Page 400 - The Mechatronics Handbook

FIGURE 19.22 A typical suspended-mass-vibrating string accelerometer.

The quantity T 1 - T 2 is proportional to ma where a is the acceleration along the axis of the strings. An
expression for the difference of the frequency-squared terms may be written as

T 1 – T 2 ma
2 2 ----------------- -----------
f 1 – f 2 = 4m s l = 4m s l (19.19)
Hence

ma
f 1 – f 2 = ------------------------------ (19.20)
(
4m s lf 1 + )
f 2
The sum of frequencies ( f 1 + f 2 ) can be held constant by serving the tension in the strings with reference
to the frequency of a standard oscillator. Then, the difference between the frequencies becomes linearly
proportional to acceleration. In some versions, the beamlike property of the vibratory elements is used
by gripping them at nodal points corresponding to the fundamental mode of the vibration of the beam,
and at the respective centers of percussion of the common proof mass. The output frequency is propor-
tional to acceleration and the velocity is proportional to phase, thus offering an important advantage.
The improved versions of these devices lead to cantilever-type accelerometers, discussed next.
In a cantilever-type accelerometer, a small cantilever beam mounted on the block is placed against the
vibrating surface, and an appropriate mechanism is provided for varying the beam length. The beam
length is adjusted such that its natural frequency is equal to the frequency of the vibrating surface, and
hence the resonance condition is obtained. Recently, slight variations of cantilever-beam arrangements
are finding new applications in microaccelerometers.
In a different type of suspended-mass configuration, a pendulum is used that is pivoted to a shaft
rotating about a vertical axis. Pickoff mechanisms are provided for the pendulum and the shaft speed.

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