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M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
1
WSachse; 3/2014;
Force
Force
M&AE 3272 - Lecture 6
Elastic Member
1
4th-8th Weeks – Load Cell Fabrication and Data Aquisition
Tasks to do during the three Weeks, March 3rd – March 21st :
M&AE 3272 - Lecture 6 6
Sections: 401-404; 409; and 413
Sections 405-408; 410; 412 and 414
Mar 3rd – Mar 7th Build Load Cellin Upson B-30
Construct LabVIEW vi
in 163 Rhodes
Mar 10th - Mar 14th ConstructLabVIEW vi
in 163 Rhodes
Build Load Cellin Upson B-30
Mar 17th – Mar 21st Test and Calibratein Upson B-30
your Load Cell(see Schedule)
Done
Done
Done
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
4
WSachse; 3/2014;M&AE 3272 - Lecture 6 7
Load Cell Hook-up and Output:
Beams
Load, P
Load, P
#1
#2
#3
C(−)
T(+)T(+) C(−)
C(−) T(+)T(+)
C(−)
WSachse; 3/2014;M&AE 3272 - Lecture 6 8
Wheatstone Bridge Output per Load:
7.20
7.20
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
5
WSachse; 3/2014;M&AE 3272 - Lecture 6 9
Expected Calibration Measurement Result:
Applied Load [lbs]
= Sensitivity [V/lb]
= Zero
Measured
Output
Voltage [V]
Non-linear
regime
WSachse; 3/2014;M&AE 3272 - Lecture 6 10
Static Load Cell Characteristics:
• Static Sensitivity •Stability
• Linearity •Resolution
• Precision/Repeatability •Hysteresis
• Accuracy •Range and Span
• Threshold• Drift; Zero Drift
• Input Impedance;Loading Effect
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
6
WSachse; 3/2014;M&AE 3272 - Lecture 6 11
Input and Output Range; Span and Zero:
WSachse; 3/2014;M&AE 3272 - Lecture 6 12
Accuracy and Error Bands; Resolution:
Resolution is the smallest,
detectable change of input
∆∆∆∆i that can be detected in
the output signal.
Error Band
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
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WSachse; 3/2014;M&AE 3272 - Lecture 6 13
Deadband; Hysteresis:
Deadband is the range of
input Xd for which the load
cell output remains at zero.
Hysteresis is the difference in
load cell response, depending
whether the applied load is
increasing or decreasing.
WSachse; 3/2014;M&AE 3272 - Lecture 6 14
Repeatability; Bias and Drift:
Repeatability describes how
well a load cell achieves the
same response under
identical conditions.
• Bias – The error between the load
cell output and the true value
(fully compensated.)
• Drift – The change of load cell
output with time with constant
input.
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
8
WSachse; 3/2014;
Type I - Example: Linear Least-squares Fit:
M&AE 3272 - Lecture 6 15
We want to find the best straight line:
to fit a set of measured data ��, �� , … ���, ��� . � � �
� ∑��∑ � ∑�∑�
∆∆∆∆ BBBB �∑� � ∑�∑
∆∆∆∆
The least-squares estimates for AAAA and BBBB are
found to be:
where: ∆ ���� � ���
Implemented in Matlab, Excel and numerous others.
( )2 2
2 ( ) 1ii
i i
y y xy a bxχ
σ σ
−= = − −
∑ ∑
WSachse; 3/2014;
Linear Least-squares Fit:
M&AE 3272 - Lecture 6 16
• The relationship between X and Y is a straight-line (linear) relationship.
• The values of the independent variable X are assumed fixed (not random); the only randomness in the values of Y
comes from the error term ε.
• The errors ε are uncorrelated (i.e. independent) in successive
observations. The errors ε are normally distributed with mean 0 and variance σ 2 (equal
variance). That is: ε ~ N(0,σ 2)
X
YLINE assumptions of the Simple
Linear Regression Model
Identical normal
distributions of errors, all centered on the
regression line.
Yy|x=ΑΑΑΑ + ΒΒΒΒ X
Y
N(Yy|x, σσσσy|x2)
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
9
WSachse; 3/2014;
Linear Least-squares Fit:
M&AE 3272 - Lecture 6 17
Example (using
Genplot):
��. �� � �. ����
x y
2.0 42.0
4.0 49.4
6.0 50.3
8.0 56.3
10.0 58.3
0 2 4 6 8 10 12
Input Data
40
45
50
55
60
Ou
tpu
tD
ata
Measured Data /w Error BarsBest Fit LineSlope (Calibration): 1.975 +/- 0.275Offset (Zero Value): 39.41 +/- 1.82
WSachse; 3/2014;
Linear Least-squares Fit:
M&AE 3272 - Lecture 6 18
Effect of Data Error Bounds on computed Line Parameters:
using Excel
using
Genplot
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
10
WSachse; 3/2014;
Linear Least-squares Fit:
M&AE 3272 - Lecture 6 19
Effect of Data Error Bounds on computed Line Parameters:
Uncertainty
in the
Coefficients:
σσσσyyyy=�
� �∑ ! � � � �! ���
"# "�∑��∆ " "�
�∆
WSachse; 3/2014;M&AE 3272 - Lecture 6 20
Beams
Load, P
Load, P
#1
#2
#3
C(−)
T(+)T(+) C(−)
C(−) T(+)T(+)
C(−)
Implementation in Upson B-30:
NI cDAQ-9172
4 Channel, Simultaneous Bridge
Module NI 9237
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
11
WSachse; 3/2014;M&AE 3272 - Lecture 6 21
Signal Collection and Processing via LabVIEW:
NI cDAQ-9172
PC
LabVIEW SoftwareLabVIEW Display
WSachse; 3/2014;
Load Cell Static Characterization:
∑=N
0
qqPaV(P)
M&AE 3272 - Lecture 6 22
Measure:
Load Cell/Bridge Output Voltage, V vs. Input Load, P
Under Standard Conditions:
• When P = 0 � V = 0 (or V = V0)
• Take measurements from 0 to Pmax in steps of Pmax /N(5 < N < 11 Readings)
• Quasi-statically
• Unload from Pmax to 0 in steps of - Pmax /N
• Reload and Unload; Repeat (3N Data Points; 4N Total).
