9.1.2 Early Accelerometers
Pendulum clocks were used in the eighteen century for measuring the acceleration
due to gravity, but these devices were not usable on moving platforms.
9.1.2.1 Drag Cup Accelerometer An early "integrating" accelerometer design
is illustrated in Fig. 9.4. It has two independent moving parts, both able to rotate
on a common shaft axis:
- A bar magnetic, the rotation rate of which is controlled by a dc motor.
- A nonferrous metal "drag cup" that will be dragged along by the currents
induced in the metal by the moving magnetic field, producing a torque on
the drag cup that is proportional to the magnet rotation rate. The drag cup
also has a proof mass attached to one point, so that acceleration along the
"input axis" direction shown in the illustration will also create a torque on
the drag cup.
The DC current to the motor is servoed to keep the drag cup from rotating, so that
the magnet rotation rate will be proportional to acceleration and each rotation of
the magnet will be proportional to the resulting velocity increment over that time
period. At very low input accelerations (e.g., during gimbaled IMU leveling),
inhomogeneities in the drag cup material can introduce harmonic noise in the
output.
This same sort of drag cup, without the proof mass and with a torsion spring
restraining the drag cup, has been used for decades for automobile speedometers.
A flexible shaft from the drive wheels drove the magnet, so that the angular
deflection of the drag cup would be proportional to speed.
9.1.2.2 Vibrating-Wire Accelerometer This is another early digital accelerometer
design, with the output a frequency difference proportional to input acceleration.
The resonant frequencies of vibrating wires (or strings) depend upon the
length, density, and elastic modulus of the wire and on the square of the tension in
the wire. The motions of the wires must be sensed (e.g., by capacitance pickoffs)
and forced (e.g., electrostatically or electromagnetically) to be kept in resonance.
The wires can then be used as digitizing force sensors, as illustrated in Fig. 9.5.
The configuration shown is for a single-axis accelerometer, but the concept can
be expanded to a three-axis accelerometer by attaching pairs of opposing wires
in three orthogonal directions.
In the "push-pull" configuration shown, any lateral acceleration of the proof
mass will cause one wire frequency to increase and the other to decrease. Furthermore,
if the preload tensions in the wires are servoed to keep the sum of their
frequencies constant, then the difference frequency
Both the difference frequency ωleft - ωright and the sum frequency ωleft + ωright
(used for preload tension control) can be obtained by mixing and filtering the
two wire position signals from the resonance forcing servo loop. Each cycle of
the difference frequency then corresponds to a constant delta velocity, making
the sensor inherently digital.
9.1.2.3 Gyroscopic Accelerometers Some of the earlier designs for accelerometers
for inertial navigation used the acceleration-sensitive precession of momentum
wheel gyroscopes, as illustrated in Fig. 9.6.
This has the center of support offset from the center of mass of the momentum
wheel, a condition known as "mass unbalance." For a mass-unbalanced design
like the one shown in the figure, precession rate will be proportional to acceleration.
If the angular momentum and mass offset of the gyro can be kept constant,
this relationship will extremely linear over several orders of magnitude.
Gyroscopic accelerometers are integrating accelerometers. Angular precession
rate is proportional to acceleration, so the change in precession angle will be
proportional to velocity change along the input axis direction.
Accelerometer designs based on gyroscopic precession are still used in the
most accurate floated system [129].
9.1.2.4 Accelerometer Performance Ranges Table 9.3 lists accelerometer and
gyroscope performance ranges compatible with the INS performance ranges listed
in Chapter 2, Section 2.2.4.3.
9.1.2 Early Accelerometers
Pendulum clocks were used in the eighteen century for measuring the acceleration
due to gravity, but these devices were not usable on moving platforms.
9.1.2.1 Drag Cup Accelerometer An early "integrating" accelerometer design
is illustrated in Fig. 9.4. It has two independent moving parts, both able to rotate
on a common shaft axis:
- A bar magnetic, the rotation rate of which is controlled by a dc motor.
- A nonferrous metal "drag cup" that will be dragged along by the currents
induced in the metal by the moving magnetic field, producing a torque on
the drag cup that is proportional to the magnet rotation rate. The drag cup
also has a proof mass attached to one point, so that acceleration along the
"input axis" direction shown in the illustration will also create a torque on
the drag cup.
The DC current to the motor is servoed to keep the drag cup from rotating, so that
the magnet rotation rate will be proportional to acceleration and each rotation of
the magnet will be proportional to the resulting velocity increment over that time
period. At very low input accelerations (e.g., during gimbaled IMU leveling),
inhomogeneities in the drag cup material...
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