Inertial Sensors and Their Applications - Signal Processing Systems - page 67

1.1 Accelerometers

An accelerometer is a device that measures translational acceleration resulting
from the forces acting on it. This acceleration is associated with the phenomenon
of weight experienced by a mass that resides in the frame of reference inside
accelerometer and can be described by Newton's second law of motion: “A force F
acting on a body of mass m causes the body to accelerate with respect to inertial
space.” A typical accelerometer consists of a small mass, also known as a proof or
seismic mass, connected via a spring to the case of the instrument as shown in Fig. 1 .
When the instrument experiences acceleration along its sensitive axis, the proof
mass is displaced with respect to the case of instrument; this is the scenario in
Fig. 1 b . Under steady state conditions, the force acting on the mass will be balanced
by the tension in the spring. The extension (or contraction) of the spring creates
a force which is proportional to the displacement. When there is no drag force to
resist the movement of the proof mass, its displacement is directly proportional to
the acceleration. This way the applied acceleration can be measured by measuring
the displacement of the proof mass.
There are many different designs for accelerometer but most of them operate in
a manner similar to the simple spring and mass system described above. In many
applications, including navigation, the three dimensional vector of acceleration is re-
quired. Normally, three single-axis accelerometers are used. In recent years, tri-axis
instruments have become very popular in the segment of low-cost accelerometers.
It is a common practice to mount the three accelerometers with their sensitive axes
mutually orthogonal, although any non-coplanar configuration is acceptable as long
as the angles between the sensitive axes are known.
Accelerometers are insensitive to the gravitational acceleration and unable to
separate the total acceleration from that caused by the presence of a gravitational
field. These sensors instead provide measurements of the difference between the
true acceleration and the acceleration due to gravity. This quantity is the non-
gravitational force per unit mass exerted on the instrument, and often called a

a b c

Fig. 1 A mass-and-spring accelerometer under different conditions: ( a )atrestorinuniform
motion, ( b ) accelerating, and ( c )atrest