Page 81 - Mechanical Engineers' Handbook (Volume 2)

70 Bridge Transducers

Transmitting System. The transmitting system typically consists of some or all of the
following devices: cable, amplifier, subcarrier oscillator, filter, analog-to-digital
(A/D) converter, transmitter, and antenna.
Receiving System. The receiving system typically consists of some or all of the following
devices: antenna, preamplifier, multicoupler, receiver, tape or disc recorder, discrim-
inator, decommutator, digital-to-analog (D/A) converter, and output filter.
Data Output and Display System. The data output and display system typically consist
of some or all of the following devices: oscilloscope, analog meter, digital meter,
graphic display, and digital printer. Either these devices may be connected directly to
the output of the receiving system or a computer may process the data from the
receiving system before display.

2 FLEXURAL DEVICES IN MEASUREMENT SYSTEMS
Bridge transducers depend on a measurand to directly modify some electrical or magnetic
property of a conductive element. For example, the thermal coefficient of impedance can
result in a change in impedance of a conductive element proportional to temperature (e.g.,
resistance thermometer). Similarly, hygroscopic materials can have their impedance change
in a deterministic fashion due to humidity (e.g., humidity sensor). Most bridge transducers,
however, depend on the displacement of a flexure to vary the impedance of a conductive
element, resulting in an electrical signal proportional to the measurand. Advantage is taken
of either the strain pattern on the surface of the flexure or the motion of this surface. Among
the gamut of flexure elements associated with bridge transducers are cantilever beams, Bour-
don tubes, and clamped diaphragms.

2.1 Cantilever Beams
Cantilever beams are routinely designed into bridge transducers. Strain near the clamped end
of the beam can be correlated to displacement of the free beam end, force or torque applied
to the free beam end, dynamic pressure associated with fluid flow acting over the beam
surface, and so on. The compliance of a cantilever beam is defined as
y L 3
(1)
F 3EI
where y is deflection of the beam free end, F is the force applied to this end, L is the beam
length, E is the modulus of elasticity of the beam material, and I is the beam area moment
of inertia. A compliant flexure will result in a bridge transducer with a large electrical signal
output. Equation (1) indicates a compliant flexure design can be achieved by a long, thin,
narrow beam of low-modulus material. The penalty attached to such a design in application
could be a transducer which is bulky, displays undesirable response to physical inputs or-
thogonal to its sensing direction, and has poor dynamic response.

2.2 Bourdon Tubes
Bourdon tubes are one of the most widely used flexures for sensing pressure. The original
patent for this device was granted to Eugene Bourdon in 1852. Bourdon tubes are hollow
tubes that are twisted or curved along their length. The application of pressure deforms the
tube wall which, depending on tube shape, causes it to untwist or unwind. Motion of the