US3382726A

US3382726A - Vibrating rotor gyroscope

Info

Publication number: US3382726A
Application number: US457740A
Authority: US
Inventors: Harold F Erdley
Original assignee: Litton Systems Inc
Current assignee: Northrop Grumman Guidance and Electronics Co Inc
Priority date: 1965-05-21
Filing date: 1965-05-21
Publication date: 1968-05-14
Anticipated expiration: 1985-05-14
Also published as: SE359918B; JPS4811257B1; DE1523213B2; DE1523213A1; GB1093549A; GB1093550A; SE326838B; NL6607061A; BE681307A

Description

May 14, 1968 H. F. ERDLEY VIBRATING ROTOR GYROSCOPE 5 Sheets-Sheet 1 Filed May 21, 1965 Rwy Y E JVQ WED/0 15 FIG w W #WL SUPPLY United States Patent 3,382,726 VIBRATING ROTGR GYROSCOPE Harold F. Erdley, Pacific Palisades, Calif, assignor to Litton Systems, Inc, Beverly Hills, Calif. Filed May 21, 1965, Ser. No. 457,740 21 Claims. (Cl. 74--5.6)

The present invention relates in general to navigational and positional instruments and in particular to improved vibrating rotor gyroscopes.

One form of vibrating rotor gyroscope, an inertial instrument possessing many advantages over conventional gyroscopes, is described in copending application entitled Vibra-Rotor Gyroscope by H. F. Erdley et 211., Serial No. 323,985, filed Nov. 15, 1963, and assigned to the same assignee as the present application. In general, a vibrating rotor gyroscope comprises an inertial element which is co axially mounted on a rotating shaft. The inertial element rotates with the shaft and has torsionally restrained vibrational freedom about its mounting axis which is angularly disposed (ordinarily perpendicular) to the shaft. The vibrating rotor gyroscope is designed so that the natural frequency of vibration of the inertial element about the mounting axis is equal to the frequency of shaft rotation (N) in order to make the inertial element very sensitive to motions at right angles to the axis of the shaft. An external angular displacement (rotation) of the vibrating rotor gyroscope around any axis, except the spin axis, causes the inertial element to vibrate at its natural frequency, the maximum amplitude of such vibration being proportional to the angular displacement. In addition, the phase of the vibration relative to a timing signal is a direct measure of the direction of the angular displacement. Hence, the vibrating rotor gyroscope may be used in place of a direct reading, two-degree-of-freedom gyroscope.

Since the vibrating rotor gyroscope requires no complicated gimbal suspension system or flotation fluid, it has an extremely low drift rate and is far superior to conventional gyrosc-opes. Due to the fact, however, that the sensitivity of the inertial element to external forces is dependent upon the natural frequency of vibration of the inertial element being equal to th frequency of shaft rotation, any spurious forces or vibrations which act in the equations of motion of the vibrating rotor gyroscope as driving forces of a frequency equal to the frequency of shaft rotation cause, as more fully explained hereafter, an output error signal to appear which is indistinguishable from the output caused by an external angular displacement. It has been found that such spurious output signals can be generated in the prior art devices by an inherent shaft wobble of frequency 2 N due to the tolerances in the bearing mechanism supporting the rotating shaft of the vibrating rotor gyroscope and, under certain circumstances, can cause undesirable errors to appear in the output signals obtained from operational angular displacements of the vibrating rotor gyroscope.

The present invention has succeeded in overcoming all of the above-mentioned disadvantages of the prior art devices by providing a vibrating rotor gyroscope in which a plurality of inertial elements are coaxially mounted on a single shaft in such a manner that the output signals therefrom maybe combined to eliminate the component of the output signals due to vibrational forces. In addition, since there are now a plurality of inertial elements on a single shaft, both rotational and accelerational information can be obtained from the same instrument.

It is therefore the primary object of the present invention to provide a new and improved vibrating rotor gyroscope.

It is another object of the present invention to provide a vibrating rotor gyroscope capable of cancelling spurious outputs caused by 2 N frequency vibrations.

'ice

It is a further object of the present invention to provide a vibrating rotor gyroscope capable of providing both rotational and accelerational information.

It is still another object of the present invention to provide a vibrating rotor gyroscope having a plurality of independently mounted inertial elements.

-It is a further object of the present invention to provide a vibrating rotor gyroscope having a plurality of coaxially mounted inertial elements whose suspension means are angularly disposed from one another.

It is another object of the present invention to provide a vibrating rotor gyroscope having a plurality of inertial elements, at least one of which has its center of mass displaced a preselected distance from its point of suspension.

