Fundamentals of
Measurement Technology
(8)
Prof,Wang Boxiong
Chapter 4 Acquisition of
measurands
4.1 Introduction
Transduction implies the conversion of a
measured or observed quantity,the
measurand,into an electrical,hydraulic,
pneumatic,or any other output by means of
a transducer or sensing element,
The device employed to accomplish this
conversion is known as a transducer or a
sensing element (sensor).
Transducer and sensing element are two
different concepts.
Sensing element,the element or unit which
directly senses and converts the measured
quantities
Transducer,the whole device consisting of a
sensing element with its associated auxiliary
components and circuits,the sensor or sensing
element being the kernel component
4.1 Introduction
Since we are mainly interested in signal
conversion laws of different devices and do
not care for whether it is a sensing element
or a transducer,so we do not distinguish
between a transducer and a sensing element
and generally refer to such a device as a
transducer if no additional explanation is
given,Since a transducer is located at the
input of measuring instrument,its quality
will influence directly the performance
characteristic of the whole instrument.
4.1 Introduction
We hope to acquire measurands with no
errors.
If the characteristic curve is a straight line,
the transducer is known as a linear
transducer.
But in most cases,the characteristic of a
transducer is not a linear one,and the
transducer is called a nonlinear transducer.
4.1 Introduction
Different ways are employed for the
classification of transducers
– One way is to classify transducers in terms of
measured quantities:
Force transducers
Velocity transducers
Temperature transducers
4.2 Classifications of transducers
– Another way is to make the classification in
terms of the operating principles of transducers
or the signal converting principles in
transduction
Structure-type transducers,transduce signals by
its structural variations
Capacitive transducer,changes capacitance by
varying gaps between two electrode plates or the
common area of the two plates
Sliding-contact resistive transducer,changes
resistance by changing the length of wire by
moving the slide
4.2 Classifications of transducers
Physical-property-type transducers,
based on the change in physical properties of
its sensing element material to realize signal
conversion
Pressure accelerometer,based on the
piezoelectric effect of its quartz crystal
material
Photo-sensitive resistor,changing its
resistance when exposed to light
4.2 Classifications of transducers
A transducer is also an energy converting element,
which converts one form of the measured energy into
another form of energy to a predefined accuracy or into
the same energy form of other values.
We also divide transducers into energy-converting and
energy-controlling transducers.
An energy-converting transducer ( passive transducer)
operates with the energy from the measurand.
An energy-controlling transducer (active transducer) is
powered by external energy source,the energy
variations being controlled by the measurand.
4.2 Classifications of transducers
Resistive transducer,a device which
converts a measurand into resistance
change
4.3 Resistive transducers
A
L
R
( 4,1 )
whe re
R the r esi st anc e (? ),
L the len gth of t he con duc tor (
cm
),
A
the cross - sec tion al area of con duc tor (
2
cm )
the r esi stiv ity of mat erial (
cm
)
4.3.1 Operating principle
4.3.1 Operating principle
S o me e x amp l e s i n c lud e s l i d in g - c o n ta c t
devices an d pot ent iomet er s,in w hich L
changes; r esistance st r ain - g a g e s,i n
w h i c h L,A,a n d? c h a n g e ; a n d
th e rmi s to rs,p h o to c o n d u c ti v e l i g h t
d e te c to rs,p i e z o res isti v e s trai n g a g e s,
a n d res i s ta n c e te mp e ratu re d e te c to rs,i n
w h i c h
c h a n g e s,
