BASIC MECHANICAL SENSORS AND SENSOR PRINCIPLES

Definitions Transducer: a device that converts one form of energy into another. Sensor: a device that converts a physical parameter to an electrical output. Actuator: a device that converts an electrical signal to a physical output.

Sensors : definition and principles

Sensors : taxonomies Measurand –physical sensor –chemical sensor –biological sensor(cf : biosensor) Invasiveness –invasive(contact) sensor –noninvasive(noncontact) sensor Usage type –multiple-use(continuous monitoring) sensor –disposable sensor Power requirement –passive sensor –active sensor

Potentiometers Translational Single turn Helical

The Wheatstone bridge

Circuit Configuration E 0 = V AC V A = E b xR 4 /(R 1 +R 4 ) V C = E b xR 3 /(R 2 +R 3 ) E 0 = V AC = V A – V C =

Null-mode of Operation At balance: R 2 R 4 = R 1 R 3 or R 1 /R 4 = R 2 /R 3 and the output voltage is zero

Example 1 9 Assume that the bridge shown is used to determine the resistance of an unknown resistance R x. The variable resistance is the resistance box that allows selection of several resistors in series to obtain the total resistance and it is set until null position in the meter observed. Calculate the unknown resistance if the variable resistance setting indicates . The bridge will be balanced if R 1 /R 4 = R 2 /R 3. Hence, R 4 = R x = R 1 /(R 2 /R 3 ) = 1000x625.4/600 = .

Deflection-mode of Operation All resistors can very around their nominal values as R 1 +  R 1, R 2 +  R 2, R 3 +  R 3 and R 4 +  R 4. Sensitivity of the output voltage to either one of the resistances can be found using the sensitivity analysis as follows

E Th = E 0 = V AC (open circuit) R Th = R 1 //R 4 + R 2 //R 3 I g = E 0 /(R Th + R g ) E g = E 0 R g /(R Th + R g ) In case of open-circuit (R g  ) E g = E 0 The equivalent circuit

Stress and strain Tension: A bar of metal is subjected to a force (T) that will elongate its dimension along the long axis that is called the axial direction. Compression: the force acts in opposite direction and shortens the length A metal bar Stress: the force per unit area  a = T/A (N/m 2 ) Bar with tension Strain Strain: The fractional change in length  a = dL/L (  m/m)

Hooke’s law Stress is linearly related to strain for elastic materials  a =  a /E y = (T/A)/E y E y : modulus of elasticity ( Young’s modulus) The stress-strain relationship

Transverse strain The tension that produces a strain in the axial direction causes another strain along the transverse axis (perpendicular to the axial axis) as  t = dD/D This is related to the axial strain through a coefficient known as the Poisson’s ratio as dD/D = - dL/L The negative sign indicates that the action is in reverse direction, that is, as the length increases, the diameter decreases and vice versa. For most metals is around 0.3 in the elastic region and 0.5 in the plastic region

Electrical Resistance of Gage Wire R=  L/A A =  r 2 = (  /4)D 2 and dA/A = 2 dD/D yields dD/D = - dL/L Piezoresistive effect Dimensional effect

Principles of strain measurement Gage factor - K K = (dR/R)/(dL/L) = (dR/R)/  a For wire type strain gages the dimensional effect will be dominant yielding K  2 For heavily doped semiconductor type gages the piezoreziztive effect is dominant yielding K that ranges between 50 and 200 dR can be replaced by the incremental change  R in this linear region yielding  R/R = K  a

Bonded Strain- Gages A bonded gage Fixing the gage

Examples of bonded gages Resistance-wire type Foil typeHelical-wire type K  2.0 R 0 = 120  or 350 . 600  and 700  gages are also available

Semiconductor strain-gage units Unbonded, uniformly doped Diffused p-type gage

Fixing the gage 20

21

Strain gage on a specimen 22

The unbonded gage 23

Unbonded strain-gage pressure sensor

Example 2 25 A strain gage has a gage factor 2 and exposed to an axial strain of 300  m/m. The unstrained resistance is 350 . Find the percentage and absolute changes in the resistance.  a = 300  m/m = 0.3x10 -3 ;  R/R = K  a = 0.6x10 -3 yielding %age change = 0.06% and  R = 350x0.6x10 -3 = 0.21 .