The novel features which are believed to be characteristic of the invention, both as to its organization and method of operation, together with further objects and advantages thereof, will be better understood from the following description considered in connection with the accompanying drawings. It is to be expressly understood, however, that the drawings are for purposes of illustration and description only and are not intended as a definition of the limits of the invention.

FIGURE 1 is a cross-section view of a preferred embodiment of the present invention;

FIGURE 2 is a simplified, perspective drawing of the embodiment of FIGURE 1 illustrating the principles of operation of the present invention;

FIGURE 3 is a block schematic diagram of a vibrating rotor gyroscope system for cancelling spurious output caused by 2 N frequency forces;

FIGURE 4 is a block schematic diagram of a vibrating rotor gyroscope system for obtaining rotational and accelerational information;

FIGURES 5 and 6 illustrate further modifications of the present invention; and

FIGURE 7 illustrates a vibrating rotor gyroscope arrangement for obtaining complete accelerational and rotational information free from spurious outputs caused by 2 N frequency forces.

In reference now to FIGURE 1, the vibrating rotor gyroscope 10 of the present invention is shown comprising a cylindrical outer casing 11 and a support member 12 attached thereto upon which is positioned the stator 14 of a constant speed synchronous hysteresis motor 16. The rotor element 18 of the synchronous motor 16 is affixed to a spin shaft 20 which is driven to rotate on ball bearings 22 about the stator 14. The outer case 11 is preferably pressure tight and in the preferred embodiment thereof is completely evacuated or alternatively contains a controlled low density atmosphere as of hydrogen or helium, and is generally constructed of a light, but rigid, material such as aluminum. The spin shaft 20 is constructed of a rigid material such as stainless steel. Inertial elements 26, 26 (shown here in the form of rings) of the vibrating rotor gyroscope are mounted on the spin shaft 20 by means of two orthogonal pairs of cruciform-

shaped torsion bars

28, 28, a pair of central supports 30, 3t) and mounting screws 29, 29'. It should be noted that since the torsion bars 28 are orthogonal to the torsion bars 28, the torsion bars 28 are not visible in this cross-sectional view. Although the inertial elements 26, 26' may be constructed completely of a rigid, lowreluctance material such as iron or steel, in the embodiment shown it has been chosen to surround a light-weight rigid material (such as titanium) with iron or

steel rings

32, 32 in order to reduce the weight of the inertial elements 26, 26'.

In the present embodiment, the center of mass (C.M.) of each of the

inertial elements

26, 26 is located at the point of suspension of each of the inertial elements 26, 26', i.e. where the axis of rotation [defined by the axis of the spin shaft 20] intersects the axis of vibration (defined by the axis of the torsion bars 28, 28). Under these conditions the gyroscope 10 is substantially insensitive to ac-celerational forces. As explained hereafter, however, the gyroscope 10 may be made sensitive to aecelerational forces (and capable of the detection thereof) by placing the center of mass a preselected distance from the point of suspension, preferably along the spin shaft 20. This may be accomplished, for example, by making the inertial element 26 heavier on one side by the addition of weights thereto or the milling of material from the other side thereof. In addition, as shown hereafter, more than two inertial elements may be placed on the spin shaft 20 in order to obtain complete information on the accelerational and rotational forces acting on the gyroscope.

In operation, the synchronous motor 16 (driven by power supply 38) causes the inertial elements 26, 26' to rotate at a predetermined frequency N. In order to better appreciate the operation of the present invention and to understand the importance of cancelling out spurious 2N frequency forces, reference may be had to FIGURE 2 and to the following mathematical analysis of the properties of the invention.

The approximating basic differential equation of motion of one of the inertial elements of the invention may be found from Eulers equations for the motion of a rigid body about a fixed point. The ordinary torque equation, L:J, where J (angular momentum) and L (torque) are both defined in a system of axes which has a fixed orientation in space, becomes when transformed into a system of axes fixed in a rotating body:

for the component of torque around the rotating y axis, I and w being the moments of inertia and the angular velocities around their respective rotating axes. If it is assumed that the rigid body is a ring rotating around the z axis, then I =I =A and I =C, where A is the transverse and C is the polar moment of inertia. If the above equation is then equated to the torques around the y axis due to restraining (spring) and damping forces, the basic equation for the system becomes:

Aw -l- (A-C)w w +D9-]-K0=O (2) where K is the angular spring constant and D is the angular damping constant of the torsion bars 28, and is the angular excursion of the inertial element 26 measured as a rotation around the y axis.

