Micromachined Rate and Acceleration Sensor

This invention relates to an apparatus and method for determining the rate of angular rotation of a moving body and, in particular, adapted to be formed, e.g. micromachined, from a silicon substrate.

Reference is made to the following commonly assigned patents:

1) entitled "Monolithic Accelerometer", U.S. Pat. No. 5,165,279 issued on Nov. 24, 1992 in the name of Brian L. Norling;

2) entitled "Accelerometer with Co-Planar Push-Pull Force Transducers", U.S. Pat. No. 5,005,413 issued on Apr. 9, 1991 in the name of Mitch Novack;

3) entitled "Coriolis Inertial Rate and Acceleration Sensor", U.S. Pat. No. 5,168,756 issued Dec. 8, 1992 in the name of Rand H. Hulsing II;

4) entitled "Translational Accelerometer with Motion Constraints", filed (SDC-BO3804), in the names of B. Norling and S. Becka.

5) entitled "Torque Coil Stress Isolator", U.S. Pat. No. 5,111,694 issued May 12, 1992 to S. Foote.

The rate of rotation of a moving body about an axis may be determined by mounting an accelerometer on a frame and dithering it, with the accelerometer's sensitive axis and the direction of motion of the frame both normal to the rate axis about which rotation is to be measured. For example, consider a set of orthogonal axes X, Y and Z oriented with respect to the moving body. Periodic movement of the accelerometer along the Y axis of the moving body with its sensitive axis aligned with the Z axis results in the accelerometer experiencing a Coriolis acceleration directed along the Z axis as the moving body rotates about the X axis. A Coriolis acceleration is that perpendicular acceleration developed while the body is moving in a straight line, while the frame on which it is mounted rotates. This acceleration acting on the accelerometer is proportional to the velocity of the moving sensor body along the Y axis and its angular rate of rotation about the X axis. An output signal from the accelerometer thus includes a DC or slowly changing component or force signal F representing the linear acceleration of the body along the Z axis, and a periodic component or rotational signal .OMEGA. representing the Coriolis acceleration resulting from rotation of the body about the X axis.

The amplitude of that Coriolis component can be produced by vibrating the accelerometer, causing it to dither back and forth along a line perpendicular to the input axis of the accelerometer. Then, if the frame on which the accelerometer is mounted is rotating, the Coriolis acceleration component of the accelerometer's output signal will be increased proportional to the dither velocity. If the dither amplitude and frequency are held constant, then the Coriolis acceleration is proportional to the rotation rate of the frame.

The linear acceleration component and the rotational component representing the Coriolis acceleration may be readily separated by using two accelerometers mounted in back-to-back relationship to each other and processing their output signals by sum and difference techniques. In U.S. Pat. No. 4,510,802, assigned to the assignee of this invention, two accelerometers are mounted upon a parallelogram with their input axes pointing in opposite directions. An electromagnetic D'Arsonval coil is mounted on one side of the parallelogram structure and is energized with a periodically varying current to vibrate the accelerometers back and forth in a direction substantially normal to their sensitive or input axes. The coil causes the parallelogram structure to vibrate, dithering the accelerometers back and forth. By taking the difference between the two accelerometer outputs, the linear components of acceleration are summed. By taking the sum of the two outputs, the linear components cancel and only the Coriolis or rotational components remain.

U.S. Pat. No. 4,590,801, commonly assigned to the assignee of this invention, describes the processing of the output signals of two accelerometers mounted for periodic, dithering motion to obtain the rotational rate signal .OMEGA. and the force or acceleration signal F representing the change in velocity, i.e. acceleration of the moving body, along the Z axis. U.S. Pat. No. 4,510,802, commonly assigned to the assignee of this invention, describes a control pulse generator, which generates and applies a sinusoidal signal of a frequency .omega. to the D'Arsonval coil to vibrate the parallelogram structure and thus the first and second accelerometer structures mounted thereon, with a dithering motion of the same frequency .omega.. The accelerometer output signals are applied to a processing circuit, which sums the accelerometer output signals to reinforce the linear components indicative of acceleration. The linear components are integrated over the time period T of the frequency .omega. corresponding to the dither frequency to provide the force signal F, which represents the change in velocity, i.e. acceleration, along the Z axis. The accelerometer output signals are also summed, whereby their linear components cancel and their Coriolis components are reinforced to provide a signal indicative of frame rotation. That difference signal is multiplied by a zero mean periodic function sgnc .omega.t. The resulting signal is integrated over a period T of the frequency .omega. by a sample and hold circuit to provide the signal n representing the rate of rotation of the frame.

The D'Arsonval coil is driven by a sinusoidal signal of the same frequency .omega. which corresponded to the period T in which the linear acceleration and Coriolis component signals were integrated. In particular, the pulse generator applies a series of pulses at the frequency .omega. to a sine wave generator, which produces the substantially sinusoidal voltage signal to be applied to the D'Arsonval coil. A pair of pick-off coils produce a feedback signal indicative of the motion imparted to the accelerometers. That feedback signal is summed with the input sinusoidal voltage by a summing junction, whose output is applied to a high gain amplifier. The output of that amplifier in turn is applied to the D'Arsonval type drive coil. The torque output of the D'Arsonval coil interacts with the dynamics of the parallelogram structure to produce the vibrating or dither motion. In accordance with well known servo theory, the gain of the amplifier is set high so that the voltage applied to the summing junction and the feedback voltage are forced to be substantially equal and the motion of the mechanism will substantially follow the drive voltage applied to the summing junction.

U.S. Pat. No. 4,881,408 describes the use of vibrating beam force transducers in accelerometers. In U.S. Pat. No. 4,372,173, the force transducer takes the form of a double-ended tuning fork fabricated from crystalline quartz. The transducer comprises a pair of side-by-side beams which are connected to common mounting structures at their ends. Electrodes are deposited on the beams and a drive circuit applies a periodic voltage signal to the electrodes causing the beams to vibrate toward and away from one another, 180 degrees out of phase. In effect, the drive circuit and beams form an oscillator with the beams playing the role of a frequency controlled crystal, i.e., the mechanical resonance of the beams controls the oscillation frequency. The vibrating beams are made of crystalline quartz, which has piezoelectric properties. Application of periodic drive voltages to such beams cause them to vibrate toward and away from one another, 180 degrees out of phase. When the beams are subjected to accelerating forces, the frequency of the mechanical resonance of the beams changes, which results in a corresponding change in the frequency of the drive signal. When subjected to acceleration forces that cause the beams to be placed in tension, the resonance frequency of the beams and thus the frequency of the drive signal increases. Conversely, if the beams are placed in compression by the acceleration forces, the resonance frequency of the beams and the frequency of the drive signal is decreased.

Above referenced U.S. Pat. No. 5,005,413 describes accelerometers using vibrating force transducers require materials with low internal damping, to achieve high Q values that result in low drive power, low self-heating and insensitivity to electronic component variations. Transducer materials for high-accuracy instruments also require extreme mechanical stability over extended cycles at high stress levels. Crystalline silicon possess high Q values, and with the advent of low cost, micromachined mechanical structures fabricated from crystalline silicon, it is practical and desirable to create vibrating beams from a silicon substrate. Commonly assigned U.S. Pat. No. 4,912,990 describes a vibrating beam structure fabricated from crystalline silicon and including an electric circuit for applying a drive signal or current along a current path that extends in a first direction along a first beam and in a second, opposite direction along a second beam parallel to the first. A magnetic field is generated that intersects substantially perpendicular the conductive path, whereby the first and second beams are caused to vibrate towards and away from one another, 180 degrees out of phase.

