SL11 Motion Measurement

ESS3271 Lecture

Twin beam

Piezoelectric accelerometer

Vertical column

(Sensors & Actuator)

Position sensor

Experimental Setup

• Actuator: a permanent magnet and coil combination placed at the base of the vertical column

• Position sensor: a variable-reluctance magnetic one placed behind one of the beams

• Displacement transducer: linear variable differential transformer (LVDT)

• Velocity transducer: another permanent magnet and coil combination placed at the upper end of the column

• Accelerometer: a piezoelectric one mounted on the upper surface of the top beam– A disc of piezo-crystal placed in a transparent case

Piezoelectric Sensors• Piezoelectric material

– Produces an electric charge when it is subjected to a force or pressure

– Such as single-crystal quartz or polycrystalline BaTiO3

– Contains molecules with asymmetric charge distribution

Piezoelectric Sensors

• Operation principle

– Pressure => crystal deformation

=> relative displacement of the positive and negative charges within the crystal

=> external charges of opposite signs on the external surfaces of the crystal

– Surfaces coated with metallic electrodes

– Charge q developed: q = CV0

Charge and Voltage Sensitivity

• q = CV0 and C = kKA/hC: capacitance, A: area of the sensor headK: relative dielectric constant for the medium in the gap k: proportionality constant

• q = SqAPCharge sensitivity Sq = f(orientation of the sensor relative to the axes of the piezoelectric crystal)q = SqAP = V0kKA/h

• V0 = (Sq/kK)hP = SvhPVoltage sensitivity Sv = Sq/kKSv = f(orientation of the sensor relative to the axes of the piezoelectric crystal)

Experiments

• 1 Phase sensitive detector

• 2 Linear variable differential transformer

• 3 Piezoelectric accelerometer

• 4 Electromagnetic velocity transducer

• 5 Relationships between acceleration, velocity, and displacement

• 6 Frequency response

Phase sensitive detector

Piezoelectric accelerometer

Electromagnetic velocity transducer

Relationships between acceleration, velocity, and displacement

Frequency response

Experimental Results• Note how the outputs of the accelerometer and velocity

transducer vary with the magnitude and frequency of the vibration of the beam system

• Sketch the waveforms obtained from the 3 signal sources and their phase relationships, and monitor how the signals vary with varying frequency and amplitude of oscillation