CA2427115C - Improved spring-based gravimeters and accelerometers - Google Patents
Improved spring-based gravimeters and accelerometers Download PDFInfo
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- CA2427115C CA2427115C CA 2427115 CA2427115A CA2427115C CA 2427115 C CA2427115 C CA 2427115C CA 2427115 CA2427115 CA 2427115 CA 2427115 A CA2427115 A CA 2427115A CA 2427115 C CA2427115 C CA 2427115C
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V7/00—Measuring gravitational fields or waves; Gravimetric prospecting or detecting
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- G01V7/04—Electric, photoelectric, or magnetic indicating or recording means
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Abstract
A spiral spring-supported proof mass for use in an accelerometer includes a plate of material having suitably high elasticity, low coefficient of thermal expansion, low magnetic susceptibility and high strength, for a proof mass. The plate has multiple spiral cuts. The spiral cuts are symmetrically disposed on a first circle of one radius and each of the spiral cuts terminate on a second, smaller circle concentric with the first circle.
Description
IMPROVED SPRING-BASED GRAVIMETERS AND ACCELEROMETERS
FIELD OF THE INVENTION
[0001] The present invention relates in general to accelerometers and more particularly to spring-based gravimeters or other accelerometers.
BACKGROUND OF THE INVENTION
FIELD OF THE INVENTION
[0001] The present invention relates in general to accelerometers and more particularly to spring-based gravimeters or other accelerometers.
BACKGROUND OF THE INVENTION
[0002] Accelerometers are instruments that measure acceleration along one or more axes.
Gravimeters are in a class of accelerometers that measure the acceleration due to the gravitational field of the earth, which, by definition, defines the vertical direction. Gravimeters measure the amplitude of this field from place to place on the earth, above the earth in aircraft or spacecraft, and below the earth's surface.
Gravimeters are in a class of accelerometers that measure the acceleration due to the gravitational field of the earth, which, by definition, defines the vertical direction. Gravimeters measure the amplitude of this field from place to place on the earth, above the earth in aircraft or spacecraft, and below the earth's surface.
[0003] There are two basic types of gravimeters, namely "absolute"
gravimeters, that measure the full amplitude of gravity, and "relative" gravimeters that measure only changes in gravity from an arbitrary base level. Gravity is usually measured in units of "Gals", after Galileo, where 1 Gal is 10-2m/s2. The Earth's gravitational acceleration is approximately 103 Gals, and is commonly denoted as "g".
gravimeters, that measure the full amplitude of gravity, and "relative" gravimeters that measure only changes in gravity from an arbitrary base level. Gravity is usually measured in units of "Gals", after Galileo, where 1 Gal is 10-2m/s2. The Earth's gravitational acceleration is approximately 103 Gals, and is commonly denoted as "g".
[0004] Relative gravimeters commonly measure changes in acceleration through changes in the extension of elastic springs which support a proof mass. Recent gravimeters are relatively light, consume little power, and are rugged enough to survive rough field USE:. As such these gravimeters are commonly used for large scale mapping of the Earth's gravitational field, on aircraft, on the ground, in vessels and in boreholes. The most sensitive of these relative gravimeters can achieve relative gravity sensitivities of the order of 1-2 Gal, i.e. 10-9 g.
[0005] Torge ("Gravimetry" Wolfgang Torge, Walter de Gruyter press, Berlin-New York, 1989, pages 232-236) describes the construction of several elastic spring-based relative gravimeters in some detail. These gravimeters typically have certain features in common (e.g.
Torge, Figure 6.38). They have a proof mass, fastened to one end of an arm.
The other end of this arm is attached to a horizontal bar that is hinged, to allow the beam and proof mass to rotate in the vertical plane. A helical elastic spring supports the bulk of the weight of the proof mass, so that the proof mass comes to rest at a horizontal, or reference level, for a specific value of gravity. Changes in gravity cause changes in the force on the proof mass (i.e. the "weight" of the proof mass), and the length of the spring changes accordingly, to adjust to the new weight. Thus, the position of the proof mass changes with changes in gravity.