Digital techniques employ stable, high frequency crystal clocks to measure a frequency change as an indication of acceleration forces applied to such vibrating beam accelerometers. To ensure precise integration or cosine demodulation, a crystal clock is used to set precisely the frequency of the dither drive signal. Outputs from two accelerometers are fed into counters to be compared to a reference clock signal produced by the crystal clock. A microprocessor reads the counters and processes the data to provide a force signal F and a rotational signal n. The main advantage of digital processing is the ability to demodulate with extreme precision. The short term stability of the reference crystal clock allows the half cycle time basis to be precisely equal. Thus a constant input to the cosine demodulator is chopped up into equal, positive half cycle and negative half cycle values, whose sum is exactly zero.

In an illustrative embodiment, the two accelerometers signals are counted in their respective counters over a 100 Hz period (corresponding to a 100 Hz of the dither frequency .omega.) and are sampled at a 400 Hz data rate corresponding to each quarter cycle of the dither motion. The two accumulated counts are subtracted to form the force signal F. Since the counters act as an integrator, the acceleration signal is changed directly to a velocity signal. Taking the difference of the acceleration signals tends to reject all Coriolis signals as does the counter integration and locked period data sampling.

The Coriolis signals are detected by a cosine demodulation. The cosine demodulated signals from the first and second accelerometers are summed to produce the .DELTA..theta. signal. Again, the counters integrate the rate data to produce an angle change. The sum also eliminates any linear acceleration and the demodulation cancels any bias source including bias operating frequency and accelerometer bias. The accelerometer temperature is used in a polynomial model to provide compensation for all the coefficients used to convert the frequency counts into output units. Thus, the scale factor, bias and misalignment of the sensor axes are corrected over the entire temperature range.

The demodulation of the frequency sample is straightforward once the data is gathered each quarter cycle. The cosine demodulation is simply the difference between the appropriate half cycles. The linear acceleration is the sum of all samples.

This invention employs the techniques of micromachining a substantially planar substrate of a material such as silicon with a high degree of accuracy to produce therefrom a pair of accelerometers, whose dither axes, accelerometer axes and input axes are so disposed that a strenuous vibration has minimal affect upon the accelerometer output signals.

This invention provides an improved rate and acceleration sensor comprised of a pair of accelerometers interconnected by a link so that extraneous motion imposed on one of the accelerometers is also imposed on the other with an equal and opposite force such that any error caused by extraneous motion in the output signals of the accelerometers tend to cancel each other.

A drive mechanism imposes a dither motion to a pair of coupled accelerometers with a simple magnetic drive circuit comprising but a single permanent magnet and a magnetic path for directing the flux through each of the accelerometers, which are both disposed in a side-by-side relation within a single plane. This magnetic circuit not only effects dither motion, but also vibrates the accelerometer sensor in the form of a pair of vibrating beams.

In an illustrative embodiment of this invention, apparatus for measuring the specific force and angular rotation rate of a moving body, comprises a silicon substrate having first and second substantially planar surfaces disposed substantially parallel to each other. A first accelerometer is formed of the substrate and has a first force sensing axis for producing a first output signal indicative of the acceleration of the moving body along the first force sensing axis. A second accelerometer is also formed of the substrate and has a second force sensing axis for producing a second output signal indicative of the acceleration of the moving body along the second force sensing axis. The substrate is micromachined to mount the first and second accelerometers such that their first and second force sensing axes are both oriented at the same angle with respect to the first and second surfaces but pointing in opposite directions, and to permit the first and second accelerometers to move along a vibration axis perpendicular to each of the first and second force sensing axes. A drive mechanism is coupled to each of the first and second accelerometers for imparting a dithering motion thereto of a predetermined frequency along the vibration axis. The substrate has a rate axis perpendicular to each of the first and second force sensing axes and the vibration axis, whereby the first and second output signals have a Coriolis component indicative of the Coriolis acceleration of the moving body about the rate axis.

In a further aspect of this invention, the apparatus includes a link having first and second points connected respectively to the first and second accelerometers, a pivoting point disposed intermediate of the first and second connected points, and a support structure for affixedly disposing the pivoting point with respect to the mounting structure formed of the substrate, to permit the link to pivot thereabout such that when one of the first and second accelerometers is moved, for imparting an equal and opposite motion to the other of the first and second accelerometers.

The measuring apparatus of this invention also includes a signal generator for producing a periodic drive signal of a predetermined frequency. The drive mechanism responds to the drive signal to imparting a dithering motion to the accelerometer along the vibration axis. The drive mechanism includes a conductive path formed on a surface of the substrate and is connected to the signal generator means to receive the drive signal therethrough, and a pole piece for directing a magnetic flux to cross the conductive path, whereby the interaction of the magnetic flux and the drive signal causes the accelerometer to vibrate along its vibration axis.

In a still further aspect of this invention, the drive mechanism of the measuring apparatus imparts a dithering motion to each of the first and second accelerometers. A first conductive path is disposed along a first portion of the first accelerometer, and a second conductive path is disposed along a second portion of the second accelerometer. A unitary magnet emanates the flux through from its first and second surfaces. A pole piece has a first surface for abutting the first surface of the unitary magnet and first and second projections having respectively second and third surfaced abutting said first substantially planar surface of the silicon substrate. These second and third projection surfaces are of reduced area compared to that of the first surface of and are aligned with the portions of the first and second accelerometers, whereby the flux density is increased and is restricted to flow through these portions of the first and second accelerometers.

FIG. 1A is a cross-sectional view illustrating the rate and acceleration sensor of this invention;

FIG. 1B is a side, cross-sectional view illustrating the rate and acceleration sensor of this invention, rotated 90 degrees from view in FIG. 1A.

FIG. 1C is a cross-sectional, side view taken along line 1C--1C of FIG. 1B.

FIG. 1D is a bottom plan view of the sensor shown in FIGS. 1A and 1B.

FIG. 1E is a top plan view of the flux path assembly included within the sensor as shown in FIGS. 1B, C and D.

FIG. 2A is a top plan view of the unitary substrate out of which are formed a pair of accelerometers disposed in a side-by-side relationship with their input axes pointing in opposite directions, as shown in FIGS. 1B, 1C, and 1D.

FIG. 2B is a perspective view of one of the accelerometers formed in the substrate as shown in FIG. 2A.

FIG. 2C is a cross-sectional view of the substrate and its accelerometer as taken along the line 2C--2C of FIG. 2B.

FIG. 3A is a circuit diagram of a first embodiment of an oscillator circuit for providing drive signals to the drive coils of the accelerometers shown in FIG. 2A.

FIG. 3B is a circuit diagram responsive to the velocity output signal of the circuit shown in FIG. 3A for gating the output signals from the accelerometer into counters.

FIG. 3C is a circuit diagram of a second embodiment of an oscillator circuit for sensing signals derived from the pick-off coils disposed on the accelerometers shown in FIG. 2A for providing drive signals to the coils of these accelerometers to effect the dither motion thereof.