Convert mechanical displacement input into
electrical output,either in voltage or in current
This is accomplished by changing the effective
length of the conductor by the movable contact,
The contact motion can be translation,rotation
or a combination of the two (helical motion in a
multi-turn rotation device),this allowing
measurement of rotary and translatory
displacements
4.3.2 Sliding-contact resistive transducers
4.3.2 Sliding-contact resistive transducers
F ig,3.1 (a) sh ow s a tra ns la tio nal
sl id in g - co nta ct de vi ce,
xkR
t
(4.2)
w he re
t
k is the resi sta nce pe r un it l en gth
an d i s a co ns tan t w he n the w ire is
arran ge d u ni formly,
T he trans du ce r sen si tiv ity is
t
k
dx
dR
s
(4.3)
Fig,3.1 Resistive
transducers
4.3.2 Sliding-contact resistive transducers
F i g,3.1 (b) d i s p l a y s a rota ti o n a l
sliding - c o n ta c t de v i c e,in w h i c h the
res i s ta n c e va rie s w i th a n g l e,S i mi l a rly,w e
g e t the tran s d u c e r se n s i ti v i ty e x p res s e d
as
r
k
d
dR
s
(4.4 )
w h e re
a n g l e o f rota ti o n (rad )
r
k
res i s ta n c e p e r rad i a n,
Fig,3.1 Resistive
transducers
4.3.2 Sliding-contact resistive transducers
Fig,3.1 Resistive transducers
4.3.2 Sliding-contact resistive transducers
Fig,3.1 Resistive transducers
4.3.2 Sliding-contact resistive transducers
Fig,3.1 Resistive transducers
The resolution of pots is dependent on the
construction of the resistance element,and
to get sufficiently high resistance values in
small space the wire-wound element is
widely used (Fig,3.1),Here the variation of
resistance proceeds in small steps as the
wiper moves from one turn of wire to the
next (Fig,3.1 (a)) and this limits resolution.
4.3.2 Sliding-contact resistive transducers
4.3.2 Sliding-contact resistive transducers
Resolution can be improved by the use of
carbon film or conductive-plastic resistance
elements,or a multi-turn pot linked to the input
shaft via a gear box,
T he p ract ical l im it fo r w ire spacing is ab ou t 25
turns/m m,and thu s f or translational dev ices
resolution is lim ited to abo ut m?40,w hile f or a
sing le - turn cm5 diam eter rotational po t best
ang ular resolution is abo ut
10,
,
Sliding-contact devices have the advantages
– Simple construction
– Stable performance
– Convenient to use
They are often used in
– Measurement of translational displacements
– Measurement of rotational displacements
They are often employed to construct
– Servo recorders
– Electronic potential-difference meter
4.3.2 Sliding-contact resistive transducers
4.3.3 Resistance strain gages
I f a c on du ct or i s s t r et ch ed o r c om pr es s ed,i t s
r es i s t an ce w i l l c ha ng e be ca us e of d i m en s i on al
ch an ge s ( l en gt h an d cr os s - s ec t i on al a r ea ) a nd
be ca us e of a f un da m en t al p r op er t y o f m at er i al s
ca l l ed p i ez or es i s t an c e,w hi ch i nd i ca t es a
dependence of r esi st i v i t y? on t he m ec ha ni ca l
s t r ai n,
Differentiate Eq,(4.1) to get
substituting into Eq,(4.6) we get
4.3.3 Resistance strain gages
2
)(
A
l dAlddlA
dR
(4.6)
L e tt in g
2
rA,r is th e r a d iu s o f r e s is ta n c e w ir e,
)
2
(
2
322
r
drd
l
dl
R
dr
r
l
d
r
l
dl
r
dR
( 4.7 )
w he r e s t r ai nun i t
l
dl
,a nd
r
dr
is the r e la tive
c ha ng e o f w ir e r a diu s
The n we ha s the f oll owing r e lations hip wit h
l
dl
,
l
dl
r
dr
( 4,8 )
4.3.3 Resistance strain gages
w h e r e P o i s s o n ’ s r a t i o o f t h e w i r e m a t e r i a l
T h e term
d
ref lect s the rela tive ch a n g e o f resis tivi ty
w ith the lon g itud in al s tr ess
ap p lie d to res ist an ce w ire
in the f o llow ing f o rm,
E
d
11
( 4,9 )
w h ere
1
lon g itud ina l p iezo resistan t c o ef f icien t
E
m o d u lus o f elasticity
4.3.3 Resistance strain gages
S ubstitut ing E qs,( 4.8 ) a nd ( 4.9 ) into E q,( 4.7 ) g ive s
)E21(
1
＋
R
dR
( 4,1 0 )
