{"id":116,"date":"2018-11-28T09:08:37","date_gmt":"2018-11-28T09:08:37","guid":{"rendered":"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=116"},"modified":"2019-05-01T04:47:19","modified_gmt":"2019-05-01T04:47:19","slug":"lvdt-transducers-iii","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/chapter\/lvdt-transducers-iii\/","title":{"rendered":"LVDT Transducers III"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/XbVROQNlswg\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n<div>\r\n\r\n<strong>\u00a0 \u00a0 Learning Objectives<\/strong>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">In this module we will study about transducers and how they are used in measuring various external forces. Our objective is<\/p>\r\n\r\n<ul>\r\n \t<li>To develop understanding about the transducers Look into instrumental design<\/li>\r\n \t<li>It\u2019s functioning based on the application.<\/li>\r\n \t<li>In the current module<span style=\"text-align: initial;font-size: 1em\"> we will study about load cell and piezo-electric transducers.<\/span><\/li>\r\n<\/ul>\r\n<strong>\u00a0 \u00a0 Introduction<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Transducers were developed for converting non-electrical quantity into electrical signal. This electrical signal is further processed by some electrical or electronic circuit that supplies output to a device for indication or recording purpose. Sometimes, transducers are used as primary transducers where input signal is sensed directly. In some cases transducer is used as a secondary transducer. Here a detector first senses the input signal and it output is supplied to secondary transducer as an input signal.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">In previous modules we studied about LVDT, Inductive and Capacitive transducers. In this modules we will study about other types of transducers like load cell, piezoelectric and photoelectric transducer.<\/p>\r\n&nbsp;\r\n\r\n<strong>Load Cell<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">A load cell is also known as pressure cell. It\u2019s a device that can covert weight (pressure) or mechanical force into electrical signal. It is widely used for measuring dynamic and static forces. The heart of this device is load (weight, force or pressure) receiving element which is a elastic element having high tensile strength. This element is bonded to strain gauge bridge network.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">The output of the load cell is derived from the deformation of the elastic element made of homogenous materials like steel alloys. One should carefully select the material and its structural configuration so that one can have linear relationship between the dimensional change and the quantity (force) under measurement.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">A desirable material should have <\/span>following<span style=\"text-align: initial;font-size: 1em\"> properties: -<\/span><\/p>\r\n\r\n<ol>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">A fairly large elastic strain limit with a linear stress-strain relationship, say upto 5000 micro-strains.<\/span><\/li>\r\n \t<li style=\"text-align: justify\">Repeated overloading should produce low strain hysteresis (less than 2 micro-strain)<\/li>\r\n \t<li style=\"text-align: justify\">Very low creep of less than 5 micro-strain over long<span style=\"text-align: initial;font-size: 1em\"> period of loading<\/span><\/li>\r\n \t<li style=\"text-align: justify\">Very low plastic flow due to strain<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div>\r\n\r\n\u00a0 \u00a0 Based on the design of the load cell element, one can have 3 different configurations\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">(i) Column (ii) cantilevered bending beam and (iii) shear element. Let us study about these configurations one by one \u2013<\/p>\r\n&nbsp;\r\n\r\n<strong>1.\u00a0 <\/strong><strong>Column<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">Figure 1. illustrates the a typical design for columnar type load cell. Such columnar type cells are usually employed in load cell having capacity of 2250 kg or more. It had 2 strain gauges called active gauges that are bonded axially. The other two additional gauges are called the Poisson Gauges and are mounted 900 to axially positioned gauges. The load cell shown in the figure 1 is used only under compression. It has a fitting at the bottom of the base for attachment to the support structure with a load-receiving button at the top.<\/p>\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-120\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-60.png\" alt=\"\" width=\"245\" height=\"203\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\"><strong>Figure 1. <\/strong>Compression Load Cell<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">During the construction of the load cell, the load-receiving element is shrunk-fit into the base in a compression type load cell. The lower most section of the load cell housing, also known as Can, is welded on to the base structure. On the top of the\u00a0<span style=\"text-align: initial;font-size: 1em\">lower Can, a diaphragm is welded to the edge of the Can and the center column. The upper can is welded to the connection between the lower can and diaphragm. This completes <\/span>outer<span style=\"text-align: initial;font-size: 1em\"> shell of the load cell structure. Finally, the upper lip of the top diaphragm and the central column is welded to the top diaphragm. This seals the inner portion of the load cell which makes it impervious to gas and moisture. All the wires from the strain gauge are carried out through a glass-to-metal seal located in the lower can wall and are connected to the external cable.