FIG. 3D is a functional block diagram illustrating the processing of the output signals from the first and second accelerometers formed within the silicon substrate, of FIG. 2A and, in particular, illustrates how a pair of counters are gated to effectively demodulate the accelerometer output signals to provide an indication of the specific force and angular rotation rate of the moving body.

Referring now to the drawings, FIGS. 1A, 1B, 1C and D show the arrangement of a rate and acceleration sensor 10 according to the present invention. The sensor 10 includes a shell 12 housing a unitary substrate 16, which is illustratively made of silicon and in which is formed, illustratively by micro-machining, a pair of accelerometers 32a and 32b disposed in side-by-side relation such that their input axes 38a and b are disposed in opposite directions (see FIG. 1D), a unitary magnet 20 and a flux path assembly 18, which provides a magnetic path for directing the flux emanating from the magnet 20 through the substrate 16 and its first and second accelerometers 32a and b. As will be explained, the configuration and disposition of the accelerometers 32a and b within the substrate 16 permits a simple, straightforward magnetic flux path to effect the operation of the dithering motion and the vibration of a sensor element of the accelerometers 32a and b.

Referring now to FIG. 2A, the details of the substrate 16 are shown. The first and second accelerometers 32a and b are micromachined from the unitary, silicon substrate 16 so that their input axes 38a and 38b are disposed in parallel but opposite directions. In FIG. 2A, the input axis 38a of the accelerometer 32a is disposed out of the page, whereas the input axes 38b of the accelerometer 32b is disposed into the page. Further, the input axes 38a and b are disposed perpendicular to a dither or vibration axis 41 and to a rate axis 39. As is well known in the art, the accelerometers 32a and b will respond to linear acceleration along their input axes 38a and b, respectively, and to rotation of the substrate 16 about its rate axis 39.

The substrate 16 includes a dither or mounting frame 30 from which each of the accelerometers 32a and b is suspended respectively by a pair of flexures 34 and 36, which upon application of a dithering force vibrate with an "S bend" motion to translate the accelerometers 32a and b in a predominantly linear relationship with each other. As will be further described, a periodic drive signal or current is applied via the external connectors 86a and b to a conductor or conductive path 92. The magnet 20 emanates a magnetic field substantially perpendicular to the surface of the substrate 16, whereby the accelerometers 32a and b are subjected to a periodic dithering motion along their dither axis 41.

A link 72 is connected to the unsupported end of each accelerometer 32 to insure that the dithering motion imparted to one of the accelerometers 32a will be of the exact same frequency and in phase with that applied to the other accelerometer 32b. Without a link 72 therebetween, the accelerometers 32a and b would tend to vibrate at slightly different frequencies due to slight mass mismatch. Even if driven by a drive signal of common frequency, the accelerometer motions would tend to be out of phase with each other. The link 72 is connected by a flexure 80a to the free moving end of the first accelerometer 32a opposite to the flexures 34a and 36a, which mount the accelerometer 32a to the dither frame 30. The link 72 resembles a lever pivotally mounted about a pivot point 73 provided by a pivot flexure 82. The link 72 includes first and second lever arms 74a and b extending in opposite directions from the pivot point 73. The second lever arm 74b is connected by a flexure 80b to the free moving end of the accelerometer 32b opposite to its end connected by the flexures 34b and 36b to the dither frame 30. The link 72 includes a pair of parallel members 76a and 76b interconnecting the pivot arms 74a and 74b to a brace 78 connected to the pivot flexure 82. In turn, the pivot flexure 82 is mounted along a center axis of the substrate 16 by a support member 84, which is in turn affixed to the dither frame 30.

As more fully shown in FIG. 2B, each accelerometer 32 includes an element 48 sensing the acceleration imposed on the sensor 10 and including a pair of vibrating beams 54 and 56, which are driven to vibrate in opposite directions as indicated by the arrows 57' and 57", respectively. It will be appreciated that the arrows 57' and 57" are aligned in a parallel relationship with the dither axis 41 and are disposed perpendicular to the input axes 38a and b and to the rate axis 39 (see FIG. 2A). One end of each of the vibrating beams 54 and 56 is affixed in a relatively stationary relationship to an accelerometer support frame 42. The remote ends of the vibrating beams 54 and 56 are connected to a proof mass 40, which is suspended by a pair of hinges 44 and 46 to the frame 42. As shown in FIG. 2B, the hinges 44 and 46 define a hinge axis 47 about which the proof mass 40 rotates. When accelerating forces are applied along the input axis 38 of each accelerometer 32, its proof mass 40 tends to pivot about its hinge axis 47. The opposite end of the proof mass 40 is pliantly or flexibly connected to the accelerometer support frame 42 by a strut 52 of reduced cross-section, whereby the proof mass 40 is free to move along its input axis 38. As shown in FIG. 2C, the hinges 44 and 46 are formed by micromachining the silicon substrate 16 into a relatively thin flexure with respect to the width of the support frame 42, whereby the proof mass 40 is permitted to pivot about the hinge axis 47.

As shown in FIGS. 2A, B and C, each of the accelerometers 32a and b has a corresponding strut 52a or b, which tends to dampen or attenuate extraneous movements applied to the proof masses 40a or b. A pendulous axis 53 is associated with each of accelerometers 32 and its proof mass 40. As best shown in FIG. 2C, each proof mass 40 has a center of gravity 50. The input axis 38 of each accelerometer 32 intersects the center of gravity 50 and is disposed perpendicular to the pendulous axis 53. The pendulous axis 53 passes through the center of gravity 50, the hinge axis 47 and the strut 52. In an illustrative embodiment of this invention, the input axis 38 is tilted at an acute angle of approximately 8.degree. with respect to the unitary substrate 16 and its support frame 42. Also the dither axis 41 intersects the centers of gravities 50a and b of both accelerometers 32a and b and is perpendicular to their input axes 38a and b. Undesired moments may be produced by acceleration forces acting along the hinge axis 47 to develop moments about the pendulous axis 53 equal to the product of such forces times a moment arm or equivalent radius of rotation 55 corresponding to the vertical distance between the rate axis 47 and the center of gravity 50. In a preferred embodiment, each strut 52 is made of reduced cross sectional dimensions, e.g., 1 millinch square. A foot 58 is disposed at right angles to the strut 52 to interconnect the end of the strut 52 to the proof mass 40. One end of the strut 52 is connected to an innerperipheral edge of the accelerometer support frame 42, and its foot 58 is connected to an edge of the free end of the proof mass 40 remote from its hinges 44 and 46 and its hinge axis 47. By maximizing the length of the strut 52, its spring rate is S reduced to provide maximum flexibility of the strut 52. The foot 58 is so configured and dimensioned to render it relatively flexible, so that the foot 58 will "S-bend" to allow rotation of the proof mass 40 substantially only about its hinge axis 47.

The vibrating beams 54 and 56 are also machined from the substrate 16 but on a surface of the substrate 16 opposite to that of the hinges 44 and 46. Thus, as acceleration forces cause the proof mass 40 to rotate upwardly as shown in FIG. 2C, both of the vibrating beams 54 are put into compression, whereas when the proof mass 40 is pivoted downwardly as shown in FIG. 2C, the vibrating beams 54 and 56 are placed in tension. When the vibrating beams 54 and 56 are placed in tension, the frequency of their natural vibration increases, and when put into compression, that frequency decreases.

