U.S. patent number 3,719,074 [Application Number 05/077,067] was granted by the patent office on 1973-03-06 for rotating-wave rotation detector and method of operating same.
This patent grant is currently assigned to General Motors Corporation. Invention is credited to David D. Lynch.
United States Patent |
3,719,074 |
Lynch |
March 6, 1973 |
ROTATING-WAVE ROTATION DETECTOR AND METHOD OF OPERATING SAME
Abstract
A bell-like high-Q member having sides capable of being flexed
in a radial vibration pattern defining an anti-nodal region that is
free to rotate about the sides in proportion to the rotation of the
sides about an input axis. A forcer is mounted adjacent and
encircling the periphery of the sides and is effective at the
instantaneous angular position of the anti-nodal region to
parametrically excite and exercise the sides. Sensor means are
located adjacent the periphery and along radii fixed with respect
to the bell sides to measure the pattern rotation with respect to
bell rotation.
Inventors: |
Lynch; David D. (Greendale,
WI) |
Assignee: |
General Motors Corporation
(Detroit, MI)
|
Family
ID: |
22135883 |
Appl.
No.: |
05/077,067 |
Filed: |
October 1, 1970 |
Current U.S.
Class: |
73/504.13 |
Current CPC
Class: |
G01C
19/5691 (20130101) |
Current International
Class: |
G01C
19/56 (20060101); G01c 019/56 () |
Field of
Search: |
;73/505 ;74/5 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Gill; James J.
Claims
What I claim as new and desire to secure by letters of patent of
the United States is:
1. A device to sense rotation of a platform about a predetermined
axis, comprising in combination:
a. a platform;
b. a high-Q member carried by said platform along said axis and
defining a perimeter about said axis, said member capable of
sustaining therein a vibration pattern rotatable about said axis
when said platform rotates about said axis, the rotation of said
pattern varying with the rotation of said platform;
c. a forcer carried by said platform adjacent said perimeter and
operative to impart thereto radial forces sustaining said pattern,
said forces having a frequency of twice the frequency of said
pattern; and
d. a sensor carried by said platform adjacent said perimeter and
operative to measure radial vibrations thereof produced by the
effects of said pattern and rotation of said platform about said
axis.
2. A device to sense rotation of a platform about a predetermined
axis, comprising in combination:
a. a platform;
b. a high-Q member carried by said platform along said axis and
defining a perimeter about said axis, said member capable of
sustaining therein a vibration pattern rotatable about said axis
when said platform rotates about said axis, the rotation of said
pattern varying with the rotation of said platform;
c. an annular forcer carried by said platform adjacent to said
perimeter and operative to impart thereto time varying forces
radial to said axis and sustaining said pattern; and
d. a sensor carried by said platform adjacent said perimeter and
operative to measure radial vibrations thereof produced by the
effects of said pattern and rotation of said platform about said
axis.
3. A device to sense rotation of a platform about a predetermined
axis, comprising in combination:
a. a platform;
b. a high-Q member carried along said axis by said platform and
defining a perimeter about said axis, said member capable of
sustaining therein a vibration pattern defining a plurality of
nodal and anti-nodal regions spaced alternately about and rotatable
on said perimeter when said platform rotates, the rotation of said
pattern varying with the rotation of said platform about said axis
to indicate said platform rotation;
c. a forcer carried by said platform adjacent said perimeter to
impart thereto periodic pulses thereto sustaining said pattern,
said pulses having a frequency of twice the frequency of said
pattern and said forcer comprising circumferential sections
effective to impart said pulses to a one of said anti-nodal regions
for substantially all positions of said pattern about said axis;
and
d. a sensor carried by said platform adjacent said perimeter and
operative to measure radial vibrations thereof produced by the
effects of said pattern and rotation of said platform about said
axis.
4. A device to sense rotation of a platform about a predetermined
axis, comprising in combination:
a. a platform;
b. a high-Q bell-like member carried along said axis and having
sides radially displaceable towards said axis and defining a
perimeter thereabout, said sides capable of sustaining therein a
vibration pattern rotatable about said axis when said platform
rotates about said axis, the rotation of said pattern varying with
the rotation of said platform;
c. a forcer carried by said platform adjacent said perimeter and
operative to impart thereto radial forces sustaining said pattern
said forces having a frequency of twice the frequency of said
pattern; and
d. a sensor carried by said platform adjacent said perimeter and
operative to measure radial vibrations thereof produced by the
effects of said pattern and rotation of said platform about said
axis.
