Transcript Bridge Circuits

Force - I
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•
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Measurement Lab
19 Feb 2003
Calibration
Force Measurement
Strain Measurement
Torque Cells
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Force - I
• Strain gages are widely used for measurement such as force, pressure,
torque, and strain.
• This is done by converting these forms of input into mechanical strain
using an elastic member, which is then converted into resistance
change.
• Finally the resistance change is converted into voltage using a bridge
circuit.
• A combination of SGs and an elastic body are also available
commercially and come in different sizes and shapes.
• Before these instruments can be used for measurement, however, they
must be properly calibrated first.
Measurement Lab
19 Feb 2003
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Calibration
• A measurement instrument must
be calibrated by applying the
inputs of known values
(standards) and measuring its
output. This process is called
calibration.
• It involves a comparison of the
instrument with a higher
standard and, thus, reduces bias
errors.
• Once this relationship is
established or verified, the input
values can be inferred from the
measured values (often voltage)
accurately.
Measurement Lab
19 Feb 2003
Bridge Circuit +
Power Source
SG
Output
Voltage
Load Cell
(Cantilever Beam)
Force (F=mg)
(Standard brass-weight)
Force
Voltage
Load Cell
Strain Gage(s)
Bridge Circuit
Excitation
Voltage
Voltage
The voltage vs force relationship
must be determined experimentally.
(Calibration)
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Force
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Calibration
• There is a hierarchy of
standards. For instance, the
following figure is one such
example for weight standards.
• A primary standard defines the
value of a unit and provides the
means to describe the unit with a
unique
number.
Secondary
standards
(inter-laboratory
transfer standard, local standard,
etc.)
are
only
reasonable
approximations to the primary
standard but can be accessed
more readily.
Measurement Lab
19 Feb 2003
The international kilogram (Paris)
National primary standard kg (Ottawa)
National secondary standard weight (Ottawa)
National transfer standard weight (portable)
Local standard weight (weight and measures dept)
Laboratory standard weight (Meas. lab. ?)
Your weight instrument
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Force Measurement
• Transducers which measure force, torque, or pressure usually contain an
elastic member that converts the mechanical quantity into a deflection or
strain.
• Elastic members employed in these transducers include link, column,
rings, beams, cylinders, tubes, washers, diaphragms, etc. For force
measurement, such members are called load cells.
• Two main types of load cell are considered in the following (actually we
have seen them already): 1) Bending-beam load-cell and 2) Axial loadcell.
Measurement Lab
19 Feb 2003
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Bending-Beam Load Cell
• A bending-beam load-cell is one
of the most popular types due to
its simple design and low cost.
To measure an applied force F,
strain gages are mounted on the
beam.
• Beam theory predicts that the
strain at the SG location is
proportional to the applied force.
In fact,
Measurement Lab
19 Feb 2003
F
H
Beam
b
l
Support
L
 
at SG
location
6L   

2

bh


geometry
of beam
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1
F
E

property
of material
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Force Measurement
• Calibration gives the true (nonlinear) relationship between the measured
voltage and the actual force, even for beams with a non-uniform shape,
for which a theoretical relationship may be difficult to find or does not
exist.
2) Axial Load-Cell
• The axial load (force) can be measured using strain gages as shown
below: Beam theory predicts that

1

bh

geometry
of beam
Measurement Lab
19 Feb 2003
1
E

F
h
F
b
property
of material
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Strain Measurement
• Ideally, calibration of measurement instrument is performed using
accurate samples of input. While making such samples is easily done for
many quantities such force, torque, and pressure, this may not be so for
others such as strain. For strain measurement, the bridge circuit can be
calibrated against force instead and the measurements (EAC) taken.
Then, the strain can be calculated from the measured data using a
theoretical equation. The bridge output, which we have obtained earlier,
can be expressed as
R
E AC  k
E
ex
R
where k is the bridge constant which depends on a particular
configuration. For instance, k=1/4 for one-arm-active bridge, ½ or 1.3/2
for two-arm-active bridge, and 1 for four-arm-active bridge, etc. Since the
gage factor is defined as (GF)=R/R/, the strain can be written as

Measurement Lab
19 Feb 2003
1
E AC
k (GF) E
ex
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Strain Measurement
• Strain gages are manufactured under carefully controlled conditions and
the gage factor is provided by the manufacturer within an indicated
tolerance of about 0.2%. Thus, accurate measurement of EAC can give
a reasonably accurate strain. Of course, there will be a propagation error.
The following figure summarizes these theoretical equations.

