts To have a close dimensional tolerance on the parts To reduce frictional wear To reduce corrosion by minimizing depth of irregularities For good appearance If the surface is not smooth enough, a turning shaft may act like a reamer and the piston

rod like a broach.

Elements of Surface Texture

The various elements of surface texture can be defined and explained with the help of fig which shows a typical surface highly magnified.

Surface: The surface of a part 'is confined by the boundary which separates that part from another part, substance or space. Actual surface. This refers to the surface of a part which is actually obtained after a manufacture ring process.

Nominal surface: A nominal surface is a theoretical, geometrically perfect surface which does not exist in practice, but it is an average of the irregularities that are superimposed on it.

Profile: Profile is defined as the contour of any section through a surface, Roughness. As already explained roughness refers to relatively finely spaced micro geometrical irregularities. It is also called as primary texture and constitutes third and fourth order irregularities.

Roughness Height: This is rated as the arithmetical average deviation expressed in micro-meters normal to an imaginary centre line, running through the roughness profile.

Roughness Width: Roughness width is the distance parallel; to the normal surface between successive peaks or ridges that constitutes the predominant pattern of the roughness.

Roughness Width cutoff: This is the maximum width of surface irregularities that is included in the measurement of roughness height. This is always greater than roughness width and is rated in centimeters.

Waviness: Waviness consists of those surface irregularities which are of greater spacing than roughness and it occurs in the form of waves. These are also termed as moon geometrical errors and constitute irregularities of first and second order. These are caused `due to misalignment of centres, vibrations, machine or work deflections, warping etc.

Effective profile: It is the real canter of a surface obtained by using instrument Laws: Flaws are surface irregularities or imperfections which occur art infrequent intervals

and at random intervals. Examples are: scratches, holes, cracks, porosity etc. These may be observed directly with the aid of penetrating dye or other material which makes them visible for examination and evaluation.

Surface Texture: Repetitive or random deviations from the nominal. Surface which forms the pattern on the surface. Surface texture includes roughness, waviness, lays and flaws.

Lay: It is the direction of predominant surface pattern produced by tool marks or scratches. It is determined by the method of production used. Symbols used to indicate the direction of lay are given below:

| | = Lay parallel to the boundary line of the nominal surface that is, lay parallel to the line representing surface to which the symbol is applied e.g., parallel shaping, end view of turning and O.D grinding.

⊥= Lay perpendicular to the boundary line .of the nominal surface, that is lay perpendicular to the line representing surface to which the symbol is applied, e.g. , end view of shaping, longitudinal view of turning and O.D. grinding.

X = Lay angular in both directions to the line representing the surface to which symbol is applied, e.g. traversed end mill, side wheel grinding.

M= Lay multidirectional e.g. lapping super finishing, honing. C= Lay approximately circular relative to the centre of the surface to which the symbol is

applied e.g., facing on a lathe. R= Lay approximately radial relative to the centre of the surface to which the symbol is

applied, e.g., surface ground on a turntable, fly cut and indexed on end mill. Sampling length: It is the length of the profile necessary for the evaluation of the

irregularities to be taken into account. It is also known as cut-off length. It is measured in a direction parallelogram general direction of the profile. The sampling length should bear some relation to the type of profile.

Evaluation of Surface Finish: A numerical assessment of surface finish can be carried out in a number of ways. These numerical values are obtained with respect to a datum. In practice, the following three methods of evaluating primary texture (roughness) of a surface are used: (1) Peak to valley height method (2) The average roughness (3) Form factor or bearing curve.

(1) Peak to valley height method: This method is largely used in Germany and Russia. It measures the maximum depth of the surface irregularities over a given sample length, and largest value of the depth is accepted as a measure of roughness. The drawback of this method is that it may read the same ℎ for two largely different textures. The value obtained would not give a representative assessment of the surface. To, overcomes this PV (Peak to Valley) height is defined as the distance between a pair of lines running parallel `to the general ‘lay' of the trace positioned so that the length lying within the peaks at, the top is 5% of the trace length, and that within the valleys at the bottom is 10% of the trace length. This is represented graphically in the Figure below.