• Fit Regression:
• We shall assume that: V(P) = K P + V0; K = Sensitivity
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
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WSachse; 3/2014;
Interfering and Modifying Sensor Inputs:
M&AE 3272 - Lecture 6 23
Interfering Inputs - Linear superposition assumption holds:
S(aX+bY) = a*S(X) + b*S(Y)
X
Y Z
Affects
Calibration Curve,
e.g. Temperature
WSachse; 3/2014;
Interfering and Modifying Sensor Inputs:
M&AE 3272 - Lecture 6 24
Question: Which changes Slope?
Which changes Zero?
X
Y Z
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
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WSachse; 3/2014;
Interfering Environmental Inputs: Affect Zero Value
IV/KI ∆∆=
M&AE 3272 - Lecture 6 25
Outp
ut
Volt
age,
V
Applied Load, P
I=0/
=V0Zero Offset +K II
=V0Zero Offset
I : Interfering Input
I=0
Hold P at Pmin (= 0?)
Vary Environmental Input: ∆I ,
e.g. Temperature;
Noise Level: Electrical,
Mechanical
Environmental Coefficient KI :
WSachse; 3/2014;
Modifying Inputs: Affect Load Cell Sensitivity
∆
∆
+=
∆
∆=
M
V
)P(P
2
M
V
P
1K
minmax
M
M&AE 3272 - Lecture 6 26
Hold P at (Pmin+Pmax)/2
Vary ModifyingInput: ∆M,
e.g. Temperature;
Noise Level: Electrical,
Mechanical
ModifyingCoefficient, KM :
Ou
tpu
t V
olt
age,
V
Applied Load, P
Slope =K
Slope =K +KM*M
M : Modifying Input
M=0
M=0/
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
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WSachse; 3/2014;
Interfering and Modifying Inputs:
−
+= I
minmax
M K∆I
∆V
PPK
2
+∆+∆=∆
2
PPIKIKV
maxminMI
M&AE 3272 - Lecture 6 27
If an Interfering Input ∆I results in a ∆V with the Environmental Coefficient KI we can calculate the corresponding non-zero KM :
then
Repeatability Test – Perform in working environment; Apply mid-level load (Pmin+Pmax)/2 ; Monitor Output Voltage for k=1, 2, 3, … ; Find rms and standard deviation of Output Voltage for given mid-level load.
WSachse; 3/2014;
Sensor Hysteresis:
M&AE 3272 - Lecture 6 28
Separate
regressions are
performed on the
two sets of data:
Loading; Unloading
V+(P)=K+P + V0
V-(P)=K-P + V0
and
Hysteresis is significant if the separation of the two calibrations
exceeds the scatter of the data points about each curve:
H(P) = KP + V0
Hysteresis is insignificant, the loading and unloading data can
be combined to generate one calibration curve:
V(P) = KP + V0 . . .You’ll check this!
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
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WSachse; 3/2014;
Dynamic Range of a Load Cell:
M&AE 3272 - Lecture 6 29
The maximum range of loads that your Load Cell can safely carry is determined by the smallest of:
PADmin = 7.451E-9/Calib_Factor >>> System Load Resolution
System uses NI-9237 4-Channel Bridge Module:
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
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WSachse; 3/2014;
Re: Load Cell System Range and Resolution:
M&AE 3272 - Lecture 6 31
• Load Cell Dynamic Range is likely NOT determined by
Vmax of ADC System – rather by σ < σYield/F.S.
• Load Cell Resolution may NOT be determined by the Voltage Resolution of the ADC but rather by the noise in the bridge circuit coupled with the noise and the chosen digitization rate of the ADC.
We are now using internal Bridge circuits in the NI-9237
WSachse; 3/2014;
Re: Load Cell System Range and Resolution:
M&AE 3272 - Lecture 6 32
• Load Cell Resolution may also be affected by the noise present in the bridge excitation voltage, Vexcit .
We are using the Agilent E3611A to provide the 5 VDC
Excitation to the Wheatstone Bridge.
200µV corresponds to an error in the strain value of 0.004%.We are now using the bridge voltage supplied
by the NI-9237
M&AE 3272 - Lecture #6 Load Cell Calibration
10 March 2014
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WSachse; 3/2014;
Using a Calibrated Load Cell to determine Loads:
M&AE 3272 - Lecture 6 33
From the Static Calibration Measurement you’ve determined the Static Calibration Constant, K (“Sensitivity” or “slope”) and the Zero,V0 (“y-intercept”):
V(P) = K P + V0
Then the estimated true Load for any loading can be found from: Pest = {Vmeas - V0}/K which has standard deviation:
σ2 = (1/N) ΣΣΣΣ[{Vmeas - V0}/K – Pin]2
WSachse; 3/2014;
Using a Calibrated Load Cell:
M&AE 3272 - Lecture 6 34
V(P) = K P + V0 Pest = {Vmeas - V0}/K
σ2 = (1/N) ΣΣΣΣ[{Vout - V0}/K – Pin]2
•For a particular, applied load, Ptrue, if the measured load cell voltage is Vmeas then the estimate of the
true load is: Pest +/- 3σ with a probability of 99.7%.
•The Bias in the measurement is given by: Pest – Ptrue
•The quantity 3σ corresponds to the Imprecision or