5. A device to sense rotation of a platform about a predetermined
axis, comprising in combination:
a. a platform;
b. a high-Q bell-like member carried along said axis and having
sides radially displaceable towards said axis and defining a
perimeter thereabout, said sides capable of sustaining therein a
vibration pattern rotatable about said axis when said platform
rotates about said axis, the rotation of said pattern varying with
the rotation of said platform;
c. A circular forcer carried by said platform adjacent to said
perimeter and operative to impart thereto radial forces sustaining
said pattern said forces having a frequency of twice the frequency
of said pattern; and
d. a sensor carried by said platform adjacent said perimeter and
operative to measure radial vibrations thereof produced by the
effects of said pattern and rotation of said platform about said
axis.
6. The device of claim 5, wherein the ratio of rotation of said
pattern to the rotation of said platform is between 0.2 and
0.4.
7. The method of detecting the rotation of a high-Q member about a
predetermined axis therethrough, said member having a perimeter
about said axis capable of sustaining natural frequency vibrations
radial to said axis, rotatable thereabout on said perimeter, and
having a substantially null region, said method comprising the
steps of:
a. applying to said perimeter forces having a frequency of twice
the frequency of the vibrations whereby said vibrations are
maintained;
b. rotating said vibrations about said axis in proportion to the
rotation of said member about said axis; and
c. sensing the change in position of said null region produced by
said vibrations and said rotation of said member.
8. The method of detecting movement of a high-Q member about a
predetermined axis therethrough, said method comprising the steps
of:
a. maintaining vibrations in said member radial to said axis and
defining a plurality of nodal and anti-nodal regions spaced
thereabout, said regions capable of rotating in said member about
said axis with rotation of said member about said axis; and
b. sensing those radial vibrations produced by the effects of said
maintained vibrations and rotations of said member about said axis,
whereby said rotation of said anti-nodal region is measured.
Description
This invention relates to rotation detectors of the type described
and claimed in U.S. Pat. applications Ser. No. 843,109, now U.S.
Pat. No. 3,625,067, Ser. No. 863,857, Ser. No. 863,861, and Ser.
No. 864,019, respectively entitled "Device for Detecting Rotation
About An Axis and Method of Using Same (Ser. No. 843,109),"
"Improved Bell Gyro and Method of Making Same (S.N. 863,857),"
"Bell Gyro and Method of Making Same (S.N. 863,861)," and "Bell
Gyro and Improved Means for Operating Same (S.N. 864,019)," the
first filed by Alfred G. Emslie on July 18, 1969 and the last three
filed by David D. Lynch and Richard E. Denis on Oct. 6, 1969,
assigned to the same assignee as the assignee of this application,
and incorporated herein by reference.
A bell-like high-Q member may have the sides thereof vibrated by a
forcer to establish thereabout a standing-wave vibration pattern
defining nodal and anti-nodal regions. Subsequent rotations of a
member so vibrated causes vibrations to appear at regions otherwise
nodal in the absence of member rotation. These nodal vibrations are
of a frequency related to the forcing frequency but of a magnitude
varying with input rate. As long as the frequencies along the nodal
and anti-nodal axes are substantially the same, i.e., degenerate,
and depending on which nodal regions are considered, the vibrations
at the nodal and anti-nodal regions add and subtract to comprise a
single standing wave that rotates about the input axis. With a
constant input rate, constant amplitude vibrations are added and
subtracted to the rotating standing wave at its instantaneous nodal
regions and the vibration pattern rotates at a constant rate. The
greater the input rate, the greater these nodal vibrations, and the
faster the pattern rotation. Conversely, when the input to the
member subsequently terminates, the pattern stops rotating.
The amount of pattern rotation is thus an integration of the
magnitude of the input rate over some duration. If the period of
integration is some interval substantially less than the duration
of input, as with the detector of the above-cited applications,
then the amount of pattern rotation corresponds to amount of
angular input over that interval, in other words, the input rate.
If, on the other hand, the period of integration is over the entire
duration of input, as possible with detectors of the present
invention, the amount of pattern rotation corresponds to the total
input angle by some fraction such as 0.3. The effect of pattern
rotation with the present invention is that, as a given radius of
the bell (i.e., a bell-referenced radius) is rotated in one
direction about the bell's input axis, the standing-wave pattern
rotates away from that radius in the other direction. Or, viewing
this rotation with respect to an axis fixed in inertial space, the
effect is that as the bell radius under consideration rotates from
the inertially fixed axis at one rate, the standing-wave pattern
rotates in the same direction but with lower rate.