A na l y z in g Eq,( 4.1 0),w e kno w tha t the r e la ti ve r e sist a nc e
c ha ng e
R
dR
is de pe nde nt on the f ollowing f a c tor s,
1,r e sist a nc e c ha n ge du e to le n g th c ha n ge ( th e f irst
te r m on the r ig ht - ha nd side )
2,r e sist a nc e c h a n g e due to a r e a c ha n ge ( the se c ond
te r m on the r ig ht - ha nd side )
3,r e sist a nc e c ha ng e du e to p ie z or e sist a nt e f f e c t
4.3.3 Resistance strain gages
It is a lso sh o w n tha t the rel at iv e res ist an ce ch an g e is
p rop o rtio n al to the s tr ain,S o m e asu rem en t o f
l
dl
allo w s m easu rem en t o f
R
dR
,T h is i s th e p rin cip l e o f the
resis tan c e st rain g ag e,
g
S is the so - c alled g ag e f acto r o r
g ag e se n sitiv ity,
E
l
dl
R
dR
S
g 1
21 ( 4,1 1 )
4.3.3 Resistance strain gages
Strain gages,in general,are applied in two types of tasks,in
experimental stress analysis of machines and structures and
in construction of force,torque,pressure,flow,and
acceleration transducers,The unbonded metal-wire gage,
used almost exclusively for transducer applications,
employs a set of preloaded resistance wires connected in a
Wheatstone bridge,as shown in fig,4.3.
4.3.3 Resistance strain gages
T he wir e s f or st r a in g a ge s a r e made of va r ious meta ls suc h
as c oppe r - nick e l,c hr om e - nicke l,or nicke l - iron a ll o y s,a r e
a bout mm,030 in diame ter,c a n sust a in a ma x im u m f or c e
of only a bout N,0020,a nd ha ve a g a g e f a c tor of 2 to 4,
4.3.3 Resistance strain gages
Fig,4.3 Unbonded strain gage
R e s i s t a n c e o f e a c h b r i d g e a r m i s 1 2 0 t o?1000,
m a x im u m e x c i t a t i o n v o l t a g e i s 5 t o V10,a n d f u l l - s c a l e
o u t p u t t y p i c a l l y i s 20 t o mV50,
4.3.3 Resistance strain gages
Fig,4.4 Metal-wire strain gage Fig,4.5 Cross-section of a metal-wire strain gage
The bonded metal-wire gage has been applied to
both stress analysis and transducers.
Embedded in a matrix of cement,the wires cannot
buckle and thus faithfully follow both the tension
and the compression strains of the specimen.
Today,the bonded metal-wire gage is largely
superseded by the bonded metal-foil construction.
4.3.3 Resistance strain gages
Bonded metal-foil gages,
–
– In addition to single-element gages,gage combinations called
rosettes (Fig,4.6) are available in many configurations for
specific stress-analysis or transducer applications,
– Theory shows that measurements with a 3-gage rosette allow
calculation of all the desired information,
– Evaporation-deposited thin-metal-film gages are used mostly
for transducers,as are the sputter-deposited variety.
4.3.3 Resistance strain gages
T h e s e n s i n g e l e m e n t s a r e f o r m e d f r o m s h e e t s l e s s t h a n
0,0 0 5 m m t h i c k by p h ot o e t c h i n g p r o c e s s e s,w h i c h a l l o w s
g r e a t f l e xi b i l i t y w i t h r e g a r d t o s h a p e,
4.3.3 Resistance strain gages
Fig,4.6 Foil strain gages
A semiconductor strain gage is based on the
piezoresistant effect of semiconductor materials,When
a mono-crystal semiconductor material is applied with
a force along a defined axis,its resistivity changes,
This effect is called the piezoresistant effect,It is
known from the semiconductor physics that,when a
force is applied to a mono-crystal semiconductor
material,its atomic lattice changes,resulting in a
change in the transition rate and the concentration of
the current-carriers and so the change in resistivity.
4.3.4 Semiconductor strain gages
Bonded semiconductor gages are used mainly in
transducers,They are made by slicing small
sections from specially processed silicon crystals
and are available in both N- and P-type,The P-
type gages increase resistance with applied tensile
strain while the N-type decrease resistance,Their
main feature is a very high gage factor – as much
as 150.
