Measurement Systems - University of Babylon · Measurement Systems Prof. Ahmed A. Al-Rajihy...
Transcript of Measurement Systems - University of Babylon · Measurement Systems Prof. Ahmed A. Al-Rajihy...
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