Resonantly vibrating accelerometer driven in multiple vibrational modes
An inventive accelerometer includes a proof mass and a pair of vibrating sensors. An excitation-and-detection circuit drives one sensor at resonant frequencies f 1 and F 1 , with f 1 ≠F 1 ; a second excitation-and-detection circuit drives the other sensor at resonant frequencies f 2 and F 2 , with f 2 ≠F 2 . The vibrational modes driven at the frequencies f 1 and f 2 are the same for each sensor; the vibrational modes driven at the frequencies F 1 and F 2 are the same for each sensor. Compressive or tensile loads oppositely applied by the proof mass to the vibrating sensors cause a difference frequency ΔF=F 1 −F 2 to vary monotonically with acceleration of the apparatus along a sensing axis, from which a measurement of acceleration can be generated.
1. An apparatus comprising:
(a) substantially identical first and second vibrating sensors, each vibrating sensor exhibiting a corresponding fundamental vibrational mode and a set of higher-order vibrational modes corresponding to that fundamental vibrational mode, each fundamental and higher-order vibrational mode of each vibrating sensor being characterized by a corresponding fundamental or higher-order resonant mode frequency;
(b) a first excitation-and-detection circuit structured and connected so as to (i) drive the first vibrating sensor at a selected resonant mode frequency f 1 of a first one of the corresponding fundamental or higher-order modes thereof, (ii) drive the second vibrating sensor at a selected resonant mode frequency f 2 of a first one of the corresponding fundamental or higher-order modes thereof that corresponds to the selected resonant mode frequency of the first vibrating sensor, and
(iii) produce an output signal indicative of a difference frequency Δf=f 1 −f 2 ;
(c) a second excitation-and-detection circuit structured and connected so as to (i) drive the first vibrating sensor at an additional selected resonant mode frequency F 1 of a second one of the corresponding fundamental or higher-order modes thereof, with F 1 ≠f 1 , (ii) drive the second vibrating sensor at an additional selected resonant mode frequency F 2 of a second one of the corresponding fundamental or higher-order modes thereof that corresponds to the additional selected resonant mode frequency of the first vibrating sensor, with F 2 ≠f 2 , and (iii) produce a second output signal indicative of a difference frequency ΔF=F 1 −F 2 ;
(d) a proof mass connected to the first and second vibrating sensors so that (i) acceleration of the apparatus in a first direction along a sensing axis causes the proof mass to apply a tensile load to the first vibrating sensor and a compressive load to the second vibrating sensor, (ii) acceleration of the apparatus in a second direction along the sensing axis, opposite the first direction, causes the proof mass to apply a compressive load to the first vibrating sensor and a tensile load to the second vibrating sensor, (iii) the corresponding tensile or compressive loads applied by the proof mass to the first and second vibrating sensors cause the difference frequency Δf=f 1 −f 2 to vary monotonically with acceleration of the apparatus along the sensing axis, and (iv) the corresponding tensile or compressive loads applied by the proof mass to the first and second vibrating sensors cause the difference frequency ΔF=F 1 −F 2 to vary monotonically with acceleration of the apparatus along the sensing axis.
2. The apparatus of claim 1 wherein, over an operational range of accelerations along the sensing axis, the difference frequency ΔF=F 1 −F 2 varies substantially linearly with acceleration of the apparatus along the sensing axis.
3. The apparatus of claim 1 wherein, at zero acceleration along the sensing axis, the difference frequency ΔF=F 1 −F 2 is non-zero.
4. The apparatus of claim 1 wherein, over an operational range of acceleration along the sensing axis, the difference frequency ΔF=F 1 −F 2 does not change sign.
5. The apparatus of claim 1 wherein: (i) the resonant mode frequencies f 1 and f 2 correspond to the fundamental vibrational modes of the first and second vibrating sensors, respectively; and (ii) the resonant mode frequencies F 1 and F 2 correspond to one of the higher-order vibrational modes of the first and second vibrating sensors, respectively.
6. The apparatus of claim 5 wherein the resonant mode frequencies F 1 and F 2 correspond to the third higher-order vibrational modes of the first and second vibrating sensors, respectively.
7. The apparatus of claim 1 wherein the first vibrating sensor is coupled to the second excitation-and-detection circuit in a corresponding phase-locked-loop arrangement, and the second vibrating sensor is coupled to the second excitation-and-detection circuit in a corresponding phase-locked-loop arrangement.