As shown in FIGS. 2A and B, a drive signal or current is applied via connector pads 62 via a conductive path or conductor 60 that extends in a first direction along the vibrating beam 54 and in a second, opposite direction along the vibrating beam 56, whereby in the presence of a magnetic field as generated by the magnet 20, the vibrating beams 54 and 56 vibrate in opposite directions. A drive circuit 64 is incorporated in the accelerometer support frame 42 to provide the current to the conductor 60. The drive circuit 64 also provides an output to the external connector path 70, indicative of the frequency at which the vibrating beams 54 and 56 are vibrating.

A significant advantage of this invention resides in the placement of the first and second accelerometers 32a and b within the silicon substrate 16, whereby a single magnet 20 may be employed to direct magnetic flux through each of the accelerometers 32a and b for the dual purposes of imparting the dithering motion to the accelerometers 32a and b, and imparting a vibrating motion to the sensor elements 48 in the form of the vibrating beams 54 and 56. FIG. 1E shows the flux path assembly 18 in its flat state, before it is folded into the configuration shown in FIG. 1D. The assembly 18 supports and retains the substrate 16, a pole piece 22 and the magnet 20 in the positions as shown in FIGS. 1C and D, and includes a bottom member 100, opposing side members 106a and 106b and top members 108a and b. In turn, the assembly 18 is supported within the housing cover 12 by a pair of support legs 110a and b, which extend downward to mate with a housing ring 14 and, in particular, a projection 15, whereby the assembly 18 is securely held within the assembled housing cover 12 and base 14.

As particularly shown in FIG. 1C, the assembly 18 provides a flux path therethrough for the flux emanating from the magnet 20, and concentrated or focused by the pole piece 22 to pass primarily through the first and second accelerometers 32a and b, before the flux returns into the restricted legs 102a and b. Thereafter, the flux passes through the side members 106a and b and their respective top members 108a and b and into the magnet 20 to complete the flux path. The structure described, and in particular the pole piece 22 and the restricted legs 102a and b, concentrate the flux to pass primarily through the accelerometers 32a and b, such that when drive signals are applied to pass through the conductors 92 and 60, a dither motion is imparted to the accelerometers 32a and b, and a natural vibration motion is imparted to the vibrating beams 54a and b, and 56a and b. The pole piece 22 has a pair of projections 118a and b of approximately the same dimensions as the corresponding cross-sectional areas of the accelerometers 32a and b such that the flux passes primarily through the accelerometers 32a and b. As shown particularly in FIGS. 1A and E, the restricted legs 102 form an opening 104 therethrough in which only a nominal flux appears, it being understood that most of the flux is concentrated to pass through the legs 102a and b. It is estimated that this configuration of the flux path assembly 18 doubles the strength of the flux passing through the accelerometers 32a and b, thus increasing proportionally the voltage appearing on the pickup coils and, thus, reducing the gain of that drive circuit 127' to be explained with respect to FIG. 3C. Thus, because of the placement of accelerometers 32a and b in a side-by-side relationship within a single substantially planar substrate 16, a single magnet 20 and a simple flux path assembly 18 may be employed to provide the magnetic flux to effect efficiently both the dithering and vibrating motion of accelerometers 32a and b.

As shown in FIG. 2A, the conductive path 92 is deposited on the top surface of the substrate 16 and extends from the external connector 86a down a leg of the dither frame 30, horizontally across the flexure 36a and the bottom peripheral edge of the accelerometer 32a, down the vertical flexure 80a, across the link arms 74a and 74b, down the vertical flexure 80b, across the upper peripheral edge of accelerometer 32b and its flexure 34b, and down the opposing leg of the dither frame 30 to the external connector 86b. The conductive path 92 has a center point, which is connected by a conductive path 92c and a ground terminal 88 to ground. In order to maximize the efficiency of generating the dither motion, the conductive path 92 follows a path along the bottom portion of accelerometer 32a and its flexure 36a and the upper portion of the accelerometer 32b and its flexure 34b, which portions are closest to the center of the substrate 16, whereby the magnetic flux emanating from the magnet 20 and focussed by the pole piece 22 and its projections 118a and b, is concentrated to pass through these portions of the conductive path 92. The conductive path 92 includes a first effective portion identified by the numeral 92a mounted on the flexure 36a and the bottom of the accelerometer frame 42a of the accelerometer 32a and a second effective portion 92b similarly but oppositely mounted on the accelerometer 32b, both effective portions 92a and b disposed within the concentrated magnetic flux produced by the magnet 20 and its pole piece 22. By so configuring the conductive path 92 and its effective portions 92a and b, the driving force of the dither motion is maximized.

As shown in FIG. 1A, the substrate 16 is provided with a pair of dust covers 17a and b disposed respectively upon the opposing surfaces of the substrate 16. The dust covers 17a and b may also be made of silicon and serve to protect the accelerometers 32a and b from dust. Illustratively, the inner surfaces of the dust covers 17a and b are recessed (not shown in the drawings) to permit movement of the proof masses 40a and b and to provide stops for them.

As described above, the input axis 38 is oriented at an acute angle with respect to a line perpendicular to the surface of the substrate 16. In an illustrative embodiment of this invention, the assembly 18 mounts the substrate 16 at a compensating angle with respect to the axis of the housing shell 12, whereby the sensor 10 and thus, the input axes 38 of the accelerometers 32a and b may be precisely oriented with respect to the vehicle or aircraft carrying the sensor 10 of this invention. The substrate 16 is mounted on a plurality of pads 114. A pair of support arms 112a and b extend from the leg 102a to support the corners of the lower surface (as seen in FIG. 1E) of the substrate 16. In turn, a support arm 116 connects the pad 114c to the leg 102b of the assembly 18, whereby the pad 114c supports a center portion of the opposite edge of the substrate 16. The numeral 113 designates the center of the opening 104 and is aligned with the pivot point 73, when the substrate 16 is mounted within the flux path assembly 18 as shown in FIG. 1A. The pivot point 73 forms the center of the silicon substrate 16 as shown in FIG. 2A. Similarly, the axis of the permanent magnet 20, shown in FIG. 1B as being of a cylindrical configuration, is also aligned with the center 113 and the pivot point 73.

The assembly 18 solves a thermal stress problem resulting from the different coefficients of thermal expansion of the silicon substrate 16 and the flux path assembly 18, i.e., the assembly 18 expands at a greater rate than the silicon substrate 16. Illustratively, the silicon substrate 16 has a temperature coefficient of expansion in the order of 2.5 PPM/.degree.C., whereas the assembly 18 is made of a silicon steel (having a silicon content of 3%), which in turn exhibits a temperature coefficient on the order of 11 PPM/.degree.C., which is considerably greater than that of the substrate 16. In the absence of thermal stress relief, the substrate 16 would tend to buckle, possibly break and/or separate from the assembly 18. If the substrate 16 warps, the critical alignment of the accelerometers 32a and b and its various parts will be thrown out of balance with the result that the desired compensation of extraneous motions applied to the sensor 10 will be defeated. As shown in FIG. 1E, each of the support arms 112a and b, and 116 is disposed perpendicular respectively to each of a corresponding plurality of radial stress lines 111a, b and c. Thus, as the assembly 16 expands and tends to place a radial stress on the arms 112a, b, and 116, their configuration as shown in FIG. 1E permits them to readily flex under the thermal stress rather than buckle or break the substrate 16. In addition, each of the mounting pads 114a, b, and c is connected to the substrate 16 by a resilient adhesive such as an epoxy.

