handbook of modern sensors

342 10 Pressure Sensors
Fig. 10.1. Mercury-filled U-shaped sensor for measuring gas pressure.
10.4 Bellows, Membranes, and Thin Plates
In pressure sensors, a sensing element is a mechanical device which undergoes structural
changes under strain. Historically, such devices were bourdon tubes (C-shaped,
twisted, and helical), corrugated [3] and catenary diaphragms, capsules, bellows,
barrel tubes, and other components whose shape changed under pressure.
A bellows (Fig. 10.2A) is intended for the conversion of pressure into a linear
displacement which can be measured by an appropriate sensor. Thus, the bellows
performs a first step in the conversion of pressure into an electrical signal. It is
characterized by a relatively large surface area and, therefore, by a large displacement
at low pressures. The stiffness of seamless metallic bellows is proportional to Young’s
modulus of the material and inversely proportional to the outside diameter and to the
number of convolutions of the bellows. Stiffness also increases with roughly the third
power of the wall thickness.
Apopular example of pressure conversion into a linear deflection is a diaphragm in
an aneroid barometer (Fig. 10.2B). A deflecting device always forms at least one wall
of a pressure chamber and is coupled to a strain sensor (e.g., a strain gauge) which
converts deflection into electrical signals. Currently, a great majority of pressure
sensors are fabricated with silicon membranes by using micromachining technology.
A membrane is a thin diaphragm under radial tension S which is measured in
Newtons per meter (Fig. 10.3B). The stiffness of bending forces can be neglected,
as the thickness of the membrane is much smaller compared with its radius (at least
200 times smaller). When pressure is applied to one side of a membrane, it shapes it