Extremely small changes in the position of the proof mass are measured by such means as capacitative position sensors, to achieve sensitivities of the order of 1-2 .t Gal, as indicated above. Such sensitivities are, however, not readily achieved and demand very precise, delicate and laborious handworking of small parts. Unfortunately, as is unavoidable with manual work, variable performance may result, as well as an uncertain yield.
Typically, the most critical parts of the gravimeter, are the ultra-thin hinges and the fine helical springs.
Torge, Figure 6.38). They have a proof mass, fastened to one end of an arm.
The other end of this arm is attached to a horizontal bar that is hinged, to allow the beam and proof mass to rotate in the vertical plane. A helical elastic spring supports the bulk of the weight of the proof mass, so that the proof mass comes to rest at a horizontal, or reference level, for a specific value of gravity. Changes in gravity cause changes in the force on the proof mass (i.e. the "weight" of the proof mass), and the length of the spring changes accordingly, to adjust to the new weight. Thus, the position of the proof mass changes with changes in gravity.
Extremely small changes in the position of the proof mass are measured by such means as capacitative position sensors, to achieve sensitivities of the order of 1-2 .t Gal, as indicated above. Such sensitivities are, however, not readily achieved and demand very precise, delicate and laborious handworking of small parts. Unfortunately, as is unavoidable with manual work, variable performance may result, as well as an uncertain yield.
Typically, the most critical parts of the gravimeter, are the ultra-thin hinges and the fine helical springs.
[0006] While these parts can be made of carefully selected metals, ultra-pure fused quartz has become a favoured basic material because of the favourable properties of quartz, including very high elasticity, low coefficient of thermal expansion, negligible magnetic susceptibility, and high strength in fine filament form. When these parts are formed by hand drawing from a silica melt, however, precise replication is very difficult to achieve. Invar is another example of a material that has many favourable properties.
[0007] It is therefore an object of an aspect of the present invention to obviate or mitigate at least some of the disadvantages of the prior art.
SUMMARY OF THE INVENTION
SUMMARY OF THE INVENTION
[0008] In one aspect of the present invention, there is provided a gravimeter comprising:
a proof mass formed from a plate of fused quartz, having multiple spiral cuts therein, each of said spiral cuts commencing and being symmetrically disposed on a first circle of one radius and each of said spiral cuts terminating on a smaller, second circle concentric with the first circle;
two metallic plates disposed in a fixed position in close proximity to said proof mass, on each side of said proof mass such that said proof mass is disposed between the two metal plates;
electronic means for measuring and comparing capacitances between the proof mass and each of the metallic plates;
electronic means for producing a direct current (DC) signal proportional to a difference between the capacitances; and electronic means for applying said DC signal between said two metallic plates as an electrostatic force to restore the proof mass to a position of balanced capacitance.
[0009-14] In yet another aspect of the present invention, there is provided a method of fabricating a gravimeter comprising:
fabricating a proof mass and supporting spiral springs from a single plate of fused quartz by creating multiple spiral cuts in the plate under computer control, each of said spiral cuts commencing and being symmetrically disposed on a first circle of one radius and terminating on a smaller, second circle concentric with the first circle;
positioning two metallic plates in a fixed position in close proximity to said proof mass, on each side of said proof mass such that said proof mass is disposed between the two metal plates;
measuring and comparing capacitances between the proof mass and each of the metallic plates;
producing a DC signal proportional to a difference between the capacitances;
and applying said DC signal between the two metallic plates, as an electrostatic force to restore the proof mass to a position of balanced capacitance.
[0015]
Advantageously, imprecise hand forming is no longer necessary and replication and performance to specific requirements is possible. The degree of precision achievable with computer-based micromachining permits the miniaturization of the accelerometer, while maintaining high performance specifications. Also, the cost of manufacture of elastic spring based accelerometers is reduced.
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] The invention will be better understood with reference to the following description and the figures, in which:
[0017] Figure 1 is a plan view of a thin plate of material machined to form a gravimeter component, according to an aspect of the present invention;
[0018] Figure 2 is a sectional view of the plate of material of Figure 1, incorporated with a supporting spring and a capacitative position sensor, for use in a relative gravimeter; and [0019] Figure 3 is a block diagram showing a D.C. circuit for the relative gravimeter including the thin plate of Figure 2.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0020] For ease of illustration and for the purpose of simplicity only, the present discussion is directed to improvements in the design of gravimeters. It will be understood that the present invention is not limited to gravimeters, however, as the present invention is also applicable to other types of spring-based accelerometers.