(2) The average roughness: For assessment off average roughness the following three statistical criteria are used: (a) C.L.A Method: In this method, the surface roughness is measured as the average deviation from the nominal surface.

Centre Line Average or Arithmetic Average is defined as the average values of the ordinates from the mean line, regardless of the arithmetic signs of the ordinates

The calculation of C.L.A value using equation (ii) is facilitated by the planimeter. CLA value measure is preferred to RMS value measure because its value can be easily determined by measuring. The areas with planimeter or graph or can be readily determined in electrical instruments by integrating the movement of the styles and displaying the result as an average. (b) R.M.S. Method: In this method also, the roughness is measured as the average deviation from the nominal surface. Root mean square value measured is based on the least squares.

R.M.S value is defined as the square root of the arithmetic mean of the values of the squares of the ordinates of the surface measured from a mean line. It is obtained by setting many equidistant ordinates on the mean line ( 1, 2, 3 … . ) and then taking the root of the mean of the squared ordinates. Let us assume that the sample length ‘L’ is divided into ‘n' equal parts and 1, 2, 3 ….are the heights of the ordinates erected at those points.

(c) Ten Point Height Method: In this method, the average difference between the five highest peaks and five lowest valleys of surface texture within the sampling length, measured from a line parallel to the mean line and not crossing the profile is used to denote the amount of surface roughness.

This method is relatively simple method of analysis and measures the total depth of surface irregularities within the sampling length. But it does not give sufficient information about the surface, as no account is taken of frequency of the irregularities and the profile shape. It is used when it is desired to control the cost of finishing for checking the rough machining. (3) Form factor and Bearing Curves: There are certain characteristic which may be used to evaluate surface texture. Form Factor: The load carrying area of every surface is often much less than might be thought. This is shown by reference to form factor. The form factor is obtained by measuring the area of material above the arbitrarily chosen base line in the section and the area of the enveloping rectangle. Then,

Conventional Method for Designing Surface finish:

As per IS: 696 surface texture specified by indicating the following (a) Roughness value i.e., Ra value in mm (b) Machining allowance in mm. (c) Sampling length or instrument cut-off length in mm. (d) Machining production method, and (e) Direction of lay in the symbol form as = ⊥, X, M, C, R

Surface roughness measuring instuments

Profilo meter:

Profilometer is an indicating and recording instrument used to measure roughness in microns. The principle of the instrument is similar to gramophone pick up. It consists of two principal units: a tracer and an amplifier. Tracer is a finely pointed stylus. It is mounted in the pick up unit which consists of an induction coil located in the field of a permanent magnet. When the tracer is moved across the surface to be tested, it is displaced vertically up and down due to the surface irregularities. This causes the induction coil to move in the field of the permanent magnet and induces a voltage. The induced voltage is amplified and recorded.

Tomlinson surface meter

The Tomlinson surface meter is a comparatively cheap and reliable instrument. It was originally designed by Dr. Tomlinson. It consists of a diamond probe (stylus) held by spring pressure against the surface of a lapped steel cylinder and is attached to the body of the instrument by a leaf spring. The lapped cylinder is supported on one side by the probe and on the either side by fixed rollers. Alight spring steel arm is attached to the lapped cylinder. It carries at its tip a diamond scriber which rests against a smoked glass. The motions of the stylus in all the directions except the vertical one are prevented by the forces exerted by the two springs.

For measuring surface finish the body of the instrument is moved across the surface by screw rotated by asynchronous motor. The vertical movement of the probe caused by surface irregularities makes the horizontal lapped cylinder to roll. This causes the movement of the arm attached to the lapped cylinder. A magnified vertical movement of the diamond scriber on smoked glass is obtained by the movement of the arm. This vertical movement of the scriber together with horizontal movement produces a trace on the smoked glass plate. This trace is further magnified at X 50 or X 100 by an optical projector for examination.

