Measurement SystemsProf. Ahmed A. Al-Rajihy

University of BabylonCollege of Engineering-Almusyyab

Department of Automobiles Engineering

Text: Measurement Systems, Application and Design by Ernest O. Doebelin.

Displacement Measurement Instruments:

1‐ Electrical Resistance potentiometer:

:

Vo  /x=Vs /AB            

Vo =xVs /AB=kx k: Sensitivity

• Es (Vs) may be AC or Dc supply.• Contact motion may be translation, rotation or combination of the two, i.e. helical motion.

• Resistance element may be wire wound, carbon film or conducting plastic.

•Error:For Rp/Rm=1, error 12%of full scale.For Rp/Rm<0.1, error= 15Rp/Rm% of full scale.•To minimize error, Rp/Rm should beminimum; But this reduce thesensitivity, where, k=Vs/L or (k=Es/L).

•To increase sensitivity, we mustincrease Vs and decrease L but thisis not the case because L is definedby the usage.

• In order to increase sensitivity,exciting voltage should be increasedwithin the safe limit, and L shouldbe decreased within the usefulrange, but:

• P: Heat dissipationps PRV max

Resolution: Length/no. wounds.Motion changes less than resolution cant be detected.

* Noise: Noise may happened due to contamination and/or resonance of sliding contact. 

For Non-open circuit;

Resistance Strain Gauges: Theoperation of strain gauges is basedon the principle that the electricalresistance of a conductor changeswhen it is subjected to a mechanicaldeformation …(1)where, R: Resistance of conductor, : resis-tivity of conductor material, , A : length and area of conductor.

AlR

δℓℓ

ρℓ

Differentiate the above Eq.(1) gives:

..(2) but &

Poisson’s ratio; and

Now:

And:

The local strain in terms of gauge factor andchange of conductor resistance is;

AdA

ldld

RdR

DdD

AdA 2 ldl/

t

ldlDdD

//

ldl

DdD

)21()2.(

dldl

ldld

RdR

RdRFG /.

d121

RR

FG

.1

** Advance alloy; 55% copper, 45% Nickel, G.F=2

** Iso-Elastic; 36% Nickel, 8% Chromium,4% manganese and others.

Types: (a) Unbounded strain gauge(b) Bounded strain gauges

unboundedbounded

The change in gauge resistance is:

And:                                                   Now,      Due to       is:

Now:

But

)(21

1

3 RRR

RRR

eeg

gexo

)(21

1

3 RRR

RRRRR

e

Re

gg

gg

ex

go

1)/(/1

)]/(/)[/(

211

2113

RRReeRRReeRR

RR

exc

excg

g

g

• Now:

• OR

• If   Rg.R2=R3.R1

Finally:

exg

go e

RRRRRRRR

e))(( 213

132

exg

g

g

go e

RR

RR

RR

RR

RRRR

e )()( 1

1

2

2

3

32

3

3

)(1

1

2

2

3

3

RR

RR

RR

RR

kee

g

g

ex

o

Temperature Compensation:

Now:

Finally: 

a

Eddy Current Transducers

A Bently Nevada proximity probe

Thank You For Listening