Regardless whether viewed from detector-referenced or
inertially-referenced axes, the difference between the rotation of
the bell and rotation of the pattern is a function of the bell
geometry and the number of nodal regions about its flexed
periphery. However, whether the pattern rotates freely about the
input axis or not depends primarily on two factors: the Q of the
bell, and, if the Q is not infinite, whether the exercising forcer
can act along any radius about the bell sides or not. If the Q of
the member were substantially infinite, the application of a single
exercising pulse would establish a vibration pattern having an
indefinite decay time, also known as ringing time. Input rotation
to the member would then result in the substantially-undamped
rotation of the standing wave pattern about the input axis as long
as there were input. At the termination of bell rotation, the
pattern would still be present and its position could be detected
to indicate the amount of bell rotation.
However, because of dissipative forces such as irreversible heat
flow between adjacent parts of the medium when heating and cooling
under periodic stresses, materials having substantially infinite
Q's are not known, and most materials having Q's sufficient to
establish standing waves for periods of hours or days before
re-excitement usually are not sufficiently stable, machinable, or
homogenous to establish standing-waves suitable for detection.
Thus, the implementation of a bell gyro in a mode requiring the
application of a single exciting force not yet being practical,
resort is taken to modes permitting the use of materials having
reasonably high Q' s but requiring the repetitive application of
energy to replace that lost by the member in vibration. One form of
such repetireplenishment of energy is, as described in the
above-cited applications, by a forcer or forcers acting along radii
fixed with respect to the bell. And in another form, that of the
present invention, the lost energy is also replaced repetitively,
but along any radii about the input axis corresponding with the
instantaneous position of the anti-nodal axis. This omniazimuth
forcing capacibility is provided by a forcer encircling the sides
of the bell so as to impart energy of the proper phase with respect
to the motion of the sides to an anti-nodal region of the lip in
any location of the region about the input axes.
If, as in the above-cited applications, the forcer is effective
along any fixed axes, the rotation is retarded so that it appears
inhibited. On the other hand, if the forcer is effective to flex
the sides along any radius where the anti-nodal axis happens to be,
as with the present invention, the pattern can rotate freely. In
either event, the angular position of points on this wave can be
determined by sensors acting along radii fixed with respect to the
bell.
Should the forcer be operative to impart attractive forces along an
a axis fixed with respect to the sides, the position of the
anti-nodal axis of the pattern is then a predetermined function of
both the position of the forcer and the input rate. Moreover, in
this configuration, the vibration pattern is constrained from any
further rotation about the input axis other than that proportional
to the input rate. This is believed due to the resolution of the
flexing forces imparted to the rotating bell continuously along the
instantaneous and mathematically-orthogonal modal and anti-nodal
axes of the standing wave pattern. Pattern rotation is therefore
stopped when that component of the flexing forces or vibrations
resolved along the instantaneous nodal axes exactly balances those
forces or vibrations produced along the same axes by the effects of
the standing wave pattern and the input rotation of the bell. The
amount of pattern rotation, as exhibited by the magnitude of
vibrations detected by sensors at regions nodal in the absence of
vibrations, is therefore in proportion to the rate of input. Should
the input-caused nodal vibrations be nulled as described in the
above-cited Lynch (Ser. No. 864,019) application, the pattern is
furthermore substantially inhibited from rotating at all and the
magnitude of the nulling vibrations may also be used as an
indication of the input rate.
The rate signal produced in either the nulled or non-nulled
variations of the restrained pattern modes may be used directly
where indications of angular rate are required or may be integrated
over periods during which the rate signal is present to indicate
the amount of angular input rotation. However, the present
invention, by allowing the vibration pattern to rotate freely about
azimuth, allows the angular displacement to be determined directly
by determining the instantaneous angular position of standing wave
pattern with sensors. Working backwards from this angular position,
angular rate may then be determined by differentiating the angular
position through a computer or differentiating circuit.
In its preferred form, the present invention includes a high-Q
bell-like member supported on a base platform by a post. The bell
member has sides flaring arcuately outwards and downwards along its
polar axis over the post and terminating adjacent the platform in
an annular lip. This lip is capable of sustaining a vibration
pattern therein and defining nodal and anti-nodal regions spaced
alternately and equiangularly thereabout. Telescoped by the
bell-like member and supported within the mouth thereof by the
platform and post adjacent to the periphery of the sides are two
circular electrodes mounted in tandem along the axis of the post.
Four other electrodes are affixed to a housing platform that
telescopes the bell, circular electrodes, and post is adjustable in
azimuth with respect to the base platform while the enclosure
defined therebetween is under vacuum.