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">2. Bending Beams<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Bending beams type load cells are used for measuring forces and weights below 225 kg. There few variations in design but the most common one is dual-guided cantilever beam, as shown in figure-2.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-121\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-61.png\" alt=\"\" width=\"179\" height=\"236\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\"><strong>Figure 2. <\/strong>Dual Guided Cantilever Beam Load Cell<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">It had four strain gauges that are mounted at the corners of a stabilized rectangle. When load is applied to the free end of this dual guided cantilever beam, the strain gauges bonded to the element undergo resistive change. This change is proportional to the forces or the load applied. In such type of cantilever beam configurations, the two gauges experience tension and two compression.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">3. Shear Element Configuration<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In this configuration, one can have 4 or 8 gauges bonded to <\/span>specifically<span style=\"text-align: initial;font-size: 1em\"> designed element and is wired to form Wheatstone bridge. A centrally loaded shear beam configuration is shown in figure 3.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-122\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-62.png\" alt=\"\" width=\"359\" height=\"230\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\"><strong>Figure 3. <\/strong>Centrally Loaded Shear Beam<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">The strain gauges used in this design differ from those used in columnar and dual-guided cantilever design. The strain gauges are designed in such a way that they get activated when they are placed under a shear force. Such elements have an advantage of have higher capacities in smaller size and have low sensitivity to side load error. i.e. when load is not placed proper orientation.<\/p>\r\n&nbsp;\r\n\r\nThe selection of a load for a particular application depends on the following factors \u2013\r\n<p style=\"text-align: justify\">(1)\u00a0 Required Accuracy (2) Scale capacity (3) Type of Loading tensile (4) Number of cells required (5) loading conditions (6) Environment (7) Space Available (8) Desired output characteristics.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong>Piezoelectric Transducers<\/strong><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">The word \u201cPiezo\u201d, is derived from a greek word, \u2018<em>piezein\u2019<\/em> which means to squeeze or press. Certain crystalline and ceramic material can generate a potential difference across the opposing faces of the material when subjected to external mechanical force.\u00a0<span style=\"text-align: initial;font-size: 1em\">Such types of materials are Piezoelectric materials and this phenomenon is called Piezoelectric effect. This effect is also reversible, i.e. on applying <\/span>potential<span style=\"text-align: initial;font-size: 1em\"> across the opposing faces of the material one can get changes in the physical dimensions of the material. This principle of electro-mechanical energy conversion is used for developing energy conversion transducers.<\/span><\/p>\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"aligncenter size-full wp-image-123\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-63.png\" alt=\"\" width=\"324\" height=\"188\" \/>\r\n\r\n&nbsp;\r\n<p style=\"text-align: center\"><strong>Figure 4. <\/strong>Piezoelectric Transducer<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">The transducer with mechanical input and electrical output are used for measuring dynamic pressure, force, shock or vibratory motion. Piezoelectric effect can only be observed in crystals having asymmetrical distribution of charge. Due to relative displacement of positive and negative charges within the lattice one can observe contraction or expansion of the material. This displacement of internal charges produces potential different across the fitted electrode. This is illustrated in figure 4. Here electrodes are placed on the opposing faces of the crystals, where output voltages are collected for measuring an external force or pressure.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">To better understand the piezoelectric properties of the transducing element in Piezoelectric Transducer let us consider a case of Quartz (SiO2) crystal. Figure 5 illustrates how opposing sides of the crystal get charged with application of external mechanical force. Under no load condition, positive and negative charges are arranged in center of the equisided triangular form.