[0021] Referring first to Figure 1, there is shown a thin plate of material from which a gravimeter component is constructed, indicated generally by the numeral 10.
The thin plate 10 is of a suitable material such as ultra-pure fused silica or an invar-like iron alloy. The plate 10 is machined using a suitable computer-controlled method such as laser machining or powder blasting, etc., to create a series of spiral cuts 12 (e.g. 3 in the present exemplary embodiment), 13, and 14. Each of the spiral cuts 12, 13, and 14 commences and is symmetrically disposed on the circumference of a first circle 15, with radius rl, and spirals inwardly to end on the circumference of a second circle 16, of radius r2. Clearly the second circle 16 is concentric with the first circle 15. The uncut central section forms a proof mass 17 of the gravimeter sensor.
The three spiral rings 18, 19, and 20, formed by the spiral cuts 12, 13, 14, are used in place of the spring and hinges of the conventional gravimeter. It will be appreciated that the thickness of each spiral spring is determined by the pitch (p= dr/d0) of the spiral, the number (n) of the spiral rings, the radius rl, and the thickness of material removed by the cutting process.
[0022] The effective sensitivity S of a gravity sensor is determined by the vertical displacement (dz) of the proof mass for a specific change of gravity (dg). In the unified component of the present embodiment of the invention, dz is the change in displacement of the proof mass 17 out of the plane of the plate 10, when the plane of the plate 10 is maintained horizontal. It can be shown that this sensitivity S=dz/dg varies directly as mrnA/133, where r is the mean of the radii r1 and r2, A is the total area of the first circle 15 containing the spiral rings 18, 19, 20, and m is the mass of the proof mass 17. It is possible to increase the mass (m) of the proof mass 17, for example by depositing a gold coating thereon, or to decrease m by etching, to achieve a desired mass and thereby achieve a desired sensitivity.
Similarly, it is possible to adjust the parameters n, r, A and 0, to achieve a desired sensitivity.
[0023] Figure 2 is a sectional view of the plate of material of Figure 1 incorporating a spring 22 and a capacitive position sensor for use in a relative gravimeter. The proof mass 17 and spiral rings 18, 19, 20 are used in place of the typical proof mass, support beam and hinges of conventional relative gravimeters. As shown in Figure 2, the plate 10 is rigidly fastened between two plates 21, with insulating spacers 23 between each of the plates 21 and 10. The spring 22 is an elastic spiral spring 22 and has a top end suspended from a rigid arm 24. The elastic spiral spring 22 supports the proof mass 17 in such a manner that the proof mass 17 is normally substantially coplanar with the plate 10 in the earth's gravity field. Changes in gravity cause the proof mass 17 to move up or down from the coplanar position.
[0024] Each of the proof mass 17 and the two plates 21 are either metallic or alternatively, are coated with a thin film of metal so that they are conductive. The three plates 10, 21 form a dual capacitor system, the capacitances of which are compared in a capacitance bridge. Any imbalance in this bridge is used to determine the displacement of the proof mass 17, which is used to determine the change in gravity causing the imbalance. The imbalance signal is then rectified and applied between the outer two plates 21, as a feedback to restore the proof mass 17 to the normal position, coplanar with the plate 10. Thus, detection of change in position of the proof mass 17 is accomplished and the feed-back restores the proof mass 17 to a standard position.
[0025] Figure 3 is a block diagram of a gravimeter, including the proof mass 17 between the two plates 21. The gravitational force on the proof mass 17 is balanced by the spring 22 and electrostatic restoring force. An AC signal is applied through a ratio transformer to the top and bottom plates 21 of the gravity sensor. The position of the proof mass 17, which is sensed by a capacitative displacement transducer bridge, is altered by a change in gravitational force. When the position of the proof mass 17 changes as a result of a change in the gravitational force, an AC signal appears from the transducer, which is amplified in an amplifier 100 and rectified in a phase sensitive detector (PSD) 102. The output of the PSD is a DC signal that is integrated in an integrator 104 and amplified in a second amplifier 106 prior to returning as a feedback voltage (+Vfb) to the top plate 21, to close the loop. The same voltage is inverted in an inverter 108 and applied to the bottom plate 21 as (-Vfb) negative feedback voltage.