E

R


ex


E
R
ex

4 E AC
(GF) E
ex
R  R
A
C
R  R
R  R
1 E AC
(GF) E
ex
R  R
2
E AC
C
 A
R
(GF) 1R+RE
ex
b g

R  R

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19 Feb 2003
C
A
ex
E
R  R
R
E
2 E AC
(GF) E
ex

R  R
R  R
A

R  R
R  R
ex

C
E AC
2
(GF) 1 +   E
ex
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Strain Gage Rosettes
• In the previous section of strain measurement, it was implicitly assumed
that the orientation of the axis of principal (maximum) stress was known.
In a more general case, this axis is not known and must be calculated
using a SG rosettes, which consists of three SGs. This is not discussed
further this year.
http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/strain
_gage_rosette.cfm
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Torque Cell
• Torque transmission through a rotating shaft can be measured using a
1) Torque cell or
2) Dynamometer.
Torque cells require the measurement of angular twist or strain of the shaft,
while dynamometers require that of reaction force with an arm.
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Torque Cell
Using a cylindrical elastic member, either the deflection or the strain
measurement may be used to determine the applied torque.
1. Torque measurement from angular deflection.
A (static) torque may be measured by observing the angular deflection
of a bar or hollow cylinder.

The torque is related to the deflection angle by
T

G r 4  r 4
o
2L
i

where, T : applied torque (Nm)
No torque applied
Torque T applied
T
ri
ro
L
G : Shear Modulus of elasticity(N/m2)
G
E
21   
E = Young’s Modulus(N/m2)
μ = Poisson’s ratio
ro = Outside radius (m)
L = Length of cylinder (m)
ri = Inside radius (m)
φ = angular deflection (rad)
Measurement Lab
19 Feb 2003
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Strain Gage Torque Cell
The above method may be suitable for non-rotating cylinder but not for
rotating one. A strain gage torque cell can be used for both cases.
The torque T applied to a solid cylindrical shaft produces tensile and
compressive strains on the shaft surface.
SG 1 is mounted with its
sensing (active) axis at 45
degrees to the shaft axis, where
the tensile strain has a
maximum value of +. Similarly,
SG2 is mounted at -45 degrees
to the shaft axis where the
compressive strain has a
maximum value of -. SG 3 and
SG4 are mounted at similar
angles on the other side of the
shaft and experience strains +
and -, respectively.
Measurement Lab
19 Feb 2003

45
3
1
4
2
45
T
r

SG3 and SG4 on
opposite side
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Strain Gage Torque Cell
• Theory predicts that this maximum strain is given by

1
1

T
3

r
G


geometry
property
• This four-arm-active bridge arrangement is temperature-compensated
and known to be insensitive to bending and axial strains.
• When SGs are used on rotating members, slip rings are often used for
signal transmission between a rotating body and a stationary instrument.
• Four SGs are connected on the shaft to form a four-arm-active bridge
and the slip-rings are used to connect the bridge, which is rotating, to
the power supply and recording instrument, which are stationary.
Measurement Lab
19 Feb 2003
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Strain Gage Torque Cell
• The slip-ring assembly consists of a shaft on which rotating conductor
rings are mounted and the outer shell which houses stationary brushes.
It is attached to the rotating member whose torque is to be measured,
such that the axes of rotation of the slip-ring shaft and the rotating
member coincide. Complete assemblies (some with speed sensors for
power calculation) are available commercially for various torque ranges.
• Brush contacts cause wear, attract dirt, and tend to produce electrical
noises. A better, but more expensive, way is to use telemetry, which
employs radio frequencies and operates in a similar manner to wireless
microphones
Measurement Lab
19 Feb 2003
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