<\/p>\r\n\r\n<\/div>\r\n<img class=\"aligncenter size-full wp-image-124\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-64.png\" alt=\"\" width=\"251\" height=\"148\" \/>\r\n<div>\r\n<p style=\"text-align: center\"><strong>Figure 5<\/strong>. Quartz Lattice Structure<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">The two opposing charges at the center point become neutral and no potential difference gets developed across the opposing face of the crystal. With the application of external force F, ions within the crystal get displaced within the structure and equi-legged triangles get deformed. This deformation of crystal lattice is shown in the figure 5b. Incase of application of tensile force, potential of opposite polarity is developed across the crystalline face adjacent to electrodes. Similarly, when piezoelectric material is under the influence of external electric field, crystal may contract or expand depending upon the polarity of the field applied.<\/p>\r\n&nbsp;\r\n\r\nThe polarity &amp; magnitude of induced surface charges is proportional to the direction &amp;\u00a0 magnitude of the applied external force. Therefore,\r\n\r\n&nbsp;\r\n\r\nQ = <em>d. F<\/em> -------- (1)\r\n\r\n&nbsp;\r\n\r\nwhere <em>d<\/em> is the crystal charge sensitivity in coulombs per newton (C\/N) which is constant for a given crystal.\r\n\r\n&nbsp;\r\n\r\nThe force <em>F<\/em> brings a change in the thickness of the crystal by\u00a0\u00a0\u00a0 t in meters\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-125\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-65.png\" alt=\"\" width=\"453\" height=\"48\" \/>\r\n<p style=\"text-align: justify\">where A is the area of crystal in m2, E is the Young\u2019s modulus of elasticity and t is the thickness of the crystal.<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\">The charge at the electrodes gives rise to the output voltage Vout and is given by the following equation \u2013<\/p>\r\n\r\n<\/div>\r\n<img class=\"aligncenter size-full wp-image-126\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-66.png\" alt=\"\" width=\"359\" height=\"55\" \/>\r\n<div>\r\n\r\n\u00a0 \u00a0 where Cc is the capacitance in between the electrodes of the crystal.\r\n\r\n&nbsp;\r\n\r\nAs capacitance is given by\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-127\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-67.png\" alt=\"\" width=\"349\" height=\"49\" \/>\r\n<p style=\"text-align: justify\">\u00a0 \u00a0 \u00a0Where A is the area of the crystal in m2, t is the thickness of the crystal and r is the relative permittivity.<\/p>\r\n&nbsp;\r\n\r\nTherefore, by solving and rearranging above equations we get\r\n\r\n<\/div>\r\n<div>\r\n\r\n<img class=\"size-full wp-image-128 alignleft\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-68.png\" alt=\"\" width=\"650\" height=\"375\" \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong>Merits.\u00a0<\/strong>Piezoelectric transducers are small in size and light. They are self-generating i.e. they do not need external power source. They operate over wide range of temperature, for quartz temperature range is of -200 to +300 0C, whereas for ceramic devices it is limited to +100 0C. Such systems have quite large outputs, for example, a quartz crystal of dimensions 2.5 mm (Thick) can have sensitivity upto 120 m V\/kPa and with crystals having area of 1000 mm2, sensitivity is of 125 V\/kN<\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong>Demerits. <\/strong>There output voltage generally gets affected by temperature variation of the crystals. When transducer is under constant deflection, it develops voltages across its terminals and slowly leaks of through its terminals. This decay of charge is very\u00a0<span style=\"text-align: initial;font-size: 1em\">slow due to high leakage resistance of 1011 ohms. <\/span>However<span style=\"text-align: initial;font-size: 1em\"> this charge leakage is very rapid when a voltage measuring device is connected across its terminals. This prevents <\/span>measurement<span style=\"text-align: initial;font-size: 1em\"> of any static displacement of the measurand. In commercial systems, quartz element of high leakage resistance is used &amp; input amplifiers of <\/span>high<span style=\"text-align: initial;font-size: 1em\"> impedance of 1014 ohms <\/span>slows<span style=\"text-align: initial;font-size: 1em\"> down the leakage allowing measurement of static displacements.<\/span><\/p>\r\n&nbsp;\r\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Applications of Piezoelectric Transducers<\/strong><\/p>\r\n\r\n<ol>\r\n \t<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">These transducers are mainly employed for estimating forces and pressure. Due to their simple and robust <\/span>construction<span style=\"text-align: initial;font-size: 1em\"> they are used for measuring forces over a wide range i.e. from 1 N to 200 N having a linearity of \u00b1 1%.