4.3.4 Semiconductor strain gages
4.3.4 Semiconductor strain gages
1,Silicon bar
2,Wire lead
3,Plastic substrate
4,P-type Si
5,N-type Si
Fig,4.7 Different types of semiconductor strain gages
Fig 4.8 shows the cross-section of a semiconductor diaphragm
absolute pressure sensor,A P-type region diffused into an N-
type base functions as a resistor whose value increases
strongly when it is strained (this behavior is called
piezoresistivity).
4.3.4 Semiconductor strain gages
E q,( 4,10 ) sho w s tha t t he r e la tive r e sista nc e c ha ng e is
a f f e c t e d ma inly b y tw o f a c tor s,
21?
E1
T he r e sista n c e c h a n g e o f a se mic on du c tor g a ge is ma inl y
de pe nd e nt on th e la tte r te r m
4.3.4 Semiconductor strain gages
Fig,4.8 Semiconductor diaphragm absolute pressure sensor
Temperature is an important interfering input for strain gages
4.3.5 Errors of strain gage and their compensation
(1) G age r esis tance change due to t em pera ture var iat ion
TRR
fT
w here
T
R
gage r esis tance change due to t em pera ture var iat ion
f
tem pera tur e coef f ici en t of re s isti vity f or m eta llic
gage,r ela ti ve r esi stance change ca used by tem pera ture var iat ion
T
tem pera ture change ( deg.)
Th en the st ra in r ela ted t o this r esis tance change is
g
f
g
T
T
S
T
SR
R?
1
( 4,1 2 )
4.3.5 Errors of strain gage and their compensation
(2) A dditiona l str a in due to tem pera tur e vari a ti on caused by th e
dif f er ent coef f ici ents of li nea r expa nsion of the m eta l w ir e and the
substra te m ate ri als,
Th e st ra in of the m eta l wire cause d by tem pera ture var iat ion,
T
gg
（ 4,13 ）
and the str a in of the subst rate m ate rial due to the tem pera ture
vari ati on,
T
ss
（ 4,14 ）
w here
g
and
s
ar e t he coef f ici ents of linear expansion of the
m eta l wire and the substr at e,r espect ivel y,
4.3.5 Errors of strain gage and their compensation
If
sg
and so
sg
,then the d if f erenc e o f strain
T
sgsg
)( （ 4,15 ）
Th e re sultant additional strain du e to tem perature variation is then
T
S
T
sg
g
f
ta
)(
（ 4,16 ）
A lso the g age sensiti vity
g
S w il l chan ge w it h tem perature
variation,and m ay cause ch ang e in strain,
Th is chan ge is usually v ery sm all and can be neg lected,
These temperature effects can be compensated in
various ways.
4.3.5 Errors of strain gage and their compensation
Fig,4.9 Strain-gage temperature compensation
Another approach to this problem involves special,
inherently temperature-compensated gages,These
gages are designed to be used on a specific material
and have expansion and resistance properties such that
the two effects very nearly cancel and no dummy gage
is required.
Another error source is related to the gage size and the
position of the point to be measured.
4.3.5 Errors of strain gage and their compensation
Th us w e have
g
f
sg
S
（ 4,17 ）
Various adhesives have been developed for
fastening strain gages to specimens,e.g,epoxy
resin,phenolic resin (at normal temperatures),
ceramic power (at high temperatures).
The quality of the adhesive joints obviously is
critical to the proper operation of the strain gage,
since we rely completely on it to transmit the
specimen strain to the gage grid.
4.3.6 Adhesion of strain gages
Strain gages are mainly used for stress analysis
and for constructing transducers
For the first application,strain gages are usually
bonded to the measured position of a structure member
to obtain the stress or strain of the member,thus
providing data for the design of the structure member,
the check of stress and the prediction of possible
damages in the structure,
For the second application,strain gages are bonded or
formed on elastic elements to construct various
transducers for the measurement of force,displacement,
pressure,torque and acceleration.
