9AEI It is defined as the change of position of a body with respect to a reference It may be Linear motion Rotational motion Displacement

9AEI Displacement Measurement Range For linear displacement A few microns to few centimeters For angular displacement A few seconds to 360 º

9AEI Linear potentiometer Fig.1

9AEI Principle It converts linear displacement into an electrical output The resistance of a wire is given as R=ρl/a Where R = resistance of wire ρ = specific resistance l = length of the wire a = area of cross section of wire

9AEI Principle Resistive displacement transducer are commonly termed as potentiometer or ‘pot’ As the wiper moves the resistance changes which in turn changes the output voltage

9AEI A pot is an electromechanical device containing an electrically conductive wiper that slides against a fixed resistive element according to the position An output voltage is generated as shown in fig The output voltage is proportional to the displacement of the wiper Operation

9AEI Equation e 0 = (e i /x i )L x i = (e 0 /e i )L where e o = output voltage in volts e i = d.c input voltage in volts x i = displacement of slider from its zero position L = total length of the potentiometer

9AEI Linear potentiometerAngular potentiometer Fig.2 Practical Potentiometers

9AEI

10 Fig.3

9AEI

9AEI Fig.4 Practical Potentiometers

9AEI Advantages and Disadvantages

9AEI Specifications

LVDT

9AEI Principle It produces an electrical output which is proportional to the displacement of the Ferro magnetic moveable core It works on the principle of electro magnetic induction

9AEI Linear Variable Differential Transformer (LVDT) Fig.1

9AEI Construction The fig. shows the construction of LVDT It consists of one primary coil Two identical secondary coils An a.c excitation voltage source A movable Ferro magnetic core

9AEI Operation When primary winding is excited with an A.C signal, voltages are induced in each secondary winding. The magnitude of the voltages depends upon the position of the iron core with respect to the center of the coil. The differential output of LVDT is given by e 0 = e s1 - e s2 Where e s1 is induced voltage in the secondary winding s1 and e s2 is induced voltage in the secondary winding s2.

9AEI Case 1: When the core is at null (centre) position e s 1 = e s 2 ( ø ps1 = ø ps2 ) e o = o (primary) core Secondary-2 Fig.2

9AEI When the core moves towards secondary winding S 1 i.e. e s 1 > e s 2 ( ø ps1 > ø ps2 ) The differential output is positive and in phase with input signal core Fig.3

9AEI When the core moves towards secondary winding S 2 i.e. e s 2 > e s 1 ( ø ps1 < ø ps2 ) The differential output is negative and 180 o out of phase With the input signal. core Fig.4

9AEI The polarity or phase induced depend upon the movement of the core the magnitude of output voltages gives the amount of displacement.

9AEI

9AEI

9AEI Transfer Characteristic Curve Fig.5

9AEI Advantages Rugged construction Extremely fine resolution High accuracy Good stability High sensitivity

9AEI Low hysteresis Good repeatability Ability to operate at high temperature Withstands shock and vibration without any adverse effect

9AEI Disadvantages Relatively large displacements are required for appreciable differential output They are sensitive to stray magnetic fields Susceptible to vibration Requires an a.c signal or demodulated network to get a d.c output Temperature sensitive

9AEI Applications of LVDT : Used 1.As basic element in Extensometers 2.In Electronic comparators 3.In Thickness measuring units 4.In Level indicators 5.In numerically – controlled machines 6.In creep testing machines

9AEI Four LVDT’s are used for measurement of weight or pressure exerted by liquid in a tank. They (LVDT ’s) are excited in parallel to increase sensitivity. Fig. 6 Practical Applications of LVDT

9AEI Two LVDT’s are used for measurement and control of thickness of a metal sheet being rolled.when the thickness equals the desired value,the two LVDT’s balanced out. Fig. 7

9AEI An LVDT being used for measurement of tension in a card. Fig. 8

9AEI Complex system where a number of LVDT’s are used in a manufacturing process. Fig. 9

LVRT

9AEI It works on the principle of self inductance The self inductance of a coil changes due to variation in the position of the core Principle

9AEI Construction It consists of Two coils A cylindrical bobbin A movable ferromagnetic core The constructional details are shown in fig.1 below.