<\/span><\/li>\r\n \t<li style=\"text-align: justify\">Piezoelectric transducers due their high frequency<span style=\"text-align: initial;font-size: 1em\"> response are mainly used in <\/span>high frequency<span style=\"text-align: initial;font-size: 1em\"> accelerometers. In <\/span>operation<span style=\"text-align: initial;font-size: 1em\"> their output voltage is <\/span>typically<span style=\"text-align: initial;font-size: 1em\"> of the order of 1-300 mV per <\/span><em style=\"text-align: initial;font-size: 1em\">g<\/em><span style=\"text-align: initial;font-size: 1em\"> of acceleration.<\/span><\/li>\r\n \t<li style=\"text-align: justify\">Quartz crystals can also be used as mass to frequency converter. A crystal controlled electronic oscillator has thin<span style=\"text-align: initial;font-size: 1em\"> quartz plate. The frequency of electrical oscillations depends on the natural frequency of mechanical oscillation of the plate.<\/span><\/li>\r\n \t<li style=\"text-align: justify\">Because of their rugged design and configuration<span style=\"text-align: initial;font-size: 1em\"> they are employed for collecting data under challenging conditions. They are used in ballistics, blasts, internal combustion, fuel injection, flow instabilities, <\/span>high intensity<span style=\"text-align: initial;font-size: 1em\"> sound hydraulic or pneumatic pulsations in connection with problems associated with guns shock tubes, closed bombs, rocket motors, internal combustion engines, pumps, compressors, pipelines <\/span>and<span style=\"text-align: initial;font-size: 1em\"> oil exploration <\/span>imploders<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/li>\r\n<\/ol>\r\n<\/div>\r\n<strong>\u00a0 \u00a0 Summary<\/strong>\r\n\r\n&nbsp;\r\n<p style=\"text-align: justify\">In this module we studied about transducers and how they are used in measuring various external forces. In the current module we studied about load cell, piezo-electric and photoelectric transducers. Our objective was to develop an understanding about the transducers and look into instrumental design and it\u2019s functioning based on the application. One should note that almost all transducer design are based on the quantity to be measured. Depending on the application and objectives of measurement one should select a transducer most suitable for that investigation.<\/p>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on  LVDT Transducers III<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/XbVROQNlswg\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n<strong>References :-<\/strong>\r\n<ol>\r\n \t<li style=\"text-align: justify\"><span style=\"font-size: 1em\">Electrical and Electronic Measurements and Instrumentation, <\/span><em style=\"font-size: 1em\">Sawhney A. K.<\/em><span style=\"font-size: 1em\">, Dhanpat Rai &amp; Sons, Reprint 1985<\/span><\/li>\r\n \t<li style=\"text-align: justify\">Measurements and Instrumentation, <em>Bakshi U.A., Bakshi A.V.,<\/em> Technical Publications, 2009<\/li>\r\n \t<li style=\"text-align: justify\">Principles of instrumental analysis, <em>Skoog, Douglas A., F. James Holler, and<\/em> <em>Stanley R. Crouc,. <\/em>Cengage learning, Edition 2017<\/li>\r\n \t<li style=\"text-align: justify\">Instrumentation, measurement and analysis. <em>Nakra, B.C. and Chaudhry, K.K.,<\/em> Tata McGraw-Hill Education, 2003.<\/li>\r\n \t<li style=\"text-align: justify\">Measurement and instrumentation: theory and application, <em>Morris, A. S., &amp;<\/em> <em>Langari, R<\/em>. , Academic Press, 2012<\/li>\r\n<\/ol>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/XbVROQNlswg\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<div>\n<p><strong>\u00a0 \u00a0 Learning Objectives<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">In this module we will study about transducers and how they are used in measuring various external forces. Our objective is<\/p>\n<ul>\n<li>To develop understanding about the transducers Look into instrumental design<\/li>\n<li>It\u2019s functioning based on the application.<\/li>\n<li>In the current module<span style=\"text-align: initial;font-size: 1em\"> we will study about load cell and piezo-electric transducers.<\/span><\/li>\n<\/ul>\n<p><strong>\u00a0 \u00a0 Introduction<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Transducers were developed for converting non-electrical quantity into electrical signal. This electrical signal is further processed by some electrical or electronic circuit that supplies output to a device for indication or recording purpose. Sometimes, transducers are used as primary transducers where input signal is sensed directly. In some cases transducer is used as a secondary transducer. Here a detector first senses the input signal and it output is supplied to secondary transducer as an input signal.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">In previous modules we studied about LVDT, Inductive and Capacitive transducers. In this modules we will study about other types of transducers like load cell, piezoelectric and photoelectric transducer.