Taylor Hobson Talysurf

Taylor-Hobson Talysurf is a stylus and skid type of instrument working on carrier modulating principle. Its response is more rapid and accurate as comparred to Temlinson Surface Meter. The measuring head of this instrument consists of a sharply pointed diamond stylus of about 0.002 mm tip radius and skid or shoe which is drawn across the surface by means of a motorised driving unit. In this instrument the stylus is made to trace the profile of the surface irregularities, and the oscillatory movement of the stylus is converted into changes in electric current by the arrangement as shown in Fig. The arm carrying the stylus forms an armature which pivots about the centre piece of E-shaped stamping. On two legs of (outer pole pieces)'the E-shaped stamping there are coils carrying an a.c. current. These two coils with other two resistances form an oscillator. As the armature is pivoted about the central leg, any movement of the stylus causes the air gap to vary and thus the amplitude of the original a.c. current flowing in the coils is

modulated. The output of the bridge thus consists of modulation only as shown in Fig. This is further demodulated so that the current now is directly proportional to the vertical displacement of the stylus only.

Profilograph

The principle of Working of a tracer type profilograph is shown in Fig. The work to be tested is placed on the table of the instrument. The work and the table are traversed with the help of a lead screw. The stylus which is pivoted to a mirror moves over the tested surface. Oscillations of the tracer point are transmitted to the mirror. A light source sends a beam of light through lens and a precision slit to the oscillating mirror. The reflected beam is directed to a revolving drum, upon which a sensitized film is arranged. This drum is rotated through two bevel gears from the same lead screw that moves the table of the instrument. A profilogram will be obtained from the sensitized film that may be sub-sequently analyzed to determine the value of the surface roughness.

Measurement of screw threads

Principles of floating carriage micrometer

It consists of three main units. A base casting carries a pair of centres, on which the threaded work-piece is mounted. Another carriage is mounted on it and is exactly at 90° to it. On this is provided another carriage capable of moving towards the centres. On this carriage one head having a large thimble enabling reading upto 0.002 mm is provided. Just opposite to it is a fixed anvil which is spring loaded and its zero position is indicated by a fiducial indicator. Thus the micrometer elements are exactly perpendicular to the axis of the centres as the two carriages are located perpendicular to each other. On the fixed carriage the centres are supported in two brackets fitted on either end. The distance between the two centres can be adjusted depending upon the length of tie threaded job. After job is fitted between the centres the second carriage is adjusted in correct position to take measurements and is located in position, The third carriage is then moved till the fiducial indicator is against the set point. The readings are noted from the thimble head. It is now obvious that the axis of the indicator and micrometer head spindle is same and is perpendicular to the line of two centres. The indicator is specially designed for this class of work and has only one index line, against which the pointer is always to be set. This ensures constant measuring pressure for all readings. Sufficient friction is provided by the conical pegs to restrain the movement of carriage along the line of centres. The upper carriage is free to float on balls and enables micrometer readings to be taken on a diameter without restraint. Squareness of the micrometer to the line of centre can be adjusted by rotating the pegs in the first carriage which is made eccentric in its mounting.

Figure –Floating carriage microscope

Above the micrometer carriage, two supports are provided for supporting the wires and Vee-pieces for measurement of effective diameter etc.

(i) Measurement of Major Diameter.

For the measurement of major diameter of external threads, a good quality hand micrometer is quite suitable. In taking readings, a light pressure must be used as the anvils make contact with the gauge at points only and otherwise the errors due to compression can be introduced. It is, however, also desirable to check the micrometer reading on a cylindrical standard of approximately the same size, so that the zero error etc., might not come into picture.

For greater accuracy and convenience, the major diameter is measured by bench micrometer. This instrument was designed by N.P.L. to estimate some deficiencies inherent in the normal hand micrometer. It uses constant measuring pressure and with this machine the error due to pitch error in the micrometer thread is avoided. In order that all measurements be made at the same pressure, a fiducial indicator is used in place of the fixed anvil. In this machine there is no provision for mounting the workpiece between the centres and it is to be held in hand. This is so, because, generally the centres of the workpiece are not true with its diameter. This machine is used as a comparator in order to avoid any pitch errors of micrometers, zero error setting etc. A calibrated setting cylinder is used as the setting standard.

