Inertial sensor and method

Abstract

An inertial sensor is disclosed that includes a central anchor, a proof mass, a flexure, and a plurality of electrodes surrounding the central anchor. The flexure has a shape that includes a first plurality of spiral arms each winding around the central anchor in a first orientation and a second plurality of spiral arms each winding around the central anchor in a second orientation, the second orientation being opposite to the first orientation. Each of the arms is connected between the central anchor and the proof mass. Advantageously, this configuration reduces energy lost through anchor losses and thermoelastic dissipation, resulting in a higher quality factor of the vibration mode.

Description

[Technical field]

[0001] The present invention relates to a gyro inertial sensor and a method of inertial sensing. [Background technology]

[0002] Inertial sensors are widely used in a variety of motion sensing applications, including but not limited to georeferencing, mapping and surveying, and stand-alone navigation systems for autonomous surface / subsurface navigation in high-end industrial, transportation, aerospace, and automotive applications.

[0003] Gyro inertial sensors are considered a subclass of inertial sensors that provide information about angular motion, such as rotation rate or angle. With the development of modern manufacturing methods, it is becoming increasingly common for these gyro inertial sensors to be MEMS-based. For example, MEMS-based gyro inertial sensors are described in US Pat. No. 7,637,156. These sensors, such as the sensor disclosed in US Pat. No. 7,637,156, typically include an axisymmetric structure coupled to a substrate at one or more anchor points by a flexure configuration, all arranged in a plane. A fully axisymmetric structure can have so-called degenerate vibration modes with matching natural frequencies, one designated as the drive mode and the other as the sense mode, in the embodiment of a Coriolis vibration gyroscope. In that case, electrodes are used to drive the ring portion in the drive vibration mode in the plane. When a rotation is applied to the sensor about an axis perpendicular to the plane, the Coriolis force couples energy to the sense vibration mode. Another set of electrodes is then used for capacitive sensing of the vibration response of the ring portion in the sense mode, allowing for detection and calculation of angular velocity or acceleration.

[0004] However, the described sensors suffer from energy losses due to several factors, including energy dissipation in the sensor flexures and substrate anchors. These energy losses result in lower quality factors for the vibrational modes of interest. High quality factors translate into superior sensor performance.

[0005] Furthermore, gyroscopic resonant sensors with high quality factor vibration modes can also be used for high-end resonant sensing and timing and frequency control applications.

[0006] It is therefore desirable to fabricate inertial sensors with flexure configurations that minimize energy dissipation and result in inertial sensors constructed from axisymmetric structures with degenerate or near degenerate vibration modes with high quality factors. Summary of the Invention

[0007] The invention is defined in the accompanying independent claims to which reference should now be made.

[0008] In a first aspect, the invention comprises an inertial sensor including a central anchor, a proof mass surrounding the central anchor, a flexure, and a plurality of electrodes. The flexure has a shape including a first set of spiral arms. The first set of spiral arms includes a first plurality of N spiral arms and a second plurality of N spiral arms, where N is an integer greater than 1. Each of the arms is connected between the central anchor and the proof mass and lies in a first plane. Each of the arms of the first plurality of N spiral arms wraps around the central anchor in a first orientation. Each of the arms of the second plurality of N spiral arms wraps around the central anchor in a second orientation. The second orientation is opposite to the first orientation. The plurality of electrodes includes at least one drive electrode for driving the proof mass in a first vibration mode and at least one sense electrode for sensing a response of the proof mass in a second vibration mode.

[0009] This arrangement of the first and second multiple spiral arms is advantageous because it contributes to minimizing anchor losses and results in an inertial sensor having a vibration mode with a high quality factor. As used herein, the term "spiral" means a shape produced by a point moving around a fixed point while continuously receding from or approaching the fixed point such that the distance from the fixed point to each and every point on the spiral is of a different length.

[0010] The flexure may be shaped such that the arms of the first plurality of N spiral arms are equally spaced at 360 / N degree intervals around the central anchor. The flexure may be shaped such that the arms of the second plurality of N spiral arms are equally spaced at 360 / N degree intervals around the central anchor. Either of these features are advantageous as they allow vibration modes with high quality factors to be generated.

[0011] The flexures may be shaped such that each arm in the first plurality of N spiral arms meets or intersects with every arm from the second plurality of N spiral arms at least once. This arrangement of the first and second plurality of spiral arms allows for a symmetric arrangement of the flexures supporting the outer mass, which provides the desired degenerate or near degenerate modes and provides robustness against both in-plane and out-of-plane shock and vibration.

[0012] The flexure may be formed from a single piece of material, such as single crystal silicon. A point where the first plurality of N spiral arms meets or intersects with an arm from the second plurality of N spiral arms may be in the first plane. Advantageously, any of these features may simplify the manufacture of the inertial sensor and / or ensure robustness of the flexure. The flexure may have a uniform thickness. The thickness is defined in a direction perpendicular to the first plane.

[0013] The flexures may exhibit N-fold rotational symmetry about an axis perpendicular to the first plane. Preferably, the central anchor, the flexures and the proof mass each exhibit N-fold rotational symmetry about an axis perpendicular to the first plane. Advantageously, this allows degenerate or near-degenerate vibration modes with high quality factors to be generated.