As the temperature of the permanent magnet 20, the assembly 18 and the substrate 16 vary, the mounting structure provided by the assembly 18 and the relative positions of the permanent magnet 20 and the substrate 16 therewith ensure that as the substrate 16 and its assembly 18 expand at different rates, the relative positions of these elements with respect to the magnet 20 remain the same. Therefore, the accelerometers 32a and b remain in the same relative relationship with the permanent magnet 20 and are exposed to a magnetic flux field of the same strength. If the magnet 20, the assembly 18 and the substrate 16 were mounted such that the magnet 20 could shift even to a small degree with respect to the accelerometers 32a and b, the flux emanating through the effective portions 92a and b and the conductive paths 60 associated with vibrating beams 54 and 56 would also vary, whereby any extraneous motion imparted to the accelerometers 32a and b, as well as the outputs derived from the conductors 60 of each of the accelerometers 32a and b, would differ from each other.

The arrangement as shown in FIG. 2A of the accelerometers 32a and b, their supporting flexures 34 and 36 and the interconnection therebetween by the link 72 provide equal and opposite dither motion to the accelerometers 32a and b, and isolate the substrate 16, its dither frame 30 and the accelerometers 32a and b from extraneous stress, such that error signals are not introduced by data processing into the resultant force signals F and rotational signals n and permits data processing using the output of the accelerometers 32a and 32b by relatively simple differentiating and scaling techniques. Further, the structure of FIG. 2A may be implemented by micromachining techniques upon a silicon substrate 16, whereby the resultant structure is produced at a low cost and with a precision of which the prior art accelerometers were simply not capable. In turn, the extreme accuracy of construction afforded by micromachining techniques permits the relative placement of accelerometers 32a and b and its link 72 to a precision in the order of 40 micro inches. As a result of such accuracy, the accelerometers 32a and b are placed in precise balance with each other such that extraneous movements imposed upon the frame 30 do not upset this balance and introduce erroneous signals into the outputs of the accelerometers 32a and b as may be otherwise caused by even slight misalignment of the accelerometers 32a and 32b.

First, the accelerometers 32a and 32b are mounted upon opposing sides of the dither frame 30 by their flexures 34a and 36a and 34b and 36b, respectively. Each of the flexures 34 and 36 is formed from the silicon substrate 16 to a height equal to the width of the substrate 16, illustratively of 20 mils, and a thickness of 1.4 mil corresponding to the vertical dimension of the flexures 34 and 36 as shown in FIG. 2A. The length of each of the flexures 34a and b and 36a and b is selected to provide a spring rate relative to the mass of accelerometers, e.g., of 0.1 gram, that will cause the flexures 34 and 36 to flex in an "S-bend" when subjected to the dither motion. The spring rate of the flexures is proportional to T.sup.3 /L.sup.3, where T is the thickness of the flexures 34 and 36 and L is the length thereof. The length L and thickness T of the flexures 34 and 36 are set such that when dither motion is applied, the flexures 34 and 36 then flex in an S configuration, as shown in FIG. 2A. Such "S-bend" flexures 34 and 36 permit the accelerometers 32a and b to translate with predominantly linear motion, i.e., the vibrating beams 48a and 48b (as well as the other elements) of accelerometers 32a and 32b remain substantially parallel to each other as they are dithered along the dither axis 41. In addition, the flexures 34 and 36 permit accelerometers 32a and 32b to move in a predominantly linear fashion with only an insignificant nonlinear frequency component imposed thereon.

The link 72 mechanically interconnects the first and second accelerometers 32a and b so that any motion, including dithering motion and extraneous motions applied to one of the accelerometers 32, will also be applied in precisely equal and opposite fashion to the other accelerometer 32. In this fashion, the outputs of the accelerometers 32a and b may be processed simply by sum and difference techniques to provide a force signal F and the rotational signal n, as well as to cancel out erroneous signals. Without the link 72, the accelerometers 32a and 32b would operate at different frequencies due to slight mass mismatch of the proof masses 40. If driven at a common frequency, the accelerometers 32a and 32b would without the link 72 operate out of phase with each other (other than 180.degree.).

The configuration and the manner of mounting the link 72 are effected to permit the link 72 to effectively pivot about the pivot point 73 intersecting an axis passing through the lever arms 74a and b. The pivot point 73 is disposed at a selected point along the length of the pivot flexure 82. As shown in FIG. 2A, the bottom end of the pivot flexure 82 is affixed to the support member 84 and extends vertically along the dither axis 41. The length of the pivot flexure 82 is selected, e.g., 100 mils, to impart a simple bending thereto, whereby that portion from the pivot point 73 to the point of interconnection to the link 72 is permitted to flex about the pivot point 73, while the remaining portion of the flexure 82 between the pivot point 73 and the support member 84, flexes in a smooth arc. In this fashion, the end points of the link 72 are disposed a radial distance from the pivot point 73 equal to the effective radius of rotation provided by the "S-bend" flexures 34 and 36 for the accelerometers 32a and 32b.

As indicated above, the length of the pivot flexure 82 is determined so that it flexes with only a simple are bending. To accommodate a pivot flexure 82 of the desired length, it is necessary to configure the link 72 with a U-shaped configuration comprised of the parallel members 76a and b and the interconnecting member 78. In addition, a portion of the support member 84 is removed to provide a cut out 85, whereby the length of the pivot flexure 82 is set to provide the simple bend motion.

The vertically oriented flexures 80a and b as shown in FIG. 2A are dimensioned and, in particular, their lengths are set such that they exhibit 50% simple arc bending and 50% "IS-bend" motion. Opposite ends of the vertical struts 80a and b are respectively interconnected between an edge of one of the accelerometers 32a and b and an end of one of the link members 74a and b. Portions of the link 72 and the accelerometers 32 are removed to provide cutouts 71 and 139, respectively, so that the precise length of the flexures 80a and b is determined to ensure that the flexures 80 have characteristics of 50 percent simple motion and 50 percent "S-bend" motion. Further with such characteristics, it is assured that any motion imparted by the flexures 80 to one of the accelerometers 32 is imparted as a sinusoidal function to the other without introducing a higher order harmonic into the translation motion. Without such flexures 80 and the link 72, the dither motion as well as other extraneous motion applied to the substrate 16, could impose high order harmonic motion to the accelerometers 32a and b, whose outputs upon demodulation would bear an undesired bias signal.

As indicated above, the flexures 34 and 36 are made of such dimensions and, in particular, their length such that they flex with an "S-bend". In particular, one end of each of the flexures 34 and 36 is respectively affixed to the inner periphery of the dither frame 30 and the other end to the accelerometer 32. An external edge portion of the accelerometer support frame 42 is removed to provide a cut out 33 so that the length of the flexures 34 and 36 is critically set to provide the desired "S-bend" motion and so that the other end of the flexures 34 and 36 are connected to a midpoint of the horizontal edges of accelerometers 32a and b. As shown in FIG. 2A, the flexures 34 and 36 support accelerometers 32a and b so that their centers of gravity 50 and the pivot point 73 lie along the central axis of the substrate 16 so that the center axis coincides with the dither axis of 41.