Example 3 26 A strain gage has an unstrained resistance of 1000  and gage factor of 80. The change in the resistance is 1  when it is exposed to a strain. Find the percentage change in the resistance, the percentage change in the length and the external strain (  m/m).  R/R (%) = 0.1 %;  L/L (%) = [  R/R (%)]/K = 1.25x10 -3 %, and  a = [  L/L (%)]/100 = 1.25x10 -5 = 12.5  m/m

Wheatstone bridge for the pressure sensor

Integrated pressure sensor

Integrated cantilever-beam force sensor

Elastic strain-gage Mercury-in-rubber strain-gage plethysmography (volume- measuring) using a four-lead gage applied to human calf. Venous-occlusion plethysmography Arterial-pulse plethysmography

Effect of Temperature and Strain in other Directions R 0 is the resistance at T 0 and  is the temperature coefficient This is very much pronounced in case of semiconductor gages due to high temperature coefficient. Effects of wanted strain (sw), unwanted strain (su) and temperature (T) add up in the change in resistance as  R =  R sw +  R su +  R T The effect of unwanted strain and temperature must be eliminated before the resistance change is used to indicate the strain

Bridge Configurations For Strain Gage Measurements The cantilever beam with a single strain-gage element A quarter bridge

Analysis of quarter-bridge circuit Let R 1 = R 2 = R 3 = R and R 4 = R x = R +  R = R(1 +  R/R), and let x =  R/R. The open circuit voltage E 0 = 0 at balance (  R = 0). At slight unbalance (  R  0) Let x =  R/R Since x<<1, higher order terms can be neglected yielding

Sensitivity analysis can also be used Sensitivity analysis

Effect of Temperature and Tensile Strain  R =  R Q +  R W +  R T The effect of unwanted strain and temperature must be eliminated. The circuit as it is provides no compensation. Using a second strain gage of the same type for R 1 can compensate effect of temperature. This second gage can be placed at a silent location within the sensor housing, hence kept at the same temperature as the first one. As a result, both R 1 and R 4 have the same amount of changes due to temperature that cancel each other in the equation yielding perfect temperature compensation

Wheatstone Bridge with Strain Gages and Temperature Compensation 36

Bridge with Two Active Elements The cantilever beam with two opposing strain gages Circuit for the half-bridge

Circuit analysis Let R 2 = R 3 = R; R 1 = R -  R; R 4 = R +  R, the open circuit voltage E 0 = 0 at balance (  R = 0). At slight unbalance (  R  0)

Insensitivity of half-bridge Effects of wanted and unwanted strains and temperature on measuring gages

Bridge with Four Active Elements (Full Bridge) The force, when applied in the direction shown, causes tension on gages at the top surface (R +  R Q ) and compression on gages at the bottom surface (R -  R Q ). The tensile force W causes (R +  R W ) on all gages. The temperature also produces (R +  R T ) on all gages. The cantilever beam with four strain gages (full bridge)

The strain gages that are working together are placed into opposite (non- neighboring) arms of the bridge. The strain gage resistors are manufactured for a perfect match to have the open circuit voltage E 0 = 0 at balance (  R = 0). At slight unbalance (  R  0) with R 1 = R 3 = R -  R; R 2 = R 4 = R +  R

L = n 2 G , where n= number of turns of coil G = geometric form factor  = effective permeability Self-inductance Inductive sensors Mutual inductance Differential transformer

LVDT transducer (a)electric diagram and (b)cross-section view

LVDT

Capacitive sensors +Q  Q x Area =A

Capacitive displacement transducer (a)single capacitance and (b)differential capacitance

Capacitive sensor for measuring dynamic displacement changes

Piezoelectric sensors k is piezoelectric constant C/N K is proportionality constant C/m K S =K/C, V/m;  = RC, s

Response to step displacement

High-frequency response High-frequency circuit model for piezoelectric sensor. R S is the sensor leakage resistance and C S the capacitance. L m, C m and R m represent the mechanical system. Piezoelectric sensor frequency response.

Quantum Tunneling Composites 51 Structure and effect of pressure for QTC

Effect of Pressure on a QTC Pill 52

QTC as a Pressure Sensor 53