Electronics connected with one of the circular electrodes provide
an energizing potential thereto of suitable frequency, magnitude,
and phase to modulate the effective spring constant of the bell
sides so as to overcome damping. Moreover, being circular and
adjacent the periphery of the bell lip, the forcer electrode is
operative to impart energy of the required phase and frequency to
at least one anti-nodal region of the rotatable vibration pattern
regardless of the azimuth position of the pattern with respect to
the input axis. The frequency of the excitation applied to and
imparted by the circular forcer is twice the natural frequency of
the bell member and therefore corresponds with twice the frequency
of the resulting vibration pattern. By this modulating a parameter
of the high-Q system at twice the natural frequency of the system
to overcome the damping thereon, the excitation is what is known as
parametric. The amplitude of this parametrically excited vibration
is detected by the second of the tandem circular electrodes at an
anti-nodal region and is utilized to develop feedback signals to
the first circular electrode whereby substantially constant
amplitude and natural frequency radial vibrations are effected in
the bell sides, such vibrations defining the pattern comprising
nodal and anti-nodal regions spaced alternately and angularly
thereabout.
In the absence of platform rotation the vibration pattern thus
parametrically excited remains stationary with respect to the input
axis and bell referenced radii. However, with rotation about the
input axis, the foregoing structure and system allows the vibration
pattern to rotate freely about the input axis with an angular
displacement proportional to that of the detector. The extent of
such rotation of the vibration pattern is detected by the sensors
mounted in the housing platform. These housing mounted electrodes
are operative in a uniradial sense as compared with the
omniazimuthal sense of the circular forcer and sensor and produce
output signals at the natural frequency of the bell. The angle of
detector displacement is then determined from the product of the
amplitude of the vibration pattern times the cosine of twice the
displaced angle times the cosine of the exercising frequency.
It is, therefore, a general object of the present invention to
provide a high-Q bell-like rotation detector having sides
encircling an input axis, where the sides are flexed in a vibration
pattern that rotates about the sides in proportion to rotation of
the detector about its input axis and where the energy to cause the
flexing is imparted repetitively to the sides at regions that
rotate with the pattern.
It is a further object to provide a device of the foregoing type
wherein the frequency of the excitation applied to the sides of the
bell member to cause the vibration pattern therein is substantially
double the natural frequency of the bell or therefore the frequency
of the pattern.
It is a further object to provide a device of the foregoing type
wherein the electrode causing the vibration pattern is operative to
exercise the sides of the high-Q member along any position of an
anti-nodal axis of the pattern about the input axis.
It is still a further and more specific object of the present
invention to provide a device of the foregoing type wherein the
repetitive energy is imparted by a continuous circular electrode
fixed to the platform supporting high-Q member.
These and other objects of the present invention will become
apparent from the following description and claims taken in
connection with the accompanying drawings, wherein:
FIG. 1 is a view in perspective partially broken away of a rotation
detector made in accordance with the invention and having a
continuous circular forcer;
FIG. 2 is a diagrammatic representation of the flexing action
exhibited by the sides, such action and the space in which the
sides flex being exaggerated for better understanding;
FIG. 2a is a representation of the rotation of the bell sides in
relation to the resulting rotation of the flexing pattern of FIG.
2; and
FIG. 3 is a section through the detector showing the electrodes
affixed in the base and housing and means in block diagram form
whereby the bell-like member may be operated to indicate rotation
about the axis.
DETAILED DESCRIPTION -- FIGURE 1
As may be seen with reference to FIG. 1, bell B is supported in an
inverted position on post 24 upstanding from platform base 10 and
is enclosed thereon by platform housing 12.
Bell B is comprised of arcuate sides that depend contiguously and
symmetrically from central area 16 about a shaft 20 along the
bell's polar or input axis ZZ and that terminate in an arcuate lip
14. In order of progression from center region 16, shaft 20 is
comprised of a neck portion 22, a hub section 26 having a lower hub
surface 28, a relief groove 30, and axially-extending stem 32, and
a terminating end 34 having a threaded portion 36 thereon.
Platform base 10 has an outer surface 42 bounded by a floor 44 and
a ledge 46. A circuit board 48 is secured to floor 44 by screws 52,
and post 24 upstands from ledge 46 along the ZZ axis. Post 24 is
comprised of a hub 54 having an upper hub surface 56 and a bore 58
therethrough concentric with the ZZ polar axis. Also concentric
therewith and counterbored in bore 58 are seat 60 and side 62. A
circular forcer ring 70 having top 72, bottom 74, inner periphery
76, and outer periphery 78 is secured to and isolated from post 24
and ledge 46 by epoxy 50 and a shield disc 80 is similarly secured
to and isolated from forcer top 72.
