Page 399 - The Mechatronics Handbook

In this way the anticipated accuracy of measurement may be predicted for frequencies of interest. A
comprehensive treatment of the analysis has been performed by McConnell [7]; interested readers should
refer to this text for further details.
Seismic instruments are constructed in a variety of ways. In a potentiometric instrument, a voltage
divider potentiometer is used for sensing the relative displacement between the frame and the seismic
mass. In the majority of potentiometric accelerometers, the device is filled with a viscous liquid that
interacts continuously with the frame and the seismic mass to provide damping. These accelerometers
have a low frequency of operation (less than 100 Hz) and are mainly intended for slowly varying
accelerations, and low-frequency vibrations. A typical family of such instruments offers many different
models, covering the range of ±1g to ±50g full scale. The natural frequency ranges from 12 to 89 Hz,
and the damping ratio ζ can be kept between 0.5 and 0.8 by using a temperature compensated liquid-
damping arrangement. Potentiometer resistance may be selected in the range of 1000–10,000 W, with a
corresponding resolution of 0.45–0.25% of full scale. The cross-axis sensitivity is less than ±1%. The
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overall accuracy is ±1% of full scale or less at room temperatures. The size is about 50 mm with a total
mass of about 1/2 kg.
Linear variable differential transformers (LVDTs) offer another convenient means of measurement of
the relative displacement between the seismic mass and the accelerometer housing. These devices have
higher natural frequencies than potentiometer devices, up to 300 Hz. Since the LVDT has lower resistance
to motion, it offers much better resolution. A typical family of liquid-damped differential-transformer
accelerometers exhibits the following characteristics. The full scale ranges from ±2g to ±700g, the natural
frequency from 35 to 620 Hz, the nonlinearity 1% of full scale. The full-scale output is about 1 V with
an LVDT excitation of 10 V at 2000 Hz, the damping ratio ranges from 0.6 to 0.7, the residual voltage
at the null position is less than 1%, and the hysteresis is less than 1% of full scale. The size is about
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50 mm with a mass of about 120 g.
Electrical resistance strain gages are also used for displacement sensing of the seismic mass. In this
case, the seismic mass is mounted on a cantilever beam rather than on springs. Resistance strain gauges
are bonded on each side of the beam to sense the strain in the beam resulting from the vibrational
displacement of the mass. A viscous liquid that entirely fills the housing provides damping of the system.
The output of the strain gauges is connected to an appropriate bridge circuit. The natural frequency of
such a system is about 300 Hz. The low natural frequency is due to the need for a sufficiently large
cantilever beam to accommodate the mounting of the strain gauges.
One serious drawback of the seismic instruments is temperature effects requiring additional compen-
sation circuits. The damping of the instrument may also be affected by changes in the viscosity of the
fluid due to temperature. For instance, the viscosity of silicone oil, often used in these instruments, is
strongly dependent on temperature.
Suspended-Mass, Cantilever, and Pendulum-Type Inertial Accelerometers
There are a number of different inertial-type accelerometers, most of which are in development stages
or used under very special circumstances, such as gyropendulum, reaction-rotor, vibrating-string, and
centrifugal-force-balance.
The vibrating-string instrument, Fig. 19.22, makes use of a proof mass supported longitudinally by a
pair of tensioned, transversely vibrating strings with uniform cross section and equal lengths and masses.
The frequency of vibration of the strings is set to several thousand cycles per second. The proof mass is
supported radially in such a way that the acceleration normal to the strings does not affect the string
tension. In the presence of acceleration along the sensing axis, a deferential tension exists on the two
strings, thus altering the frequency of vibration. From the second law of motion the frequencies may be
written as

T 1 2 T 2
2
f 1 = ----------- and f 2 = ----------- (19.18)
4m s l 4m s l
where T is the tension, m are the mass, and l is the lengths of strings.
s
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