The advantage of using cylinder as setting standard and not slip gauges etc., is that it gives greater similarity of contact at the anvils. The diameter of the setting cylinder must be nearly same as the major diameter. The cylinder is held and the reading of the micrometer is noted down. This is then replaced by threaded workpiece and again micrometer reading is noted for the same reading of fiducial indicator. Thus, if the size of cylinder is approaching, that of major diameter, then for a given reading the micrometer thread is used over a short length of travel and any pitch errors it contains are virtually eliminated.

Figure-bench micrometer

(ii) Measurement of Minor Diameter

This is also measured by a comparative process using small Vee-pieces which make contact with a root of the thread. The Vee-pieces are available in several sizes having suitable radii at the edges. The included angle of Vee-pieces is less than the angle of the thread to be checked so that it can easily probe to the root of the thread. To measure the minor diameter by Vee-pieces is suitable for only Whitworth and B.A. threads which have a definite radius at the root of the thread. For other threads, the minor diameter is measured by the projector or microscope.

(iii) Effective Diameter Measurements.

The effective diameter or the pitch diameter can be measured by any one of the following methods: (i) The micrometer method (ii) The one wire, two wire, or three wire or rod method.

Two Wire Method.

The effective diameter of a screw thread may be ascertained by placing two wires or rods of identical diameter between the flanks of the thread, as shown in Figure below, and measuring the distance over the outside of these wires. The effective diameter E I s then calculated as

The wires used are made of hardened steel to sustain the wear and tear in use. These are given a high degree of accuracy and finish by lapping to suit different pitches. Dimension T can also be determined by placing wires over a standard cylinder of diameter greater than the diameter under the wires and noting the reading R1 and then taking reading with over the gauge, say R2. Then T=S—(R1—R2).

P=It is a value which depends upon the diameter of wire and pitch of the thread.

If P= pitch of the thread, then P= 0.9605p−1.1657d (for Whitworth thread). P= 0.866p—d (for metric thread).

Actually P is a constant Value which has to be added to the diameter under the wires to give the effective diameter. The expression for the value of P in terms of p (pitch), d (diameter of wire) and x (thread angle) can be derived as follows :

Two wire methods can be carried out only on the diameter measuring machine described for measuring the minor diameter, because alignment is not possible by 2 wires and can be provided only by the floating carriage machine. In the case of three wire method, 2 wire, on one side help in aligning the micrometer square to the thread while the third placed on the other side permits taking of readings.

Gear Measurement Gears is a mechanical drive which transmits power through toothed wheel. In this gear drive, the driving wheel is in direct contact with driven wheel. The accuracy of gearing is the very important factor when gears are manufactured. The transmission efficiency is almost 99 in gears. So it is very important to test and measure the gears precisely.

Gear Tooth Caliper In gear tooth vernier method the thickness is measured at the pitch line. Gear tooth thickness varies from the tip of the base circle of the tooth, and the instrument is capable of measuring the thickness at a specified position on the tooth. The tooth vernier caliper consists of vernier scale and two perpendicular arms. In the two perpendicular arms one arm is used to measure the thickness and other arm is used to measure the depth. Horizontal vernier scale reading gives chordal thickness (W) and vertical vernier scale gives the chordal addendum. Finally the two values e compared. The theoretical values of W‘ and d‘ can be found out by considering one tooth in the gear and it can be verified.

In fig note that w is a chord ADB and tooth thickness is specified by AEB. The distance d is noted and adjusted on instrument and it is slightly greater than addendum CE. Therefore, W‘is chordal thickness and d‘ is named as chordal addendum.

Vernier method like the chordal thickness and chordal addendum are depends upon the number of teeth. Due to this for measuring large number of gears different calculations are to be made for each gear. So these difficulties are avoided by this constant chord method.