Conductive brass guard cage 82 comprised of a top disc 84, a
cylinder 86, and a bottom disc 88 are secured to and isolated from
post 24 and shield 80 and a circular sensor electrode 90 is secured
to and electrically isolated from cage 82 by epoxy 50 inserted in
the 0.01 inch spaces between the various elements as shown. The
outer periphery of base 10 at surface 42 as well as the
radially-outwardly facing portions of electrode 70, shield 80,
guard 82, electrode 90, and epoxy 50 are contoured to provide an
arcuate surface 78 to receive the inner surface of bell lip 14 in
close spaced-relation therefrom upon assembly therewith. Having
axially-open portions facing radially outwards from the ZZ axis
towards lip 14, guards 82 expose just the face 94 of the electrode
90 to just the inner periphery of lip 14, electrode 90 being
elsewhere isolated from platform 10 by guard 82.
A hole 96 drilled into electrode 70 through floor 44 is potted with
epoxy and then tapped with threads 98 to receive feedthrough
connector 102 comprised of a probe 104 supported in an
electrically-isolated guard sleeve 106 having threads to mate
threads 98. Guard sleeve 106 is threaded into epoxy 50 so that
connector probe tip 104 is in pressure contact with electrode 70.
Another hole 108 having counterbored seat 109a and side 109b is
drilled into electrode 90 through floor 44, electrode 70, shield
80, and guard bottom disc 88, and is similarly potted and tapped
with thread 110. A shield sleeve 92 is then secured in hole 108 by
epoxy 50 so as to be in contact with seat 109a and side 109b of
hole 108 and with shield disc 80. Feedthrough connector 112 having
a probe 114 and a guard sleeve 116 is potted into shield sleeve 92
and engaged with threads 110 so that probe 114 is in pressure
contact with electrode 90 and so that connector guard 116
terminates a guard bottom 88 without contacting electrode 90.
Bell B is secured to post 24 and base 10 by means of a nut 38
threaded onto threads 36 of shaft 20 inserted into post bore 58 to
urge washer 40 against counterbore seat 60, thereby also urging
lower bell hub surface 28 against upper post hub 56. A groove 64
extending about stem 32 of shaft 20 carries an O ring 66 to permit
bell B to be adjusted axially and circumferentially with respect to
post 24 and axis ZZ.
Housing platform 12 is comprised of an end wall or roof 118 and
cylindrical side walls 120. Roof 118 has a central hub 122 and a
surface 124 recessed thereabout to receive a circuit board 126
secured thereto by screws 128. Side walls 120 terminate in an edge
130, have a clamping flange 132 on their outer periphery, and on
their inner periphery have a counterbored seat 134 and side 136,
the latter having O ring groove 138 therein. As may be seen more
clearly in conjunction with FIG. 3, guard 140 and electrode 142 are
secured by 0.01 inch layers of epoxy 50 in space 150 that protrudes
axially and equiradially about the ZZ axis into walls 120 from roof
118.
Guard 140 has an axially-open portion facing radially inwards to
expose just sensor face 152 to the outer periphery of lip 14 and
terminate at end 154. Elsewhere, the guard, electrode, and housing
are isolated from each other by epoxy 50. The inner periphery of
walls 120 and portions of sleeve 140 and end 154 as well as
electrode 142 and epoxy 50 are removed to provide an arcuate
surface 156 to receive the outer periphery of bell lip 14 in close
spaced relationship therefrom upon assembly. Also, to reduce
damping between housing 12 and the outer periphery of lip 14,
twelve axial openings 158, FIG. 3, protrude into walls 120
equiradial with spaces 150 and terminate short of roof 118. A port
160 coaxial with an opening 158 extends through surface 118 and is
sealed by plug 162 after the apparatus has been assembled and
evacuated.
A feedthrough connector 164 is screwed into sleeve 140 so that the
connector probe tip 166 is in pressure contact with the electrode
and the connector guard 168 is in contact with and terminates at
the guard sleeve 140 short of the electrode. Signals developed on
probe tips 104, 114, and 166 and guards 106, 116, and 168 of
connectors 102, 112, and 164 respectively are brought out thereby
to circuit board 48 in base 10 and board 126 in housing 12. These
circuit boards carry suitable pads for connection with the probes
and guards of the connectors and also carry suitable circuit paths
and elements for interconnecting the electrodes and operating the
rotation detector as to be more fully described below with
reference to FIG. 3. Moreover, being electrically-isolated and
physically separated by epoxy 50 from housing 12 and the
electrodes, the guards around the sensor electrodes are main-tained
electrically by these circuits at substantially the same potential
as these electrodes to provide a constant capacitance cage
thereabout, thereby enhancing the sensitivity of the sensors to
radial lip vibrations.
