Measurement of Motion

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

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)

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)

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)

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

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

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

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

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