Download force measurement – strain gauges k

FORCE MEASUREMENT – STRAIN GAUGES
For the resistive strain gauge - the relation between the relative resistor’s change and the
relative extension (or contraction):
∆R
∆l
=K
, where K is so called “gauge factor” (“the deformation sensitivity” – the main
R
l
gauge strain parameter).
I.
STRAIN GAUGE –SHUNT CALIBRATION – see fig. P.30
1/ For weight G used as load between supports, constant bending torque Mo the relative
elongation of the surface filaments of a bar can be calculated as
M0
∆l
4 yh
=
= 2 , where y … the bar deflection, h, b, r … see fig. P.30,
l
W0 E
r
E … elasticity modulus (Young's modulus)
h 2b
1 M 0r 2
h 3b
(for W0 =
,
(r >>y),
y=
,
J=
)
6
EJ 8
12
2/ If weight G is substituted (simulated) with the resistor Rc (shunt resistor) see fig. P.31 –
the change of resistance is
2
RR
R0
∆R = R0 − c 0 =
Rc + R 0 R c + R0
R0
∆R
∆l
,
(if substituted) …
=
=K
R0 Rc + R0
l
the gauge factor …
Fig. P.30
correct: d = h
K=
R0
r2
Rc + R0 4 yh
where R0 = 120 Ω
Fig. P.31
Task:
a/ To determine the GAUGE FACTOR K of the foil strain gauge which is cemented on
the duralumin bar - loaded in agreement with the fig. P.30. The measurement should be
repeated 3 times and GAUGE FACTOR K calculated as average from those 3
measurements. The compensating strain gauge has to be used – see fig. P.31.
b/ In the limits of Hook’s law, measure and plot the bar deflection vs. load - dependency
y = f (G), and the bridge output voltage vs. load G, what means Fu = f (G), But –Note: the
output voltage of the quarter bridge (Wheatstone bridge with the one active strain gauge,
only) – is proportional to loading force Fu in (N).
Use metal discs (7pcs x 0,63 kg, each) – as the load. First, add the metal discs then
remove them to determine if hysteresis has to be taken into consideration; Calculate
sensitivity for the ½ Gmax (from the plotted graph), the correction factor k for the
Fu = f(G) dependency – so that the statements Fu would be in agreement with the real
loading G ( Fu = kG ).
c/ Verify as the DEMO, only:
- repeatability (e.g.: by the 5 times – loading with the same load – from 0 – step change
- up to 20 N about).,
- short-time stability (e.g.: in the range from 30 to 60 s for the selected load),
- the possibility to increase the sensitivity by using a half-bridge instead of the one
active strain gauge (quarter bridge); can be done by light pressure on the bar with
compensating strain gauge.
- the temperature influence (!! As the last DEMO!! – to allow enough time to cool down
for the next group). The spot light (from the distance about 0,3 m) realizes the heating,
!! short time only, please !!
Instruments:
- Geometric Quantities Measurement System – INTRONIX – NX 3030 + sensor
(LVDT-probe ± 0,5 mm – accuracy 1 %),
- Digital Precision Measuring Amplifier – SCOUT 55 + strain gauge quarter bridge
with the compensating gauge strain RK = RM = 120 Ω,
- The loading system with 7 pcs metal discs (0,63 kg ± 1% each, about),
- The resistor with resistive decade Rc = 567 k Ω + R, where R … 0-100 kΩ, (1%).
Attention:
The main switch ON – on the rear panel SCOUT 55: front panel: 1-st “right” button – ON,
0 – “zero” button ON,
the main switch ON – on the rear panel INTRONIX, front panel: (MENU – by means of
↑↓ ↵ - to select: Current measurement). The display values – can be taken as starting
values.
When the measurement is finished - the main switches – OFF!!
Manipulation – (for task a) – strain gauge factor K):
- put all 7 discs on the plateau – calculate what is load Gmax, measure bar´s deflection y
- remove the load Gmax and simulate it by the “electric” way – that means, connect the
parallel (shunt) resistor Rc (the connecting terminals are marked on the resistive
decade Rc). On this resistive decade, the R-value has to be set – to reache the original
value (as by loading with Gmax), then Rc = R + 567 kΩ. (resistor 567kΩ is connected
in series with the decade)
Note: ! The manipulation with the discs has to be done carefully – don´t let the
mechanism fall down the support edges!