Limit, fit and Gauges

Zero Line: It is a line along which represents the basic size and zero (or initial point) for measurement of upper or lower deviations.

Basic Size: It is the size with reference to which upper or lower limits of size are defined. Shaft and Hole: These terms are used to designate all the external and internal features of any shape and not necessarily cylindrical. Hole Designation: By upper case letters from A, B, … Z, Za, Zb, Zc (excluding I, L, O, Q, W and adding Js, Za, Zb, Zc) - 25 nos. Shaft Designation: By lower case letters from a, b, … z, za, zb, zc (excluding i, l, o, q, w and adding js, za, zb, zc) - 25 nos. Upper Deviation: The algebraic difference between the maximum limit of size (of either hole or shaft) and the corresponding basic size, like ES, es. Lower Deviation: The algebraic difference between the minimum limit of size (of either hole or shaft) and the corresponding basic size, like EI, ei. Fundamental Deviation: It is one of the two deviations which is chosen to define the position of the tolerance zone. Tolerance: The algebraic difference between upper and lower deviations. It is an absolute value.

Limits of Size: There are two permissible sizes for any particular dimension between which the actual size lies, maximum and minimum Basic Shaft and Basic hole: The shafts and holes that have zero fundamental deviations. The basic hole has zero lower deviation whereas, the basic shaft has zero upper deviation.

Fit It is the relation between dimensions of two mating parts before their assembly.

Systems of Fit: There are two systems by which a fits can be accomplished – 1. Hole basis system 2. Shaft basis system

Classes of fit

a) Clearance fit b) Transition fit c) Interference fit

Tolerance: Various grades of tolerances are defined using the ‘standard tolerance unit’, (i) in μm, which is a function of basic size.

Where, D (mm) is the geometric mean of the lower and upper diameters of a particular diameter step within which the chosen the diameter D lies.

Grade of Tolerance: It is an indication of the level of accuracy. There are 18

Grades of tolerances – IT01, IT0, IT1 to IT16 IT01 to IT4 - For production of gauges, plug gauges, measuring instruments IT5 to IT 7 - For fits in precision engineering applications IT8 to IT11 – For General Engineering

IT12 to IT14 – For Sheet metal working or press working IT15 to IT16 – For processes like casting, general cutting work

IT6 – 10 i; IT7 – 16i; IT8 – 25i; IT9 – 40i; IT10 – 64i; IT11 – 100i; IT12 – 160i; IT13 – 250i; IT14 – 400i; IT15 – 640i; IT16 – 1000i.

Measurement of straightness and flatness

Autocollimators This is an optical instrument used for the measurement of small angular differences. For small angular measurements, autocollimator provides a very sensitive and accurate approach. Auto-collimator is essentially an infinity telescope and a collimator combined into one instrument. The principle on which this instrument works is given below. O is a point source of light placed at the principal focus of a collimating lens in Fig. 8.30. The rays of light from O incident on the lens will now travel as a parallel beam of light. If this beam now strikes a plane reflector which is normal to the optical axis, it will be reflected back along its own path and refocused at the same point O. If the plane reflector be now tilted through a small angle 0, [Refer Fig] then parallel beam will be deflected through twice this angle, and will be brought to focus at O‘ in the same plane at a distance x from O. Obviously OO‘=x=2θ.f, where f is the focal length of the lens.

Principle of the Autocollimator. A cross line ―targetǁ graticule is positioned at the focal plane of a telescope objective system with the intersection of the cross line on the optical axis, i.e. at the principal focus. When the target graticule is illuminated, rays of light diverging from the intersection point reach the objective via a beam splitter and are projected-from the objective as parallel pencils of light. In this mode, the optical system is operating as a “collimator”

A flat reflector placed in front of the objective and exactly normal to the optical axis reflects the parallel pencils of light back along their original paths. They are then brought to focus in the plane of the target graticule and exactor coincident with its intersection. A proportion of the returned light passes straight through the beam splitter and the return image of the target cross line is therefore visible through the eyepiece. In this mode, the optical system is operating as a telescope focused at infinity. If the reflector is tilted through a small angle the reflected pencils of light will be deflected by twice the angle of tilt (principle of reflection) and will be brought to focus in the plane of the target graticule but linearly displaced from the actual target cross lines by an amount 2θ * f.