[0014] Each arm may have a first end connected to the central anchor and a second end connected to the proof mass, the first end connecting to the central anchor at a point on the central anchor furthest from the second end of the arm.

[0015] Each arm may have a first end connected directly to the central anchor. Advantageously, this feature may result in a higher quality factor of the vibration mode. Alternatively, each arm may have a first end connected to the central anchor via another component of the inertial sensor.

[0016] Each arm may have a second end connected directly to the proof mass. Alternatively, each arm may have a second end connected to the proof mass via another component of the inertial sensor. Advantageously, this may result in a higher quality factor of the vibration mode.

[0017] The bend may have a shape including a second spiral arm set concentrically nested around the first spiral arm set. The second spiral arm set advantageously includes a first plurality of N spiral arms and a second plurality of N spiral arms, each of the arms of the first plurality of N spiral arms winding around the central anchor in a first orientation and each of the arms of the second plurality of N spiral arms winding around the central anchor in a second orientation, the second orientation being opposite to the first orientation. The arms of the second spiral arm set may have a different curvature or shape to the arms of the first spiral arm set.

[0018] The bend may have a shape that includes further spiral arm sets, the spiral arm sets being concentrically nested one inside the other.

[0019] The bend may have a shape including multiple nested quatrefoils. Each quatrefoil may be rotated 45 degrees with respect to an adjacent quatrefoil. A quatrefoil is defined as the perimeter of four overlapping identical shapes. Thus, a quatrefoil includes four lobes and has four-fold rotational symmetry around the center of the quatrefoil. Examples of identical shapes may include, but are not limited to, circles, ellipses, Reuleaux triangles, and other Reuleaux polygons. A central anchor may be located at the center of the quatrefoil. The proof mass may surround all the quatrefoils. The proof mass may be connected to the quatrefoils at four points. Preferably, the proof mass is connected to the outermost quatrefoil. More preferably, the proof mass is connected to the outermost quatrefoil at the outermost points of each lobe of the outermost quatrefoil.

[0020] Preferably, the bent portion has a shape including four nested quatrefoils, each quatrefoil rotated 45 degrees relative to an adjacent quatrefoil. The bent portion may have a shape including a plurality of nested quatrefoils, each quatrefoil rotated 45 degrees relative to an adjacent quatrefoil as a result of the arrangement of the first plurality of N spiral arms and the second plurality of N spiral arms as described above.

[0021] The proof mass may be ring-shaped. The proof mass may have an inner diameter of between 0.1 millimeters and 10 millimeters. Preferably, the proof mass has an inner diameter of between 0.5 millimeters and 9 millimeters.

[0022] The proof mass may have an outer diameter of between 1 millimeter and 20 millimeters. Preferably, the proof mass has an outer diameter of between 1 millimeter and 10 millimeters.

[0023] The width of the proof mass may be measured from the inner diameter to the outer diameter. The width of the proof mass may be between 19 millimeters and 0.05 millimeters. The width of the proof mass may be between 10 millimeters and 0.1 millimeters. Preferably, the width of the proof mass is between 5 millimeters and 0.5 millimeters. More preferably, the width of the proof mass is between 4 millimeters and 1 millimeter. Even more preferably, the width of the proof mass is between 2.5 millimeters and 1 millimeter. Advantageously, these widths of the proof mass, and in particular the preferred widths of the proof mass, may achieve low thermoelastic dissipation and a high quality factor of the inertial sensor. This enables high mechanical sensitivity and excellent signal-to-noise ratio of the gyroscope.

[0024] The thickness of the proof mass may be greater than the thickness of the flexure. Advantageously, this improves the sensitivity and noise performance of the inertial sensor. The proof mass may have a thickness between 0.5 micrometers and 1000 micrometers. The flexure may have a thickness between 0.5 micrometers and 400 micrometers.

[0025] The proof mass may have a first mass. The flexure may have a second mass. The proof mass and the flexure may together have a total mass equal to the sum of the first mass and the second mass. The first mass may be between 50% and 99.9% of the total mass. The first mass may be between 75% and 99.5% of the total mass. Preferably, the first mass is between 90% and 99% of the total mass. More preferably, the first mass is between 95% and 99% of the total mass.

[0026] The proof mass may have a first volume. The flexure may have a second volume. The proof mass and the flexure may together have a total volume equal to the sum of the first volume and the second volume. The first volume may be 50% to 99.9% of the total volume. The first volume may be 75% to 99.5% of the total volume. Preferably, the first volume is 90% to 99% of the total volume. More preferably, the first volume is 95% to 99% of the total volume.

[0027] Advantageously, having the first mass be a significant percentage of the total mass or the first volume be a significant percentage of the total volume can result in an inertial sensor with low thermomechanical noise and can provide good tolerance to manufacturing tolerances, thus achieving low frequency division during fabrication between degenerate and near-degenerate vibration modes. This can make mode matching during device operation relatively easy. This allows for high mechanical sensitivity and excellent signal-to-noise ratio of the gyroscope.