Base platform 10 carrying bell B fastened thereto is assembled and
rigidly secured to housing platform 12 by clamp ring 170 having a
counterbored seat 172 and side 174. Clamp ring 170 is fastened to
housing platform 12 at edge 130 thereof by eight screws 176
threaded into holes 178. As the screws 176 are tightened,
counterbored seat 172 of ring 170 urges bottom surface 44 of base
platform 10 and ledge 46 towards seat 134 counterbored in the inner
periphery of housing side 120, and base surface 42 slides axially
along counterbored side 136. Side 136 having a radial gap of 0.0005
inch from surface 42 centers the latter coarsely therewith, fine
centering and sealing therebetween being effected by O ring 139 in
groove 138.
Prior to the final tightening of screws 176, the atmosphere
internal to the cavity about the bell B defined by platforms 10 and
12 is evacuated as desired to effect a high-Q for bell B and the
relative azimuth positions of the bell B, platform base 10, and
platform housing 12 are adjusted. Air may thus be withdrawn from
housing 12 through port 160 and the atmosphere therein backfilled
with another gas such as helium so as to increase the Q of the bell
by decreasing air damping. For instance, it has been found that by
maintaining the bell vacuum on the order of 10.sup..sup.-2 torrs
increases the Q of the device fourfold and hence comparably
increases the time constant, or ringing time, of oscillations in
relation to the energy input per cycle.
The platform structures, electrodes, and especially bell B are made
from a high-Q or low-loss material. By high-Q I refer to the ratio
of the energy stored in the oscillating system to the energy
dissipated in one cycle. Materials that exhibit favorable Q's,
elastic limits, and modulus of elasticity, and yet are readily
machinable, include aluminum alloys, such as 2024-T4. This alloy
has a composition generally of 93.4 percent aluminum, 4.5 percent
copper, 1.5 percent magnesium, and 0.6 percent manganese. Also,
silicon aluminum bronze or "Everdur" alloys, having 96 percent
copper, 3 percent silicon, and 1 percent manganese or 91 percent
copper, 7 percent aluminum and 2 percent silicon have favorable
properties.
Thus, bell B shown in FIG. 1, is preferably constructed from
2024-T4 aluminum having a modulus of elasticity E of 10.6 .times.
10.sup.6 psi and a Q of 3,000 in air, 3,000 in helium and up to
12,000 in 10.sup..sup.-2 torr vacuum. The inner and outer
peripheries of sides 18 both have a mean radius of 1 inch swung at
different points along the ZZ axis and vary in thickness in the
arcuate region from maximum h.sub.o of 0.20 inches in the center
region 16 to some finite thickness h in accordance with the formula
h = h.sub.o (1 + cos .theta.).sup.2 / 4, where .theta. is the
spherical angle subtended from the polar axis through center 16.
This thickness contour is believed to provide surfaces of uniform
maximum strain when flexed. When assembled to platforms 10 and 12,
lip 14 clears the arcuate faces of the sensor and forcer electrodes
by nominally 0.005 inch.
The feedthrough connectors 102, 112, and 164 are "Microdot"
connectors DC-051-007 available from Microdot Incorporated of South
Pasedena, California. Potting adhesive or epoxy 50 may, for
example, be that known as "P38" obtainable from Bacon Industries of
Watertown, Massachusetts. This adhesive is an epoxy resin base
compound chosen because of the stability of its composition and
dimensions with time and temperature and its high dielectric
strength. Moreover, such epoxy has high adhesion, low tendency to
crack, low coefficient of linear thermal expansion, low creep, and
high tensile strength.
GENERAL OPERATION -- FIG. 2
As may be understood generally with reference to FIG. 2, the
operation of bell B requires that sides thereof be exercised or
forced radially so as to flex lip 14 between two extreme positions,
shown exaggerated by the dotted and dashed lines, about a neutral
unflexed circular position, shown by the solid lines. These
exercising vibrations establish about the circumference of the lip
a standing wave pattern defining nodal regions of normally
quiescent radial vibrations and anti-nodal regions of normally
maximum radial vibrations. The flexing of the bell sides is due
predominantly to their bending in contrast to extension and
compression as would be the case if the sides expanded and
contracted uniformly. Moreover, since the energy required to effect
bending is significantly less than that to effect extension and
compression and since the energy imparted by the forcer is
sufficient to effect bending but not extension, the
nodal/anti-nodal pattern obtains.
Such flexing is initiated and sustained by an electromechanical
self oscillation loop comprised generally of circular forcer 70,
circular sensor 90, and feedback means 184 shown schematically
adjacent the sides of the bell, the bell in turn being connnected
to a source of constant potential. The forcer 70 is energized at a
potential varying at twice the natural frequency of the bell to
modulate the electrical contribution to the spring constant of the
bell introduced by the energy stored in the electrode. As a result
lip 14 flexes in a standing wave pattern having an instantaneous
set of anti-nodal regions 14a-14e and 14c-14g, respectively, along
each of two mutually perpendicular directions AA--AA and AB--AB
radial to the input or polar axis ZZ and an instantaneous set of
nodal regions 14b-14f and 14d-14h, respectively, along each of two
mutually perpendicular directions NA--NA and NB--NB midway between
those associated with the anti-nodes. These sets of nodal and
anti-nodal regions rotate about the sides of the lip as the bell is
rotated but are stationary with respect to the bell when it is not
rotated.