Linear displacement of the graticule image in the plane of the eyepiece is therefore directly proportional to reflector tilt and can be measured by an eyepiece graticule, optical micrometer no electronic detector system, scaled directly in angular units. The autocollimator is set permanently at infinity focus and no device for focusing adjustment for distance is provided or desirable. It responds only to reflector tilt (not lateral displacement of the reflector)

Optical Flat:

Optical flat are flat lenses, made from quartz, having a very accurate surface to transmit light.

They are used in interferometers, for testing plane surfaces. The diameter of an optical flat varies from 50 to 250mm and thickness varies from 12 to

25 mm. Optical flats are made in a range of sizes and shapes. The flats are available with a coated surface. The coating is a thin film, usually titanium oxide, applied on the surface to reduce the

light lost by reflection. The coating is so thin that it does not affect the position of the fringe bands, but a coated

flat

Module –III Bath-tub-curve The 'bathtub curve' hazard function (blue, upper solid line) is a combination of a decreasing hazard of early failure (red dotted line) and an increasing hazard of wear-out failure (yellow dotted line), plus some constant hazard of random failure (green, lower solid line). The bathtub curve is widely used in reliability engineering. It describes a particular form of the hazard function which comprises three parts:

The first part is a decreasing failure rate, known as early failures. The second part is a constant failure rate, known as random failures.

The third part is an increasing failure rate, known as wear-out failures. The name is derived from the cross-sectional shape of a bathtub: steep sides and a flat bottom.

The bathtub curve is generated by mapping the rate of early "infant mortality" failures when first introduced, the rate of random failures with constant failure rate during its "useful life", and finally the rate of "wear out" failures as the product exceeds its design lifetime.

Figure –Bath-tub Curve

In less technical terms, in the early life of a product adhering to the bathtub curve, the failure rate is high but rapidly decreasing as defective products are identified and discarded, and early sources of potential failure such as handling and installation error are surmounted. In the mid-life of a product—generally speaking for consumer products—the failure rate is low and constant. In the late life of the product, the failure rate increases, as age and wear take their toll on the product. Many consumer product life cycles strongly exhibit the bathtub curve.

While the bathtub curve is useful, not every product or system follows a bathtub curve hazard function, for example if units are retired or have decreased use during or before the onset of the wear-out period, they will show fewer failures per unit calendar time (not per unit use time) than the bathtub curve.

The term "Military Specification" is often used to describe systems in which the infant mortality section of the bathtub curve has been burned out or removed. This is done mainly for life-critical or system-critical applications as it greatly reduces the possibility of the system failing early in its life. Manufacturers will do this at some cost generally by means similar to environmental stress screening.

Reliability Reliability is defined as the probability that an item will perform a required function without failure under stated conditions for a stated period of time. Objectives:

i. To increase product/equipment life. ii. To increase the operational availability of an equipment.

iii. To reduce the frequency of failure.

Maintainability and Availability Maintainability is defined as the probability of performing a successful repair action within a given time. In other words, maintainability measures the ease and speed with which a system can be restored to operational status after a failure occurs. This is similar to system reliability analysis except that the random variable of interest in maintainability analysis is time-to-repair rather than time-to-failure. For example, if it is said that a particular component has a 90% maintainability for one hour, this means that there is a 90% probability that the component will be repaired within an hour. When you combine system maintainability analysis with system reliability analysis, you can obtain many useful results concerning the overall performance (availability, uptime, downtime, etc.) that will help you to make decisions about the design and/or operation of a repairable system. Availability is defined as the probability that a repairable system or system element is operational at a given point in time under a given set of environmental conditions. Availability depends on reliability and maintainability.