[0028] The proof mass may have an aspect ratio of 1 to 20. The aspect ratio may be defined as the ratio of the width of the proof mass to the thickness of the proof mass. Preferably, the proof mass has an aspect ratio of 2 to 10. More preferably, the proof mass has an aspect ratio of 4 to 8. Advantageously, such an aspect ratio allows the first mass to be a significant fraction of the total mass, thereby resulting in an inertial sensor with a high quality factor, while also allowing the inertial sensor to maintain a relatively thin thickness.

[0029] Advantageously, these dimensions allow the inertial sensor to correspond to dimensions used in common MEMS manufacturing techniques, making it easy to manufacture.

[0030] The flexure may have a shape further including a plurality of N radial spokes, each of the radial spokes being connected to the proof mass. Advantageously, the plurality of N radial spokes contributes to minimizing anchor losses, resulting in an inertial sensor having a vibration mode with a high quality factor.

[0031] Each of the radial spokes may be connected to at least one arm from the first plurality of N spiral arms or the second plurality of N spiral arms. Preferably, each of the radial spokes is connected to at least one arm from the first plurality of N spiral arms and at least one arm from the second plurality of N spiral arms. The N radial spokes may be connected to the proof mass and spaced at 360 / N degree intervals around the central anchor. Each of the N radial spokes may be connected to an outermost quad-leaf. Preferably, each of the N radial spokes is connected to an outermost quad-leaf at the outermost point of each lobe of the outermost quad-leaf.

[0032] The width of each of the plurality of N radial spokes may be between 2 micrometers and 500 micrometers. Preferably, the width of each of the plurality of N radial spokes is between 2 micrometers and 500 micrometers. The width of each of the first plurality of N arms and the second plurality of N arms may be between 2 micrometers and 500 micrometers. Preferably, the width of each of the first plurality of N arms and the second plurality of N arms is between 5 micrometers and 200 micrometers. The width is defined in a direction parallel to the first plane. The plurality of N radial spokes contributes to minimizing anchor losses, resulting in an inertial sensor having a vibration mode with a high quality factor.

[0033] N may be an integer multiple of 4. Preferably, N is equal to 4.

[0034] Advantageously, the flexures and the proof mass may be integrally formed. Also advantageously, the flexures and the proof mass may be formed from a single piece of material. Either or both of these two features allow for simplified manufacturing, reduce the possibility of manufacturing defects, and minimize splitting of vibrational modes. Preferably, the material is silicon. Silicon may be selected for its ease of manufacturing and etching. If the starting substrate is a silicon-on-insulator (SOI) wafer, the material may also include a buried silicon dioxide layer integrated between two separate layers of single crystal silicon.

[0035] The plurality of electrodes may include at least one electrode disposed outside the proof mass. The plurality of electrodes may include X electrodes disposed outside the proof mass, where X is an integer multiple of 4. X may be equal to 24. In this regard, the exterior of the proof mass is defined by components located outside a region defined by an outer periphery of the proof mass when the inertial sensor is viewed perpendicular to the first plane.

[0036] A plurality of electrodes, including an integer multiple of four electrodes, arranged on the outside of the proof mass allows for independent driving of a first vibration mode and measurement of the response from a second vibration mode. Furthermore, a plurality of electrodes, including 24 electrodes, arranged on the outside of the proof mass allows for selective tuning of the frequency of one vibration mode relative to the other to match the frequencies of the two vibration modes. This is called mode matching. Mode matching increases the sensitivity of the inertial sensor.

[0037] The plurality of electrodes may include at least one electrode disposed inside the proof mass. The plurality of electrodes may include Y electrodes disposed inside the proof mass, where Y is an integer multiple of 4. Y may be equal to 12. In this regard, the interior of the proof mass is defined by components located within a region defined by an inner periphery of the proof mass when the inertial sensor is viewed perpendicular to the first plane. Advantageously, having at least one electrode disposed inside the proof mass in addition to electrodes on the exterior of the proof mass provides further tunability and increased transduction area of ​​the inertial sensor and may counter capacitive feedthrough effects.

[0038] The inertial sensor may be a Micro-Electro-Mechanical System or MEMS device. The inertial sensor may be a gyro sensor.

[0039] The first vibration mode and the second vibration mode may both be cos(nθ) modes, n being an integer equal to or greater than 1. Preferably, the first vibration mode and the second vibration mode are cos(3θ) modes. Advantageously, the cos(3θ) modes of the described inertial sensor exhibit a high quality factor.

[0040] In a second aspect, the invention is an inertial sensor comprising a central anchor, a proof mass surrounding the central anchor, and a flexure connected between the proof mass and the central anchor, the proof mass being suspended from the central anchor by the flexure, the flexure having a shape including a plurality of nested quatrefoils.

[0041] Each quatrefoil may be rotated 45 degrees relative to an adjacent quatrefoil. A quatrefoil is defined as the perimeter of four overlapping identical shapes. A quatrefoil also includes four lobes and has four-fold rotational symmetry around the center of the quatrefoil. Examples of identical shapes may include, but are not limited to, circles, ellipses, Reuleaux triangles, and other Reuleaux polygons. A central anchor may be located at the center of the quatrefoil. A proof mass may surround all the quatrefoils. The proof mass may be connected to the quatrefoils at four points. Preferably, the proof mass is connected to the outermost quatrefoil. More preferably, the proof mass is connected to the outermost quatrefoil at the outermost points of each lobe of the outermost quatrefoil.