Rotation of this pattern as the instrument rotates may be
understood with reference to FIG. 2 and 2a. As shown in FIG. 2,
prior to rotation perpendicular axes XX and YY referenced to and
rotating with the bell are aligned with anti-nodal axes AA--AA and
AB--AB respectively of the pattern. Rotation of the bell in a
counterclockwise direction by some angle .beta. displaces the XX
and YY axes a similar amount and direction to a new position X'X'
and Y'Y'. In the course of this rotation, the standing wave pattern
is also rotated in the same direction, but only at some angle
.alpha., where .alpha. equals 0.3.beta. . Thus, anti-nodal axes
AA--AA and AB--AB are rotated to A'A'--A'A' and A'B'--A'B' and
nodal axes NA--NA and NB--NB are rotated to N'A'--N'A' and
N'B'--N'B'. For example, as shown in FIG. 2a, if the bell is
rotated in a counterclockwise sense for 100.degree. (.beta.), the
pattern rotates only 30.0.degree. (.alpha.). Moreover, this pattern
rotation is retrograde with respect to the rotated instrument axes
but posigrade with respect to the initial (inertial) orientation of
the instrument axes.
Deflections of the lip are detected by sensors located adjacent
thereto and measuring either the varying capacitance or varying
potential therebetween depending on the input impedance of the
circuits connected with the sensors. A sensor 90 detects the
amplitude of radial vibrations of lip 14 anti-nodes, and electrical
feedback means 184 connect anti-nodal sensor 90 to anti-nodal
forcer 70 thereby closing a loop operative to flex the anti-nodal
lip regions at constant maximum amplitude. Other sensor means 142
detect those radial lip vibrations due to the motion of the lip
associated with the standing wave pattern and the rotation of the
wave pattern about the input axis. Sensor 142, moreover, is
connected to readout circuit 186 and develops in conjunction
therewith signals usable for indicating the amount and direction of
bell rotation.
A feature of the nodal and anti-nodal regions of the vibration
pattern imparted and maintained by forcer 70 and sensor 90 is that
radial vibrations produced along the anti-nodal AA--AA and AB--AB
directions cause the bell to produce substantially no radial
vibrations along nodal directions NA--NA and NB--NB in the absence
of bell rotation. Similarly, radial vibrations imparted along the
nodal directions produce substantially no effects along the
anti-nodal directions. In terms of the present invention, the
vibrations imparted by forcer 70 at an anti-nodal region causes
substantially no additional vibration along the nodal axes.
Another feature inherent in the imparted radial vibration pattern
is that radial vibrations along any one anti-nodal axis are
mathematically and substantially physically identical in magnitude
and frequency to those along any other anti-nodal axis even though
such axes are physically separated, and radial vibrations along one
nodal axis are similarly identical to those along any other nodal
axis even though physically separated. The effect of this feature
is that all nodal and anti-nodal axes may be considered as
equivalent respectively to just one nodal and one anti-nodal axis.
Thus, radial vibrations applied at one anti-nodal region produce
substantially identical radial vibrations at the other anti-nodal
regions, and radial vibrations to sustain the standing wave may be
imparted with equal effect at any anti-nodal region. To be
effective to apply forcing potential at lip anti-nodes, forcer 70
may therefore be a continuous element encircling the lip or may be
comprised of segments connected to the same source of varying
potential and located about the perimeter of the lip 14 so that one
segment of the forcer is always opposite one anti-nodal region
regardless of pattern orientation.
DESCRIPTION OF OPERATION -- FIG. 3
The means comprising the self oscillation and readout loops are
shown interconnected in block form in FIG. 3 with the bell sides
and electrodes shown schematically in plan view using like
designations for similar elements in FIG. 1. Thus, forcer electrode
70 and sensor electrode 90 are disposed on base 10 between post 24
and lip 14 as shown, and electrode 142 is mounted in housing
12.