This automatic feedback circuit applies DC voltage to the capacitor plates 21, producing an electrostatic force on the proof mass 17 that brings the proof mass 17 back to a null position.
The feedback voltage, which is a measure of the relative value of gravity at the reading site, is converted to a digital signal for further processing.
[0026] It will be understood that the present invention has been described by way of example and modifications and variations to the embodiment described herein may occur to those skilled in the art. For example, the present invention is not limited to gravimeters and can be used in accelerometers also. The present invention extends to accelerometers employing metal components or fused silica components. Other embodiments may also be possible. All such modifications and variations are believed to be within the sphere and scope of the present invention.
a proof mass formed from a plate of fused quartz, having multiple spiral cuts therein, each of said spiral cuts commencing and being symmetrically disposed on a first circle of one radius and each of said spiral cuts terminating on a smaller, second circle concentric with the first circle;
two metallic plates disposed in a fixed position in close proximity to said proof mass, on each side of said proof mass such that said proof mass is disposed between the two metal plates;
electronic means for measuring and comparing capacitances between the proof mass and each of the metallic plates;
electronic means for producing a direct current (DC) signal proportional to a difference between the capacitances; and electronic means for applying said DC signal between said two metallic plates as an electrostatic force to restore the proof mass to a position of balanced capacitance.
[0009-14] In yet another aspect of the present invention, there is provided a method of fabricating a gravimeter comprising:
fabricating a proof mass and supporting spiral springs from a single plate of fused quartz by creating multiple spiral cuts in the plate under computer control, each of said spiral cuts commencing and being symmetrically disposed on a first circle of one radius and terminating on a smaller, second circle concentric with the first circle;
positioning two metallic plates in a fixed position in close proximity to said proof mass, on each side of said proof mass such that said proof mass is disposed between the two metal plates;
measuring and comparing capacitances between the proof mass and each of the metallic plates;
producing a DC signal proportional to a difference between the capacitances;
and applying said DC signal between the two metallic plates, as an electrostatic force to restore the proof mass to a position of balanced capacitance.
[0015]
Advantageously, imprecise hand forming is no longer necessary and replication and performance to specific requirements is possible. The degree of precision achievable with computer-based micromachining permits the miniaturization of the accelerometer, while maintaining high performance specifications. Also, the cost of manufacture of elastic spring based accelerometers is reduced.
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] The invention will be better understood with reference to the following description and the figures, in which:
[0017] Figure 1 is a plan view of a thin plate of material machined to form a gravimeter component, according to an aspect of the present invention;
[0018] Figure 2 is a sectional view of the plate of material of Figure 1, incorporated with a supporting spring and a capacitative position sensor, for use in a relative gravimeter; and [0019] Figure 3 is a block diagram showing a D.C. circuit for the relative gravimeter including the thin plate of Figure 2.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0020] For ease of illustration and for the purpose of simplicity only, the present discussion is directed to improvements in the design of gravimeters. It will be understood that the present invention is not limited to gravimeters, however, as the present invention is also applicable to other types of spring-based accelerometers.
[0021] Referring first to Figure 1, there is shown a thin plate of material from which a gravimeter component is constructed, indicated generally by the numeral 10.
The thin plate 10 is of a suitable material such as ultra-pure fused silica or an invar-like iron alloy. The plate 10 is machined using a suitable computer-controlled method such as laser machining or powder blasting, etc., to create a series of spiral cuts 12 (e.g. 3 in the present exemplary embodiment), 13, and 14. Each of the spiral cuts 12, 13, and 14 commences and is symmetrically disposed on the circumference of a first circle 15, with radius rl, and spirals inwardly to end on the circumference of a second circle 16, of radius r2. Clearly the second circle 16 is concentric with the first circle 15. The uncut central section forms a proof mass 17 of the gravimeter sensor.
