Page 128 - An Introduction to Microelectromechanical Systems Engineering

Sensors and Analysis Systems 107

small size and low cost, currently less than $10. They are slowly gaining acceptance
in automotive applications, in particular, for vehicle stability systems. The sensor
detects any undesired yaw of a vehicle due to poor road conditions and feeds the
information to a control system, which may activate the antilock braking system
(ABS) or the traction control system (TCS) to correct the situation. The Mercedes
Benz ML series of sport utility vehicles incorporates a silicon angular-rate sensor
from Robert Bosch GmbH for vehicle stability.
The selection of commercially available micromachined yaw-rate sensors
remains limited, but many manufacturers have publicly acknowledged the existence
of development programs. The sensors from Delphi Delco Electronics Systems,
Robert Bosch GmbH, Daimler Benz AG, and Silicon Sensing Systems illustrate four
vibratory-type angular-rate sensors distinct in their structure as well as excitation
and sense methods.

Micromachined Angular-Rate Sensor from Delphi Delco Electronics Systems
The sensor from Delphi Delco Electronics Systems of Kokomo, Indiana [29], a divi-
sion of Delphi Corporation of Troy, Michigan, includes at its core a vibrating ring
shell based on the principle of the ringing wine glass discovered in 1890 by G. H.
Bryan. He observed that the standing-wave pattern of the wine glass did not remain
stationary in inertial space but participated in the motion as the glass rotated about
its stem.
The complete theory of vibrating-ring angular-rate sensors is well developed
[30]. The ring shell, 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 (see Figure 4.23). The points on the shell that remain stationary are
called nodes, whereas the points that undergo maximal deflection are called anti-
nodes. The nodes and antinodes form a vibration pattern—or standing-wave pat-
tern—around the ring. The pattern is characteristic of the resonance mode. Because
of symmetry, a ring shell possesses two frequency-degenerate resonant modes with
their vibration patterns offset by 45º with respect to each other. Hence, the nodes
of the first mode coincide with the antinodes of the second mode. The external con-
trol electronics excite only one of the two modes—the primary mode. But under
rotation, the Coriolis effect excites the second resonance mode, and energy transfer
occurs between the two modes. Consequently, the deflection amplitude builds up
at the antinodes of the second mode—also, the nodes of the first mode. 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. It is this lag that Bryan heard in his spinning
wine glass. In an open-loop configuration, the deflection amplitude at the nodes
and antinodes is a measure of the angular rate of rotation. Alternatively, the
angular shift of the vibration pattern is another measure. In a closed-loop
configuration, electrostatic actuation by a feedback voltage applied to the
excitation electrodes nulls the secondary mode and maintains a stationary vibra-
tion pattern. The angular rate becomes directly proportional to this feedback
voltage.