A transducer having compensation for a deflection due to an applied stress. The transducer includes a support ring (32) having a proof mass (34) cantilevered on a pair of flexures (38) between the magnets (26,28) of a stator in which the transducer is mounted. deflection of the support ring due to an imbalanced applied force is compensated by either moving the pads (30) used to mount the support ring, moving the centroid of capacitance (42) of the proof mass, or by modifying the support ring to provide a pair of moment arms (152), each approach insuring that an axis of deflection (102,130) of the support ring is coaligned with the centroid of capacitance, thereby minimizing a bias error in the transducer output.
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7. A method for minimizing a bias error in an output signal of a transducer, where the transducer has a pick-off capacitance plate mounted on a cantilever arm extending from a support that is itself mounted as a cantilever from a plurality of spaced apart pads, said method comprising the steps of:
providing at least one slot that is integral to the support and which divides the support into a fixed portion mounted to the pads and a cantilevered portion attached to the cantilever arm, wherein said cantilevered portion deflects about a deflection axis when an imbalanced force is applied to the cantilevered portion of the support; and positioning said at least one slot so that the deflection axis is aligned with a centroid of capacitance of the pick-off capacitance plate, whereby the imbalanced force is prevented from displacing the centroid of capacitance, thereby minimizing the bias error that would otherwise be caused by such displacement.
12. A transducer comprising:
(a) a movable proof mass to which is applied a pick-off capacitance plate; (b) a support within which the proof mass is mounted, said support including a fixed portion and a cantilevered portion, said proof mass being attached by a compliant cantilever arm to a side of the support and thus movable in a generally transverse direction relative to a plane aligned with a surface of the support; (c) a stator assembly in which the fixed portion of the support is mounted, the cantilevered portion of the support deflecting around a deflection axis with respect to the stator assembly in response to an imbalanced force acting on the cantilevered portion of the support, where said imbalanced force has a component in the transverse direction, said deflection axis being disposed adjacent the cantilevered portion of the support; (d) means for detecting a change in the motion of the transducer along the transverse direction by sensing a displacement of the pick-off capacitance plate, including means for producing a restoring signal to eliminate the displacement and operative to produce an output signal that is a function of the restoring signal and thus indicative of the change in the motion; and (e) means for determining the position of the deflection axis about which the cantilevered portion of the support deflects under the applied unbalanced force, said deflection axis position determining means including an arcuate slot having first and second ends formed in the support for dividing the support into the fixed and cantilevered portions, whereby the deflection axis intersects said first and second ends.
1. A transducer comprising:
(a) a movable proof mass to which is applied a pick-off capacitance plate having a centroid of capacitance; (b) a support within which the proof mass is mounted, said support including a fixed portion and a cantilevered portion, said proof mass being attached by a compliant cantilever arm to the cantilevered portion of the support and thus movable in a generally transverse direction relative to a plane aligned with a surface of the support; (c) a stator assembly in which the fixed portion of the support is mounted, the cantilevered portion of the support deflecting around a deflection axis with respect to the stator assembly in response to an imbalanced force acting on the cantilevered portion of the support, where said imbalanced force has a component in the transverse direction; (d) means for detecting a change in the motion of the transducer along the transverse direction by sensing a displacement of the pick-off capacitance plate, including means for producing a restoring signal to eliminate the displacement and operative to produce an output signal that is a function of the restoring signal and thus indicative of the change in the motion; and (e) means for mechanically compensating for a deflection of the support caused by the imbalanced force, said means comprising slot means for dividing the support into the fixed portion and the cantilevered portion and operative to align the centroid of capacitance with the deflection axis about which the support deflects under the applied imbalanced force, whereby the centroid of capacitance is not displaced due to deflection of the cantilevered portion by the imbalanced force and bias shift in the output signal that would otherwise be caused by displacement of the pick-off capacitance plate is substantially prevented.