The three spiral rings 18, 19, and 20, formed by the spiral cuts 12, 13, 14, are used in place of the spring and hinges of the conventional gravimeter. It will be appreciated that the thickness of each spiral spring is determined by the pitch (p= dr/d0) of the spiral, the number (n) of the spiral rings, the radius rl, and the thickness of material removed by the cutting process.
[0022] The effective sensitivity S of a gravity sensor is determined by the vertical displacement (dz) of the proof mass for a specific change of gravity (dg). In the unified component of the present embodiment of the invention, dz is the change in displacement of the proof mass 17 out of the plane of the plate 10, when the plane of the plate 10 is maintained horizontal. It can be shown that this sensitivity S=dz/dg varies directly as mrnA/133, where r is the mean of the radii r1 and r2, A is the total area of the first circle 15 containing the spiral rings 18, 19, 20, and m is the mass of the proof mass 17. It is possible to increase the mass (m) of the proof mass 17, for example by depositing a gold coating thereon, or to decrease m by etching, to achieve a desired mass and thereby achieve a desired sensitivity.
Similarly, it is possible to adjust the parameters n, r, A and 0, to achieve a desired sensitivity.
[0023] Figure 2 is a sectional view of the plate of material of Figure 1 incorporating a spring 22 and a capacitive position sensor for use in a relative gravimeter. The proof mass 17 and spiral rings 18, 19, 20 are used in place of the typical proof mass, support beam and hinges of conventional relative gravimeters. As shown in Figure 2, the plate 10 is rigidly fastened between two plates 21, with insulating spacers 23 between each of the plates 21 and 10. The spring 22 is an elastic spiral spring 22 and has a top end suspended from a rigid arm 24. The elastic spiral spring 22 supports the proof mass 17 in such a manner that the proof mass 17 is normally substantially coplanar with the plate 10 in the earth's gravity field. Changes in gravity cause the proof mass 17 to move up or down from the coplanar position.
[0024] Each of the proof mass 17 and the two plates 21 are either metallic or alternatively, are coated with a thin film of metal so that they are conductive. The three plates 10, 21 form a dual capacitor system, the capacitances of which are compared in a capacitance bridge. Any imbalance in this bridge is used to determine the displacement of the proof mass 17, which is used to determine the change in gravity causing the imbalance. The imbalance signal is then rectified and applied between the outer two plates 21, as a feedback to restore the proof mass 17 to the normal position, coplanar with the plate 10. Thus, detection of change in position of the proof mass 17 is accomplished and the feed-back restores the proof mass 17 to a standard position.
[0025] Figure 3 is a block diagram of a gravimeter, including the proof mass 17 between the two plates 21. The gravitational force on the proof mass 17 is balanced by the spring 22 and electrostatic restoring force. An AC signal is applied through a ratio transformer to the top and bottom plates 21 of the gravity sensor. The position of the proof mass 17, which is sensed by a capacitative displacement transducer bridge, is altered by a change in gravitational force. When the position of the proof mass 17 changes as a result of a change in the gravitational force, an AC signal appears from the transducer, which is amplified in an amplifier 100 and rectified in a phase sensitive detector (PSD) 102. The output of the PSD is a DC signal that is integrated in an integrator 104 and amplified in a second amplifier 106 prior to returning as a feedback voltage (+Vfb) to the top plate 21, to close the loop. The same voltage is inverted in an inverter 108 and applied to the bottom plate 21 as (-Vfb) negative feedback voltage.
This automatic feedback circuit applies DC voltage to the capacitor plates 21, producing an electrostatic force on the proof mass 17 that brings the proof mass 17 back to a null position.
The feedback voltage, which is a measure of the relative value of gravity at the reading site, is converted to a digital signal for further processing.
[0026] It will be understood that the present invention has been described by way of example and modifications and variations to the embodiment described herein may occur to those skilled in the art. For example, the present invention is not limited to gravimeters and can be used in accelerometers also. The present invention extends to accelerometers employing metal components or fused silica components. Other embodiments may also be possible. All such modifications and variations are believed to be within the sphere and scope of the present invention.