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Load Cell<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">A load cell is also known as pressure cell. It\u2019s a device that can covert weight (pressure) or mechanical force into electrical signal. It is widely used for measuring dynamic and static forces. The heart of this device is load (weight, force or pressure) receiving element which is a elastic element having high tensile strength. This element is bonded to strain gauge bridge network.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The output of the load cell is derived from the deformation of the elastic element made of homogenous materials like steel alloys. One should carefully select the material and its structural configuration so that one can have linear relationship between the dimensional change and the quantity (force) under measurement.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">A desirable material should have <\/span>following<span style=\"text-align: initial;font-size: 1em\"> properties: &#8211;<\/span><\/p>\n<ol>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">A fairly large elastic strain limit with a linear stress-strain relationship, say upto 5000 micro-strains.<\/span><\/li>\n<li style=\"text-align: justify\">Repeated overloading should produce low strain hysteresis (less than 2 micro-strain)<\/li>\n<li style=\"text-align: justify\">Very low creep of less than 5 micro-strain over long<span style=\"text-align: initial;font-size: 1em\"> period of loading<\/span><\/li>\n<li style=\"text-align: justify\">Very low plastic flow due to strain<\/li>\n<\/ol>\n<\/div>\n<div>\n<p>\u00a0 \u00a0 Based on the design of the load cell element, one can have 3 different configurations<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">(i) Column (ii) cantilevered bending beam and (iii) shear element. Let us study about these configurations one by one \u2013<\/p>\n<p>&nbsp;<\/p>\n<p><strong>1.\u00a0 <\/strong><strong>Column<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">Figure 1. illustrates the a typical design for columnar type load cell. Such columnar type cells are usually employed in load cell having capacity of 2250 kg or more. It had 2 strain gauges called active gauges that are bonded axially. The other two additional gauges are called the Poisson Gauges and are mounted 900 to axially positioned gauges. The load cell shown in the figure 1 is used only under compression. It has a fitting at the bottom of the base for attachment to the support structure with a load-receiving button at the top.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-120\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-60.png\" alt=\"\" width=\"245\" height=\"203\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-60.png 245w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-60-65x54.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-60-225x186.png 225w\" sizes=\"auto, (max-width: 245px) 100vw, 245px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><strong>Figure 1. <\/strong>Compression Load Cell<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">During the construction of the load cell, the load-receiving element is shrunk-fit into the base in a compression type load cell. The lower most section of the load cell housing, also known as Can, is welded on to the base structure. On the top of the\u00a0<span style=\"text-align: initial;font-size: 1em\">lower Can, a diaphragm is welded to the edge of the Can and the center column. The upper can is welded to the connection between the lower can and diaphragm. This completes <\/span>outer<span style=\"text-align: initial;font-size: 1em\"> shell of the load cell structure. Finally, the upper lip of the top diaphragm and the central column is welded to the top diaphragm. This seals the inner portion of the load cell which makes it impervious to gas and moisture. All the wires from the strain gauge are carried out through a glass-to-metal seal located in the lower can wall and are connected to the external cable.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">2. Bending Beams<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">Bending beams type load cells are used for measuring forces and weights below 225 kg. There few variations in design but the most common one is dual-guided cantilever beam, as shown in figure-2.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-121\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-61.png\" alt=\"\" width=\"179\" height=\"236\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-61.png 179w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-61-65x86.png 65w\" sizes=\"auto, (max-width: 179px) 100vw, 179px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><strong>Figure 2. <\/strong>Dual Guided Cantilever Beam Load Cell<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">It had four strain gauges that are mounted at the corners of a stabilized rectangle. When load is applied to the free end of this dual guided cantilever beam, the strain gauges bonded to the element undergo resistive change. This change is proportional to the forces or the load applied. In such type of cantilever beam configurations, the two gauges experience tension and two compression.