If the shaft 20, spinning at a frequency N, experiences an angular displacement around an axis orthogonal to the shaft 20 then:

where sin 9:0, cos 0:1, @5 0. Inserting

Equations

6, 7, and 8 into Equation 2, the basic equation of motion becomes:

A D+ K+N c A 0=cN sin Nz Al;3 cos Nr which can be recognized as the equation of a damped forced harmonic oscillator. Since it is desirable that the system have its natural frequency of oscillation at the driving frequency N, the spring constant K must be chosen so that:

AN =K+N (CA) 10 K=N2(2AC) and the basic equation of motion becomes:

A'+D0'+AN 0=cN sin Nr-A i' cos Nt 12) If it is assumed that the rate of change of the angular displacement is a constant (which inherently makes :0), the damping constant D is small, and the time constant of the system T, defined as 2A/D, is very much greater than t, the solution to Equation 12 can be approximated by:

to z =2-- T 6(1) D T cos At (13) This equation demonstrates that for small angles the angular excursion of the inertial element 26 is directly proportional to the rotational displacement git of the shaft 20, multiplied by a cosine term representing the vibrations. Although it is not expressly stated in the above equation, the cosine term contains phase information which can be extracted by means of a timing signal to yield the angle between the direction of the rotational displacement of the shaft 20 and a coordinate system fixed in the outer case 11 of the gyroscope.

If the shaft 29 of the gyroscope is subjected to vibrations of a 2 N frequency, the vibrations are rectified by the system and appear in the angular excursion 0 of the inertial element 26 as a spurious rotational displacement. This fact can be made more apparent by the follow ing mathematical analysis. The vibrations can be represented by:

Substituting

Equations

14, 15, and 16 into Equation 12 and noting the identities:

sin 2Nt sin Nt= /z (cos Nt-cos 3N1) cos 2Nt sin Nt= /z (sin Nzsin 3Nr) cos 2Nt cos Nt= /2 (cos Nt+cos 3Nt) sin 2Nt cos NZ= /2 (sin N1. sin 3Nt) and the fact that the system is very insensitive to vibrations of frequency 3N, the following equation of motion is obtained:

A +D0 +AN 0 =N (2A-C) (G cos Nz+H sin N!) (18) Using the previous assumptions, the solution to Equation 18 can be approximated by:

cos Nt+tarr It is apparent the Equation 19 is identical in form to Equation 13 and thus an output signal is generated by the spurious 2 N frequency forces Which cannot be separated by prior art devices from the ouput generated by true rotational displacement.

In the preferred embodiment of the present invention, however, the spurious output signal is cancelled by using two inertial elements 26, 26' mounted on the shaft 20 with their torsion bars 28, 28' at substantially right angles to one another. In this case, the basic equation of motion for the second inertial element is given by:

into which

Equations

14, 15, and 16 can be inserted, as before, to yield:

A0 -{-D!) +AN 0 :N (2AC) (G sin Nt-H cos N!) K o +H t Q cos (Ni tan 1 H (22) If Equations 19 and 22 are then summed:

but since then:

and thus the spurious output signal does not appear in the summed output signals generated (as hereafter shown) by the inertial elements 26, 26'.

In FIGURE 1, E-shaped sensor arrangements 40, 40', each composed of a C-shaped ferrite material with a permanent magnet central leg, are positioned adjacent to inertial elements 26, 26 (and iron rings 32, 32') and are attached to the outer case 11 of the vibrating rotor gyroscope by

support members

32, 42. The permanent magnet central legs of the E-shaped sensor arrangements 40, 49 cause D.C. magnetic fields to exist in the closed fiux paths defined by the central and outer legs of the

sensor arrangements

40, 40 and the iron rings 32, 32. Any vibratory motions of the iron rings 32, 32' cause a change in the reluctance of the portions of the paths between the central and outer legs of the

sensor arrangements

40, 40. Consequently, the vibrations of the iron rings 32, 32 cause A.C. magnetic fields to be generated in the windings (and output leads) 47, 47, which fields in turn generate A.C. signals (the outputs of the sensor arrangement 40, 40) representative of the vibratory motion of the

inertial elements

26, 26. While the sensing signals have been obtained by using D.C. magnets for the central legs of the sensor arrangements 40, 46, many other techniques are possible. For example, A.C. magnetic fields can be generated (in the closed flux paths) by coupling A.C. generators to ferrite central legs of the sensor arrangements 49, 40'. Since the edges of the iron rings 32, 32 nearest the sensor arrangements 49, 40' are not only vibrating but also rotating, the frequency of the electromotive forces generated by the positional or velocity changes of the iron rings 32, 32' is a function of both such motions and is primarily equal to the sum of the frequency of rotation and the frequency of vibration (a small difference frequency term also being present). Thus, in the sensor arrangement of the present embodiment, the sensing signal has (in the ideal case) a frequency of 2 N.