[0042] Preferably, the bent portion has a shape including four nested quatrefoils, each quatrefoil rotated 45 degrees relative to an adjacent quatrefoil. The bent portion may have a shape including a plurality of nested quatrefoils, each quatrefoil rotated 45 degrees relative to an adjacent quatrefoil as a result of the arrangement of the first plurality of N spiral arms and the second plurality of N spiral arms as described above.

[0043] In a third aspect, the present invention comprises a navigation system including an inertial sensor as described in any embodiment according to the first or second aspect of the invention.

[0044] In a fourth aspect, the present invention includes a method of inertial sensing using an inertial sensor as described in any embodiment according to the first or second aspect of the present invention, the method comprising driving a proof mass in a first vibration mode using at least one drive electrode, sensing a response of the proof mass in a second vibration mode using at least one sense electrode, adjusting a frequency of the first vibration mode relative to the second vibration mode or adjusting a frequency of the second vibration mode relative to the first vibration mode to match a frequency of the first vibration mode and a frequency of the second vibration mode, and calculating a value of an input measurand based on the response of the proof mass in the second vibration mode.

[0045] The value of the input measurand may be calculated based on the difference between the resonant frequency of the first mode and the resonant frequency of the second mode. Advantageously, this allows for high dynamic range measurements and offers the potential for reducing the temperature dependence of the magnification.

[0046] Features described with reference to one aspect may also be applied to any other aspect of the invention.

[0047] The example will now be further explained with reference to the figures. [Brief description of the drawings]

[0048] [Figure 1] FIG. 2 shows a plan view of an inertial sensor according to a first embodiment of the first or second aspect of the present invention; [Diagram 2] FIG. 1 shows a perspective view of an inertial sensor according to a first embodiment of the first or second aspect of the present invention. [Diagram 3] FIG. 2 shows a plan view of an inertial sensor according to a first alternative embodiment of the first or second aspect of the present invention; [Figure 4] FIG. 2 shows a plan view of an inertial sensor according to a second alternative embodiment of the first or second aspect of the present invention; [Diagram 5] FIG. 2 shows a plan view of an inertial sensor according to a first embodiment of the first or second aspect of the invention, showing the electrode arrangement; [Figure 6a] 3 shows the degenerate vibration modes of a first embodiment of the first or second aspect of the present invention. [Figure 6b] 3 shows the degenerate vibration modes of a first embodiment of the first or second aspect of the present invention. [Figure 7a] The ring-down response of the degenerate vibration modes of 6a and 6b is shown. [Figure 7b] The ring-down response of the degenerate vibration modes of 6a and 6b is shown. [Figure 8] 4 shows an Allan variance plot of an inertial sensor according to the first or second embodiment of the first or second aspect of the present invention; [Figure 9]1 shows a first alternative vibration mode of a first embodiment of the first or second aspect of the present invention. [Figure 10] 1 shows a second alternative vibration mode of the first embodiment of the first or second aspect of the present invention. [Figure 11] FIG. 2 is a schematic diagram of a navigation system according to a third aspect of the invention, including an inertial sensor as described in any embodiment according to the first or second aspects of the invention. [Figure 12] 1 illustrates a first method of inertial sensing according to a fourth aspect of the invention using an inertial sensor as described in any embodiment according to the first or second aspects of the invention; [Figure 13] 4 illustrates a second method of inertial sensing according to a fourth aspect of the invention, using an inertial sensor as described in any embodiment according to the first or second aspects of the invention. [Figure 14] 1 illustrates a further method of inertial sensing according to a fourth aspect of the invention, using an inertial sensor as described in any embodiment according to the first or second aspect of the invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0049] 1 and 2 are schematic diagrams of a top view and a perspective view, respectively, of an inertial sensor 100 according to a particular embodiment of the present invention. The inertial sensor 100 includes a central anchor 130, a ring-shaped proof mass 110, and a flexure 120. The central anchor 130 is attached to a substrate (not shown). The flexure 120 is connected to both the central anchor and the proof mass. The flexure 120 further includes a first plurality of four spiral arms 121, a second plurality of four spiral arms 122, and four radial spokes 123. The first plurality of four spiral arms 121, the second plurality of four spiral arms 122, and the four radial spokes 123 all lie in a first plane, which is the plane of the paper in FIG. 1.

[0050] Each of the arms of the first plurality of four spiral arms 121 winds around the central anchor 130 in a first clockwise direction when viewed from the perspective of Figure 1. Each of the arms of the second plurality of four spiral arms 122 winds around the central anchor 130 in a second counterclockwise direction when viewed from the perspective of Figure 1. Thus, the second direction is opposite to the first direction.

[0051] Each of the arms from the first plurality of four spiral arms 121 and the second plurality of four spiral arms 122 is directly connected at a first end to a central anchor 130 .

[0052] Each of the arms of the first plurality of four spiral arms 121 and the second plurality of four spiral arms 122 is also indirectly connected at a second end to the proof mass 110. This indirect connection is via four radial spokes 123. Each of the four radial spokes 123 is directly connected to the proof mass 110, one arm from the first plurality of four spiral arms 121, and one arm from the second plurality of four spiral arms 122. The four radial spokes 123 are equally spaced at 90 degree intervals around the central anchor 130.