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">3. Shear Element Configuration<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">In this configuration, one can have 4 or 8 gauges bonded to <\/span>specifically<span style=\"text-align: initial;font-size: 1em\"> designed element and is wired to form Wheatstone bridge. A centrally loaded shear beam configuration is shown in figure 3.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-122\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-62.png\" alt=\"\" width=\"359\" height=\"230\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-62.png 359w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-62-300x192.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-62-65x42.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-62-225x144.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-62-350x224.png 350w\" sizes=\"auto, (max-width: 359px) 100vw, 359px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><strong>Figure 3. <\/strong>Centrally Loaded Shear Beam<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The strain gauges used in this design differ from those used in columnar and dual-guided cantilever design. The strain gauges are designed in such a way that they get activated when they are placed under a shear force. Such elements have an advantage of have higher capacities in smaller size and have low sensitivity to side load error. i.e. when load is not placed proper orientation.<\/p>\n<p>&nbsp;<\/p>\n<p>The selection of a load for a particular application depends on the following factors \u2013<\/p>\n<p style=\"text-align: justify\">(1)\u00a0 Required Accuracy (2) Scale capacity (3) Type of Loading tensile (4) Number of cells required (5) loading conditions (6) Environment (7) Space Available (8) Desired output characteristics.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong>Piezoelectric Transducers<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The word \u201cPiezo\u201d, is derived from a greek word, \u2018<em>piezein\u2019<\/em> which means to squeeze or press. Certain crystalline and ceramic material can generate a potential difference across the opposing faces of the material when subjected to external mechanical force.\u00a0<span style=\"text-align: initial;font-size: 1em\">Such types of materials are Piezoelectric materials and this phenomenon is called Piezoelectric effect. This effect is also reversible, i.e. on applying <\/span>potential<span style=\"text-align: initial;font-size: 1em\"> across the opposing faces of the material one can get changes in the physical dimensions of the material. This principle of electro-mechanical energy conversion is used for developing energy conversion transducers.<\/span><\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-123\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-63.png\" alt=\"\" width=\"324\" height=\"188\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-63.png 324w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-63-300x174.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-63-65x38.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-63-225x131.png 225w\" sizes=\"auto, (max-width: 324px) 100vw, 324px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center\"><strong>Figure 4. <\/strong>Piezoelectric Transducer<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The transducer with mechanical input and electrical output are used for measuring dynamic pressure, force, shock or vibratory motion. Piezoelectric effect can only be observed in crystals having asymmetrical distribution of charge. Due to relative displacement of positive and negative charges within the lattice one can observe contraction or expansion of the material. This displacement of internal charges produces potential different across the fitted electrode. This is illustrated in figure 4. Here electrodes are placed on the opposing faces of the crystals, where output voltages are collected for measuring an external force or pressure.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">To better understand the piezoelectric properties of the transducing element in Piezoelectric Transducer let us consider a case of Quartz (SiO2) crystal. Figure 5 illustrates how opposing sides of the crystal get charged with application of external mechanical force. Under no load condition, positive and negative charges are arranged in center of the equisided triangular form.<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-124\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-64.png\" alt=\"\" width=\"251\" height=\"148\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-64.png 251w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-64-65x38.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-64-225x133.png 225w\" sizes=\"auto, (max-width: 251px) 100vw, 251px\" \/><\/p>\n<div>\n<p style=\"text-align: center\"><strong>Figure 5<\/strong>. Quartz Lattice Structure<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The two opposing charges at the center point become neutral and no potential difference gets developed across the opposing face of the crystal. With the application of external force F, ions within the crystal get displaced within the structure and equi-legged triangles get deformed. This deformation of crystal lattice is shown in the figure 5b. Incase of application of tensile force, potential of opposite polarity is developed across the crystalline face adjacent to electrodes. Similarly, when piezoelectric material is under the influence of external electric field, crystal may contract or expand depending upon the polarity of the field applied.