In order to resolve the output signals from the

sensor arrangements

40, 40 into components along the set orthogonal axes fixed in the outer case 11 (to determine the direction of the angular displacement of the shaft 20 relative to such axes), a timing signal having a frequency 2 N is generated. A C-shaped timing generator 51 is shown aflixed to the outer case 11 by supporting member 12 and comprises a C-shaped permanently magnetized ferrite structure with a sensing coil (and output lead) -11 Wound thereon. A rotating ferrite member 36 (which forms part of the closed flux path) is constructed with a very slight ellipsoidal conformation so as to vary the reluctance of the magnetic path between the legs of the C-shaped timing generator 51. Since the C-shape-d timing generator 51 is stationary, the position of the rotating member 36 over the two ferrite legs oscillates radially during each revolution of the shaft 20. For each revolution of the shaft 20, the radial oscillation of the member 36 causes it to assume maximum and minimum spacings from the timing generator 51 twice during each revolution. Thus, during each revolution of the shaft 20 alternate minimum reluctance and maximum reluctance paths are twice formed between the two legs of the C-shaped timing generator 51. Since the reluctance of the magnetic path varies through two maximums and two minimums each revolution, an A.C. electromotive force is generated in sensing coil (and output lead) 51' having a frequency twice that of the frequency of revolution of the shaft 20. This A.C. electromotive force is used to provide a timing signal of frequency of 2 N. By circumferentially varying the position of the timing generator 51 around the shaft 20, the two maximum amplitude points (or minimum amplitude points) of the timing signal can be made to occur when the torsion bars 28, 28 are parallel and orthogonal, respectively, to one of the case-referenced orthogonal axes. If such coincidence does not occur, the timing signal will be resolved into components along orthogonal axes rotated a determinable angle from the case-referenced axes. These two set of axes can be brought into coincidence, however, by shifting the phase of the timing signal.

As illustrated in FIGURE 3 wherein the gyroscope 10 is depicted in symbolic form, the timing signal from the timing generator is fed via lead 51' into a standard phase shifter 54 which provides two timing signals, one shifted in phase from the other by In an alternative embodiment, a second timing generator may be employed displaced 45 circumferentially from timing generator 51 to provide the second timing signal shifted in phase by 90. The timing signals are coupled along with the sensing signals from the sensor arrangements 40, 40' (via leads 47, 47') to standard demodulators 50, 50 (of the type, for example, described in the above-cited patent application). The demodulato-rs 50, 50- provide signals 0(X) :2N(X), 0(Y):2N(Y) which represent the magnitudes of the components of the rotational displacement plus or minus the components of the 2N frequency movements of the shaft 20 along the X and Y coordinates of the case-referenced axes. Since demodulators 50, 50' receive each two timing signals and provide each two output signals, demodulators 50, 50' may each consist of two separate demodulators or a single composite demodulator with two input and output channels. In addition, demodulators 50, 50' may also include R-C networks to filter the signals generated thereby.

As stated previously (and as shown above), each of the output signals from the vibnating rotor gyroscope is composed of signals generated by true rotational displacement forces and spurious 2N frequency forces. Since, however, the output signals caused by such spurious forces are generated by two inertial elements having their axes of vibration (i.e. suspension means) orthogonal and thus are opposite in polarity, the output from demodulator 50' contains spurious signals of one polarity while the output from demodulator 50 contains the same spurious signals but of opposite polarity. The output signals from

demodulators

50 and 50 are thus coupled to standard summing

circuits

70, 70, composed of addition circuit 97 and sign inverter 99, which add the Y and X components, respectively, of the sensor outputs and, in so doing, provide signals 0(X), 9(Y) representative of the magnitudes of the rotational displacement free from the spurious signals 2N (X), 2N(Y) generated by the 2N frequency forces.

It should be noted that, as previously stated with respect to the angle between the shaft and mounting axis, the suspension means do not have to be orthogonal but may be angulariy disposed. In such a case, however, the 2N frequency tennis are not completely eliminated but partially remain with their magnitude being proportional to the cosine of the angle between the suspension means.