[0053] The connection point of each of the arms to the central anchor 130 is at a point on the central anchor 130 that is furthest from the second end of the arm in question. This may be described as the arm completing a 180 degree turn, as the length of each arm of both the first and second pluralities of four spiral arms 121, 122 describes a 180 degree arc about a point centered on the central anchor.

[0054] In this particular embodiment of the invention, the first plurality of four helical arms 121, the second plurality of four helical arms 122, and the four radial spokes 123 are integrally formed from a single piece of material. Because these components of the flexure all lie in a first plane, and the flexure has a constant thickness, the points where the arms from the first plurality of four helical arms 121 and the second plurality of four helical arms 122 meet or intersect also lie in the first plane. This may be referred to as the overlapping of the first plurality of four helical arms 121 and the second plurality of four helical arms 122.

[0055] In the embodiment of Figures 1 and 2, the proof mass is also integrally formed with the flexure. The proof mass and the flexure may be formed from silicon. The dimensions of the flexure and the proof mass are such that 90% or more of the combined mass of the flexure and the proof mass is contained in the proof mass.

[0056] An alternative way to describe the shape of the portion of the flexure 120 in Figures 1 and 2 is that it is a plurality of concentrically nested quatrefoils. The arms of the first plurality of four spiral arms 121 and the arms of the second plurality of four spiral arms 122 intersect such that the flexure comprises concentrically nested quatrefoils, with concentrically adjacent quatrefoils appearing to be rotated 45 degrees relative to each other. The contact or intersection points where the arms from the first plurality of four spiral arms 121 and the second plurality of four spiral arms 122 meet are the points where the concentrically adjacent quatrefoils meet. Those skilled in the art will appreciate that a similar flexure shape may be formed from a different integer number of concentrically nested quatrefoils and provide the same advantage of a high quality factor.

[0057] The nested quatrefoils need not be shaped to provide continuous spiral arms extending from one quatrefoil to the next, as shown in Figures 1 and 2. Instead, the quatrefoils may be shaped to produce a concentrically nested arrangement of spiral arm sets, with the spiral arms in each spiral arm set having a different shape or curvature than the spiral arms in an adjacent spiral arm set. Each spiral arm set includes a first plurality of N spiral arms and a second plurality of N spiral arms, where N is an integer greater than 1, and each of the arms of the first plurality of N spiral arms wraps around the central anchor in a first orientation, and each of the arms of the second plurality of N spiral arms wraps around the central anchor in a second orientation, the second orientation being opposite to the first orientation. Each spiral arm set may define a quatrefoil. Each spiral arm in each spiral arm set connects at least one end to two spiral arms in another spiral arm set.

[0058] 3 is a schematic diagram of a plan view of an inertial sensor 200 according to an alternative embodiment of the present invention. The inertial sensor 200 of this alternative embodiment also includes a central anchor 230, a ring-shaped proof mass 210, and a flexure 220. The proof mass 210 and the central anchor 230 are identical to those of the embodiment shown in Figures 1 and 2. The flexure 220 further includes a first plurality of four spiral arms 221, a second plurality of four spiral arms 222, and four radial spokes 223, similar to those of the embodiment shown in Figures 1 and 2.

[0059] The embodiment of Figure 3 differs from the embodiment shown in Figures 1 and 2 in the number of turns of each of the arms around the central anchor. In the embodiment shown in Figure 3, the length of each arm of both the first and second pluralities of four spiral arms 221, 222 describes a 270 degree arc about a point centered on the central anchor 230, such that each of the arms completes 270 degrees of turns.

[0060] The arms of the first plurality of four spiral arms 221 and the arms of the second plurality of four spiral arms 222 intersect such that the bends include five concentrically nested quatrefoils, with concentrically adjacent quatrefoils rotated 45 degrees relative to each other. As with the embodiment shown in Figures 1 and 2, the points where the arms from the first plurality of four spiral arms 221 and the second plurality of four spiral arms 222 meet or intersect are the points where concentrically adjacent quatrefoils meet.

[0061] 4 is a schematic diagram of a plan view of an inertial sensor 300 according to an alternative embodiment of the present invention. The inertial sensor 300 of this alternative embodiment also includes a central anchor 330, a ring-shaped proof mass 310, and a flexure 320. The proof mass 330 is identical to that of the embodiment shown in FIGS. 1, 2, and 3.

[0062] This embodiment differs from that shown in Figures 1 and 2 in that the embodiment shown in Figure 4 includes a bend 320 that further includes a first plurality of eight spiral arms 321, a second plurality of eight spiral arms 322, and eight radial spokes 323. The eight radial spokes 323 are equally spaced at 45 degree intervals around a central anchor 330. Additionally, the central anchor 330 has a different shape than that of the central anchors of the embodiments shown in Figures 1, 2, and 3 to accommodate the different number of arms.

[0063] In the embodiment shown in FIG. 4, the length of each arm of both the first and second pluralities of eight spiral arms 321, 322 describes a 90 degree arc about a point centered on the central anchor 330, so that each of the arms completes a 90 degree turn.

