Download 09 force measurement

9. Force Measurement with a Strain gage Bridge
Task
1. Measure the transfer characteristics of strain-gage based force sensor in a range 0 – 10
kg1.
2. Determine the mass of an unknown weight.
3. Check whether it is possible to obtain more precise measurement by polarity
commutation of the bridge excitation voltage.
4. (optional) Measure the mass of other objects (back-pack, notebook...)
5. Connect the sensor to the Omega measurement module and determine in which unit it
presents the output (with the use of known weight).
6. (optional) Measure the force you are able to develop with your arms (use handrails,
max. force 1000N).
7. Measure the resistance of the bridge with an ohmmeter and check whether the
resistance changes while the applied load is changed. Explain the results.
8. Determine the base value of resistance of each strain-gage element in the bridge.
Determine the change of resistance for applied load of 100kg. Calculate the
prolongation of the strain gage element if you know the coefficient of deformation
sensitivity k = 2 (gage factor) and the length of the strain-gauge is 5 mm.
Questions
1. What is the principle of a resistance based strain-gage? What is the definition of the
deformation sensitivity coefficient k?
2. What are the advantages of using full-bridge circuit (with 4 active elements)?
3. Make a simple chart showing a flexible support in a bended position with a four active
elements bridge; indicate which of the strain-gages are stressed in “strain” and which
in “compression”; relate them to an electrical circuit.
4. What is the resolution in weight you are able to achieve with this sensor? What is the
corresponding change of resistance of a single element strain-gage? In case you would
measure the resistance change without the use of a bridge circuit, how many digits
would have to have the used ohmmeter? How many effective bits it corresponds to?
Theoretical and practical background
Force sensors with flexible elements of different shapes are often used as weight scales. The
advantages are relatively high accuracy and flexibility of measurement ranges – the range can
be adjusted by changing the shape or size of the flexible element. The mechanical stress in the
flexible element is sensed by resistive strain-gages. The strain-gages are typically glued on
spots where the stress is maximal (highest sensitivity). Let’s consider a conductor with length
l and cross-section S which is stressed in strain by force F, the force causes the prolongation
of the length and cross section reduction and also micro-structural changes in the material
which alters the material’s resistivity ρ.
The total resistance of a conductor with cross section S and length l is given by following
equation:
1
The unit of force is Newton. The manufacturer uses a unit KgF, 1 KgF = 9.8 N, 9.8 m.s-2 is a normal gravity.
R=
l
⋅ρ
S
The total change of resistance can be expressed with the use of total differential:
∆R ∆l ∆S ∆ρ
= −
+
R
l
S
ρ
Coefficient of deformation sensitivity (gage factor):
∆l
∆R
⋅k =
l0
R0
A typical strain-gage is shown on Fig.1. The dimension of the strain-gage is maximized in the
direction of applied stress, in order to get the highest sensitivity and to suppress the sensitivity
in the perpendicular direction.
Fig. 1 Resistance based strain-gage
The set of four resistance based strain-gages forms full Wheatstone bridge (Fig.2). The set is
glued on to a flexible element. One of the most often used elements is an “S” shaped support
(Fig. 3). If there is a tension applied to the support, the strain-gages 1 and 4 are strained (R is
increased), while the 2 and 3 strain-gages are compressed (R is decreased).
The output voltage is given by following equation, where UEXC is the bridge excitation
voltage and ∆R/R0 is the relative change of resistance of each strain-gage.
U out =
U EXC ⋅ ∆R
R0
Fig. 2 Full Wheatstone bridge
F
R1
R2
R3
R4
F
Fig. 3 Strain-gage based force sensor
Instructions
1) Measure the output voltage UOUT (bridge diagonal voltage) by DMM. Power up the sensor
with a 10VDC stabilized power supply UEXC. Use the available weights to load the sensor.
Important!
The pinout of the sensor is:
UEXC+ … red
UEXC - … black
UOUT + … green
UOUT - … white
Fig. 4 Circuit for tasks 1 - 3
4) The Omega module uses 10VDC excitation voltage and measures the diagonal voltage.
The voltage is scaled with pre-programmed calibration constant and shown on display.
Fig. 5 Circuit for tasks 4 and 5
Attachment: calibration datasheet of the used load cell sensor