!! Don´t touch the wires connecting the strain gauges at all and especially during the
measurement!!!
Tab. 1
for R0=120Ω ;
Gmax … m ≅ 7x 0,63 kg
No. FU load [ N] y deflection [mm]
1
2
3
RC = R + 567 kΩ
K
[-]
Kawg
[-]
ad b)
Tab.2.
G
load No.
disc
0
1
2
3
4
5
6
7
Tab. 2
for … y = f(G) ; … FU = f(G)
Bridge output
[V]
average
↑
↓
loading
unloading
y
↑
loading
deflection
[mm]
average
↓
unloading
The transducer sensitivity – from the graph:
∆F
∆y
c F = U = … [N/N] or [V/N] ; c y =
= … [mm/N] ;
∆G
∆G
Fig.P.25
II.
Fig.P.26
Fig.P.27
STRAIN GAUGE BRIDGE - TEMPERATURE COMPENSATION
Fig. P.25: The condition of bridge balance: R1R4 = R2 R3 , then Uv = 0, e.g.: for R1-4 =
R0 … the standstill value (without load).
¼ - quarter bridge: 1 measuring strain gauge, can have 1 compensating strain gauge – this
one has to be situated in the neighbouring branch – see fig. P.26,
½ - half bridge: 2 measuring strain gauges, may have also 2 compensating strain gauges.
Theoretically it has 2-times sensitivity compared to ¼ bridge for:
- the same stressed strain gauges (tensile – tensile, or compressive – compressive) –
have to be situated in the opposite branches – see fig. P.27,
- the opposite stressed compressive – tensile strain gauges – have to be situated in the
neighbouring branches – see fig. 28,
The full bridge: 4 measuring strain gauges (and these ones are the compensating strain
gauges, in the same time, too.) – can reach theoretically 4 times sensitivity compared to ¼
bridge – see fig. P.29
Fig.P.28
Fig.P.29
TASK:
a/ To compare the theoretical sensitivity with the practical one - for the half bridge and the
quarter bridge. To measure the output voltage Uv vs. the deflection y - dependency:
Uv = f (y) – for the one side stressed belt (as the built in beam) in the range y є (-5 mm, +5
mm) – step 1mm
b/ To determine (from the graphs): the transducer range, the sensitivity, to compare the
sensitivity either for the compressive stress and either for the tensile stress (it means the
symmetry in the I. and in the III. quadrant), to interpolate with a straight line by means of the
linear regression method.
Instruments:
- 2 pieces - the jig strain gauge half bridge, R0 = 120Ω ± 0,35 ‰, K – factor 2,08 ± 1%,
type 10/120 LY 11 for the steel,
Precision Measuring Amplifier – SPIDER (acc. class 0,1) – full control by PC,
without external setting and controlling elements, connected by means of the parallel
port PC/Master (IEE – 1284), or by means of RS 232-C. This device is intended for
the electric measuring of the mechanical quantities as: distance, force, pressure,
relative elongation, acceleration, temperature, speed. It possible to connect up to 8
sensors.
PC
min. demands: MS Windows 3.1., 80486, 8MB RAM, HD 35 MB, parallel port
(LPT 1), serial (COM 1,2) port, mouse.
Instructions for usage:
PC – “ON”, then SPIDER – “ON”, Click – programme CONMES (LPT1, NIBBLE) –
"MERENI" (MEASUREMENT); then the configuration 7 window appears (or ten 55)
to check the settings; and the belt without load; then to check:
the sensitivity measuring range 3mV/Vm
4th-channel (the transducer type … full bridge) instead here is installed the complete
bridge, where 2 strain gauges are active, only : it is ½ - bridge from the measurement
point of view) … ten 44, (or ten 55)
5th-channel (the transducer type… half bridge) instead here is installed the half bridge…
where 1 strain gauge is active, only : what is ¼ - bridge from the measurement point of
view)… ten 55,
if non-zero value appears – try to RESET ("NULOVANI"),(if no-success, then consider
this value as offset and take it as “0”),
Change deflection with the step 1 mm from – 5 mm to + 5 mm, and measure Uv – tab. 3.
