1. Measurement of Motion

2. Self-Induction Transducers
Coil is activated by the supply and the current produces a magnetic flux which is linked with the coil
The level of flux linkage (self-inductance) can be varied by moving a ferromagnetic object within the magnetic field AC
Supply
vref ~
Inductance
Measuring
Circuit
Ferromagnetic
Target Object x
(Measurand)
Self-Induction Proximity Sensor

3. Permanent Magnet Transducers
A permanent magnet transducer uses a permanent magnet to generate the magnetic field
A relative motion between the magnetic field and an electrical conductor induces a voltage
This voltage is proportional to the speed at which the conductor crosses the magnetic field
Depending on the configuration either rectilinear speeds or angular speeds can be measured
Rectilinear
Permanent
Magnet
Output vo
(Measurement)
Moving Coil
Velocity v
(Measurand)

4. DC Tachometer (Angular Velocity)
Commutator
Speed
Permanent
Magnet + - N S h
Rotating
Coil
Rotating
Coil 2r vo
The rotor is directly connected to the rotating object.
The output signal that is induced at the rotating coil is picked up using a commutator device (consists of low resistance carbon brushes)
Commutator is stationary but makes contact with the split slip rings
Generated voltage is (Faraday’s Law)

5. Example 3.5
A dc tachometer is shown below. The field windings are powered by dc voltage vf. Angular speed ω and torque Ti are the input variables. The output voltage vo of the armature circuit and the corresponding current io are the output variables. Obtain a transfer-function model for this device. Discuss the assumptions needed to “decouple” this result into a practical input-output model for a tachometer. What are the corresponding design implications? In particular discuss the significance of the mechanical time constant and the electrical time constant of the tachometer. i R L R i f f a a o + + T + g
(Output Port)
Inertia
J, b J v L f v v f g o T w i
Damping b - - - T w i
(Input Port)

7. Permanent Magnet AC Tachometer
When the rotor is stationary or moving in a quasi-static manner the output voltage will be constant
As the rotor moves, an additional voltage, proportional to the speed of the rotor will be induced
The output is an amplitude modulated signal proportional to the rotor speed and demodulation is necessary
Direction is obtained from the phase angle AC
Carrier Source
vref ~
Output vo
Permanent-Magnet
Rotor
Primary
Stator
Secondary
Stator
For low frequency applications (~5Hz), supply with 60Hz is adequate
Sensitivity is in the range 50 – 100mV/rad/s

8. AC Induction Tachometer
Similar in construction to an induction motor. Rotor windings are shorted.
The induced voltage in the rotor windings is a modulated signal of the supply. Modulation is due to the speed of the rotor.
The output voltage on the secondary is a result of primary and rotor windings and is supply modulated by the speed AC
Carrier Source
vref ~
Output vo
Shorted
Rotor Coil
Primary
Stator
Secondary
Stator
Main advantage of AC tachometers is that they have no slip rings or brushes

9. Eddy Current Transducers
Conducting materials when subjected to a fluctuating magnetic field produce Eddy currents
When a target object is moved closer to the sensor the inductance of the active coil changes
The two coils on the probe head form two arms of an inductance bridge
The output of the bridge is amplitude modulated signal
Coaxial Cable
Compensating
Coil
(Measurand) x
Output vo
Impedance Bridge
Demodulator
Low-Pass Filter
Calibrating
Unit
Target Object
Conducting
Surface
RF Signal
(100 MHz)
Active
Coil
Radio Freq. Converter
(Oscillator)
20 V DC
Supply

10. Impedance Bridge The bridge is balanced when there is no object
Bridge Output
(to Demodulator) C R1 R2
Compensating
Coil L
RF Generator ~
Active
Coil
L + ΔL R1 R2 C
The bridge is balanced when there is no object
The change in inductance creates an imbalance in the circuit and results in the output signal
The modulated signal needs to be demodulated to determine the displacement
For large displacements output is not linearly related to the displacement

11. Typical diameter of the probe is about 2mm (large 75mm)
The target object has to be slightly larger than the frontal area of the probe
Output impedance is about 1 kΩ (medium impedance)
Sensitivity is around 5V/mm
Range .25mm – 30mm
Suitable for high transient (100 kHz) measurements
Applications include
Displacement
Fault detection
Metal detection
Braking