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  • 8/11/2019 Lecture 11Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 Lecture 1 vv

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    RESISTIVE TRANSDUCERS

    Lecture 11Instructor : Dr Alivelu M Parimi

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    RESISTIVE

    POTENTIOMETERS Loading Effect of Potentiometers

    The usual situation with use of potentiometer is that output

    voltage is fed to a meter or recorder that draws some current

    from the potentiometer. Thus a more realistic circuit is as

    shown in Figure

    2

    Schematic of Loaded

    Potentiometer

    Using concept of voltage divider concept,

    K1mK1

    K

    R||RRR

    R||R

    e

    e

    xmxp

    xm

    ex

    0

    where

    K =m

    p

    t

    i

    p

    x

    R

    Rm&

    x

    x

    R

    R

    When K = 0, i.e. x i=0, e0= 0 V , wiper is on one extreme [negative side of supply] and

    whole of eexis dropped across resistor.

    When K=1, i.e. xi = xt, e0 = eex, wiper is on other extreme [ positive side of supply ] and

    whole of supply is tapped

    Choice of Rp thus must be influenced by a

    tradeoff between loading and sensitivity

    considerations

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    RESISTIVE

    POTENTIOMETERS

    3

    Rm = detector is of infinite impedance( ideal detector) i.e. m = 0 ; Ke

    e

    ex

    0

    When m = 0 , input-output curve is a straight line and e0is open circuit voltage.

    When Rm , m >0 , there is a nonlinear relation between e0 and xi. This deviation from

    linearity is shown in Figure 4.3.

    Error = (output voltage under no load) - ( output voltage at loaded condition )

    = eex.K - K1mK1K.eex

    =

    m

    KK

    KKeex1

    1

    12

    At K = 0 and K = 1, error = 0. At all other points error is positive, since voltage of loaded

    potentiometer is less than unloaded potentiometer. The position of wiper at which maximum

    error occurs could be found by differentiating error expression w.r.t. K. For all values of m,

    maximum error is encountered for values of K around 0.6 - 0.7.

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    RESISTIVITE

    POTENTIOMETERS

    4

    A variable pot has a total resistance of 2.2 kand is fed from 10 V DC supply. The output is

    connected to a load resistance of 5.1 k. Tabulate errors for wiper positions from 0 to 1.0 in

    increments of 0.1

    Error = eex.

    p

    m

    2

    R

    RK1K

    1KK

    K 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

    Error/Eex 0 0.037 0.013 0.25 0.37 0.48 0.573 0.58 0.52 0.3363 0.0

    It may be observed that maximum error is for K between 0.7 and 0.8

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    Resolution of Potentiometers

    The resolution of potentiometer is strongly influenced by the

    construction of the resistance element.

    A single slide-wire as the resistance element gives an

    essentially continuous step less resistance variation as the

    wiper travels over it.

    Slide wire resistance elements, also called non-wire wound

    resistance elements provide improved resolution and life;

    however, they are more temperature-sensitive, have a high

    wiper contact resistance.

    Elements of both cermet and conductive plastic are available

    in the form of flat strips or films and thus present a smooth

    surface to the wiper. They are conventionally described as

    having infinitesimal resolution.5

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    Resolution of Potentiometers

    To get sufficiently high resistancevalues in small space, the wire woundresistance element is widely used.

    The resistance wire is wound in amandrel or card which is then formed

    into a circle or helix if a rotationaldevice is desired as shown in Figure

    With such a construction the variation

    of resistance is not a linear continuouschange, but actually proceeds in smallsteps as the wiper moves from oneturn of the wire to the next as shownin figure 6

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    Resolution of Potentiometers

    This phenomenon results in a fundamental limitation on the resolutionin terms of resistance-wire size.

    For instance, if a translational device has 500 turns of resistance wire ona card 1 inch long, motion changes smaller than 0.002 inch cannot bedetected. The actual limit for wire spacing according to current practiceis between 500 and 1,000 turns per inch. For translational devices,

    resolution is thus limited to 0.001 to 0.002 inches. Another approach to increased resolution involves the use of multiturn

    potentiometers.

    The resistance element is in the form of a helix, and the wiper travelsalong a lead screw. The number of wires per inch of element is stilllimited, but an increase in resolution can be obtained by introducinggearing between the shaft whose motion is to be measured and thepotentiometer shaft.

    For example, one rotation of the measured shaft could cause 10rotations of the potentiometer shaft; thus the resolution of measured-shaft motion is increased by a factor of 10.

    For translational devices, various motion-amplifying mechanisms couldbe used in similar fashion.

    7

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    Example

    8

    Suppose we have two resistors of 10 and 330 both having power rating of 0.25W. I

    both resistors are connected to 6V battery then power dissipated by 330 resistor is PD=

    W109.0330

    66

    R

    V 2

    and power dissipated by 10 resistors is

    10

    66= 3.6W.

    Then 10 resistor will burn, since power dissipated by it exceeds its rated capacity. Smaller

    resistance will carry more current and burnout (principle used in fuse)

    A control potentiometer is rated as 150 Ohm, 1W (derate at 10 mW/oC above 65

    oC).

