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Torque Sensors

Common Sensing Methods

Measuring strain in a sensing member between the drive element and the driven

load, using a strain gage bridge

Measuring displacement in a sensing member either directly, using a

displacement sensor, or indirectly, by measuring a variable, such as magneticinductance or capacitance, that varies with displacement

Measuring reaction in support structure or housing (by measuring a force) and the

associated lever arm length

In electric motors, measuring the field or armature current that produces motor

torque; in hydraulic or pneumatic actuators, measuring actuator pressure

Measuring torque directly piezoelectric sensors

Measuring the angular acceleration caused by the unknown torque in a knowninertia element

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Strain Gage Torque Sensors

Drive Unit

(Motor)

Bridge

Circuit

Torque

Reading

Torsion

Member

Strain

Gages

Driven Unit

(Load)

For circular shaft the torque-strain

relationship

=r

GJT

2

T= torque transmitted through the

member

= principal strain (45 to axis) at radius rof the member

J= polar moment of area of cross-section

of the member

G = shear modulus of the material

Also, the shear stress at a radius

rof the shaft is given by

TrJ

= = A dArJ2

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Using the general bridge equation

4

s

ref

o Sk

v

v=

=

r

GJT

2

GJ

krTS

v

v s

ref

o

8=

ref

o

s v

v

krS

GJT

8=

Strain gages are mounted on the shaft along the principle stress

directions (45o to the shaft axis)

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Mounting Configurations

T

1

1

2

T

1

1

2

2

T

1

12

2

3

3

4

4

vref(Constant Voltage)

R1

R3

R4

B

- +

v

o

+

R2

2

Strain Gage BridgeBridge Constant (k): 2 2 4

Axial Loads Compensated: Yes Yes Yes

Bending Loads Compensated: Yes Yes Yes

(a) (b) (c)

Both axial and bending are compensated with the given configurations

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Jm

StatorTransmitted

Torque

Tm

Motor

Torque

m L

Ks

JL

Rotor

Motor Torsion

Member Load

Jm

Tm

m L

JL

Ks(m - L)

Consider a rigid load with inertia JL, and driven by a motor with a rigid rotor, which

has inertia Jm. A torsion member of stiffness K

sis connected between the rotor and

the load, as shown below, in order to measure the torque transmitted to the load.

Determine the transfer function between the motor torque Tm

and the twist angle of

the torsion member. What is the torsional natural frequency n of the system?Discuss why the system bandwidth depends on

n. Show that the bandwidth can be

improved by increasing Ks, by decreasing J

m, or by decreasing J

L. Mention some

advantages and disadvantages of introducing a gearbox at the motor output.

Example 4.6

Ks(m -L)

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)( Lmsmmm KJT += && LLLms JK &&= )(For Motor: For Load:

m

mLm

Lm

sLmJ

T

JJK +

+= )(11

&&&&

Lm =Let

m

m

Lm

sJ

T

JJK =

++

11&&

)(

)()(

sT

ssG

m

=

+=

Lm

snJJ

K11

BW can be increased by

increasing Ks and bydecreasing Jm and JL

)11(

1)(

2

Lms

m

JJKs

JsG

++=

When gears are added equivalent inertia

increases and equivalent stiffness

decreases resulting reduction in BW

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Design Requirements

Strain capacity limit specified by the strain gage manufacturer is not exceeded

A specified upper limit on nonlinearity for the strain gage is not exceeded for

linear operation

Sensor sensitivity is acceptable in terms of the output signal level of the

differential amplifier in the bridge circuit

The overall stiffness (bandwidth) of the system is acceptable

maxmax2

2

1

max

50S

SNp2

1

maxmax

502 S

SNT

GJ

r p=

oa vKv = v K kS rvGJTo

a s ref8

maxo

sa

vT

GrvkSKJ maxref

8

PN

T

GS

rSJ max

1

225

LJ K

G

s

T GJK

L= =r

L

=

Gr

L

=Shear

strain

Shear

stress

Torsional

stiffness

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Design criteria for a strain gage torque-sensing element