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The present invention generally pertains to a transducer for detecting acceleration, and more particularly, to a transducer wherein a proof mass is mounted in cantilever fashion to a supporting structure that is subject to an imbalanced applied force.
In certain transducers of the prior art, one side of a supporting annular ring is clamped in cantilever fashion between two opposed stators. A pair of flexures extend inwardly from the opposite side of the ring to support a is a result, the imbalanced force 44 does not cause the centroid of capacitance 42 to deflect from its normal position and torque coil 36 does not produce a restoring force. Thus, the output of the transducer is free of any bias signal error due to the deflection of support ring 32.
Turning now to FIGS. 6 and 7, a second embodiment of the present invention, generally represented by reference numeral 120, is shown wherein a deflecting force 132 is applied to support ring 32 at a point which is substantially closer to one edge of the cantilever arm than to its other edge, i.e., closer to one of flexures 38 than to the other. Absent any provision for compensating force 132, the prior art transducer shown in FIGS. 2 and 3 would produce a bias error signal as a result of the applied imbalanced force 132. To compensate for the "off centered" deflection of support ring 32 caused by force 132, the second embodiment of the subject invention 120 is provided a centroid of capacitance 128 which is shifted from the previous centroid of capacitance 42. The change in the disposition of the centroid of capacitance 128 results from provision of an asymmetrical distribution of the pick-off capacitance area. A relatively larger plated capacitance area 124 is disposed on a portion of proof mass 34 that is relatively farther away from the point at which force 132 is applied than is a second smaller pick-off capacitance area 122. The relative sizes and arrangement of pick-off capacitance areas 124 and 122 are selected so that the centroid of capacitance 128 is shifted onto an axis of deflection 130 associated with the deflection of support ring 32 caused by the applied force 132. Due to the coincidence of the centroid of capacitance 128 with the axis of deflection 130, the centroid of capacitance 128 is not displaced from its normally centered position between first and second stators 22 and 24 of support ring 32; therefore, an output signal from the transducer to which the second embodiment 120 is applied does not include a bias error. A mechanical effect similar in result can be obtained by making the support ring (on the side closes t closest to the load) stiffer by increasing its width or thickness or reducing its length, while using pick-off capacitance area 40 instead of areas 124 and 122.
A third embodiment of the subject invention is generally denoted by reference numeral 150 as shown in FIGS. 8 and 9. In this embodiment, moment arms 152 are provided on a support ring 54 154, and are defined by "L" shaped slots 156, which, in a first leg, extend radially outward from the internal circumference of support ring 154, and in a second leg, are aligned parallel with the circumference. Mounting pads 30 are applied to the extending ends of moment arms 152, generally lying on a line extending through the centroid of capacitance 42. Centered between moment arms 152 and disposed opposite flexures 38 are other mounting pads 30, as in the first embodiment. As shown in FIG. 9, provision of moment arms 152 shifts the axis of deflection 102 so that it is aligned with the centroid of capacitance 42. Again, a force 44 applied to support ring 154 causes it to deflect about axis 102, but dies not cause any displacement of the centroid of capacitance 42 from its normal position. As a result, the output from a transducer incorporating the third embodiment 150 does not include a bias error due to the applied imbalanced force 44.
Turning to FIGS. 12 and 13, a fourth embodiment of the present invention is generally denoted by reference numeral 160. A support ring 162 includes an arcuate slot 164 disposed adjacent flexures 38, centered in the radial extent of the ring, and terminating at each end approximately at axis 102. A pair of mounting pads 30 are disposed opposite flexures 38, on each side of ring 162. Additional pairs of narrow mounting pads 166 are provided on each side of support ring 162, spaced apart from mounting pads 30 approximately on one third of the circumference of the support ring. A force 44 applied to support ring 162 adjacent flexures 38 (i.e., on the portion radially inside slot 164) causes the support ring to deflect downwardly about axis 1023 102, but the centroid of capacitance does not deflect from its normal position. Slot 164 thus shifts the bending axis 102 into alignment with the centroid of capacitance 42.