Since the validity of Equation 13 describing the angular excursion 0 of the inertial elements 25, 26 is predicated upon the time of application of a particular shaft displacement rate being very much less than the time constant of the system, it is desirable that torquing forces be applied to the vibrating rotor gyroscope to null such vibratory motion. In an inertial guidance system, the vibratory motion is usually nulled by rotating the platform upon which the vibrating rotor gyroscope is mounted (and hence applying a mechanical torquing force to displace the shaft The X and Y outputs are thus shown as coupled to networks 74, 76 (which may, for example, be standard switching circuits or s-witchin circuits coupled with mixing circuits) adapted to apply via terminals 71, 71' such signals to the rotators of the inertia guidance platform, as illustrated in the above-cited patent application. In many other instances, however, it is desirable to be able to null the vibratory motion of the

inertial elements

26, 26 without displacing the shaft 20. This occurs, for example, when the vibratory rotor gyroscope is fixedely mounted in an aircnaft or on the earth and the vibratory motion induced by the aircraft motion or the earth rate must be nulled in order to use the sensing signal generated thereby for reference purposes. On the other hand, it is desirable to be able to directly induce vibratory motion of the

inertial elements

26, 26 to correct for positional or guidance errors and use the sensing signal generated thereby to effect mechanical torquing of the shaft 20 (to null the induced vibratory motion). For this purpose, feedback leads 7?, 80 are shown leading from networks 7 76 to the vibrating rotor gyroscope itself to apply X axis and Y axis torquing forces, respectively, as explained hereafter, to the

inertial elements

26, 26. In addition, inputs 82, 84 are coupled to the

networks

74, 76 to allow external biasing signals to be introduced (via such switching circuits) when desired into the system.

In the present invention, the vibratory motion of the

inertial elements

26, 26 can be nulled (or induced) by applying torquing forces directly to the inertial elements 26, 26 (and the iron rings 32, 32) of the vibrating rotor gyroscope. As shown in FIGURE 1, two

E-shaped torquer arrangements

62, 62 are mounted to the outer case 11 of the vibrating rotor gyroscope by support arrangements 66, 66' along, for example, the X axis of the case-referenced coordinate system. Mounted 90 therefrom, but not illustrated, are two more torquer arrangements which act along the Y axis of the case-referenced coordinate system. The E-shaped torquer arrangements 62, 62' are composed of C-shaped ferrite pieces with permanent magnet central legs. The network 74 provides torquing signals via leads 78, 78 to the outer legs of the

torquer arrangements

62, 62 acting along the X axis; similarly, the network '76 provides torquing signals via leads 80, G9 to the outer legs of the torquer arrangements acting along the Y axis. Depending upon the polarity of the torquing signals applied by the network 74, the magnetic field between the central leg and one of the two outer legs of each of the E-shaped X axis torquer arrangements 62, 52 is increased, while the magnetic field between the central leg and the other outer leg is decreased. Network 76 effects a like result in the Y 'axis torquing arrangements. Thus, the selective application of torquing signals by the

networks

74, 76 to the X axis and Y axis torquer arrangements generate magnetic torquing fields which can oppose, reinforce, or induce vibnatory motion of the inertial elements 25, 26 in the same manner as if an angular displacement were applied to the shaft 20.

A modification of the vibrating rotor gyroscope of the present invention is illustrated (symbolically) in FIGURE 4. In FIGURE 4, two

inertial elements

26, 26 are shown with their suspension means 28, 28' parallel to one another. One of the inertial elements (26) has its center of mass (C.M.) displaced (as described previously), a preselected distance along the shaft 2% from the point of suspension of the inertial element. Since the center of mass is displaced from the point of suspension, an acceleration along any direction, except that of the shaft, produces a moment on the inertial element. This moment. it can be shown, appears in equations of motion of the vibrating rotor gyroscope exactly like an angular displacement it; since, however, the moment produced by an acceleration is orthogonal to the acceleration causing it, an angular displacement about and an acceleration along a particular axis appear 90 out of phase in the equations of motion. In a typical case, for a pendulosity of .4 grn.-crn. (the product of the pendulous mass and the length of the pendulum arm) and an inertial element weighing 40 gms., the center of mass would be displaced approximately .01 cm. from the point of suspension.

Thus, the output signal from the sensor of a vibrating rotor gyroscope with its center of mass displaced contains components not only of rotational displacement but also of acceleration. In order to separate out the component of acceleration without the use of a separate accelerometer, a second inertial element is used which is substantially identical to the first but with its center of mass at its point of suspension. As shown in FIGURE 4, output signals H(X)+2N(X), 6(Y) +2N(Y) are derived by phase shifter 54 and demodulator 50 from inertial element 26 having its center of mass at its point of suspension while output signals 6(X) +A (X) +2N(X), 0(Y) +A(I) +2N(Y) representative of the magnitude of the components of the rotational displacement plus the acceleration plus the 2N frequency movements of the shaft 213 are derived by phase shifter 54 and demodulator 50 from inertial element 26 having its center of mass displaced a preselected distance from its point of suspension. The output signals from the inertial element 26 are then subtracted from those of inertial element 26' by standard differencing networks, 0, 9i) to yield the signals A(X), A(Y) representative of the components of the acceleration.

