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Torque Measuring
Torque fundamental concepts
Outline
Basics Physical definition of torque
Use of torque measuring
Mechanical basics
Different methods to measure torque
Principal assembly of strain gage torque transducer
Strain gage and measure bridge Function
Compensation
Definition of Torque
Torque:
The vector product of position
vector and force called torque
sin
FrM
FrM
r
F
x
y
z
Uses of Torque Measuring
Test Rigs (electric, combustion) Power
Efficiency factor
Torque over angle rotation measuring
Etc.
Screw application Detent torque
Calibrate torque key
Etc.
Stress and Strain
Strain is caused by torque
Elastic strain
If balanced forces act on a solid body from outside, a change in form
and volume occurs, which can be measured.
Once these forces stop acting the distortions go back completely,
provided that the deformation has not exceeded a certain limit
(adherence to the elastic range).
Otherwise the body of measurement becomes useless.
Stress and Strain
Strain ε is defined as the
relative change of length Δl / l
l
l
Hook’s Law
With torsion applies to shear stress :
The modulus of elasticity E
is the proportionality factor.
It is a material constant
with the unit [N / mm²].
It influences the sensor performance
regarding its sensitivity. The module
itself is influenced by temperature.
At one axle stress condition the following
relations apply :
= Normalspannung
shear stress
shear module
slip
normal stress
modulus of elasticity
Hook’s range of the curve can be written as:
µ = poisson’s ratio
(0,3 by metal)
Stress and Strain
The elastic range is influenced
by strain and the modulus of
elasticity. There is an overstrain
in the plastic range, making the
body of measurement useless
elastic range
plastic range
Hook’s
straight line
B = break strength
S = elastic limit
= break stress
B
Conversion English/Metric
Symbol When you know
Multiply by To find Symbol
lb-ft Pound-feet 0.1383 kilogram meters kgm
0z-in Ounce-inches 720 gram millimeters gmm
kgm Kilogram meters 7.233 gram millimeters lb-ft
gmm Gram millimeters 0.0014 Ounce-inches oz-in
lb-ft Pound-feet 192 Ounce-inches oz-in
Nm Ounce-inches 0.00521 Pound-feet lb-ft
Nm Newton-meters 8.85 Pound-inch lb-in
Kpm Kilopond-meters 7.233 Pound-feet lb-ft
Kpm Kilopond-meters 86.8 Pound-inch lb-in
Different Methods to Measure
Torque
mechanic
(oscillating string)
resistive
strain gage
surface wave
resonator
piezo electric resistive
thick film sensor
magneto elastic
Ring magnet
optical
Pattern
recognition
Photo elasticity
capacitive
capacitive
strain gage
angle difference shield
optical
phase shift
Differential
transformer
yoke
Eddy-current
coil slotted sleeves
eddy current
segment disks absolute
capacitive
differential
transformer
resonators
Mechanical Strain Torsion Angle
Torque Measurement via
Differential Transformer
Due to torsion a coil leaves
its original position and like
that the induction/coupling
changes.
The illustration shows an
idealized coil system, in
practice the system is
positioned on a radius, i.e.
the signal is not linear.
Mt = 0
Mt ≠ 0
Torque Measurement via
Differential Transformer
Applied for over 50 years
Very small measuring ranges
possible
No active components, low
inductivities
High temperature range
Accuracy is less than strain
gage transducer
Mechanical construction is very
complex
Torque Measurement with
Magneto-Flexible Toric Magnet
Passive system
Low cost
Less accuracy (0,5-1%)
A magnetic field is generated by a ring of magneto elastic material, which is magnetized
in circumferential direction. Influenced by stress a magnetic reorientation occurs,
and an extern magnetic field develops, which is measured with magnetic field sensors.
Torque Measurement using
Torsion Angle
In the range of elastic strain the following
correlation between the torsion angle and
torque M applies :
At circular-cylindrical shaft
applies:
Polar moment of inertia Shear modulus 80.000 N/mm² at steel).
Length of the torsion sector
Principal of Torque Transducer
Torque measuring
body
strain strain-
gage
mV/V V
ADC transmission processing conversion
V Digit Digit Digit
Voltage
Frequency
RS-232C
Field Bus
Strain Gages
In the strain gage method the
electric resistance of a wire is
changed by the influence of
strain ε. The length l of the
wire is increased to the
length l+dl. The diameter D
is reduced by the amount dD.
The change of resistance of
a wire is proportional to the
strain of the wire.
Fig:
Standard strain gage
Cover Connecting bands
measuring grid Support
length of
measuring grid
Wheatstone-Bridge
Minor changes of Resistance generate a output voltage
KSM uses exclusively the full bridge. In a full bridge R1 and R4 must
be strained and R2 and R3 compressed.
UB US
R1
R2
R3
R4
Wheatstone-Bridge
Bridge sensitivity EB is the quotient of bridge voltage UB and bridge
supply voltage US
The bridge voltage UB is proportional to the strain, which is
measured
1000
k
U
UE
S
BB
Factorkk
m
mVUmVU
V
mVE SBB
][;][;][;][
Example for Strain Gage
Measurement
strain gage
width b
Ehb
Fl
2
6
On the upside and bottom side
of a bending beam (width b and
height h) strain gages are
arranged at l intervals from the
power flow. In the illustration the
upper strain gage is strained
and the lower strain gage is
compressed.
The strain ε of the bending
beam at the position l is
calculated as follows:
Application of Strain Gage in
Industry
The measuring technology with strain gage is universally
applied in practice. This method helps to obtain maximum
accuracies (0,1% or better)
Advantages: Can be applied in calibration devices
No drift, static measurement are possible
Disadvantages: Application of strain gage and the evaluation of the signal are complex
An energy supply is required
The ambient temperature for STM torque sensors is maximally 100°C
Strain gage application at STM is only performed by
specialists in a clean room
Strain Gage Application
Marking lines on the measuring body to place the strain gage
Pasting the strain gage on the measuring body
Wiring the strain gage
Cover the strain gage
Make the compensation
Strain Gage Application and
Clean Room
Clean Room Cell Class 100
Particle size Particle no. / dm³ Particle no. / dm³
inside outside
1,0 µ 0 ~110.000
Fig:
Endoscope for quality
assurance +
humidity sensor
Fig:
Workplace for
strain-gage application
Pasting in the Clean Room
The body of measurement is
cleaned carefully
Glue is thinly brushed on the strain
gage and contact spot on the body of
measurement, then the product is
aire for 10 minutes
The strain gage is precisely
positioned on the contact spot and
pressed on
Soldering tags are affixed together
with the strain gage in the same
manner
Pasting in the Clean Room
Strain gages are covered with Teflon foil and silicone rubber
pad.
Contact pressure is applied
The applied body of measurement is hardened in the oven
The body of measurement is cleaned carefully again
Wiring
The strain gage bridge is
interconnected with wires of the
same length and the leads
soldered On.
The connecting leads are
covered with Coat.
Wires must fit closely to the
body of measurement. After the
wiring, a temperature
compensation and a zero point
compensation are carried out.
Compensation
Copper wire (positive
temperature coefficient) is
connect in series to one of the
resistor to compensate the
temperature influence
Manganin wire (zero temperature
coefficient) is connect in series to
compensate Zero-Point
UB US
R1
R2
R3
R4
Application Examples