Availability is of three types: a) Inherent Availability

b) Achieved Availability c) Operational Availability Inherent availability (Ai) is

i

MTBFMTBF MTTRA

Where, MTBF= Mean time between Failure MTTR= Mean time to repair

Achieved Availability (Aa) is:

a

MTBMMTBM MA

Where MTBM= Mean time between maintenance

M = mean maintenance down time

Operational Availability (Ao) is: Ao= (Uptime of a system) / (Operating cycle)

Acceptance Sampling Acceptance sampling involves both the producer (and supplier) of materials and the consumer (or buyer). Consumers need acceptance sampling to limit the risk of rejecting good-quality materials or accepting bad-quality materials. Consequently, the consumer, sometimes in conjunction with the producer through contractual agreements, specifies the parameters of the plan. Any company can be both a producer of goods purchased by another company and a consumer of goods or raw materials supplied by another company.

Types of sampling plans

Single sampling plan Double sampling plan Sequential sampling plans

The single-sampling plan is a decision rule to accept or reject a lot based on the results of one random sample from the lot. The procedure is to take a random sample of size (n) and inspect each item. If the number of defects does not exceed a specified acceptance number (c), the consumer accepts the entire lot. Any defects found in the sample are either repaired or returned to the producer. If the number of defects in the sample is greater than c, the consumer subjects the entire lot to 100 percent inspection or rejects the entire lot and returns it to the producer. The single-sampling plan is easy to use but usually results in a larger ANI than the other plans. After briefly describing the other sampling plans, we focus our discussion on this plan. In a double-sampling plan, management specifies two sample sizes (n1 and n2) and two acceptance numbers (c1 and c2). If the quality of the lot is very good or very bad, the consumer can make a decision to accept or reject the lot on the basis of the first sample, which is smaller than in the single-sampling plan. To use the plan, the consumer takes a random sample of size . If the number of defects is less than or equal to , the consumer accepts the lot. If the number of defects is greater than, the consumer rejects the lot. If the number of defects is between , the

consumer takes a second sample of size . If the combined number of defects in the two samples is less than or equal to , the consumer accepts the lot. Otherwise, it is rejected. A double-sampling plan can significantly reduce the costs of inspection relative to a single-sampling plan for lots with a very low or very high proportion defective because a decision can be made after taking the first sample. However, if the decision requires two samples, the sampling costs can be greater than those for the single-sampling plan.

A further refinement of the double-sampling plan is the sequential-sampling plan, in which the consumer randomly selects items from the lot and inspects them one by one. Each time an item is inspected, a decision is made to (1) reject the lot, (2) accept the lot, or (3) continue sampling, based on the cumulative results so far. The analyst plots the total number of defectives against the cumulative sample size, and if the number of defectives is less than a certain acceptance number (c1), the consumer accepts the lot. If the number is greater than another acceptance number (c2), the consumer rejects the lot. If the number is somewhere between the two, another item is inspected. The figure below illustrates a decision to reject a lot after examining the 40th unit. Such charts can be easily designed with the help of statistical tables that specify the accept or reject cut-off values c1 and c2 as a function of the cumulative sample size.

The ANI is generally lower for the sequential-sampling plan than for any other form of acceptance sampling, resulting in lower inspection costs. For very low or very high values of the proportion defective, sequential sampling provides a lower ANI than any comparable sampling plan. However, if the proportion of defective units falls between the AQL and the LTPD, a sequential-sampling plan could have a larger ANI than a comparable single- or double-sampling plan (although that is unlikely). In general, the sequential-sampling plan may reduce the ANI to 50 percent of that required by a comparable single-sampling plan and, consequently, save substantial inspection costs.

Figure-Sequential Sampling Chart

Operating Characteristic Curves Analysts create a graphic display of the performance of a sampling plan by plotting the probability of accepting the lot for a range of proportions of defective units. This graph, called an operating characteristic (OC) curve, describes how well a sampling plan discriminates between good and bad lots. Undoubtedly, every manager wants a plan that accepts lots with a quality level better than the AQL 100 percent of the time and accepts lots with a quality level worse than the AQL 0 percent of the time. This ideal OC curve for a single-sampling plan is shown in Figure below. However, such performance can be achieved only with 100 percent inspection. A typical OC curve for a single-sampling plan, plotted in red, shows the probability a of rejecting a good lot (producer’s risk) and the probability of accepting a bad lot (consumer’s risk). Consequently, managers are left with choosing a sample size n and an acceptance number to achieve the level of performance specified by the AQL, , LTPD, and .