Criterion Specification Governing Formula

for Polar Moment of

Area (J)

Strain capacity of strain

gage element

Strain gage nonlinearity Np and Tmax

Sensor sensitivity vo and Tmax

Sensor stiffness (system

bandwidth and gain)K

max maxand Tmax

max2

Tr

G >

max2

1

25p

TrSGS N

>

ref max

8

a s

o

K kS rv T

G v

LK

G

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Example 4.7

A joint of a direct-drive robotic arm is sketched below. Note that the rotor of thedrive motor is an integral part of the driven link, without the use of gears or any

other speed reducers. Also, the motor stator is an integral part of the drive link. A

tachometer measures the joint speed, and a resolver measures the joint rotation.

Gearing is used to improve the performance of the resolver. Neglecting mechanical

loading from sensors and gearing, but including bearing friction, sketch the torque

distribution along the joint axis. Suggest a location (or locations) for measuring the

net torque transmitted to the driven link using a strain gage torque sensor.

Driven Link

GearingTachometer

Ball

Bearings

Resolver

Motor

Rotor

Motor

Stator

ABCD

Drive Link

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Driven

Link

ABCD

Tf1 TL Tf2 TI

Tm

Bearing Bearing Motor

Axial Location

TmTm TI

Tm TI Tf2

Tf1 = Tm TI Tf2 TLTL

0

Torque

For accurate results two strain gages at locations B and C should be installed

A single sensor at B is also a good approximation since the bearing friction is

small

Motor torque Tm

is also approximately equal to transmitted torque when inertia

and friction are small

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Example 4.8

Consider the design of a tubular torsion element. The following design

specifications are given: and for a system

bandwidth of 50 Hz, K= 2.5x103 N.m/rad. A bridge with four active strain gages is

used to measure torque in the torsion element. The following parameter values areprovided:

1. For strain gages: Ss

= S1 = 115, S2 = 3500

2. For the torsion element: Outer radius r = 2 cm, Shear modulus G = 3x1010 N/m2

Length L = 2 cm

3. For the bridge circuitry: vref = 20 V and Ka = 100The maximum torque that is expected is Tmax = 10 N.m.

Using these values, design a torsion element for the sensor. Compute the

operating parameter limits for the designed sensor.

max 3,000 ; 5%; 10 V;p oN v = = =

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1. For max , := 3 000

4 9 4

10 3

0.02 10m 1.11 10 m

2 3 10 3 10

J

= =

2. For Np = 5

4 9 4

10

25 0.02 3500 10m 1.01 10 m

3 10 115 5

J = =

3. For vo = 10V

4 8 4

10

100 4 115 0.02 20 10m 7.67 10 m

8 3 10 10

J = =

4. For

32.5 10 N.m/rad:K=

34 9 4

10

0.02 2.5 10m 1.67 10 m3 10J

= =

( ) ( ) ( )9 -9 -9 8 41.11 10 and 1.01 10 and 1.67 10 and 7.67 10 mJ J

Pick this

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Bending Element for Torque Sensing

It is difficult to mount semiconductor strain gages on cylindrical/tubular element

Tubular elements are not optimal with rigidity (stiffness) for both bending and

tensile loads

The element shown below can overcome these disadvantages and has highinsensitivity to cross-loading

A

A

Connected to

Drive Member

Connected toDriven Member

A = Torque Sensing Elements

Strain

Gage

A

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Direct Deflection Torque Sensor

Direct measurement of the twist angle can be used to measure the torque

Proximity probes produce pulse sequences as the shaft rotates

The phase shift of the two signals determines the angular deflection which is a

measure of the transmitted torque Both the magnitude and the direction of the torque can be measured

Output

Ferromagnetic ToothedWheel

Phase Shift

Processor

Variable-Inductance

Probes

Torque

T

T

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Variable Reluctance Torque Sensor

This sensor operates like a differential transformer

Torque sensing element is a ferromagnetic tube with two slits placed in the

direction of principle stresses

When a torque is applied one slit opens and other closes causing a change inreluctance

Output voltage is a measure of the transmitted torque

T

Torque

TSlits

FerromagneticTube

AC Reference

Supply

Output

vo

Secondary Coils Primary Coil

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Reaction Torque Sensors

A torque sensing element modifies the original system. It reduces the systemstiffness

It decreases the system bandwidth and adds extra loading to the system

Reaction torque sensors eliminate these problems.