8. The apparatus of claim 7 wherein (i) the second excitation-and-detection circuit is structured and connected so that the second output signal is filtered by at least one low-pass filter characterized by a low-pass cut-off frequency f LP , and (ii) f 1 <F 1 , f 2 <F 2 , and Δf<ΔF.
9. The apparatus of claim 8 wherein f LP <ΔF.
10. The apparatus of claim 9 wherein 2·f LP <ΔF.
11. The apparatus of claim 9 wherein Δf<f LP <ΔF.
12. The apparatus of claim 9 wherein f LP <Δf<2·f LP <ΔF.
13. The apparatus of claim 9 wherein f LP is greater than about 1.0×10 2 Hz.
14. The apparatus of claim 1 further comprising a processing module that is structured, connected, or programmed so as to receive one or more output signals from the second excitation-and-control circuit and to generate therefrom a measurement, based at least in part on the difference frequency ΔF, or a linear or nonlinear function of F 1 and F 2 , of the acceleration of the apparatus along the sensing axis.
15. The apparatus of claim 1 further comprising a processing module that is structured, connected, or programmed so as to receive one or more output signals from one or both of the first or second excitation-and-detection circuits and to generate therefrom a measurement, based at least in part on one or more of Δf, ΔF, or a linear or nonlinear function of one or more or all of f 1 , f 2 , F 1 , or F 2 , of the acceleration of the apparatus along the sensing axis.
16. The apparatus claim 15 , the processing module being further structured, connected, or programmed so as to compensate or self-calibrate, in the measurement of the acceleration, for (i) variations of temperature of the apparatus, (ii) variations of pressure or humidity around the apparatus, (iii) vector components of acceleration of the apparatus perpendicular to the sensing axis, or (iv) aging of the apparatus.
17. The apparatus of claim 16 , the processing module being programmed and trained, for compensation or self-calibration, using one or more statistical algorithms, machine learning algorithms, or hybrids or combinations thereof.
18. The apparatus of claim 16 , the compensation or self-calibration being based at least in part on one or more of f 1 , f 2 , F 1 , F 2 , or a linear or nonlinear function of one or more or all of f 1 , f 2 , F 1 , or F 2 .
19. The apparatus of claim 16 , the measurement of the acceleration along the sensing axis being based at least in part on Δf or a linear or nonlinear function of f 1 and f 2 , and the compensation or self-calibration being based at least in part on one or more of F 1 , F 2 , or a linear or nonlinear function of one or both of F 1 or F 2 .
20. The apparatus of claim 16 , the measurement of the acceleration along the sensing axis being based on at least in part on ΔF or a linear or nonlinear function of F 1 and F 2 , and the compensation or self-calibration being based at least in part on one or more of f 1 , f 2 , or a linear or nonlinear function of one or both of f 1 or f 2 .
21. The apparatus of claim 1 wherein each vibrating sensor comprises a pair of elongated beams and, for each vibrating sensor, the corresponding fundamental vibrational mode and set of higher-order vibrational modes are symmetric transverse vibrational modes of the pair of elongated beams.
22. The apparatus of claim 1 wherein the first vibrating sensor is coupled to the first excitation-and-detection circuit in a corresponding phase-locked-loop arrangement, and the second vibrating sensor is coupled to the first excitation-and-detection circuit in a corresponding phase-locked-loop arrangement.
23. The apparatus of claim 1 , the proof mass and the first and second vibrating sensors being integrally formed from a single continuous volume of a single material or from a single continuous volume of multiple adhered layers of one or more materials.
24. The apparatus of claim 1 wherein the proof mass and the first and second vibrating sensors include crystalline quartz or one or more other piezoelectric materials.
25. The apparatus of claim 1 wherein the proof mass and the first and second vibrating sensors include crystalline silicon or one or more other non-piezoelectric materials.
26. The apparatus of claim 1 , the first and second vibrating sensors being arranged substantially collinearly and substantially parallel to the sensing axis.
27. The apparatus of claim 1 further comprising an elongated linking member connected to the proof mass so that the linking member and the proof mass are arranged as a pendulum constrained to move in a plane defined by the linking member and the sensing axis.
28. The apparatus of claim 27 , the linking member, the proof mass, and the first and second vibrating sensors being formed from a single continuous volume of a single material or from a single continuous volume of multiple adhered layers of one or more materials.