Figure- OC curve

B.Tech (Mechanical Engineering) detail Syllabus for Admission Batch 2015-16

4th Semester PME4I104 MECHANICAL MEASUREMENT, METROLOGY & RELIABILITY MODULE – I (16 HOURS) Definition and methods of measurement, classification of measuring instruments, Measuring systems, performance characteristics of measuring devices, types of errors. Functional elements of measuring system. Static and Dynamic Characteristics of Instruments: Static Performance Parameters, Impedance Loading and Matching, Selection and Specifications of Instruments, Dynamic Response, Compensation. Transducer Elements: Analog Transducers, Digital Transducers, Basic detector transducer elements : Electrical transducer, Sliding Contract devices, Variable-inductance transducer elements, the differential transformer, Variable-reluctance transducers, Capacitive transducers. The piezoelectric effect, photo-electric transducer, electronic transducer element. Intermediate Elements: Amplifier, Operational Amplifier, Diffential and Integrating Elements, Filters, A-D and D-A Converters Strain Measurement The electrical resistance strain gauge. The metallic resistance strain gauge, Selection and Installation factors for metallic strain gauge, Circuitry, metallic strain gauge. The strain gauge ballast circuit, the staring gauge bridge circuit, Temperature compensation. Measurement of Pressure Pressure measurement systems, Pressure measurement transducers, Elastic diaphragms, strain gauge pressure cells, measurement of high pressure, Measurement of low pressures, dynamic characteristics of pressure measuring systems. Measurement of Fluid Flow Flow characteristics obstruction meters, Obstruction meter for compressible fluids- Orifice, Venturi meter and Pitot tube, The variable-area meter, Turbine Flow meters. Temperature Measurement Use of bimetals pressure thermometers, Thermocouples, Pyrometry, Calibration of temperature measuring devices. Force, Power, Speed and Torque Measurement : Load Cell, Dynamometers, Tachometer and Tacho-generator, Stroboscope, The seismic instrument.- Vibrometers and accelerometers MODULE – II (10 HOURS) Principles of Measurements, Line and End & optical Standards, Calibration, accuracy and Precision, Random error and systemic error. Measurement of Surface Roughness, Screw Thread and Gears. Limits, Fits and Gauges, Assembly by full, partial and group interchangeability, geometric tolerances. Measurement of straightness, Flatness and circularity. MODULE – III (10 HOURS) Definition, bath-tub-curve, system reliability, reliability improvement, maintainability and availability, Availability of single repairable system using Markov model, Life tests, acceptance

sampling plan based on life tests, Sequential acceptance sampling plan based on MTTF & MTBF. B.Tech (Mechanical Engineering) detail Syllabus for Admission Batch 2015-16 TEXT BOOKS : 1. Engineering Metrology & Measurement, N.V.Raghavendra and L. Krishnamurthy, OXFORD University Press 2. Instrumentation Measurement and Analysis, B.C.Nakra and KK.Chaudhry, Tata Mc Graw Hill, Third Edition. 3. Engineering Metrology,R.K. Jain, Khanna Publisher, Delhi 4. Reliability Engg. And Terotechnology , A.K. Gupta, Macmillan India. Reference Books: 1. Metrology & Measurement, A. K. Bewoor and V.A.Kulkarni, Mc Graw hill 2. Mechanical Measurements, T.G. Beckwith and N. Lewis Buck, Oxford and IBH Publishing Co. 3. A text book of Engineering Metrology I.C. Gupta, Dhanpat Rai & sons, Delhi.

4. Introduction to /reliability and Maitainability Engg E. Ebeling, MC-Graw Hill.