The housing of the rotating machine is cradled and the effort necessary to keep

the structure stationary is measured.

R RT F L== reaction force measured using load cell

= lever arm length.

RF

L

Frictionless

Bearing

Lever

Arm

L

Motor Housing

(Stator) F

Force Sensor

(Load Cell)FR

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A drawback of reaction torque sensors is under acceleration and deceleration

conditions the measured torque is not accurate

Apply Newtons second law to the entire system

R LJ T T =&&

T T JL R= &&

This can be compensated by measuring shaft acceleration

Reaction

Torque

TR

Motor

Torque

Tm

Frictional

Torque

Tf1

Tf1 Tf2

Frictional

Torque

Tf2

To Load

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Motor Current Torque Sensors

For a DC Motor with armature windings on the rotor and field windings on the stator

am fT ki i=

field current

armature current

= torque constant.

f

a

i

i

k

=

=

Motor torque can be determined by measuring iforia

Magnetic torque is only an approximation of the transmitted torque. It includes the inertial torque and the frictional torque

f C

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Torque of an AC motor can also be determined by measuring motor current

For an AC synchronous motor

2 4sin sin sin1 2 33 3m

fT ki i i i = + +

i i ta2

2

3=

sin

i i ta3

4

3=

sin

i i ta1 = sin

( )tikiT afm = cos5.1

Stator

Phase 1

1i

Rotor

Stator

Phase 2

2i

Stator

Phase 33i

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Tactile Sensing

Typical Specifications for an Industrial Tactile Sensor

Spatial resolution of about 2 mm

Force resolution (sensitivity) of about 2 gm

Force capacity (maximum touch force) of about 1 kg

Response time of 5 ms or less

Low hysteresis (low energy dissipation)

Durability under harsh working conditions

Robustness and insensitivity to change in environmental conditions

(temperature, dust, humidity, vibration, etc.)

Capability to detect and even predict slip

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Construction and Operation of Tactile Sensors

Position 1 of Reflecting Surface

x

Light (or Laser)

Receiver

Position 2 of Reflecting Surface

Image

Processor

Beam

Splitter

Reflecting

Surface

Tactile Forces

Elastomeric

Touch PadLight (or Laser)

Source

Transparent

Elastomeric

LayerFixed Array of

Optical FiberIntensity

at Receiver

Positionx0

Light (or Laser)

Source

Solid-StateCamera

Deflection or

Force Profile

O ti l T til S ith L li d Li ht S d Ph t

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Optical Tactile Sensor with Localized Light Sources and Photosensors

Pin

LED

(Light Source)

Photodiode

(Light Receiver)

x

Elastomeric

Touch Pad

Piezoresistive tactile sensors use an array of semiconductor strain gages

mounted under the touch pad to measure forces

Ultrasound tactile sensors are based on pulse echo ranging tactile surface istwo membranes separated by an air gap

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Strain Gage Tactile Sensor

Useful in parts-mating applications

P R R R R= + + +1 2 3 4

aRaRPy 34 +=Px R a R a= +2 3

( )xa

PR R= +2 3 ( )y a

PR R= +

3 4

Contact

Force

p

R2

R4

p

x

y

12

34

a

a

Sensing

Plate

R3

R1

Strain Gage

Load Cells

G i S

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Gyroscopic Sensors

Spinning

Disk

Frictionless

Bearings

Gimbal

Spin

Axis

Torque

Motor

JH=

Output

H1

H2H

Angular Momentum GimbalAxis

Applications: Angular orientation and speed of aircraft, ships, vehicles, and

various mechanical devices

O i l S

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Optical Sensors

Laser, LCD, etc.

PowerSource

Signal

Processor

Position

Measurement

Photodiode,

Phototransistor,

etc.

