Applications: Angular Rate Sensors

1. Applications:Angular Rate Sensors CSE 495/595: Intro to Micro- and Nano- Embedded Systems Prof. Darrin Hanna

2. Angular Rate Sensors

3. Angular Rate Sensors – Good Ole Gyroscopes • large angular momentum that is proportional to the heavy mass of the flywheel • substantial size • high rate of spin • Won’t work in • MEMS

4. Angular Rate Sensors • Coriolis Effect • deflection of a moving object • in a rotating frame of reference • Coriolis acceleration • a = 2Ω x v • V is the velocity of the particle in the rotating system • ω is the angular velocity vector of the rotating system • magnitude equal to the rotation rate • points in the direction of the axis of rotation. • Multiply by the mass of the object to produce the Coriolis force.

5. Angular Rate Sensors

6. Angular Rate Sensors • Coriolis acceleration is perpendicular both to the direction of the velocity of the moving mass and to the rotation axis • if the velocity is zero, the Coriolis acceleration is zero • if the velocity is parallel to the rotation axis, the Coriolis acceleration is zero • if the velocity is perpendicularly inward to the axis, the acceleration will follow the direction of rotation (i.e., be perpendicular to the rotation axis and the particle velocity) • if the velocity is following the rotation, the acceleration will be (perpendicularly) outward from the axis

7. Angular Rate Sensors • Two tines of the fork normally vibrate in opposite directions in the plane of the fork • flexural mode • Rotating it: Coriolis acceleration subjects the tips to a displacement perpendicular to the primary mode of oscillation, forcing each tip to describe an elliptical path. • excites a secondary vibration torsional • mode around the stem with energy transferred from the primary flexural vibration of the tines.

8. Angular Rate Sensors

9. Angular Rate Sensors • Main specifications of an angular-rate sensor • full-scale range (expressed in º/s or º/hr) • scale factor or sensitivity [V/(º/s)] • noise, °/(s ∙ (Hz)1/2) • bandwidth (Hz) • resolution (º/s) • dynamic range (dB) • dynamic range and resolution are a function of noise and bandwidth. • Short- and long-term drift of the output, known as bias drift (º/s) or (º/hr) • withstand shocks of at least 1,000G.

10. Angular Rate Sensors Delphi Delco Electronic Systems • Primary and secondary mode resonance

11. Angular Rate Sensors Delphi Delco Electronic Systems

12. Angular Rate Sensors Delphi Delco Electronic Systems • Ring shell is anchored at its center to the substrate • deforms as it vibrates through a full cycle from a circle to an ellipse, back to a circle, then to an ellipse rotated at right angles to the first ellipse, then back to the original circle

13. Angular Rate Sensors Delphi Delco Electronic Systems • Points on the shell that remain stationary are called nodes • Points that undergo maximal deflection are called antinodes. • The nodes and antinodes form a vibration pattern—or standing-wave pattern—around the ring • The pattern is characteristic of the resonance mode

14. Angular Rate Sensors Delphi Delco Electronic Systems • Because of symmetry, a ring shell possesses two frequency-degenerate resonant modes with their vibration patterns offset by 45º with respect to each other. • The nodes of the first mode coincide with the antinodes of the second mode.

15. Angular Rate Sensors Delphi Delco Electronic Systems • The external control electronics excite only one of the two modes—the primary mode. • Under rotation, the Coriolis effect excites the second resonance mode, and energy transfer occurs between the two modes. • The deflection amplitude builds up at the antinodes of the second mode—also, the nodes of the first mode.

16. Angular Rate Sensors Delphi Delco Electronic Systems • The overall vibration becomes a linear combination of the two modes with a new set of nodes and antinodes forming a vibration pattern rotated with respect to the pattern of the primary mode.

17. Angular Rate Sensors Delphi Delco Electronic Systems • Open-loop configuration • deflection amplitude at the nodes and antinodes is a measure of the angular rate of rotation. • the angular shift of the vibration pattern is another measure. • Closed-loop configuration • electrostatic actuation by a feedback voltage applied to the excitation electrodes • nulls the secondary mode and maintains a stationary vibration pattern • Angular rate is directly proportional to this feedback voltage.

18. Angular Rate Sensors Delphi Delco Electronic Systems • 32 electrodes positioned around the suspended ring shell • of this eight electrodes positioned at 45º intervals—at the nodes and antinodes—capacitively sense the deformation of the ring shell • A phased-locked loop (PLL) drives the ring into resonance through the electrostatic drive electrodes • maintains a lock on the frequency

19. Angular Rate Sensors Delphi Delco Electronic Systems • Preprocessed CMOS control circuitry • Electroplated nickel ring shell • 15 to 50 µm thick • Packaging completed in vacuum • minimize air damping of the resonant ring • provide a large quality factor

20. Angular Rate Sensors Delphi Delco Electronic Systems • Specifications over the temperature range of –40° to +125ºC • resolution of 0.5º/s • bandwidth of 25 Hz • limited by noise in the electronic circuitry • nonlinearity in a rate range of ±100 º/s is less than 0.2º/s • sensor survives the standard automotive shock test • a drop from a height of one meter

21. Angular Rate Sensors