9AEI Linear variable reluctance transducer (LVRT) Fig.1

9AEI Fig.2

9AEI Two coils L 1 and L 2 are wound continuously over a cylindrical bobbin with a ferromagnetic core moving within it Any variation in the position of the core will change the self inductances of the coils L 1 and L 2. Operation

9AEI Operation The fractional change ∆L in the inductance L is approximately related to the fractional change ∆x in position x of the core for small displacements as

9AEI The measurements are carried out for this transducer with a Wheatstone bridge circuit as shown in Fig.2. The coils L 1 and L 2 form half of the bridge, and The other two arms are completed with two fixed Resistors R 1 and R 2 with Capacitors C 1 and C 2 in parallel R 1, R 2 C 1 & C 2 are to achieve both amplitude and phase. Operation

9AEI Detector circuit

9AEI Under balance condition the output voltage is zero If there is any change in self inductance of the coil the bridge will become unbalance and the corresponding output is produced The output voltage is proportional to the displacement of the core Operation

Inductive Proximity Sensor

9AEI It operates on the principle, That the inductance of a coil is considerably changed in the presence of magnetic material. Principle

9AEI Inductive proximity sensor Fig 1

9AEI A basic inductive sensor consists of a magnetic circuit. It is made with a ferromagnetic core. A coil wounded on it.

9AEI

9AEI

9AEI When the object moves closer to the coil the air gap reduces The reluctance of the magnetic circuit is also reduces then the inductance of the coil increase The change of inductance can be measured by an a.c bridge The magnitude of inductance is a measure of displacement Operation

Inductive Proximity Sensor

9AEI It operates on the principle, That the inductance of a coil is considerably changed in the presence of magnetic material. Principle

9AEI Inductive proximity sensor Fig 1

9AEI A basic inductive sensor consists of a magnetic circuit. It is made with a ferromagnetic core. A coil wounded on it.

9AEI

9AEI

9AEI When the object moves closer to the coil the air gap reduces The reluctance of the magnetic circuit is also reduces then the inductance of the coil increase The change of inductance can be measured by an a.c bridge The magnitude of inductance is a measure of displacement Operation

Proximity Sensor

9AEI The principle of operation of capacitive proximity sensor is based upon the equation of parallel plate capacitor. The capacitance of a parallel plate capacitor is given by Where, A = over lapping area d = distance between plates ε = dielectric constant Principle

9AEI Fig.1

9AEI

9AEI Principle The capacitance of a capacitor changes in two ways. Changing the distance between the two plates. Changing the overlapping area of the two plates.

9AEI Changing the displacement between two plates Fig 2

9AEI This consists of a fixed plate and movable plate. The displacement to be measured is applied to the arm which is connected to the movable plate. Due to movement of the arm the distance between the plates changes and accordingly the capacitance changes. Operation

9AEI This capacitance is inversely proportional to the distance between the plates. This capacitance can be converted into electrical signal by an a.c bridge circuit.

9AEI The response of this Transducer is non-linear. Fig 3

9AEI Changing the overlapping area of the Plates Fig 3

9AEI This consists of two plates a fixed and movable plate. As displacement changes the overlapping area of the plates changes Accordingly the capacitance also changes. The capacitance change is proportional to the overlapping area of the plates. Operation

9AEI The capacitance can be converted into output voltage by a ac bridge circuit. The output voltage e o is proportional to the overlapping area A of the plates. i.e.

9AEI The response of this Transducer is linear. Fig 5

9AEI advantages, Low cost and power usage Good stability, High Resolution, Fast response. Near-zero temperature coefficient, Easy to integrate into ICs or onto printed- circuit boards (pc boards)..

9AEI Applications Capacitive sensors can detect Motion, Acceleration, Flow, Density and many other variables

Strain Gauge 9AEI

9AEI Resistance transducer These type of transducers have slow dynamic response susceptible to vibration Noise wear etc.

9AEI Equation

9AEI Strain Gauge Principle ΔL is elongation in length of wire (i.e., L) G f is gage factor, which defines the sensitivity. It is defined as change in resistance for unit strain.

9AEI Strain Gauge Principle Gauge factor can vary from 2-6 for metallic strain gages. For semiconductor it varies from 40 to 200. Gauge factor value is supplied by the manufacturer

9AEI Strain Gauge Principle When a wire is stretched, it gets thinner and longer and the resistance changes. More the wire is strained more the change in resistance.

9AEI Resistive Sensors - Strain Gauges Gauge factor derivation Resistance is related to length and area of cross-section of the resistor and resistivity of the material as By taking logarithms and differentiating both sides, the equation becomes Dimensional piezoresistance

9AEI Resistive Sensors - Strain Gauges Strain gage component can be related by poisson’s ratio as

9AEI Resistive Sensors - Strain Guages Gage Factor of a strain gage G is a measure of sensitivity.

9AEI Resistive Sensors - Strain Gauges

9AEI Resistive Sensors - Strain Gauges Strain gauges are generally mounted on cantilevers and diaphragms and measure the deflection of these. More than one strain gauge is generally used and the readout generally employs a bridge circuit.

9AEI Strain Gage Mounting Applications!  Surgical forceps  Blood pressure transducer (e.g. intracranial pressure

9AEI Bridge Circuits Wheatstone’s Bridge

9AEI Bridge Circuits Wheatstone’s Bridge R-dR R+dR R Rf Vs R Vo Real Circuit and Sensor Interface