The "S-bend" flexures 34 and 36 have respectively pivot points 35 and 37, which are disposed a distance 1/6th of the flexure length from the inner periphery of the dither frame 30. The "S-bend" flexures 34 and 36 form respectively an effective radius from their pivot points 35 and 37 to their points of connection with their support frames 42. That effective radius equals to 5/6 of the length of the flexures 34 and 36, which in turn precisely equals the radius provided by the lever arms 74 from their pivot point 73 to the points of interconnection of the upright flexures 80a and b to the extremities of the lever arms 74a and b. By providing the link 72 and the accelerometers 32a and b with equal radii of rotation about the respective pivot points 73, and 37 and 35, it is assured that the link 72 will provide equal and opposite motion to the accelerometers 32a and b. As a result, if any extraneous noise is applied to one-of the accelerometers 32a and b, a like and opposite motion will be applied to the other, so that upon processing any noise in the outputs of the accelerometers 32 is effectively removed by sum and difference techniques.

Upon application of the dithering motion to the accelerometers 32a and b, the "S-bend" flexures 34 and 36 move up and down in a substantially parallel relationship to each other due to the "S-bend" flexing of their flexures 34 and 36. Each flexure 34 and 36 has a center point 239 and 240, respectively. The bending motion resembles two smooth curves, the first terminating at the center point in one direction and the second curve with an opposite curve meeting the first at the center point. The "S-bend" flexures ensure that the horizontal and vertical edges of the support frames 42a and b remain precisely parallel with the inner horizontal and vertical peripheral edges of the dither frame 30.

As indicated above, the "S-bend" flexures 34 and 36 provide an effective rotation of the accelerometers 32a and b about their pivot points 35 and 37. In an illustrative embodiment, the commonly applied dithering forces move accelerometers 32a and b through a positive and negative angular rotation with respect to their rest positions, whereby the center of gravities 50a and b move from the center axis of the substrate 16 a distance of only 37 microinches for a dithering motion having an amplitude of 1 mil along the dithering axis 41.

The construction of accelerometers 32a and b from the silicon substrate 16 results in extremely close alignment of the accelerometers 32. This results from the high degree of flatness of the silicon substrate 16 and the relative proximity of the accelerometers 32a and b micromachined from the substrate 16. The flexures 34, 36, 80 and 82 are produced by etching near the surfaces of the substrate 16. Such micromachining ensures that the input axes 38a and b will be precisely perpendicular to the dither axis 41, at least as good as the flatness and parallel relationship of the surfaces of the silicon substrate 16, which can typically be achieved to a high degree. Thus, this invention achieves close alignment of the input and dither axes 38 and 41, thus overcoming the problem of prior art Coriolis sensors with regard to such alignment. The suspension of the accelerometers 32a and b by their flexures 34a and 36a, and 34b and 36b from opposing sides of the dither frame 30 so that their input axes 38a and b point in opposite directions and the use of the link 72 provide excellent nonlinearity motion cancellation.

The well known Euler-Buckling curves represent the structural tensioning and compression characteristics of the accelerometers their vibrating beams 54 and 56. The back-to-back orientation ensures that when the vibrating beams 54 and 56 of the accelerometer 32a are in tension, the beams of the other accelerometer 32b are in compression, and vice versa. As will be explained, the outputs of the accelerometers 32a and 32b are summed together to provide an indication of linear acceleration. This orientation insures that the beams 54 and 56 are operating in complementary portions of these curves and the summed outputs of the accelerometers 32a and b provide an accurate indication of the linear acceleration by canceling the higher order nonlinearities of the vibrating beams 54 and 56. In addition, extraneous movements acting on the accelerometers 32a and b will at least to a first order of measure, tend cancel or dampen each other, whereby extraneous signals do not appear in the summed accelerometer outputs. In an analogous fashion when the difference of the accelerometer outputs is taken, the canceling characteristics of these curves ensure that second order nonlinearities in the resultant angular rotation signal will also average.

The construction of the two accelerometers 32a and b from the silicon substrate 16 offers other advantages. First, the S configuration and the dimensions of the accelerometers 32, the various flexures and the link 72 may be determined with an extreme degree of accuracy, e.g., 40 microinches, so that the relative position of these elements is controlled to a like degree. Second, the construction of the flexures in the plane of the silicon substrate 16 ensures that the accelerometers 32 are dithered in that plane. As noted above, the link 72 ensures that the accelerometers 32a and b move in equal and opposite directions under the influence of the applied dithering motion. Thus, the centers 50a and b of gravity of the accelerometers 32a and b are placed precisely upon the center axis of the substrate 16, which is aligned with the dither axis 41 with a high degree of precision, whereby the dither motion caused by the current passing through the drive coils a and b causes the dithering motion to be applied precisely along the center axis of the substrate 16. Such accuracy ensures that extraneous motions otherwise resulting from the dither motion are not imposed upon the accelerometers 32a and b.

Secondly, the suspension of accelerometers 32a and b by the "S-bend" flexures 34 and 36, which are also formed in the plane of the silicon substrate 16, produces a motion of the accelerometers 32a and b of relatively small, opposing arcs as a result of this dithering motion. In one illustrative embodiment, dithering at maximum displacement (amplitude) of 1 millinch (corresponding to 1 degree of the total peak to peak angular travel), displaces the accelerometers 32a and b from their center axis by a mere 37 microinches. During a single cycle of motion of each of the accelerometers 32a and b up and down along the dither axis 41, each accelerometer 32 is subjected to 2 translations as it rotates about its effective radius provided by its flexures 34 and 36. However, since these double translations or "bobbings" occur within the plane of the silicon substrate 16 and not along the input axes 38a and b, the problems that have occurred with the prior art sensors of parallelogram configuration are avoided. First, a corresponding double frequency error signal is not imposed upon the inputs of the accelerometers 32, which required a phase servo adjustment in the processing as described in U.S. Pat. No. 4,799,385. Second, there is no need to offset the center of oscillation or to couple turn-around acceleration into the accelerometer input axis. As a result, for any position of the accelerometers 32a and b during their dithering motion, there is very little double frequency motion imposed upon their input axis 50. Thus, there is no need to "steer" out the misalignment by adding a bias to the dither drive signal.

The various features of the silicon substrate 16 may be micromachined by various techniques well known in the prior art such as a wet chemical etch or a dry chemical etch such as plasma etching, sputter etching or reactive ion etching. For a detailed discussion of such techniques, reference is made to the following publications, which are incorporated herein by reference: VLSI Fabrication Principles by Sorab K. Ghandhi and Silicon Processing for the VLSI Era. Vol. 1--Process Technology by S. Wolf & R. J. Tauber.

In this illustrative embodiment of the silicon substrate 16, the maximum misalignment of the accelerometers 32 from the substrate center axis would be less than 0.1 mrad. This has the benefit of not fully imposing second harmonic distortion resulting from the dither drive into the rotational component signal outputted by the accelerometers 32a and b. Otherwise, as is disclosed by the prior art parallelogram drive arrangements, such second harmonic drive distortion could be multiplied by the squaring action of double dipping to generate primary and third harmonics, which can be coupled into the rate channels as error. These errors are avoided by the side-by-side placement and accurate micromachining of the accelerometers 32a and b within the substrate 16.