Note: The values from + 5 mm to + 1 mm have to be realized by the belt´s bending –
(merely !! – pressure) towards the setting point of the micrometrical screw.
The values from – 1 mm to – 5 mm – have to be realized by the light belt holding over
this one demanded limit (e.g. – 1 mm), what is followed with the micrometrical screw
setting on this limit and then the belt releasing, so that this one is in the contact with the
end of the micrometrical screw. By the similar way would be realized the return to the
standstill position of the micrometrical screw !!
For the distortion reason – DON´T SET – the deflection – BY MEANS of the SETTING
SCREW ALONE!!
For the reading display comfort – it´s possible to use MONITOR – in menu – PANEL –
(return back ≡ ZPET … to the KONFIGUR 7. ctn.)
!When the measurement is finished – in menu SOUBOR – KONEC (end), START – PC –
off (VYPNOUT), then PC-Main switch OFF, and SPIDER 8, too, BOTH – measuring
BELTS –release any load!
Tab.3
y deflection
[mm]
½UV
[V]
bridge
¼bridge
III.
-5
-4
-3
-2
-1
0
+1
+2
+3
+4
+5
THE STRAIN – GAUGES – APPLICATION – THE WEIGHT CELL
Task:
a/ Verify the transducer linearity Fu = f (G), what is the dependency of output voltage (as
the shown loading force Fu [N]) v.s. the real loading G = mg [N] , in the range of the
weights from 0 to 2 kg, about) for 3 different, places of the transducer (e.g.: centre, corner,
edge).
b/ Determine the resolution for the selected weights (e.g.: 0 kg, 0,5 kg, 1 kg) as the
smallest step shown on the display ∆ = … [N].
∆Gmax
c/ Determine the accuracy class : T p =
⋅ 100%
for
Gmax
the rated weight range 7,2 kg = Gmax, and ∆ Gmax – the max. absolute error in the
measuring range (for simplification, only Your measured values can be taken in Your
consideration).
Instruments:
- the strain – gauges weight HBM – WE 2110 – with the weight cell PW 2 – 2 – 7,2kg!!
- weight sets – hardwood boxed set in 1, 2, 2,5 sequence.
Instructions for usage:
- ON – push the plug in the socket. Automatically is set the measuring MODE (in about
8 seconds).
- OFF – pull out the plug out off the socket
Note:
- !! – 0- button – is damaged!, if you need 0, then by means of T-button (tarra).
TORQUE
Tasks:
1) measure and plot dependence of strain ε = f(T) and bridge output voltage V0 = g(T) as a
function of torsion load T on a steel tube.
2) compare measured results with results from theoretical calculations and explain
eventual differences
Task description:
The loaded tube has internal
diameter d = 20 mm, external
diameter D = 25 mm, material
is steel with Young's modulus E
= 200 GPa, Possion number ν =
0,3. The tube is loaded with
know load force by adding
weights of weight m on a
known length l = 170 mm.
Strain ε is measured with strain
gauges in a full bridge
configuration.
The
bridge
output voltage V0 is measured
with a precision voltmeter. The
gauge factor of used strain
gauges is K = 2,03. The bridge
is powered with voltage VS.
Used instruments: RLC bridge, power supply Diametral P230R51D (5V part)
Measured and calculated values:
Weight Load force Load torque
m (g)
F(N)
T (Nm)
Strain
ε(-)
Bridge unbalance
∆R/R0 (-)
Measured
bridge output
voltage
Calculated
bridge output
voltage
V0 (mV)
V0 (mV)
0
500
1000
1500
2000
2500
3000
3500
Used equations:
load force: F = m· g
shear modulus: G =
strain: ε =
load torque: T = l· F
4
E
π ⋅ D3   d  
; Torsional Resisting Moment Wk =
1 −   
16   D  
2·(1 + ν )
2T
; bridge unbalance ∆R / R = ε ⋅ K ;
G ⋅ Wk
bridge output voltage V0 = VS ⋅
K
⋅ε
4