    Thermal resistance is 30oC/W. Can it be used with a 10V supply at 80

    otemperature?

    Problem

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    RESISTANCE STRAIN GAGES

    Strain measurement is generally used for testing the performance ofa particular device when subjected to vibration, bending,compression and tension, torque etc.

    They are used in industry, aerospace, medical, automotive sector,material testing research etc

    . Strain Gages in general are applied in two types of tasks, one ofthem being experimental stress analysis of machines and structuresand the other being in the development of force, torque, pressure,flow and acceleration transducers.

    Strain Gage works on the basic principle of change in the resistanceupon application of strain.

    Both Strain Gages and Potentiometer are resistive transducers. Thebasic difference is that Potentiometer resistance is varied manuallyor automatically by wiper motion, while Strain Gages exhibitschange in resistance by mechanical deformation or stress. 9

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    RESISTANCE STRAIN GAGES

    10

    Consider a conductor of uniform cross sectional area A and length L, as shown in Figure 4.7.

    Fig. 4.7: Wire with length L and area of cross--section A

    It is made of a material with resistivity () and the resistance R of such a conductor is given

    by

    R =A

    L

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    Basic Concepts, RESISTANCE

    STRAIN GAGES

    11

    If this conductor is now stretched or compressed, its resistance will change because of

    dimensional changes (length and cross sectional area) and because of a fundamental property

    of materials called piezoresistance which indicates a dependence of resistivity () on the

    mechanical strain. R depending on the basic parameters. Taking natural logarithmic and

    differentiating expression of resistance. To find expression for sensitivity of gage, it is

    required to findL/dL

    R/dRwhich is fractional change in resistance per unit applied strain.

    ln R = ln + ln Lln A

    A

    dA

    L

    dLd

    R

    dR

    R =A

    L

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    12

    A

    dA

    L

    dLd

    R

    dR

    D

    dD2

    A

    dA;

    L/dL

    /d

    L/dL

    A/dA1

    L/dL

    R/dR

    = Poissons ratio =L/dL

    D/dD

    soL/dL

    R/dR= 1 + 2+

    L/dL

    /d

    L/dL

    R/dR

    is called Gage factor, so

    Gage factor =

    effectcepiezoresistoduechangeceresischangeareatodue

    changeceresis

    changelengthtodue

    changeceresisLdL

    d

    LdL

    RdR

    tantan

    tantan/

    /21

    /

    /

    Basic Concepts, RESISTANCE

    STRAIN GAGES

    This is the principle of the resistance gage. The termLdL

    d

    /

    /can also be expressed as ,E

    where is the longitudinal piezoresistance and E is the modulus of elasticity. Poissonsratio is always between 0 and 0.5 for all the materials.

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    Strain Gages

    Desirable features of Strain Gages are:

    High value of gage factor which will lead to enhanced

    sensitivity

    High Gage resistance to minimize the effects of

    undesirable variation of resistance in measurement circuitry(connecting leads, terminals, etc.)

    Linear relationship between resistance vs strain

    Good spatial resolution, ideally measuring strain at a

    point Insensitive to changes in ambient temperature

    High frequency response for dynamic strain

    measurements 13

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    Problem

    14

    A Strain Gage is bonded to a steel beam which is 10 cm long having cross-sectional area o

    4 cm2. Youngs modulus of elasticity (Ysteel) is 20.7 x 10

    102m

    N.

    Gage resistance is 240 ,

    Gage factor is 2.2. Upon application of load, resistance changes by 0.0013 . Calculate the

    change in length and amount of force applied.

    Solution

    =L

    Land Gage factor = 2.2

    L/L

    R/R

    m

    m

    L

    L 61046.22.2

    240/0013.0

    Y = Youngs Modulus =Strain

    Stressso Stress = Y.= (20.7 x 10

    10) N/

    m

    2( 2.46 x 10

    -6)

    = 50.922 x 104

    2m

    N

    F = Stress x Area = (50.922 x 104 2mN )x ( 4 x 10-4m2)= 203.688 N

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    Classification of Strain Gages

    Unbonded Metal Wire Gage

    Bonded Metal Wire Gage

    Bonded Metal Foil Gage

    Vacuum Deposited Thin Metal Film Gage.

    Sputter Deposited Thin Metal Film Gage.

    Bonded Semiconductor Gage

    Diffused Semiconductor Gage 15

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    The Unbonded Metal Wire

    Gage

    16

    It employs a set of preloaded resistance wires

    connected in a Wheatstone Bridge

    configuration as shown in the Figure

    At the initial preload resistance the strains and the resistances of the four wires are nominally equal, which gives a

    balanced bridge, and e0 = 0. Application of a small input motion increases the tension in the two wires ( 1 & 3) and

    decreases in the other two ( 2& 4) causing corresponding resistances to change and making the bridge unbalanced. The

    output voltage of bridge being proportional to the input motion.

    The wires may be made of various Copper-Nickel, Manganin, Chrome Nickel, or Nickel-Iron alloys.

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    The Bonded Metal-Wire Gage

    A grid of fine wire is cemented to the specimen surface where

    the strain is to be measured.