As noted above, each of the accelerometers 32a and b is suspended by "S-bend" flexures 34 and 36, which provide effective radii of rotation equal to that radius provided by the link arms 74a and b; without such construction, the accelerometers 32a and b would dither with a non-sinusoidal motion, which would introduce high order harmonic distortion in the rate signal. It is contemplated that there will be some coupling due to the offset of the input axis 50 resulting from the centers 50 of gravity being disposed above the flexures; however, such coupling is minor compared to that introduced by the parallelogram structures of the prior art.

Referring now to FIG. 3A, there is shown a dither drive circuit 127 for providing a sinusoidal voltage to be applied across the effective portions 92a and b. The conductive path 92 forms the first effective portion 92a for imparting a vibrating motion to the accelerometer 32a and the second effective portion 92b for imparting a vibrating motion to the accelerometer 32b. The center point of the conductor 92 is connected to ground via the conductor 92c and a ground terminal 88. As shown in FIGS. 1A and 1D, a magnetic field is generated perpendicular to the surfaces of the substrate 16 and is focused by the pole piece 22 through the accelerometers 32a and 32b. Illustratively, the conductor 92 takes the form of a deposit of gold. In an illustrative embodiment of this invention wherein the length of the conductor 92 extending between terminals 86a and 88 (or 86b and 88) is approximately 1 inch and is deposited to a depth of 1 .mu.meter and a width of 10 .mu.meter, the resistance offered by such a length of the conductor 92 is in the order of 100 ohms. When the magnetic flux crosses the conductive path 92, a voltage is induced thereacross of approximately 0.5 volt, which is approximately 2500 times the voltage amplitude of the velocity signal which is outputted by the dither drive circuit 127 of FIG. 3A on its output 86-91. To effectively remove this resistance voltage, a bridge 125 shown in FIG. 3A is employed with one leg thereof being formed by the effective portions 92a and b connected in parallel, and a second leg by a reference conductor 93 which is disposed on the dither frame 30 and has ends connected to terminals 91 and 95, as shown in FIG. 2A. The effective portions 92a and b are connected in parallel by connecting the terminals 86a and b together; in turn, the terminal 88 forms one node of the bridge 125 and the connected terminals 86a and b another node. The conductive path 92 forms the two effective portions 92a and b connected, with the interconnecting portion of conductor 92 being connected via the conductive path 92c to the ground terminal 88. The effective portions 92a and 92b are connected in parallel to form one leg of the bridge 125. The other leg of the bridge 125 is formed of the reference conductor 93 having one-half the length of the conductor 92 between the terminals 86a and 88 (or 86b and 88), e.g., one-half inch. The reference conductor 93 is made of the same material as that of conductor 92, e.g., gold, and is deposited to a like depth, whereby a like voltage, e.g., 0.5 v, is developed across both of the parallel connected effective portions 92a and b, and the reference conductor 93. A single drive voltage is applied from a first bridge node 129 to ground, whereas an output of the bridge 125 as developed across bridge nodes 86 and 91 is taken and applied to a first operational amplifier 128, which subtracts the voltage developed across the reference conductor 93 from that developed across the parallel connected effective portions 92a and b. A second operational amplifier 130 provides the remaining gain to boost the output of the first operational amplifier 128 to approximately 2.5 v peak at the output 132. A feedback path is connected to the bridge circuit 125 providing position feedback plus an excess phase shift due to the high-order operational amplifier poles, whereby an oscillating circuit is established to provide the sinusoidal signal to drive the effective portions 92a and b. The output 132 is clamped by a pair of Zener diodes D1 and D2 connected in opposition between the output 132 and ground, to clamp the output 132 and thereby stabilize the drive signal applied to the effective portions 92a and b.

As shown in FIG. 3B, the velocity signal appearing on the output 132 of the dither drive circuit 127 is applied to a zero-crossing detector circuit 133, whose outputs are used to gate the counters for counting the crystal clock signal, whereby the Coriolis rate signal and acceleration force signal can be demodulated. The velocity signal is coupled to an operation amplifier 134 by a capacitor C1 and resistor R10 to generate a zero-crossing signal. The open loop gain of the operational amplifier 134 "squares" the velocity signal and applies the "squared" signal to a pair of CMOS logic gates 136 and 138 connected in parallel with each other; these gates effect a voltage shift of the signal to levels compatible with the counters, e.g., 0 to + or -5 v. Another inverting logic gate 140 inverts the signal. The signals illustrated in FIG. 3B are applied to the counters 152 and 154, as shown in FIG. 3 D, to count a signal indicative of the resonant, natural frequency for each half cycle of the dithering frequency f, whereby the Coriolis rate component is demodulated by inverting every other sample. As described in detail in U.S. Pat. No. 4,590,801, the acceleration is the sum of each such sample.

Referring now to FIG. 3C, there is shown an alternative of embodiment of the dither drive circuit 127', which provides a dither drive signal across the external connectors 86a and 86b to the effective portions 92a and b. As described above, a magnetic field is generated and directed by the magnet 20 and its flux path assembly 18 perpendicular to the surfaces of the substrate 16 and the effective portions 92a and b disposed thereon, whereby a force is generated by the current flowing through the effective portions 92a and b to move the accelerometers 32a and b in a substantially rectilinear, vibrating movement up and down along the dither axes 41 as shown in FIG. 2A. The accelerometers 32a and b vibrate or dither at the frequency f determined by the mechanical characteristic including the spring rates of the flexures 34, 36, 80 and 82 the mass of the accelerometers 32a and b. The dither drive signal outputted by the dither drive circuit 127' is of a frequency corresponding to the frequency f of dither vibration and, as explained above, is used in the further processing of the accelerometer outputs to demodulate those signals to provide a force signal F and a rotational signal n. Further, a wire (not shown) is disposed on the opposite side of the substrate 16 (from that shown in FIG. 2A) and forms first and second pick-off portions 92a' and 92b'. The innerconnection of the pick-off portions 92a' and 92b' deposited an the opposite side to ground is more clearly shown in FIG. 3C. As accelerometers 32a and b are vibrated, the pick-off portions 92a' and b' move through the magnetic field created by the unitary magnet 20 and its assembly 18, a current is induced therein and the resultant voltage is applied via resistors R11 and R12 to a pair of operational amplifiers 142 and 144 to be successively amplified with a relatively high gain, before being applied as the dither drive signal to the effective portions 92a and b. Zener diodes D4 and D5 serve to clamp the dither drive voltage as derived from the output of the operational amplifier 144 to a known voltage level.

