unit 4

Vibratory Gyroscope

• Low cost miniature companion with micromachined accelerometers for inertial navigation.
• Applications:
  • Automotive: Ride stabilization and rollover detection.
  • Consumer electronics: Video-camera stabilization, inertial mouse.
  • Robotics.
  • Military: Guided missiles.

Tuning Fork Vibratory Gyroscope

• Operating principle: Tines are differentially resonated, and rotation induces Coriolis force, causing differential sinusoidal force on the tines, orthogonal to the main vibration.
• Detection: Differential bending of the tuning fork stem.
• Actuation/Sensing: Electrostatic, electromagnetic, or piezoelectric mechanisms.

Coriolis Force

• Formula: $F_c = k v \times \Omega$ where:
  • $F_c$ is the Coriolis force
  • $k$ is a constant,
  • $v$ is the velocity,
  • $\Omega$ is the angular velocity.
• Maximum sensitivity: Achieved when actuation and Coriolis force frequencies are nearly equal.

Ideal Gyroscope Model

• Drive and detection axes are orthogonal.
• Mass-spring-damping system:
  • Driving mode: Mass $m$ vibrates along the x-axis.
  • Angular velocity subjects the mass to Coriolis force, causing vibration along the z-axis.

Tuning Fork Gyroscope: Working Principle

• Composed of driving and detecting tuning forks.
• Driving tuning fork: Two masses vibrate toward each other (x-axis) near resonance frequency via the inverse piezoelectric effect.
• Rotation around the y-axis induces Coriolis force, causing vibration in the z-axis.
• Coriolis force movement is transmitted to the detection tuning fork via V-shaped beams.
• Detection tuning fork vibrates perpendicular to the plane of the tuning forks.
• Electrical signal (proportional to angular velocity $\Omega$) is generated via the piezoelectric effect and conditioned to calculate the input angular velocity.

Vibratory Gyroscope: Fabrication Techniques

• Silicon bulk micromachining and wafer bonding.
• Polysilicon surface micromachining.
• Metal electroforming and LIGA.
• Combined bulk-surface micromachining.

Parameters of Vibratory Gyroscope

• Resolution: Standard deviation of equivalent rotation rate per square root of bandwidth of detection $\left[ (\frac{\sigma}{\text{hour}}) / \sqrt{\text{Hz}} \right]$.
• Angle Random Walk: Measured in $\degree \sqrt{\text{Hz}}$, alternative to resolution.
• Scale Factor: Change in output signal per unit change of rotation rate, expressed in V/($\degree$/S).
• Zero Rate Output (ZRO): Output in the absence of rotation.
• Short- or Long-term Drift: Peak-to-peak value of slowly varying function influencing output without rotation.
• Gyroscope Categories: Inertial-grade, tactical-grade, and rate-grade.

Piezoelectric Energy Harvester

• Energy harvesting: Extracting energy from external sources and storing it.
• External sources:
  • High-level: Solar, wind, tidal.
  • Low-level: Vibrations, heat, noise.

Piezoelectric Energy Harvesting

• Reliable and energy-efficient method.
• Piezoelectric materials: Transform mechanical strain energy into electrical energy, and vice versa.
• Process:
  • Piezo ceramic generates AC wave.
  • Rectifier circuit converts AC to DC.
  • Boost converter steps up the voltage.
  • Lithium-ion battery charger circuit charges the battery.

Applications of Harvested Energy

• Powering:
  • Remote sensing systems (automotive electronics).
  • Wireless sensor nodes (WSNs).
• Sensing:
  • Environmental, structural, biological, and automobile health.

Applications of Piezoelectric Energy Harvester

• Roadway Generator: Slabs installed at the London Olympic games (Pavegen systems).
• Railroad Generator and Runway Generator: Piezoelectric generators for road, rail, and runway (Innowattech, Israel).
• Flexible Piezoelectric Energy Harvesters: 200 microW @1.5g vibration amplitude (University of Michigan), flexible harvesters (KAIST, Republic of Korea).

Why Piezoelectricity over Batteries?

• Piezoelectric energy must be stored in significant amounts.
• Disadvantages of Batteries:
  • Limited lifetime.
  • Physical dimensions.
• Advantages of Piezoelectricity:
  • Small size.
  • Ability to be fabricated in custom shapes.
• Enables compact, maintenance-free, and cost-effective systems using human activities (walking, jogging, running) for electrical energy generation.

Piezoelectric Energy Harvester: Basic Block Diagram

• Components:
  • Piezoelectric generator.
  • Rectifier.
  • DC-DC Converter (Buck or Buck-boost).
  • Storage capacitor.
  • Load.
  • PZT thin film
  • Interface circuits

Piezoelectric Energy Harvester: Circuit Details

• Piezoelectric ceramic converts mechanical energy (vibration) into AC electrical energy.
• AC signal is rectified and filtered to produce a DC voltage.
• Regulator circuit removes ripples and maintains a constant DC value.
• DC-DC Boost Converter steps up the voltage.
• Battery charging circuit (e.g., MCP 73862 IC) charges lithium-ion/lithium polymer batteries.
• Lithium polymer battery stores the charge for electrical applications.