4.3.7 Applications
4.3.7 Applications
Fig,4.10 Strain gage transducers for force and torque measurements
Measurement Technology
(8)
Prof,Wang Boxiong
Chapter 4 Acquisition of
measurands
4.1 Introduction
Transduction implies the conversion of a
measured or observed quantity,the
measurand,into an electrical,hydraulic,
pneumatic,or any other output by means of
a transducer or sensing element,
The device employed to accomplish this
conversion is known as a transducer or a
sensing element (sensor).
Transducer and sensing element are two
different concepts.
Sensing element,the element or unit which
directly senses and converts the measured
quantities
Transducer,the whole device consisting of a
sensing element with its associated auxiliary
components and circuits,the sensor or sensing
element being the kernel component
4.1 Introduction
Since we are mainly interested in signal
conversion laws of different devices and do
not care for whether it is a sensing element
or a transducer,so we do not distinguish
between a transducer and a sensing element
and generally refer to such a device as a
transducer if no additional explanation is
given,Since a transducer is located at the
input of measuring instrument,its quality
will influence directly the performance
characteristic of the whole instrument.
4.1 Introduction
We hope to acquire measurands with no
errors.
If the characteristic curve is a straight line,
the transducer is known as a linear
transducer.
But in most cases,the characteristic of a
transducer is not a linear one,and the
transducer is called a nonlinear transducer.
4.1 Introduction
Different ways are employed for the
classification of transducers
– One way is to classify transducers in terms of
measured quantities:
Force transducers
Velocity transducers
Temperature transducers
4.2 Classifications of transducers
– Another way is to make the classification in
terms of the operating principles of transducers
or the signal converting principles in
transduction
Structure-type transducers,transduce signals by
its structural variations
Capacitive transducer,changes capacitance by
varying gaps between two electrode plates or the
common area of the two plates
Sliding-contact resistive transducer,changes
resistance by changing the length of wire by
moving the slide
4.2 Classifications of transducers
Physical-property-type transducers,
based on the change in physical properties of
its sensing element material to realize signal
conversion
Pressure accelerometer,based on the
piezoelectric effect of its quartz crystal
material
Photo-sensitive resistor,changing its
resistance when exposed to light
4.2 Classifications of transducers
A transducer is also an energy converting element,
which converts one form of the measured energy into
another form of energy to a predefined accuracy or into
the same energy form of other values.
We also divide transducers into energy-converting and
energy-controlling transducers.
An energy-converting transducer ( passive transducer)
operates with the energy from the measurand.
An energy-controlling transducer (active transducer) is
powered by external energy source,the energy
variations being controlled by the measurand.
4.2 Classifications of transducers
Resistive transducer,a device which
converts a measurand into resistance
change
4.3 Resistive transducers
A
L
R
( 4,1 )
whe re
R the r esi st anc e (? ),
L the len gth of t he con duc tor (
cm
),
A
the cross - sec tion al area of con duc tor (
2
cm )
the r esi stiv ity of mat erial (
cm
)
4.3.1 Operating principle
4.3.1 Operating principle
S o me e x amp l e s i n c lud e s l i d in g - c o n ta c t
devices an d pot ent iomet er s,in w hich L
changes; r esistance st r ain - g a g e s,i n
w h i c h L,A,a n d? c h a n g e ; a n d
th e rmi s to rs,p h o to c o n d u c ti v e l i g h t
d e te c to rs,p i e z o res isti v e s trai n g a g e s,
a n d res i s ta n c e te mp e ratu re d e te c to rs,i n