The FIG. 3 self oscillator loop is comprised generally of the
anti-nodal regions of the standing wave in lip 14, electrode 90,
oscillator pickoff amplifier 200, level detector 202, amplifier
206, filter 208, dc-to-dc converter 210, demodulator 212,
multivibrator 214, flip flop 216, oscillator forcer circuit 218,
electrode 70, bell B, and its anti-nodal regions. Electrode 70 is
the oscillator forcer electrode connected from oscillator forcer
circuit 218 and operative to impart radial exercising vibrations to
bell B by applying varying attractive electrical potential at the
anti-nodal wave regions along an anti-nodal axis normal to the
polar or input axis ZZ. Electrode 90 is the oscillator pickoff
electrode connected to oscillator pickoff amplifier 200 and
operative to detect radial vibrations of bell B by measuring the
varying potential of anti-nodal lip regions with respect to
electrode 90 along an anti-nodal axis normal to the ZZ axis.
The output of oscillator pickoff amplifier 200 is connected
parallely both to level detector 202 and to demodulator 212. A
source of adjustable reference potential 204 is also connected to
an input terminal of level detector 202, the output of which is
connected to dc-to-dc converter 210 through amplifier and
compensator 206 and filter 208 to regulate the amplitude of the
exercising wave. Demodulator 212 is connnected to multivibrator 214
and therefrom to frequency dividing flip flop 216. Synchronization
pulses are provided by frequency dividing flip flop 216 to start up
converter 210 and also to operate demodulator 212, oscillator
forcer circuits 218, and monostable 232. The output of demodulator
212 regulates the frequency of multivibrator 214 at four times the
natural frequency of the bell so that frequency dividing flip flop
216, in turn, slaves converter 210, demodulator 212, forcer circuit
218, and monostable 232 at substantially twice the resonant
frequency.
At start-up, the difference in amplitude between reference
potential 204 and the signal from amplifier 200 corresponding to
the maximum amplitude of lip 14 is of sufficient magnitude and a
polarity to cause an output from dc-to-dc converter 210 to
oscillator forcer circuit 218. The amplitude and frequency of the
varying potential to oscillator forcer electrode 70 and anti-nodal
wave regions therefore tends to increase the amplitude of lip
vibrations. As the amplitude of lip vibrations increase, the input
to detector 202 increases the difference from that provided by
reference 204. The output from level detector 202 to converter 210
consequently increases to ultimately stabilize at a value
corresponding to a substantially constant maximum amplitude of lip
vibration, such amplitude being adjustable by setting reference
potential 204.
Free-running multivibrator 214 is biased at start-up to cause the
output from frequency divider 216 to oscillator forcer circuit 218
to be at a frequency less than the twice resonant frequency of lip
14. Thereafter, the bias to multivibrator 214 is adjusted by the
output of demodulator 212 to effect a frequency which produces a
maximum amplitude at lip 14 for the converter regulated forcing
potential. The forcing potential applied by oscillator forcer
circuit 218 to electrode 70 is then a substantial dc bias generated
from converter 210 modulated by the double frequency pulses
generated in response to flip flop 216. The amplitude of these
pulses is continuously controlled by converter 210, and the
un-linearities in the components regulating it, to maintain the
vibration pattern, thus parametrically excited, at constant
amplitude.
The readout loop is comprised generally of readout pickoff
electrode 142, readout amplifier 220, demodulator 222, phase
shifting monostable vibrator 232, frequency dividing flip flop 236,
and compensation amplifier 224. The pulses applied to monostable
232 from flip flop 216 are phase shifted by adjustment means 234
and then applied to demodulator 222 after frequency division by
flip flop 236. Electrodes 142 and 146 are readout pickoff
electrodes connected to readout amplifier 220 and operative to
detect radial vibrations of bell B by measuring the varying
potential at regions of the lip. The output of readout amplifier
220 is connected to demodulator 222, the output of which after
amplification and compensation in amplifier 224 provides a signal
226 proportional to the rotation of bell B about axis of symmetry
ZZ.
In the configuration shown in FIG. 3, signal 226 developed by
amplifier 224 varies substantially as the cosine of twice the angle
through which the pattern has rotated times the product of the
maximum flexing amplitude times the cosine of the exercising
frequency. The angle through which platform 10 and bell B mounted
thereon are rotated during any given period can be determined from
signal 226 as for instance by a computer.
The subject invention has application wherever it is desired to
detect motion of a structure about an axis. Applications where the
device may be used include those to indicate horizontal and
vertical directions, to provide a strapped down or gimballed
reference platform, to stabilize a structure against external
motions, or to navigate a vehicle over desired course. Moreover,
having described one embodiment of the present invention it is
understood that the specific terms and examples are employed in a
descriptive sense and not for the purpose of limitation. It will be
obvious to those skilled in the art that modifications and changes
may be made without departing from my invention and I, therefore,
aim in the appended claims to cover such modifications and changes
as fall within the true spirit and scope of my invention.
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