Claims (4)
1. A gravimeter comprising:
a proof mass formed from a plate of fused quartz, having multiple spiral cuts therein, each of said spiral cuts commencing and being symmetrically disposed on a first circle of one radius and each of said spiral cuts terminating on a smaller, second circle concentric with the first circle;
two metallic plates disposed in a fixed position in close proximity to said proof mass, on each side of said proof mass such that said proof mass is disposed between the two metal plates;
electronic means for measuring and comparing capacitances between the proof mass and each of the metallic plates;
electronic means for producing a direct current (DC) signal proportional to a difference between the capacitances; and electronic means for applying said DC signal between said two metallic plates as an electrostatic force to restore the proof mass to a position of balanced capacitance.
a proof mass formed from a plate of fused quartz, having multiple spiral cuts therein, each of said spiral cuts commencing and being symmetrically disposed on a first circle of one radius and each of said spiral cuts terminating on a smaller, second circle concentric with the first circle;
two metallic plates disposed in a fixed position in close proximity to said proof mass, on each side of said proof mass such that said proof mass is disposed between the two metal plates;
electronic means for measuring and comparing capacitances between the proof mass and each of the metallic plates;
electronic means for producing a direct current (DC) signal proportional to a difference between the capacitances; and electronic means for applying said DC signal between said two metallic plates as an electrostatic force to restore the proof mass to a position of balanced capacitance.
2. A gravimeter as in Claim 1 wherein said fused quartz plate has gold or other inert metal deposited thereon.
3. A gravimeter as in Claim 1 or 2, further comprising a main spiral spring formed from fused quartz, one end of said main spring being attached to the centre of said proof mass and the other end of said main spring being attached to a rigid arm, thereby to support said proof mass in such a manner that said proof mass is normally substantially coplanar with said plate of fused quartz, in the earth's gravitational field.
4. A method of fabricating a gravimeter comprising:
fabricating a proof mass and supporting spiral springs from a single plate of fused quartz by creating multiple spiral cuts in the plate under computer control, each of said spiral cuts commencing and being symmetrically disposed on a first circle of one radius and terminating on a smaller, second circle concentric with the first circle;
positioning two metallic plates in a fixed position in close proximity to said proof mass, on each side of said proof mass such that said proof mass is disposed between the two metal plates;
measuring and comparing capacitances between the proof mass and each of the metallic plates;
producing a DC signal proportional to a difference between the capacitances;
and applying said DC signal between the two metallic plates, as an electrostatic force to restore the proof mass to a position of balanced capacitance.
fabricating a proof mass and supporting spiral springs from a single plate of fused quartz by creating multiple spiral cuts in the plate under computer control, each of said spiral cuts commencing and being symmetrically disposed on a first circle of one radius and terminating on a smaller, second circle concentric with the first circle;
positioning two metallic plates in a fixed position in close proximity to said proof mass, on each side of said proof mass such that said proof mass is disposed between the two metal plates;
measuring and comparing capacitances between the proof mass and each of the metallic plates;
producing a DC signal proportional to a difference between the capacitances;
and applying said DC signal between the two metallic plates, as an electrostatic force to restore the proof mass to a position of balanced capacitance.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA 2427115 CA2427115C (en) | 2003-04-28 | 2003-04-28 | Improved spring-based gravimeters and accelerometers |
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| Application Number | Priority Date | Filing Date | Title |
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| CA 2427115 CA2427115C (en) | 2003-04-28 | 2003-04-28 | Improved spring-based gravimeters and accelerometers |
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| CA2427115A1 CA2427115A1 (en) | 2004-10-28 |
| CA2427115C true CA2427115C (en) | 2013-12-10 |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP1949142B1 (en) * | 2006-11-23 | 2015-05-13 | Technological Resources PTY. Limited | Gravity gradiometer |
| US8650950B2 (en) | 2008-09-25 | 2014-02-18 | Technological Resources Pty, Ltd. | Detector for detecting a gravity gradient |
| CA2729571C (en) | 2008-09-25 | 2017-05-09 | Technological Resources Pty Ltd | A gravity gradiometer |
| CN111830588B (en) * | 2020-06-29 | 2022-10-28 | 中国船舶重工集团公司第七0七研究所 | Centering mechanism, centering installation method and maintaining method of zero-length spring type gravimeter |
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