w h i c h
c h a n g e s,
Convert mechanical displacement input into
electrical output,either in voltage or in current
This is accomplished by changing the effective
length of the conductor by the movable contact,
The contact motion can be translation,rotation
or a combination of the two (helical motion in a
multi-turn rotation device),this allowing
measurement of rotary and translatory
displacements
4.3.2 Sliding-contact resistive transducers
4.3.2 Sliding-contact resistive transducers
F ig,3.1 (a) sh ow s a tra ns la tio nal
sl id in g - co nta ct de vi ce,
xkR
t
(4.2)
w he re
t
k is the resi sta nce pe r un it l en gth
an d i s a co ns tan t w he n the w ire is
arran ge d u ni formly,
T he trans du ce r sen si tiv ity is
t
k
dx
dR
s
(4.3)
Fig,3.1 Resistive
transducers
4.3.2 Sliding-contact resistive transducers
F i g,3.1 (b) d i s p l a y s a rota ti o n a l
sliding - c o n ta c t de v i c e,in w h i c h the
res i s ta n c e va rie s w i th a n g l e,S i mi l a rly,w e
g e t the tran s d u c e r se n s i ti v i ty e x p res s e d
as
r
k
d
dR
s
(4.4 )
w h e re
a n g l e o f rota ti o n (rad )
r
k
res i s ta n c e p e r rad i a n,
Fig,3.1 Resistive
transducers
4.3.2 Sliding-contact resistive transducers
Fig,3.1 Resistive transducers
4.3.2 Sliding-contact resistive transducers
Fig,3.1 Resistive transducers
4.3.2 Sliding-contact resistive transducers
Fig,3.1 Resistive transducers
The resolution of pots is dependent on the
construction of the resistance element,and
to get sufficiently high resistance values in
small space the wire-wound element is
widely used (Fig,3.1),Here the variation of
resistance proceeds in small steps as the
wiper moves from one turn of wire to the
next (Fig,3.1 (a)) and this limits resolution.
4.3.2 Sliding-contact resistive transducers
4.3.2 Sliding-contact resistive transducers
Resolution can be improved by the use of
carbon film or conductive-plastic resistance
elements,or a multi-turn pot linked to the input
shaft via a gear box,
T he p ract ical l im it fo r w ire spacing is ab ou t 25
turns/m m,and thu s f or translational dev ices
resolution is lim ited to abo ut m?40,w hile f or a
sing le - turn cm5 diam eter rotational po t best
ang ular resolution is abo ut
10,
,
Sliding-contact devices have the advantages
– Simple construction
– Stable performance
– Convenient to use
They are often used in
– Measurement of translational displacements
– Measurement of rotational displacements
They are often employed to construct
– Servo recorders
– Electronic potential-difference meter
4.3.2 Sliding-contact resistive transducers
4.3.3 Resistance strain gages
I f a c on du ct or i s s t r et ch ed o r c om pr es s ed,i t s
r es i s t an ce w i l l c ha ng e be ca us e of d i m en s i on al
ch an ge s ( l en gt h an d cr os s - s ec t i on al a r ea ) a nd
be ca us e of a f un da m en t al p r op er t y o f m at er i al s
ca l l ed p i ez or es i s t an c e,w hi ch i nd i ca t es a
dependence of r esi st i v i t y? on t he m ec ha ni ca l
s t r ai n,
Differentiate Eq,(4.1) to get
substituting into Eq,(4.6) we get
4.3.3 Resistance strain gages
2
)(
A
l dAlddlA
dR
(4.6)
L e tt in g
2
rA,r is th e r a d iu s o f r e s is ta n c e w ir e,
)
2
(
2
322
r
drd
l
dl
R
dr
r
l
d
r
l
dl
r
dR
( 4.7 )
w he r e s t r ai nun i t
l
dl
,a nd
r
dr
is the r e la tive
c ha ng e o f w ir e r a diu s
The n we ha s the f oll owing r e lations hip wit h
l
dl
,
l
dl
r
dr
( 4,8 )
4.3.3 Resistance strain gages
w h e r e P o i s s o n ’ s r a t i o o f t h e w i r e m a t e r i a l
T h e term
d
ref lect s the rela tive ch a n g e o f resis tivi ty
w ith the lon g itud in al s tr ess
ap p lie d to res ist an ce w ire
in the f o llow ing f o rm,
E
d
11
( 4,9 )
w h ere
1
lon g itud ina l p iezo resistan t c o ef f icien t
E
m o d u lus o f elasticity
4.3.3 Resistance strain gages
S ubstitut ing E qs,( 4.8 ) a nd ( 4.9 ) into E q,( 4.7 ) g ive s