Terminals

73, 73 are provided to couple the signals A(X), A(Y) to an external recording means, such as a computer.

It should be noted, however, that in accordance wtih the solutions of the vibrating rotor gyroscope, the accelerational information is really the acceleration times the time it has been applied, or the velocity. In order to obtain true acceleration information, the output signals A(X), A(Y) are fed back via leads 78, to the torquing elements of the vibrating rotor gyroscope to operate it in a closed loop operation. Since the angular excursion of the inertial element is constantly being torqued back to null, the informational output is therefore a true acceleration. In addition, the signals 0(X), 6(Y) may be fed back to the torquers by coupling the signals from terminals 71, '71 to

terminals

91, 93.

It should be noted in FIGURE 4 that the outputs of both of the

inertial elements

26, 26" contain 2N frequency terms of the same polarity since the suspension means 28, 28 are parallel. Because of this, the rotational displacement terms 6(X)+2N(X), 0(Y)+2N(Y) retain 2N frequency terms in their final form while the accelerational terms A(X), A(Y) upon subtraction of the two outputs, emerge free from any 2N frequency terms. If, moreover, the suspension means 28, 28' were orthogonal, it is easily seen that the rotational displacement terms would retain the 2N frequency term while the accelerational terms would have 2N frequency terms added to it. If it is considered more desirable to eliminate the 2N frequency terms from the rotational displacement terms and to allow them to remain in the accelerational terms, the embodiment of the gyroscope 10 and the circuitry therefor shown in FIGURE 5 can be used. In this embodiment, the suspension means 23, 28' for the

inertial elements

26, 26 are orthogonal, while the centers of mass of the

inertial elements

26, 26 are displaced in opposite directions from their respective axes of vibration, i.e. towards one another or away from one another rather than in the same direction (as in FIGURE 7). The output signals obtained from each of the sensors 43, 4d of the inertial elements 26, 26' are demodulated and mixed in a manner similar to that in FIGURES 3 and 4 to yield the output signals K )l It can easily be recognized that with only four outputs available from a two inertial element vibrating rotor gyroscope (X and Y terms from each inertial element), the six variables in the output signals, i.e., (X), 0(Y), A(X), A(Y), 2N(X), and 2N(Y) cannot be individually determined. This limitation, however, is overcome by the embodiment of the gyroscope 10 (and the circuitry therefor) shown in FIGURE 6 in which three

inertial elements

26, 26, 26" are coaxially mounted on a single shaft 20. One of the elements (26) has its center of mass displaced a preselected distance from its point of suspension, while the other two inertial elements (26, 26") have their suspension means 28', 28" orthogonally disposed. Since there are now 6 outputs (X and Y terms from each inertial element), the six variables recited above can be individually determined. The output signals of each of the three inertial elements are demodulated and mixed in a manner similar to the previous embodiments to yield the signals 0(X), 0(Y), A(X), A(Y), 2N(X), 2N(Y) on

terminals

71, 71', 73, 73' and 75, 75. It should be noted that the signals 2N(X), 2N(Y) are coupled back to the torquers via leads 78, 80 to prevent undue oscillations being built up by the 2N vibrational forces.

It is apparent that the embodiments illustrated in FIGURES 3 through 6 can be used as the sensing elements on an inertial platform. Since, however, a single vibrating rotor gyroscope can only measure acceleration and rotational displacement -(or rate) along two axes, two or more of such gyroscopes must be combined to give complete three-dimensional information. As stated above, moreover, unless there are sufficient outputs from the inertial elements of the gyroscope all of the rotational, accelerational, and 2N frequency terms cannot be individually determined. If, for example, two of the vibrating rotor gyroscopes illustrated in FIGURE 3 are placed orthogonal to one another, the eight outputs therefrom (X and Y terms from each inertial element) yield a sulficient amount of information to individually determine the seven variables, i.e. the three rotational terms and the four 2N frequency terms (two from each gyroscope). If the gyroscopes in FIGURES 4 and 5 are utilized, however, it can be easily recognized that the eight outputs therefrom will be unable to yield sufficien-t information to separate the ten variables, i.e. three rotational terms, the three accelerational terms, and the four 2N frequency terms. If, however, two of the vibrating rotor gyroscopes illustrated in FIGURE 6 are placed orthogonal to one another, the twelve outputs obtainable therefrom are more than suflicient to resolve the three accelerati nal, three rotational, and four 2N frequency terms.