[0064] An alternative way to describe the shape of the bend 320 in FIG. 4 is that it comprises a plurality of similar concentrically nested shapes each containing eight lobes. Each of the concentrically nested shapes has eight-fold rotational symmetry. Each of the concentrically nested shapes containing eight lobes may be considered to be formed by the perimeter of two identical overlapping quatrefoil shapes offset by a 45 degree rotation from each other. The arms of the first plurality of eight spiral arms 321 and the arms of the second plurality of eight spiral arms 322 intersect such that the bend comprises four concentrically nested shapes containing eight lobes, with the concentrically adjacent shapes appearing to comprise eight lobes rotated 22.5 degrees relative to each other. The points where the arms from the first plurality of eight spiral arms 321 and the second plurality of eight spiral arms 322 meet or intersect are equivalent to the points where the concentrically adjacent shapes containing eight lobes meet.

[0065] 5 is a schematic diagram of an electrode arrangement of an inertial sensor 100 in accordance with a particular embodiment of the present invention. The arrangement of the proof mass 110, flexures 120, and central anchor 130 is identical to that shown in FIGS.

[0066] In this particular embodiment, the plurality of electrodes consists of a set of 12 electrodes 160 disposed inside the proof mass 110 and a set of 24 electrodes 150 disposed outside the proof mass 110. Each set of 12 electrodes and 24 electrodes is disposed in one of two concentric circles centered about the central anchor 130. The electrodes in each set are equally spaced around each of the circles. Each of the electrodes in the set of 12 electrodes 160 disposed inside the proof mass 110 are substantially identical to each other. Also, each of the electrodes in the set of 24 electrodes 150 disposed outside the proof mass 110 are substantially identical to each other.

[0067] Each electrode in the plurality of electrodes may be used to perform a function of the inertial sensor during use, including, but not limited to, driving the proof mass 110 in a first or second vibration mode, sensing a change in capacitance as the proof mass 110 vibrates in the first or second vibration mode, or applying a bias voltage to help match the resonant frequencies of the first and second vibration modes. The electrodes used to perform these functions may be referred to as drive electrodes, sense electrodes, and mode matching electrodes, respectively.

[0068] Each drive electrode is disposed adjacent to the proof mass 110. Each drive electrode is configured to generate an electrostatic force acting on the proof mass 110. Each sense electrode is disposed adjacent to the proof mass 110. Each sense electrode is configured to detect a variation in capacitance when the proof mass 110 vibrates in a vibration mode.

[0069] In use, a DC bias voltage is applied to the inertial sensor 100 such that the central anchor 130, the flexures 120, and the proof mass 110 are electrostatically biased. The DC bias voltage is applied to the inertial sensor at bias point 140. The DC bias voltage enables electrostatic actuation and capacitive sensing of both vibration modes using signals at the frequencies of both vibration modes. The method of operation of the inertial sensor 100 is explained in detail in Figures 12 and 13 and their respective descriptions.

[0070] 5, first drive electrode set 151 and first sense electrode set 153 are disposed adjacent antinodes of the drive mode of proof mass 110. Second drive electrode set 152 and second sense electrode set 154 are disposed adjacent antinodes of the sense mode of proof mass 110. However, the configuration of which electrodes perform which function may vary.

[0071] The embodiment of Figure 5 includes mode-matching electrodes 155. The mode-matching electrodes 155 may be located either outside or inside the proof mass 610, but in this particular embodiment shown in Figure 5, they are located outside the proof mass 610. Each mode-matching electrode 155 is disposed adjacent to the proof mass 110. Each mode-matching electrode 155 is configured to generate an electrostatic force acting on the proof mass 110 to locally adjust the stiffness of the proof mass 110.

[0072] 6a and 6b are COMSOL Multiphysics® simulations of two of the degenerate vibration modes that may be used to drive and sense the inertial sensor 100 during use. These two vibration modes may be referred to as cos3θ modes. During use, one of these degenerate vibration modes may be driven by a first set of drive electrodes 151, not shown in Figs. 6a and 6b. This first vibration mode is referred to as the drive mode as described above. As a result of the Coriolis forces generated by the angular velocity of the inertial sensor, energy is coupled into the other of the two degenerate vibration modes, which is then referred to as the sense mode as described above. An outline of the stationary inertial sensor 100 is also included for reference. It can be seen that significant local distortions of the proof mass 110 occur during vibration in these two modes. Furthermore, the simulation shows significant distortions of the four radial spokes 123. Advantageously, the distortions present in both the degenerate vibration modes at the central portion of the flexure 120, near the second end of the arm, and on the central anchor 130 are relatively low. This localized relatively low strain in both of the degenerate vibration modes reduces the energy loss due to anchor losses and increases the quality factor of these vibration modes. The actual strains experienced by an inertial sensor in use may be less than or greater than those represented in Figures 6a and 6b.

[0073] Figures 7a and 7b are data plots showing the ring-down response of the drive and sense vibration modes, respectively. The measured drive and sense vibration modes are the same as those shown in Figures 6a and 6b.

[0074] The output voltage 701 is directly proportional to the amplitude of vibration of the drive and sense vibration modes. The output voltage 701 is measured using a lock-in amplifier. The quality factors of the drive and sense vibration modes are calculated from the ring-down response using equation (1). Q = π × τ × f(1)

[0075] The decay time 720, τ, is the time it takes for the output voltage to decay to 1 / e of the output voltage 701 at time 710 when the output voltage equals zero. The frequency of the vibration modes is represented by f. Both the drive and sense vibration modes exhibit measured quality factors of over 1.1 million.

