MAE 3272 - Lecture 6 Notes - Load Cell Calibration

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

M&AE 3272: Mechanical Propertyand Performance Laboratory

Excitation

Signal Conditioning and Processing

Display and Analysis via LabVIEW

Strain Gage

Load Cell

Wireless USB S-Beam Load Cell

WSachse; 3/2014;M&AE 3272 - Lecture 6 2

Idea: A portable Scale for iPod/iPad ??


10 March 2014

2

WSachse; 3/2014;

i-Clicker Survey

1. I hated it. It was a waste of time.

2. I know it’s good for me but I didn’t enjoy it.

3. It was ok.

4. I see the value of it and sort of liked it.

5. I think that it was a good way for me to learn how to write better

M&AE 3272 - Lecture 6 3


Part of Module 1 was writing an Abstract which

summarized what you did and what results you

obtained. It was intended as a writing exercise.

Please select the response which best describes

your experience:

WSachse; 3/2014;

i-Clicker Survey

1. It was a difficult task for me to do.

2. I feel that I really didn’t do a good job.

3. It took a long time for me to do the job with little benefit to me.

4. It took some time for me to do the job but I did learn how to improve my own Abstract

5. It didn’t take much time for me to do the job and I also learned how to improve my own Abstract.



You served as a “Peer Reviewer” for two of your

classmates’ Abstracts. Which of the choices below

best characterizes your experience:


10 March 2014

3

WSachse; 3/2014;

i-Clicker Survey

1. Not worth the effort. Would prefer not to do it.

2. Very reluctantly would like to do it.

3. Don’t care. Either is fine with me.

4. It’ll be work but it’s good for me to practice some more.

5. By all means, let’s do it.



Having completed the Abstract for Module 1, what

are your opinions about writing an Abstract for

Module 2, the Load-cell Lab?

WSachse; 3/2014;

Tasks to do during the three Weeks, March 3rd – March 21st :


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


10 March 2014

4


Load Cell Hook-up and Output:

Beams

Load, P

Load, P

#1

#2

#3

C(−)

T(+)T(+) C(−)

C(−) T(+)T(+)

C(−)


Wheatstone Bridge Output per Load:

7.20

7.20


10 March 2014

5


Expected Calibration Measurement Result:

Applied Load [lbs]

= Sensitivity [V/lb]

= Zero

Measured

Output

Voltage [V]

Non-linear

regime


Static Load Cell Characteristics:

• Static Sensitivity •Stability

• Linearity •Resolution

• Precision/Repeatability •Hysteresis

• Accuracy •Range and Span

• Threshold• Drift; Zero Drift

• Input Impedance;Loading Effect


10 March 2014

6


Input and Output Range; Span and Zero:


Accuracy and Error Bands; Resolution:

Resolution is the smallest,

detectable change of input

∆∆∆∆i that can be detected in

the output signal.

Error Band


10 March 2014

7


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.


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.


10 March 2014

8

WSachse; 3/2014;

Type I - Example: Linear Least-squares Fit:


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:


• 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)


10 March 2014

9

WSachse; 3/2014;



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;



Effect of Data Error Bounds on computed Line Parameters:

using Excel

using

Genplot


10 March 2014

10

WSachse; 3/2014;



Effect of Data Error Bounds on computed Line Parameters:

Uncertainty

in the

Coefficients:

σσσσyyyy=�

� �∑ ! � � � �! ��

"# "�∑��∆ " "�

�∆


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


10 March 2014

11


Signal Collection and Processing via LabVIEW:

NI cDAQ-9172

PC

LabVIEW SoftwareLabVIEW Display

WSachse; 3/2014;

Load Cell Static Characterization:

∑=N

0

qqPaV(P)


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


10 March 2014

12

WSachse; 3/2014;

Interfering and Modifying Sensor Inputs:


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:


Question: Which changes Slope?

Which changes Zero?