<\/p>\n<p>&nbsp;<\/p>\n<p>The polarity &amp; magnitude of induced surface charges is proportional to the direction &amp;\u00a0 magnitude of the applied external force. Therefore,<\/p>\n<p>&nbsp;<\/p>\n<p>Q = <em>d. F<\/em> &#8212;&#8212;&#8211; (1)<\/p>\n<p>&nbsp;<\/p>\n<p>where <em>d<\/em> is the crystal charge sensitivity in coulombs per newton (C\/N) which is constant for a given crystal.<\/p>\n<p>&nbsp;<\/p>\n<p>The force <em>F<\/em> brings a change in the thickness of the crystal by\u00a0\u00a0\u00a0 t in meters<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-125\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-65.png\" alt=\"\" width=\"453\" height=\"48\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-65.png 453w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-65-300x32.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-65-65x7.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-65-225x24.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-65-350x37.png 350w\" sizes=\"auto, (max-width: 453px) 100vw, 453px\" \/><\/p>\n<p style=\"text-align: justify\">where A is the area of crystal in m2, E is the Young\u2019s modulus of elasticity and t is the thickness of the crystal.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The charge at the electrodes gives rise to the output voltage Vout and is given by the following equation \u2013<\/p>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-126\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-66.png\" alt=\"\" width=\"359\" height=\"55\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-66.png 359w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-66-300x46.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-66-65x10.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-66-225x34.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-66-350x54.png 350w\" sizes=\"auto, (max-width: 359px) 100vw, 359px\" \/><\/p>\n<div>\n<p>\u00a0 \u00a0 where Cc is the capacitance in between the electrodes of the crystal.<\/p>\n<p>&nbsp;<\/p>\n<p>As capacitance is given by<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-127\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-67.png\" alt=\"\" width=\"349\" height=\"49\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-67.png 349w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-67-300x42.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-67-65x9.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-67-225x32.png 225w\" sizes=\"auto, (max-width: 349px) 100vw, 349px\" \/><\/p>\n<p style=\"text-align: justify\">\u00a0 \u00a0 \u00a0Where A is the area of the crystal in m2, t is the thickness of the crystal and r is the relative permittivity.<\/p>\n<p>&nbsp;<\/p>\n<p>Therefore, by solving and rearranging above equations we get<\/p>\n<\/div>\n<div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-128 alignleft\" src=\"http:\/\/msp04.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-68.png\" alt=\"\" width=\"650\" height=\"375\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-68.png 650w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-68-300x173.png 300w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-68-65x38.png 65w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-68-225x130.png 225w, https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-content\/uploads\/sites\/103\/2018\/11\/Untitled-68-350x202.png 350w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong>Merits.\u00a0<\/strong>Piezoelectric transducers are small in size and light. They are self-generating i.e. they do not need external power source. They operate over wide range of temperature, for quartz temperature range is of -200 to +300 0C, whereas for ceramic devices it is limited to +100 0C. Such systems have quite large outputs, for example, a quartz crystal of dimensions 2.5 mm (Thick) can have sensitivity upto 120 m V\/kPa and with crystals having area of 1000 mm2, sensitivity is of 125 V\/kN<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong>Demerits. <\/strong>There output voltage generally gets affected by temperature variation of the crystals. When transducer is under constant deflection, it develops voltages across its terminals and slowly leaks of through its terminals. This decay of charge is very\u00a0<span style=\"text-align: initial;font-size: 1em\">slow due to high leakage resistance of 1011 ohms. <\/span>However<span style=\"text-align: initial;font-size: 1em\"> this charge leakage is very rapid when a voltage measuring device is connected across its terminals. This prevents <\/span>measurement<span style=\"text-align: initial;font-size: 1em\"> of any static displacement of the measurand. In commercial systems, quartz element of high leakage resistance is used &amp; input amplifiers of <\/span>high<span style=\"text-align: initial;font-size: 1em\"> impedance of 1014 ohms <\/span>slows<span style=\"text-align: initial;font-size: 1em\"> down the leakage allowing measurement of static displacements.