The configuration of the accelerometers 32a and b within their silicon substrate 16 and the flux path assembly 16 and its unitary magnet 20 develop a considerable force in excess of that minimum turn-around acceleration required to effect the dither motions of accelerometers 32a and b. It is understood in the art that a minimum turn-around acceleration is needed to cause each of the accelerometers 32a and b to stop going in one direction and to accelerate in the opposite, whereby the dithering motion may occur. The acceleration force F tending to cause the dithering motion of accelerometers 32a and b is set out by the following equation:

where i is the current passing through the conductive path 92 making up the effective portions 92a and b, l is the effective length of that portion of the conductive path 92 within the magnetic flux passing through the accelerometers 32a and b, i.e., the length of the effective portions 92a and b, and B is the magnitude of the flux. In an illustrative embodiment of this invention, a current of 5 milliamp may be applied to each of the effective portions 92a and b, the effective portions 92a and b may have an effective length l of 6 mm and 8 kilogauss may be readily provided by the magnet 20 and its assembly 18. Solving equation (1) for mass m, where g is the universal gravity constant, it is shown that a force of 2.4 milligrams may be readily developed by this illustrative embodiment. In such an embodiment, the resonant frequency of the dithering motion imposed upon the accelerometers 32a and b is approximately 500 hz and a displacement D of accelerometers of 1 milliinch. The drive acceleration a may be calculated by the following: ##EQU1## where D is the displacement, f is the dither frequency and K is a conversion factor. The calculated force for 1 millinch of displacement D at 500 Hz is 25 g's peak acceleration. Where the mechanical gain of the spring mass system formed by accelerometers Q is set at a modest value of 1,000, the force developed by the interaction of a current passing through the conductive path 92 and the magnetic flux directed through the accelerometers 32, is 0.025 g's (25 g's/1,000). This force is sufficient to accelerate the calculated mass force of 0.024 grams. It is noted that the Q of pure crystals may be as high as 10,000, demonstrating that the dithering system described above is more than capable of developing sufficient force to effect the required dithering drive motion.

The following calculations demonstrate that the values of the voltage induced in the pick-off portions 92a' and 92b', is relatively high compared to the noise found in those operational amplifiers as would be incorporated into the drive circuit 127', as shown in FIG. 3C. Values of .epsilon. are provided by the following equation:

where v is the amplitude of the velocity output signal of the accelerometers 32, B is the strength of the magnetic field crossing the effective portions 92a and b, l is the effective length of the conductor within the magnetic flux field. For a dither displacement D of 1 milliinch, a natural frequency of accelerometer of 500 Hz, a velocity signal v of approximately 8 cm/sec., a length l of the effective portions 92a and b of 6 mm, and a flux strength of 8 kilogauss, the output of a single pick-off portion 92a' is 0.4 mv. If the outputs of accelerometers 32a and b are connected in series, the output voltage is doubled to 0.8 mv. An operational amplifier, as may be incorporated into the drive circuits of FIGS. 3A and C, typically has a noise of 0.1 .mu.v for a bandwidth of 10 K Hz. If the operational amplifier has a gain of 3.times.10.sup.3, its output may typically be 2.4 v peak, providing a noise to peak signal ratio of 0.01%, which is a good indicator that the sensor 10 of this invention is a good velocity sensor for the inherent of noise level found in the available operational amplifiers.

The accuracy with which the rate and acceleration sensor 10 may be made, the symmetry of the accelerometers 32a and b and their suspension by the flexures 34 and 36, and the interconnection of the link 72 to impose equal and opposite motions on the accelerometers 32a and b, have an accumulative effect to greatly simplify the processing of the accelerometer output signals, essentially reducing it to a cosine demodulation step. This can be done every half cycle, since neither sine nor double frequency sine demodulation is needed as was the case with the parallelogram structures of the prior art. Basically, the outputs of accelerometers 32a and b are subtracted from each other to provide the linear acceleration signal and to average both signals while inverting every other sample to demodulate for the cosines to produce a rate of rotation signal .omega.. Neither an alignment servo nor a phase servo is needed for such processing thus increasing the band width of the rotational. acceleration signal n to be 1 K Hz in one illustrative embodiment of this invention.

The rate and acceleration sensor 10 has a sensitivity to rotational acceleration imposed about its rate axis 39, i.e. the moment of each of accelerometers 32a and b about the rate axis 39, which acceleration sensitivity will introduce an undesired noise component in the subsequent demodulation processing of the accelerometer output signals. That noise component can be effectively eliminated by differentiating the rotation rate signal .omega. and scaling it. In effect, as indicated above, the demodulated outputs of accelerometers 32 are a measure of its rotation rate signal .omega., which can be differentiated to obtain an indication of the angular acceleration of each accelerometer 32. Since the dimensions and, in particular, the distance between the rate axis 39 and each of the centers 50a and b of gravity is known to a high degree of precision, e.g., 40 microinches, that equivalent radius of rotation is multiplied by a measured angular acceleration force to obtain an accurate indication thereof of the linear acceleration caused by the angular acceleration. The calculated acceleration moment is subtracted from the accelerometer outputs to reduce or substantially eliminate such acceleration sensitivity.

Referring now to FIG. 3D, there is shown how the output signals f1 and f2 as derived from the respective drive circuits 127a and c are processed and, in particular, are applied respectively to counters 152 and 154. As explained above, as the vibrating beams 54 and 56 are placed in tension or in compression due to accelerations being applied along the force sensing axes 38 of the respective accelerometers 32, the frequencies of the output signals f1 and f2 change. The dither drive circuit 127b may preferably take the form of that circuit shown in FIG. 3C or alternatively FIG. 3A. The drive circuits or signal generators 127a and c may illustratively take the form of that circuit shown in FIG. 3A.

The dither drive circuit 127b provides an output signal, which is applied to the gating circuit 133 as discussed above with regard to FIG. 3B. The output of the gating circuit 133 is a pair of squared gating signals which are applied to the counters 152 and 154. This pair of gating signals occur at the velocity zero-crossings to gate the counters 152 and 154. This is approximately a reading at 1 k Hz or both edges of the velocity zero-crossings. The counters 152 and 154 count the frequencies of the accelerometer output signals f1 and f2 with respect to a reference clock signal generated and applied by a reference clock 150 to each of the counters 152 and 154. In turn, a microprocessor reads the output of the counters 152 and 154 at an illustrative frequency of 1 k Hz and process these counts to provide an indication of .DELTA.v and .DELTA..theta..

As explained in detail in commonly assigned U.S. Pat. No. 4,786,861, .DELTA.v is provided by the following equation:

where v.sub.i is the "ith" sample of the velocity signal, A and F are scale factors, N1.sub.i is the count derived from the counter 152 over a 1 k Hz (1 m sec) period for the "ith" sample, N2.sub.i is the count obtained from the counter 154 for the "ith" sample, T is the time period and B is the bias correction term. As well known in the art, .DELTA..theta..sub.i is provided by the following equation:

where a is a scale factor and b is a bias/correction term, and

Angular acceleration a is equal to the linear acceleration as derived from the output of either of the accelerometers 32a or b, divided by the equivalent radius of rotation, r.sub.eq in accordance with the following equation: ##EQU2## In turn, angular acceleration .alpha. is a function of the measured rotation rate .omega. in accordance with the following equation: ##EQU3## In turn, the rotation rate may be expressed as follows: ##EQU4## Since the derivative of the rotation rate .omega. is equal to acceleration .alpha., acceleration may be expressed by the following equation: ##EQU5## Thus, correction for linear acceleration A.sub.linear is provided by the following equation: ##EQU6## In turn, the microprocessor 156 is programmed in a conventional fashion to subtract values of A.sub.linear correction from the accelerometer outputs f1 and f2 to correct for angular acceleration.

While the invention has been shown and described in detail, it is obvious that this invention is not to be considered as being limited to the exact form disclosed, and that changes in detail and construction may be made therein within the scope of the invention, without departing from the spirit thereof.