Finally, a fifth embodiment is shown in FIGS. 14 and 15 and is identified by reference numeral 170. As clearly shown in FIG. 14, a proof mass 172 is trimmed to provide a flat side 174 opposite flexures 38. A support ring 176 is mounted with support pads 30, in a generally conventional manner. Pick-off capacitance area 178 is applied to the proof mass in a generally symmetrical pattern relative to the center of the torque coil 36, making the centroid of capacitance 42 coincident with the center of the torque coil, and with axis 102. A force 44 applied to deflect support ring 176 about axis 102 merely causes the torque coil to pivot about that axis, but does not deflect the centroid of capacitance.
Although it may appear that compensation for an applied imbalanced force 44 or 132, by appropriately shifting either the axis of deflection or the centroid of capacitance into alignment depends upon the magnitude of the applied force, it can be shown that this is not the case. Proof of the preceding premise is presented herein for a simplistic rectangular shaped support and proof mass assembly, as shown in FIGS. 10 and 11; however, the result applies equally well to a circular or more complex shaped support and proof mass assembly.
Referring now to FIGS. 10 and 11, two parallel supports 200, each of thickness "h" and width b/2 extend over a length L. Supports 200 are cantilevered from a supporting structure 202 at one end, and at their other end, are connected along a line from which a proof mass 205 204 is cantilevered by means of a flexure 206. A central point 208 (corresponding to a centroid of capacitance) is selected within the interior of proof mass 204 at a distance "a" from the outwardly extending ends of support arms 200, and a force "P" is applied, as shown by arrow 210, to deflect support arms 200 by a distance "δ" as shown at 212. The angle of deflection or slope is equal to "θ".
The standard equation for deflection of a rectangular beam having a modulus of elasticity, "E" is given as:
δ=4PL3 /Ebh3 =Kδ P.
The slope at the free end of arms 200 is:
θ=6PL2 /Ebh3 =Kθ P.
However, since a=δ/tanθ, for small angles where tan θ=θ (radians), a=δ/θ. Substituting from the previous equations,
a=Kδ P/Kθ P=Kδ /K74
a=Kδ P/Kθ P=Kδ /Kθ
Therefore, the position of point 208 described by the length "a" is the ratio of two constants which depend on invariant characteristics of a given support and proof mass assembly and which, for small angles, are not a function of the magnitude of the displacement. The position where the central point 208 crosses the no load position line is independent of the magnitude of the load P that is applied. Thus, it is always possible to align a centroid of capacitance with an axis of deflection regardless of the magnitude of the imbalanced force applied to the support ring (so long as the deflection of the support ring subscribes a small angle).
It will be apparent to one skilled in the art that the above proof holds true for beams of different cross-section and taper. Taking that a step further, it will be apparent that for small displacements of any linearly elastic structure, the displacement and the local slope are linear functions of load. Therefore, with an appropriate free proof mass structure, a point of zero relative translation can be found, because the distance to this point (similar to "a" in the equation above) is independent of the applied load. It will further be apparent that compensation for an applied force on the support ring 32 or 154 can be achieved by either moving the pads 30 as in the first embodiment 100, moving the centroid of capacitance 128 as in the second and fifth embodiment 120 and 170, or by modifying the support ring 154 as in the third and fourth embodiment 150 and 160, respectively.
Although the present invention has been disclosed with respect to several preferred embodiments modifications thereto will be apparent to those skilled in the art. Accordingly, it is not intended that the invention be limited by the disclosure or by such modifications, but instead that its scope should be determined entirely by reference to the claims which follow hereinbelow.
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| Nov 17 1993 | Sundstrand Corporation | AlliedSignal Inc | ASSIGNMENT OF ASSIGNORS INTEREST SEE DOCUMENT FOR DETAILS | 006796 | /0571 |
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