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\"><strong style=\"text-align: initial;font-size: 1em\">Applications of Piezoelectric Transducers<\/strong><\/p>\n<ol>\n<li style=\"text-align: justify\"><span style=\"text-align: initial;font-size: 1em\">These transducers are mainly employed for estimating forces and pressure. Due to their simple and robust <\/span>construction<span style=\"text-align: initial;font-size: 1em\"> they are used for measuring forces over a wide range i.e. from 1 N to 200 N having a linearity of \u00b1 1%.<\/span><\/li>\n<li style=\"text-align: justify\">Piezoelectric transducers due their high frequency<span style=\"text-align: initial;font-size: 1em\"> response are mainly used in <\/span>high frequency<span style=\"text-align: initial;font-size: 1em\"> accelerometers. In <\/span>operation<span style=\"text-align: initial;font-size: 1em\"> their output voltage is <\/span>typically<span style=\"text-align: initial;font-size: 1em\"> of the order of 1-300 mV per <\/span><em style=\"text-align: initial;font-size: 1em\">g<\/em><span style=\"text-align: initial;font-size: 1em\"> of acceleration.<\/span><\/li>\n<li style=\"text-align: justify\">Quartz crystals can also be used as mass to frequency converter. A crystal controlled electronic oscillator has thin<span style=\"text-align: initial;font-size: 1em\"> quartz plate. The frequency of electrical oscillations depends on the natural frequency of mechanical oscillation of the plate.<\/span><\/li>\n<li style=\"text-align: justify\">Because of their rugged design and configuration<span style=\"text-align: initial;font-size: 1em\"> they are employed for collecting data under challenging conditions. They are used in ballistics, blasts, internal combustion, fuel injection, flow instabilities, <\/span>high intensity<span style=\"text-align: initial;font-size: 1em\"> sound hydraulic or pneumatic pulsations in connection with problems associated with guns shock tubes, closed bombs, rocket motors, internal combustion engines, pumps, compressors, pipelines <\/span>and<span style=\"text-align: initial;font-size: 1em\"> oil exploration <\/span>imploders<span style=\"text-align: initial;font-size: 1em\">.<\/span><\/li>\n<\/ol>\n<\/div>\n<p><strong>\u00a0 \u00a0 Summary<\/strong><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">In this module we studied about transducers and how they are used in measuring various external forces. In the current module we studied about load cell, piezo-electric and photoelectric transducers. Our objective was to develop an understanding about the transducers and look into instrumental design and it\u2019s functioning based on the application. One should note that almost all transducer design are based on the quantity to be measured. Depending on the application and objectives of measurement one should select a transducer most suitable for that investigation.<\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on  LVDT Transducers III<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/XbVROQNlswg\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>References :-<\/strong><\/p>\n<ol>\n<li style=\"text-align: justify\"><span style=\"font-size: 1em\">Electrical and Electronic Measurements and Instrumentation, <\/span><em style=\"font-size: 1em\">Sawhney A. K.<\/em><span style=\"font-size: 1em\">, Dhanpat Rai &amp; Sons, Reprint 1985<\/span><\/li>\n<li style=\"text-align: justify\">Measurements and Instrumentation, <em>Bakshi U.A., Bakshi A.V.,<\/em> Technical Publications, 2009<\/li>\n<li style=\"text-align: justify\">Principles of instrumental analysis, <em>Skoog, Douglas A., F. James Holler, and<\/em> <em>Stanley R. Crouc,. <\/em>Cengage learning, Edition 2017<\/li>\n<li style=\"text-align: justify\">Instrumentation, measurement and analysis. <em>Nakra, B.C. and Chaudhry, K.K.,<\/em> Tata McGraw-Hill Education, 2003.<\/li>\n<li style=\"text-align: justify\">Measurement and instrumentation: theory and application, <em>Morris, A. S., &amp;<\/em> <em>Langari, R<\/em>. , Academic Press, 2012<\/li>\n<\/ol>\n","protected":false},"author":3,"menu_order":7,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["prof-vinay-gupta"],"pb_section_license":""},"chapter-type":[],"contributor":[58],"license":[],"class_list":["post-116","chapter","type-chapter","status-publish","hentry","contributor-prof-vinay-gupta"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/116","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":6,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/116\/revisions"}],"predecessor-version":[{"id":511,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/116\/revisions\/511"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapters\/116\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/media?parent=116"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/pressbooks\/v2\/chapter-type?post=116"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/contributor?post=116"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/msp04\/wp-json\/wp\/v2\/license?post=116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}