)E21(
1
＋
R
dR
( 4,1 0 )
A na l y z in g Eq,( 4.1 0),w e kno w tha t the r e la ti ve r e sist a nc e
c ha ng e
R
dR
is de pe nde nt on the f ollowing f a c tor s,
1,r e sist a nc e c ha n ge du e to le n g th c ha n ge ( th e f irst
te r m on the r ig ht - ha nd side )
2,r e sist a nc e c h a n g e due to a r e a c ha n ge ( the se c ond
te r m on the r ig ht - ha nd side )
3,r e sist a nc e c ha ng e du e to p ie z or e sist a nt e f f e c t
4.3.3 Resistance strain gages
It is a lso sh o w n tha t the rel at iv e res ist an ce ch an g e is
p rop o rtio n al to the s tr ain,S o m e asu rem en t o f
l
dl
allo w s m easu rem en t o f
R
dR
,T h is i s th e p rin cip l e o f the
resis tan c e st rain g ag e,
g
S is the so - c alled g ag e f acto r o r
g ag e se n sitiv ity,
E
l
dl
R
dR
S
g 1
21 ( 4,1 1 )
4.3.3 Resistance strain gages
Strain gages,in general,are applied in two types of tasks,in
experimental stress analysis of machines and structures and
in construction of force,torque,pressure,flow,and
acceleration transducers,The unbonded metal-wire gage,
used almost exclusively for transducer applications,
employs a set of preloaded resistance wires connected in a
Wheatstone bridge,as shown in fig,4.3.
4.3.3 Resistance strain gages
T he wir e s f or st r a in g a ge s a r e made of va r ious meta ls suc h
as c oppe r - nick e l,c hr om e - nicke l,or nicke l - iron a ll o y s,a r e
a bout mm,030 in diame ter,c a n sust a in a ma x im u m f or c e
of only a bout N,0020,a nd ha ve a g a g e f a c tor of 2 to 4,
4.3.3 Resistance strain gages
Fig,4.3 Unbonded strain gage
R e s i s t a n c e o f e a c h b r i d g e a r m i s 1 2 0 t o?1000,
m a x im u m e x c i t a t i o n v o l t a g e i s 5 t o V10,a n d f u l l - s c a l e
o u t p u t t y p i c a l l y i s 20 t o mV50,
4.3.3 Resistance strain gages
Fig,4.4 Metal-wire strain gage Fig,4.5 Cross-section of a metal-wire strain gage
The bonded metal-wire gage has been applied to
both stress analysis and transducers.
Embedded in a matrix of cement,the wires cannot
buckle and thus faithfully follow both the tension
and the compression strains of the specimen.
Today,the bonded metal-wire gage is largely
superseded by the bonded metal-foil construction.
4.3.3 Resistance strain gages
Bonded metal-foil gages,
–
– In addition to single-element gages,gage combinations called
rosettes (Fig,4.6) are available in many configurations for
specific stress-analysis or transducer applications,
– Theory shows that measurements with a 3-gage rosette allow
calculation of all the desired information,
– Evaporation-deposited thin-metal-film gages are used mostly
for transducers,as are the sputter-deposited variety.
4.3.3 Resistance strain gages
T h e s e n s i n g e l e m e n t s a r e f o r m e d f r o m s h e e t s l e s s t h a n
0,0 0 5 m m t h i c k by p h ot o e t c h i n g p r o c e s s e s,w h i c h a l l o w s
g r e a t f l e xi b i l i t y w i t h r e g a r d t o s h a p e,
4.3.3 Resistance strain gages
Fig,4.6 Foil strain gages
A semiconductor strain gage is based on the
piezoresistant effect of semiconductor materials,When
a mono-crystal semiconductor material is applied with
a force along a defined axis,its resistivity changes,
This effect is called the piezoresistant effect,It is
known from the semiconductor physics that,when a
force is applied to a mono-crystal semiconductor
material,its atomic lattice changes,resulting in a
change in the transition rate and the concentration of
the current-carriers and so the change in resistivity.
4.3.4 Semiconductor strain gages
Bonded semiconductor gages are used mainly in
transducers,They are made by slicing small
sections from specially processed silicon crystals
and are available in both N- and P-type,The P-
type gages increase resistance with applied tensile
strain while the N-type decrease resistance,Their
main feature is a very high gage factor – as much
as 150.