LightSource

Photodetector

Target

Object

Transmitting

Fibers

Receiving

Fibers

x

(Measurand)

Optical fiber diameter ~m 0.01mm

Laser Interferometer

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Laser Interferometer

Light

Source

Light

Sensor

Reflector

xBeam

Splitter

(B)

Signal

Processor

BeamSplitter

(A)

Target

Object

Optical Fiber

Bundle

Part of the beam is reflected back to the sensor from Beam splitter A

The other part travels an extra distance of2x

The phase shift between the two components

2

2x

=

L D l I t f t

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Laser Doppler Interferometer

Reflector

Laser

TargetObject

Speed v

Beam

Splitter

Photosensor

Signal

Processor

Speed,

Position

Readings

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Ultrasound Sensors

Ultrasound

GeneratorTarget

Object

Transmitter/

Receiver

SignalProcessor

Distance

Reading

Ultrasound waves are pressure waves like sound waves but their frequency is

higher than (40kHz, 75kHz, ~ 10MHz) audible waves

Ultrasound waves can be generated by piezoelectric or magnetostrictive

devices (ferromagnetic material deform when subject to a magnetic field).

2

vtx =

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Pressure Sensors

pref

h

p x

p

pxp

refp p gh = Measure deflection/displacement using a displacementsensor (LVDT or capacitive)

p

Piezoresistors

(Semiconductor

Strain Gages)

F

Frictionless

pp A

pFpA

= Measure angular displacement using anRVDT, resolver, or potentiometer

Fl S

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A

r

Qv

,

Motor Tube

Bundle

Flow Sensors

m

Q Q= Q Av= 21

constant2p v+ =h

Qm

2d

pQ c A

= 2v gh= 2 mr Q =

v

v

v

Displacement

Sensor

Motion

Sensor

Q

h

FloatConic

Cylinder

Coriolis

Torque

Restrained

by spring

v2onAcceleratiCoriolis =hQ

T t S

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Temperature SensorsThermocouple

Hot

Junction

(Measured

Temperature T)

Voltage

Acquisition

Circuit

Cold

Junction

(Reference)

Metal A

Metal B Metal B

Conductor

C

Conductor

C

Electron configuration due to heat transfer produces a voltage Seebeck Effect

Two metals Fe and Constantan, Cu and Constantan, Chrome and Alumel

Sensitivity 10mV/oC

Resistance Temperature Detector

Metal element in a ceramic tube resistance changes with the temperature

Metals used Platinum, Nickel, Cu

0 (1 )R R T= +

Rating Parameters of Sensors and Transducers

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Rating Parameters of Sensors and Transducers

Transducer Measurand MeasurandFrequency

Max Min

OutputImpedance

TypicalResolution

Accuracy Sensitivity

Potentiometer Displacement 10 Hz/ DC Low 0.1 mm 0.1% 200 mV/mm

LVDT Displacement 2,500 Hz/ DC Moderate 0.001 mm orless

0.1% 50 mV/mm

Resolver Angulardisplacement

500 Hz/ DC

(limited by

excitation freq.)

Low 2 min. 0.2% 10 mV/deg

Tachometer Velocity 500 Hz/ DC Moderate

(50

)

0.2 mm/s 0.5% 5 mV/mm/s

75 mV/rad/s

Eddy current

proximity sensor

Displacement 100 kHz/ DC Moderate 0.001 mm

0.05% full

scale

0.5% 5 V/mm

Piezoelectric

accelerometer

Acceleration (and

velocity, etc.)25 kHz/ 1Hz High 1 mm/s2 0.1% 0.5 mV/m/s2

Semiconductor

strain gage

Strain

(displacement,

acceleration, etc.)

1 kHz/ DC

(limited

by fatigue)

200 1-10

(1=10-6

unity strain)

0.1% 1 V/ max

2000

Loadcell Force(10 - 1000N)

500 Hz/ DC Moderate 0.01 N 0.05% 1 mV/N

Laser Displacement/Shape

1 kHz/ DC 100 1.0 m 0.5% 1 V/mm

Optical encoder Motion 100 kHz/ DC 500 10 bit bit 104 Pulses/rev.