    Embedded in the matrix of cement, the wires cannot buckle

    and thus faithfully follow both the tensile and the compressive

    strains of the specimen. Since materials and wire sizes are similar to those of the

    unbonded gage, gage factors and resistances are comparable.

    17

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    The Bonded Metal-Foil Gage

    Bonded Metal Foil Gages use identical or similar materials to

    wire gages that are used today for most general purpose

    stress analysis tasks and many transducers. The sensing

    elements are formed from sheets less than 0.0002 inches

    thick by Photoetching process which allows greater flexibilitywith regard to the shape. The various shapes of this type of

    the Strain Gage

    18

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    Evaporation-deposited and sputtering -

    deposited thin-metal film gages

    Thin-film gages exhibit improved time and temperature

    stability.

    Both evaporation-deposited and sputter-deposited form all

    the gage elements directly on the strain surface; they are not

    separately attached as with bonded gages. Resistances and gage factors of film gages usually are similar

    to those of the bonded foil strain gages.

    19

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    To study

    Bonded Semiconductor Gage

    Diffused Semiconductor Gage

    20

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    Strain Gage Bridge

    Arrangements Strain Gage Bridge Arrangements

    Quarter Bridge

    Half Bridge

    Full bridge

    21

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    Problem

    A resistance strain gage having gage factor 3.5 has

    contribution of 1.7 due to piezoresistive effect. Calculate the

    contribution of Poissons ratio in Gage Factor.

    22

    Solution

    (G.F.) = 1 + 2 + E

    2 = (G.F.)1E

    = 3.511.7 = 0.8

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    Problem

    Strain Gage with gage resistance of 350and gage factor of 2

    is used in Wheatstone Bridge with resistances of other three

    arms being 350. If strain of 1450 microns is applied, find the

    bridge output voltage if excitation voltage is 10V.

    23

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    Bonded Semiconductor Gage

    strain sages depend on the piezoresistive effects of Silicon or

    Germanium and measure the change in resistance with stress

    as opposed to strain. The semiconductor bonded strain gage is

    a wafer with the resistance element diffused into a substrate

    of Silicon. The wafer element usually is not provided with abacking, and bonding it to the strained surface requires great

    care as only a thin layer of epoxy is used to attach it as shown

    in Figure

    24

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    Strain Gage Bridge

    Arrangements Strain Gage Bridge Arrangements

    Quarter Bridge

    Half Bridge

    Full bridge

    25

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    Quarter Bridge

    26

    Quarter Bri dge

    The strain gage bridge circuit shown in Figure 4.14, in which one arm is occupied by strain

    gage is known as Quarter Bridge. The strain gage may be measuring deflection caused by

    orce, pressure, vibration, torque etc.

    Fig. 4.14: Quarter Bridge Strain Gage Circuit

    Physical realization of this is shown in Figure 4.15, where strain gage bonded on cantilever

    orms one arm of the bridge.

    Fig. 4.15 : Quarter Bridge Arrangement for Cantilever Beam

    We analyze this circuit for finding the expression for output voltage in terms of change in

    resistance.

    Assume RRRR 321

    Voltage source = Vs

    Output voltage = Vo

    If due to tensile force strain gauge resistance changes to RR

    2

    1

    RR2

    RRVV so

    RR22

    RR2R2R2Vs

    R2R4

    RVs

    if RR ,

    R

    RVV so

    4 ( as 2R

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    Half Bridge

    27

    The strain gage bridge circuit shown in Figure 4.16, in which two arms are occupied bystrain gages is known as Half Bridge .

    Fig. 4.16 : Half Bridge Strain Gage Circuit

    Physical realization of half bridge is shown in Figure 4.17, where strain gages bonded on

    pper and lower side of cantilever form two arms of the bridge. Figure 4.17(a) shows the

    cantilever under no load leading and corresponding balanced bridge. Figure 4.17(b) shows

    he loaded beam and unbalanced bridge.

    Suppose one strain gauge(upper one ) undergoes tension RR and the other(lower one)

    undergoes compression, RR

    Voltage source = Vs

    Output voltage = V0

    2

    1

    R2

    RRVV

    so

    R

    RRR

    2

    Vs

    R

    R

    2

    Vs

    output voltage is directly proportional to R, resulting in linear relationship between V0and

    R.

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    Full bridge

    28

    Figure 4.18 shows the Full bride circuit in which all the arms of the bridge are constituted by

    active strain gages. One possible physical arrangement of strain gages can be thought of as:

    wo strain gages on the upper side of cantilever undergoing tension, and the two on lower

    side of cantilever beam undergoing compression.

    Fig. 4.18 : Full Bridge Strain Gage Circuit

    Voltage source = Vs

    Output voltage = Vo

    R2

    RR

    R2

    RRVV so

    R2R2

    Vs

    R

    RVs

    It can be observed that Sensitivity of Quarter bridge < Half bridge< Full bridge.

    Full bridge always gives linear output while for quarter bridge and half bridge where the two

    arms are occupied by opposite arms, linear relationship is attained only for small changes in

    R .