4.3.4 Semiconductor strain gages
4.3.4 Semiconductor strain gages
1,Silicon bar
2,Wire lead
3,Plastic substrate
4,P-type Si
5,N-type Si
Fig,4.7 Different types of semiconductor strain gages
Fig 4.8 shows the cross-section of a semiconductor diaphragm
absolute pressure sensor,A P-type region diffused into an N-
type base functions as a resistor whose value increases
strongly when it is strained (this behavior is called
piezoresistivity).
4.3.4 Semiconductor strain gages
E q,( 4,10 ) sho w s tha t t he r e la tive r e sista nc e c ha ng e is
a f f e c t e d ma inly b y tw o f a c tor s,
21?
E1
T he r e sista n c e c h a n g e o f a se mic on du c tor g a ge is ma inl y
de pe nd e nt on th e la tte r te r m
4.3.4 Semiconductor strain gages
Fig,4.8 Semiconductor diaphragm absolute pressure sensor
Temperature is an important interfering input for strain gages
4.3.5 Errors of strain gage and their compensation
(1) G age r esis tance change due to t em pera ture var iat ion
TRR
fT
w here
T
R
gage r esis tance change due to t em pera ture var iat ion
f
tem pera tur e coef f ici en t of re s isti vity f or m eta llic
gage,r ela ti ve r esi stance change ca used by tem pera ture var iat ion
T
tem pera ture change ( deg.)
Th en the st ra in r ela ted t o this r esis tance change is
g
f
g
T
T
S
T
SR
R?
1
( 4,1 2 )
4.3.5 Errors of strain gage and their compensation
(2) A dditiona l str a in due to tem pera tur e vari a ti on caused by th e
dif f er ent coef f ici ents of li nea r expa nsion of the m eta l w ir e and the
substra te m ate ri als,
Th e st ra in of the m eta l wire cause d by tem pera ture var iat ion,
T
gg
（ 4,13 ）
and the str a in of the subst rate m ate rial due to the tem pera ture
vari ati on,
T
ss
（ 4,14 ）
w here
g
and
s
ar e t he coef f ici ents of linear expansion of the
m eta l wire and the substr at e,r espect ivel y,
4.3.5 Errors of strain gage and their compensation
If
sg
and so
sg
,then the d if f erenc e o f strain
T
sgsg
)( （ 4,15 ）
Th e re sultant additional strain du e to tem perature variation is then
T
S
T
sg
g
f
ta
)(
（ 4,16 ）
A lso the g age sensiti vity
g
S w il l chan ge w it h tem perature
variation,and m ay cause ch ang e in strain,
Th is chan ge is usually v ery sm all and can be neg lected,
These temperature effects can be compensated in
various ways.
4.3.5 Errors of strain gage and their compensation
Fig,4.9 Strain-gage temperature compensation
Another approach to this problem involves special,
inherently temperature-compensated gages,These
gages are designed to be used on a specific material
and have expansion and resistance properties such that
the two effects very nearly cancel and no dummy gage
is required.
Another error source is related to the gage size and the
position of the point to be measured.
4.3.5 Errors of strain gage and their compensation
Th us w e have
g
f
sg
S
（ 4,17 ）
Various adhesives have been developed for
fastening strain gages to specimens,e.g,epoxy
resin,phenolic resin (at normal temperatures),
ceramic power (at high temperatures).
The quality of the adhesive joints obviously is
critical to the proper operation of the strain gage,
since we rely completely on it to transmit the
specimen strain to the gage grid.
4.3.6 Adhesion of strain gages
Strain gages are mainly used for stress analysis
and for constructing transducers
For the first application,strain gages are usually
bonded to the measured position of a structure member
to obtain the stress or strain of the member,thus
providing data for the design of the structure member,
the check of stress and the prediction of possible
damages in the structure,
For the second application,strain gages are bonded or
formed on elastic elements to construct various
transducers for the measurement of force,displacement,
pressure,torque and acceleration.
4.3.7 Applications
4.3.7 Applications
Fig,4.10 Strain gage transducers for force and torque measurements