In certain instances, however, it may not be desirable to place three inertial elements on a single shaft; In FIGURE 7 an embodiment of the vibrating rotor gyroscope utilizing only two inertial elements on a single shaft to determine rotational, acce'lerational and 2N frequency terms is illustrated. In this embodiment, three vibrating rotor gyroscopes 19a, 12, 0 (each with two inertial elements) are mounted on an inertial element 13 orthogonal to one another. Since a single vibrating rotor gyroscope (such as shown in FIGURE 4) can determine acceleration only along two coordinate axes, at least two of the gyroscopes r1042, 11, 0 must have the center of mass of an inertial element spaced a preselected distance from the point of suspension to determine A(X), A(Y), A(Z). Since there are now three sucn gyroscope-s, it can be recognized that there are twelve variables, i.e. three rotational terms, three accelerational terms, and six 2N frequency terms (two for each gyroscope). Thus, the twelve outputs of the three gyroscopes yield just enough information to separate all the variables. However, the centers of mass of the inertial elements of the various gyroscopes must be properly placed so as to avoid duplication of output signals. If the inertial elements of one of the three gyroscopes generate the same information as the inertial elements of another one of the three gyroscopes, then all of the variables cannot be individually determined. In the particular embodiment shown, the gyr0scope (10a) supplying the X and Z coordinate rotational and accelerational terms has the centers of mass of the inertial elements displaced from the points of sus ension a preselected distance away from the origin O of the stationary reference coordinate system located in the inertial elernent 13. On the other hand, the gyroscope (10c) supplying the Y and Z coordinate rotational and accelerationa'l terms has the centers of mass of the inertial elements displaced from the point of suspension a preselected distance towards the center of such coordinate system. If the centers of mass of the inertial elements of the gyroscopes 10a and were not displaced in an opposite manner with respect to the origin of the reference coordinate system, the A(Z) terms would be of the same polarity and the 0(Z)+A (Z) ter'm could not be separated. As is seen from the circuitry illustrated in FIGURE 7, the rota tional and accelerational output signals generated by each of the gyroscopes 1012:, b, 0 can be demodulated and mixed to yield all six rotational and accelerational variables; since each of the gyroscopes has its suspension means orthogonal, it is apparent that all six of the 2N frequency terms can be eleminated (and solved for if desired). The output signals, available on terminals 71, 71', 711" 73, 73', 73", can be fed back to X, Y, Z torquer

terminals

91, 93, 95, respectively, coupled to the rotators of an inertial platform such as shown in the aforementioned patent application, or stored in a computer for processing.

Having thus described the invention, it is obvious that numerous modifications and departures may be made by those skilled in the art; thus, the invention is to be construed as being limited only by the spirit and scope of the appended claims.

What is claimed is: I

1. An inertial instrument comprising: a frame; a plurality of inertial elements rotatable with respect to said frame about a first axis, said inertial elements being capable of rotationally restrained vibratory motion about axes of vibration rotating with said inertial elements and angularly disposed 'with respect to said first axis; and means for rotating said inertial elements about said first axis.

2. The inertial instrument of claim 1 further comprising sensor means responsive to the vibratory motion of said inertial elements for generating signals representative of said vibratory motion.

'3. The inertial instrument of claim 2 further comprising means coupled to said sensor means and responsive to signals therefrom for generating output signals representative of rotational movements of said inertial instrument.

4. The inertial instrument of claim 3 further comprising means for reducing the magnitude of the components of said output signals caused by vibrational forces acting on said inertial elements.

5. The inertial instrument of claim 3 wherein said means coupled to said sensor means further comprises means for generating signals representative of vibrational forces acting on said inertial elements.

6. The inertial instrument of claim 5 further comprising means operable on said inertial elements and responsive to said output signals representative of said vibrational forces for substantially continuously nulling the vibratory motion of said inertial elements caused by said vibrational forces.

7. The inertial instrument of claim 1 wherein at least one of said inertial elements has its center of mass displaced a preselected distance from its axis of vibration.

8. The inertial instrument of claim 7 further comprising means responsive to the vibratory motion of said inertial elements for generating output signals representative of accelerational movements of said inertial instrument.