[0076] Figure 8 is an Allan variance plot showing the previously described data collected from the inertial sensor as in Figures 1, 2, and 5. The data is measured at zero input rotation about an axis perpendicular to the first plane. The ARW is shown to be 0.019° / √h and the BI is shown to be 0.88° / h.

[0077] Angular random walk (ARW) and bias instability (BI) are important metrics for evaluating and comparing the performance of gyro inertial sensors. Bias may be defined as the average over a specified time of the gyro output measured at specified operating conditions that are uncorrelated with the input rotation or acceleration. Bias is typically expressed in degrees per time (° / h). Bias instability may be defined as the random fluctuation of bias calculated over a specific finite sample time and average time interval. Bias instability is also typically expressed in degrees per time (° / h). Angular random walk may be defined as the accumulation of angular error with time due to white noise in the angular rate. Angular random walk is typically measured in degrees per square root of time (° / √h).

[0078] 9 and 10 are COMSOL Multiphysics® simulations of two alternative vibration modes of the inertial sensor of the aforementioned FIGS. 1, 2, and 5. FIG. 9 shows a vibration mode that may be referred to as the 560 KHz vibration mode. FIG. 10 shows a vibration mode that may be referred to as the primary wine-glass vibration mode, or alternatively as the cos(2θ) vibration mode. Both the 560 KHz vibration mode and the primary wine-glass vibration mode show lower strain relative to the strain of the proof mass 110 and the radial spokes 123 at the central portion of the flexure 120, near the second end of the arm, and at the central anchor 130. This is similarly advantageous to the vibration modes shown in FIGS. 6a and 6b. The effect of reduced strain close to the central anchor 130 results in reduced energy loss due to anchor losses, resulting in an increase in the quality factor of both vibration modes.

[0079] Since both the 560 KHz vibration mode and the first order wine-glass vibration mode have been shown to demonstrate high quality factors, inertial sensors utilized with either the 560 KHz vibration mode or the first order wine-glass vibration mode may be implemented in high end resonant sensor as well as timing and frequency control applications.

[0080] The aforementioned inertial sensors may be used in a navigation system. FIG. 11 is a schematic diagram of an exemplary navigation system 800 according to a third embodiment of the present invention, including three inertial sensors 801 according to the first or second embodiment of the present invention. The navigation system 800 further includes a navigation computer 802 including a memory. Signals from the three inertial sensors are input to the navigation computer. The navigation computer processes the signals from the three inertial sensors and calculates the acceleration, velocity and position of the navigation system 800 based on the signals. The navigation system may be used in autonomous surface or subsurface navigation, georeferencing, mapping and surveying, transportation, aerospace, and automotive applications.

[0081] 12 is a schematic diagram of a method of operation according to a fourth aspect of the invention of an inertial sensor according to the first or second aspect of the invention. The inertial sensor is first driven in a first vibration mode 901, called the drive mode. This is achieved by a combination of AC and DC voltages applied to a first set of drive electrodes relative to the proof mass.

[0082] The first set of sense electrodes senses a response of the proof mass to being driven in the drive mode. The first feedback loop 902 utilizes the first set of sense electrodes and the first set of drive electrodes. The first feedback loop 902 is configured to adjust a frequency, amplitude, phase, or other characteristic of the drive mode.

[0083] The variation in capacitance as the proof mass vibrates in the sense mode may be detected by a second set of sense electrodes 903. An amplitude of the sense mode vibration may then be calculated from the variation in capacitance as the proof mass vibrates in the sense mode. To accomplish this, the amplitude of the sense mode vibration may first have to be separated from the amplitude of the drive mode vibration. An angular rotation may then be calculated 904 from the amplitude of the sense mode vibration.

[0084] Mode matching 905 may be used to increase the sensitivity of the gyroscope. This process involves detecting the difference in frequency between the drive mode and the sense mode and applying a voltage to the mode matching electrodes. In use, when a voltage difference exists between the mode matching electrodes and the proof mass, an electrostatic force is generated. This allows the stiffness of the proof mass to be locally adjusted. Thus, the mode matching electrodes can be used to relatively adjust the frequencies of the drive mode and the sense mode of the inertial sensor to ensure that the frequencies of the drive mode and the sense mode are precisely matched.

[0085] This method of detecting angular rotation is called open-loop sensing.

[0086] 13 is a schematic diagram of an alternative method of operation of an inertial sensor according to the first or second aspects of the invention, according to a fourth aspect of the invention. Similar to open-loop sensing, the inertial sensor is first driven in a first vibration mode 901, a first feedback loop 902 is configured to adjust the frequency, amplitude, phase or other characteristic of the drive mode, and the variation in capacitance as the proof mass vibrates in the sense mode may be detected by a second set of sense electrodes 903. Furthermore, similar to the open-loop sense mode control, a process of mode matching 905 may be used.

