Page 397 - The Mechatronics Handbook

The Transient Response
Shocks are characterized as sudden releases of energy in the form of short-duration pulses exhibiting
various shapes and rise times. They have high magnitudes and wide frequency contents. In applications
where transient and shock measurements are involved, the overall linearity of the measuring system may
be limited to high and low frequencies by a phenomena known as zero shift and ringing, respectively.
The zero shift is caused by both the phase nonlinearity in the preamplifiers and the accelerometer not
returning to steady-state operation conditions after being subjected to high shocks. Ringing is caused by
high-frequency components of the excitation near-resonance frequency, preventing the accelerometer
from returning back to its steady-state operation condition. To avoid measuring errors due to these
effects, the operational frequency of the measuring system should be limited to the linear range.

Full Scale Range and Overload Capability
Most accelerometers are able to measure acceleration in both positive and negative directions. They are
also designed to be able to accommodate overload capacity. Manufacturers also supply information on
these two characteristics.
Environmental Conditions
In selection and implementation of accelerometers, environmental conditions such as temperature ranges,
temperature transients, cable noise, magnetic field effects, humidity, and acoustic noise need to be con-
sidered. Manufacturers supply information on environmental conditions.

Inertial Accelerometers
Inertial accelerometers are mechanical accelerometers that make use of a seismic mass that is suspended
by a spring or a lever inside a rigid frame as shown in Fig. 19.17. The frame carrying the seismic mass
is connected firmly to the vibrating source whose characteristics are to be measured. As the system
vibrates, the mass tends to remain fixed in its position so that the motion can be registered as a relative
displacement between the mass and the frame. An appropriate transducer senses this displacement and
the output signal is processed further. The displacement sensing element can be made from a variety of
materials exhibiting resistive, capacitive, inductive, piezoelectric, piezoresistive, and optical capabilities.
In practice, the seismic mass does not remain absolutely steady, but it can satisfactorily act as a reference
position for selected frequencies.
By proper selection of mass, spring, and damper combinations, the seismic instrument may be used
for either acceleration or displacement measurements. In general, a large mass and soft spring are suitable
for vibration and displacement measurement, while a relatively small mass and a stiff spring are used in
accelerometers. However, the term seismic is commonly applied to instruments, which sense very low
levels of vibration in the ground or structures.
In order to describe the response of the seismic accelerometer in Fig. 19.17, Newton’s second law, the
equation of motion, may be written as
2
d x 2 dx 2 dx 1
=
2 +
m ---------- c -------- + kx 2 c -------- + kx 1 + mg cos θ () (19.12)
dt dt dt
where x 1 is the displacement of the vibration frame, x 2 is the displacement of the seismic mass, c is the
velocity constant, θ is the angle between the sense axis and gravity, and k is the spring constant.
2
2
Taking md x 1 /dt from both sides of the equation and rearranging gives
2
2
m d z 2 + c dz + kz mg cos θ () m d x 1 (19.13)
-----
----------
-------
=
–
dt dt dt 2
where z = x 2 - x 1 is the relative motion between the mass and the base.
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