9. The inertial instrument of claim 8 further comprising means operable on said inertial elements and responsive to said signals representative of said accelerational movements for substantially continuously nulling the vibratory motion of said inertial elements caused by said accelerational movements.

10. The inertial instrument of claim 1 further comprising means for applying torquing forces to said inertial elements to control the vibratory motion thereof.

11. An inertial instrument comprising: a frame; a plurality of inertial elements rotatable with respect to said frame about a first axis, said inertial elements being capable of rotationally restrained vibratory motion about axes of vi ration rotating with said inertial elements and substantially orthogonal to said first axis; and means for rotating said inertial elements about said first axis.

12. The inertial instrument of claim 11 wherein said axes of vibration are substantially orthogonal.

13. A gyroscope comprising: support means; first and second inertial elements; first and second suspension means for t-orsionally coupling said first and second inertial elements, respectively, to said support means, said first and second suspension means being orthogonal; and means for rotating said support means.

14. The gyroscope of claim 13 further comprising means responsive to the vibrations of each of said inertial elements for generating output signals representative of rotational movements of said inertial instrument and means coupled to the last recited means for reducing the magnitude of the components of said output signals gen erated by vibrational forces acting on said support means.

15. A gyroscope comprising: support means; a pair of inertial elements; first and second suspension means for torsionally coupling said inertial elements to said support means, said first and second suspension means being substantially parallel and one of said inertial elements having its center of mass displaced a preselected distance from its point of suspension; means for rotating said inertial elements; and means responsive to vibratory motions of said inertial elements for generating output signals representative of rotational and accelerational movements of said gyroscope.

36. An inertial instrument comprising: a frame; first and second inertial elements rotatable with respect to said frame about a preselected axis, said first and second inertial elements being capable of vibratory motion about first and second axes of vibration angularly disposed with respect to said preselected axis and each of said inertial elements having its center of mass displaced a preselected distance from its axis of vibration, the centers of mass of said inertial elements being displaced in opposite directions from their respective axes of vibration; and means 12. for rotating said first and second inertial elements about said preselected axis.

17. A gyroscope comprising: support means; a plurality of inertial elements; suspension means for torsionally coupling said inertial elements to said support means, at least one of said suspension means being angularly disposed to the others of said suspension means and at least one of said inertial elements having its center of mass displaced a preselected distance from its center of suspension; and means for rotating said plurality of inertial elements.

18. A gyroscope comprising: support means; a trio of inertial elements; suspension means for t-orsionally coupling said inertial elements to said support means, two of said inertial elements having their suspension means parallel to one another and orthogonal to the suspension means of said third inertial element and one of said trio of inertial elements having its center of mass displaced a preselected dista cc from its center of suspension; and means for rotating said support means.

19. in an inertial guidance system the combination comprising: a stable element; and a plurality of gyro scopes positioned on said stable element along preselected axes, each of said gyroscopes comprising a plurality of inertial elements and means for rotating said plurality of inertial elements with respect to said stable element about one of said preselected axes, said plurality of inertial elements being capable of vibratory motion about axes of vibration angularly disposed with respect to the axes of rotation of said plurality of inertial elements.

29. The combination of claim 19 wherein the center of mass of at least one of the plurality of inertial elements in each of said gyroscopes is displaced a preselected distance from its axis of vibration.

21. The combination of claim 19 wherein the center of mass of at least one of the plurality of inertial ele tents of one of said gyroscopes is displaced toward the point of intersection of said preselected axes and the center of mass of at least one of the inertial elements of another of said gyroscopes is displaced away from the point of intersection of said preselected axes.

References Cited UNITED STATES PATENTS 2,716,893 9/1955 Birdsall 745 3,077,785 2/1963 Stiles 745 3,147,627 9/1964 Hunn 745.6 3,241,377 3/1966 Newton 74-5.6

C. I. HUSAR, Primary Examiner.

FRED C. MATTERN, Examiner.

I. D. PUFFER, Assistant Examiner.

Claims

1. AN INERTIAL INSTRUMENT COMPRISING: A FRAME; A PLURALITY OF INERTIAL ELEMENTS ROTATABLE WITH RESPECT TO SAID FRAME ABOUT A FIRST AXIS, SAID INERTIAL ELEMENTS BEING CAPABLE OF ROTATIONALLY RESTRAINED VIBRATORY MOTION ABOUT AXES OF VIBRATION ROTATING WITH SAID INERTIAL ELEMENTS AND ANGULARLY DISPOSED WITH RESPECT TO SAID FIRST AXIS; AND MEANS FOR ROTATING SAID INERTIAL ELEMENTS ABOUT SAID FIRST AXIS.