[0087] The method of FIG. 13 differs from the method of FIG. 12 in that a second set of drive electrodes is used to generate electrostatic forces acting on the proof mass. A second feedback loop 906 utilizes a second set of sense electrodes, to which a second AC voltage is applied. These second AC voltages from the second set of drive electrodes exert forces on the proof mass, and are configured to reduce the amplitude of the sense mode response to zero using the second feedback loop 906. An angular rotation is then calculated in step 907. The amplitude of the second AC voltage required to reduce the amplitude of the sense mode vibration to zero is used to calculate the angular rotation experienced by the inertial sensor.

[0088] This method of detecting angular rotation is called closed loop sensing mode control or force-to-rebalance sense mode control.

[0089] 14 is a schematic diagram of a further alternative method of operation of an inertial sensor according to the first or second aspects of the invention, according to a fourth aspect of the invention. Similar to the open-loop and closed-loop sense mode control, the inertial sensor is initially driven in a first vibration mode 1001, and a first resonance tracking feedback loop 1002 is configured to adjust the amplitude, phase or other characteristics of the drive mode.

[0090] Similar to the operation of the drive mode of Figure 14, a second set of drive electrodes is used to generate an electrostatic force acting on the proof mass. A second feedback loop 1006 utilizes a second set of sense electrodes, and a second AC voltage is applied to the second set of drive electrodes. The second resonance tracking feedback loop 1006 is configured to adjust the amplitude, phase, or other characteristic of the sense mode 1003.

[0091] Additionally, a mode matching process 1005 may be used, as well as open-loop and closed-loop sense mode control.

[0092] The method of Figure 14 differs from the methods of Figures 12 and 13 in that the rotation is calculated 1007 based on the resonant frequencies of the first and second vibration modes, denoted as f1 and f2, respectively. To estimate the angular rotation rate, the difference in the resonant frequencies, denoted as f1-f2, is calculated.

Claims

1. The central anchor and a proof mass surrounding the central anchor; and A bend portion; A plurality of electrodes; Equipped with the bend has a shape including a first set of spiral arms; the first set of spiral arms includes a first plurality of N spiral arms and a second plurality of N spiral arms; N is an integer greater than 1, each of the arms is connected between the central anchor and the proof mass and lies in a first plane; each of the arms of the first plurality of N spiral arms winds around the central anchor in a first orientation; each of the arms of the second plurality of N spiral arms winds around the central anchor in a second orientation; the second orientation is opposite to the first orientation; The plurality of electrodes at least one drive electrode for driving the proof mass in a first vibration mode; at least one sense electrode for sensing a response of the proof mass in a second vibration mode; Including, Inertial sensors.

2. the arms of the first plurality of N spiral arms are equally spaced at 360 / N degree intervals around the central anchor; The inertial sensor according to claim 1 .

3. the arms of the second plurality of N spiral arms being equally spaced at 360 / N degree intervals around the central anchor; 3. The inertial sensor according to claim 1.

4. each of the arms in the first plurality of N spiral arms meets or intersects with every arm from the second plurality of N spiral arms at least once; The inertial sensor according to claim 1 .

5. the bent portion exhibits N-fold rotational symmetry about an axis perpendicular to the first plane; The inertial sensor according to claim 1 .

6. the central anchor, the flexures, and the proof mass each exhibit N-fold rotational symmetry about an axis perpendicular to the first plane; The inertial sensor according to claim 1 .

7. the bend has a shape including a plurality of nested quatrefoils, each quatrefoil rotated 45 degrees relative to an adjacent quatrefoil; The inertial sensor according to claim 1 .

8. the bend has a shape including a second spiral arm set concentrically nested around the first spiral arm set; the second set of spiral arms includes a first plurality of N spiral arms and a second plurality of N spiral arms; each of the arms of the first plurality of N spiral arms winds around the central anchor in a first orientation; each of the arms of the second plurality of N spiral arms winds around the central anchor in a second orientation; the second orientation is opposite to the first orientation; the arms of the second spiral arm set may have a different curvature or shape than the arms of the first spiral arm set; The inertial sensor according to claim 1 .

9. the bent portion has a shape including additional spiral arm sets, the spiral arm sets being concentrically nested within each other; The inertial sensor according to claim 8 .

10. Each arm is a first end connected to the central anchor; a second end connected to the proof mass; and and the first end connects to the central anchor at a point on the central anchor farthest from the second end of the arm. The inertial sensor according to claim 1 .

11. the proof mass is ring-shaped; The inertial sensor according to claim 1 .

12. the bent portion has a shape further including a plurality of N radial spokes, each of the radial spokes is connected to the proof mass; The inertial sensor according to claim 1 .

13. A navigation system including the inertial sensor of claim 1.

14. A method of inertial sensing using the inertial sensor of claim 1, comprising: driving the proof mass in a first mode using at least one drive electrode; sensing a response of the proof mass in a second mode using at least one sense electrode; adjusting the frequency of the first mode relative to the second mode or adjusting the frequency of the second mode relative to the first mode to match the frequency of the first mode and the frequency of the second mode; calculating a value of an input measurand based on the response of the proof mass in the second mode; A method of inertial sensing, comprising:

15. the value of the input measurand is calculated based on a difference between a resonant frequency of the first mode and a resonant frequency of the second mode.

15. The method of inertial sensing of claim 14.

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