X

Y Z


10 March 2014

13

WSachse; 3/2014;

Interfering Environmental Inputs: Affect Zero Value

IV/KI ∆∆=


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


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/


10 March 2014

14

WSachse; 3/2014;

Interfering and Modifying Inputs:

−

+= I

minmax

M K∆I

∆V

PPK

2

+∆+∆=∆

2

PPIKIKV

maxminMI


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:


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!


10 March 2014

15

WSachse; 3/2014;

Dynamic Range of a Load Cell:


The maximum range of loads that your Load Cell can safely carry is determined by the smallest of:

• Start of inelastic deformation of the “elastic

members” comprising your load cell, i.e. εyield

with a Factor of Safety of 2.0 . For 6061-T6 Al,

εyield = σyield/E = 35ksi/10.1Msi = approx 3500µε ;

with Factor of Safety, use approx 1700µε .

• Failure of the strain gage and/or its attachment adhesive. εgage-fail approx 3% or 30000µε .

• Load cell signal exceeds dynamic range of digitizing A/D unit.

WSachse; 3/2014;

Dynamic Range / Resolution of Load Cell:


• A/D Converter Resolution: 24 bits = 16,777,216 voltage levels

• A/D Converter Input Signal Range: +/-25 mV/V

• Bridge excitation is 2.5 V

• Maximum Input Voltage: ±25 mV/V•2.5 V= ±62.5 mV � Vmax

• Voltage Resolution: 2•62.5 mV/16777216 = 7.451E-9 V

PADmax = Vmax/Calib_Factor >>> System Maximum Load

This will correspond to the Maximum Allowable Load if A/D

Converter controls Dynamic Range.

Load Resolution: Smallest theoretically detectable Load

Resolution corresponding to one level or . . .

PADmin = 7.451E-9/Calib_Factor >>> System Load Resolution

System uses NI-9237 4-Channel Bridge Module:


10 March 2014

16

WSachse; 3/2014;

Re: Load Cell System Range and Resolution:


• 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:


• 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


10 March 2014

17

WSachse; 3/2014;

Using a Calibrated Load Cell to determine Loads:


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:


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

Uncertainty of the load determination.


10 March 2014

18

WSachse; 3/2014;

Load Cell: Testing Schedule

(March 17th – 21st)


WSachse; 3/2014;

Module 2 Deliverable:

Load Cell Calibration

Data and Curve:


0 20 40 60 80

Applied Load [lbs]

0

5

10

15

20

Bri

dg

eO

utp

ut

Vo

ltag

e[m

V]

Measured Calibration DataLinear Fit: 0.215 [mV/lb]

Load Cell Calibration

4Calibration

Data Points

2Linear Fit

Line

3aSlope: Sensitivity =

1/Calibration Constant3b Zero

6


10 March 2014

19

WSachse; 3/2014;

Load Cell: Calibration

Sheets


3.

1.

4.

5.

2.

Due:Week of April 7th

to 11th

Two weeksafter you did

the Calibration

WSachse; 3/2014;

Tasks to do during the three Weeks, March 3rd – March 21st :


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


10 March 2014

20

WSachse; 3/2014;

• Everyone should now have familiarity with LabVIEW.

• Sections #401, #402, #403, #404, #409, and #413

can go to the Lab to check out their LabVIEW vi.

(Go at times when the Sections above are not

session.) Thanks. Enjoy the week!

• Sections #405, #406, #407, #408, #410 , #412 and

#414 meet in B30 Upson to fabricate your Load Cell.

Come prepared to show your design to your TA so

that you can receive parts. Then: Prep. Glue. Wire.

• Everyone should now have familiarity with LabVIEW.

• Sections #401, #402, #403, #404, #409, and #413

can go to the Lab to check out their LabVIEW vi.

(Go at times when the Sections above are not

session.) Thanks. Enjoy the week!

• Sections #405, #406, #407, #408, #410 , #412 and

#414 meet in B30 Upson to fabricate your Load Cell.

Come prepared to show your design to your TA so

that you can receive parts. Then: Prep. Glue. Wire.

Tasks to do THIS Week, March 10th - 14th:


Documents

MAE 3272 - Lecture 6 Notes - Load Cell Calibration