CN107643423B - Three-degree-of-freedom weak coupling resonant accelerometer based on modal localization effect - Google Patents
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Abstract
The invention discloses a micro resonant accelerometer based on a mode localization principle, and belongs to the field of Micro Electro Mechanical Systems (MEMS). An accelerometer comprises two identical movable masses and three resonators connected together by mechanical coupling beams. The three-degree-of-freedom weak coupling resonator is used, so that the sensitivity of the resonator is further increased, and the sensitivity of the accelerometer is increased; capacitor plates are designed on the inner side and the outer side of each resonator, so that differential detection of the amplitude of a single resonator can be realized, the signal strength can be enhanced, feed-through capacitance signal interference caused by potential difference between a driving electrode and a detection electrode can be eliminated, and the stability and the accuracy of a measurement signal can be greatly improved; and a rigidity adjusting electrode is added, so that flexible selection of a working point and adjustment of a linear working range are realized.
Description
Belongs to the field of:
the invention relates to an acceleration sensor, in particular to a micro resonant accelerometer based on modal localization effect, and belongs to the technical field of sensors.
Background art:
the accelerometer is an instrument for measuring the acceleration of a carrier, is a basic core component of an inertial navigation system, and has important application value in the fields of aerospace, automobile industry, consumer electronics, engineering machinery and the like. MEMS accelerometers have become a major development direction for accelerometers due to their advantages of small size, light weight, low cost, and ease of mass production. The working principle of most MEMS accelerometers is based on Newton's second law, the inertia force is generated by utilizing a movable mass block, and the inertia force is converted into parameters such as voltage, current or frequency change and the like to be output through sensing mechanisms such as static electricity, piezoresistance, piezoelectricity or resonance and the like, so that the acceleration is measured. The common MEMS resonant accelerometer has the working principle that a sensitive mass block generates displacement under the action of inertia force, and axial pressure or electrostatic force is generated on a resonator which is directly or indirectly contacted with the sensitive mass block, so that the effective rigidity of a resonator beam is changed, the resonant frequency of the resonator is changed, and the acceleration is measured by detecting the change of the resonant frequency.
In recent years, a new sensing mechanism based on modal localization effect has begun to appear in the field of MEMS resonant sensors. The main difference with the conventional resonant sensor is that this type of sensor does not use the resonant frequency as output, but rather uses the amplitude ratio of the two coupled resonators as output of the sensor. The sensitivity mechanism is applied to sensors such as mass sensors and electrometers, and the sensitivity of the resonant sensor can be remarkably improved by 2-3 orders of magnitude.
A paper entitled "An acquisition sensing method based on the mode localization of the accelerometer localization of the first accelerometer based on the modal localization principle" published by the Journal of microelectronic Systems, Changhong, 4 months, 2016, and the like, shows the first accelerometer based on the modal localization principle in the world. The accelerometer uses amplitude ratio output, and the sensitivity is improved by about 302 times compared with the sensitivity of frequency output. There are many aspects to be improved in terms of structural design of the accelerometer. For example, a differential detection mode is not adopted for a single resonator, so that an output signal during testing can be interfered by a feed-through capacitance signal existing between a resonator driving electrode and a detection electrode, and the effective signal amplitude is greatly reduced; the weak coupling resonator of the accelerometer is composed of a double-end fixed tuning fork structure and is driven from two ends of the outer side of the resonator at the same time, so that the resonator structure has four working modes, and great difficulty is brought to the selection of the working modes and the design of a closed-loop circuit; due to the fact that the structures of the two weakly coupled resonators are not matched due to machining errors, the initial working point of the accelerometer cannot be determined, and the working point and the linear measurement range are difficult to flexibly adjust. More importantly, the core sensitive structure of the accelerometer is a two-degree-of-freedom weakly coupled resonator, the mode localization degree of the two-degree-of-freedom weakly coupled resonator is limited, and the further improvement of the accuracy of the accelerometer is limited.
The invention content is as follows:
the purpose of the invention is: the modal localization accelerometer based on the three-degree-of-freedom weak coupling resonator is provided, the sensitivity is further enhanced, the self-elimination of feed-through signals is realized, the adjustment of the effective rigidity of the resonator and the flexible selection of working points are realized, and the like.
In order to achieve the above object, the present invention provides a novel three-degree-of-freedom weakly-coupled resonant accelerometer based on modal localization effect. In the accelerometer, two identical sensitive masses, namely a first mass 301 and a second mass 302, are symmetrically arranged left and right; two elastic support beams 307 supporting the first mass block 301 on the first fixed anchor points 303 at two sides thereof, and two elastic support beams 306 supporting the second mass block 302 on the second fixed anchor points 304 at two sides thereof, so that the first mass block 301 and the second mass block 302 only move in the sensitive direction of the accelerometer, namely the left-right direction; the center of the first mass block 301 and the mass block 302 is the core structure of the accelerometer, namely a three-degree-of-freedom weakly coupled resonator, the resonator comprises a first resonator 308, a second resonator 309 and a third resonator 310, wherein the first resonator 308 and the third resonator 310 are symmetrical left and right around the center of the second resonator 309, the first resonator 308, the second resonator 309 and the third resonator 310 are connected by a mechanical coupling beam 307 to realize weak coupling, the electrostatic force application capacitive plate 408 of the first mass connected to the first mass 301 and the capacitor outer plate connected to the first resonator 308 form a first load application capacitance 311 that applies an electrostatic negative stiffness to the first resonator 308, the electrostatic force applying capacitive plate 409 of the second mass 302 and the capacitor outer plate connected to the resonator three 310 form a second load applying capacitance 312 that applies an electrostatic negative stiffness to the resonator three 310.
The invention has the beneficial effects that: the accelerometer comprises two identical movable masses and a weakly coupled resonator with three degrees of freedom connected together by a mechanical coupling beam. Compared with the prior structure, the invention uses the design of the three-degree-of-freedom weakly coupled resonator, further reduces the coupling of the two outer resonators as the output resonator, and strengthens the degree of mode localization, thereby further increasing the sensitivity of the resonator; the design of a single resonant beam is adopted, so that the working modes of the resonator are reduced from four to two, and the mode interference is greatly reduced; the capacitor polar plates are designed on the inner side and the outer side of each resonator, so that the amplitude of the same resonator can be detected from the two sides simultaneously, and the differential detection of the amplitude of the single resonator is realized, the detection method can enhance the signal strength, more importantly, the feed-through capacitance signal interference caused by the potential difference between the driving electrode and the detection electrode can be eliminated, and the stability and the accuracy of the measurement signal can be greatly improved; the rigidity adjusting electrode is added, and the effective rigidity of the resonator is adjusted through the electrostatic negative rigidity effect, so that the flexible selection of the working point and the adjustment of the linear working range are realized.
Description of the drawings:
FIG. 1 is a simplified model diagram of a three-degree-of-freedom resonant system.
FIG. 2 is an accelerometer frequency response curve versus sensitivity curve: FIG. 2- (a) is a sensor input-output characteristic curve when no acceleration is input; FIG. 2- (b) is a sensor input-output characteristic curve with 1g acceleration input; FIG. 2- (c) is a resonance frequency versus amplitude ratio sensitivity curve over a range of + -1g acceleration input.
Fig. 3 is a schematic diagram of the general structure of the accelerometer designed by the invention.
Figure 4 is a block diagram of the weakly coupled resonator of the core of the accelerometer shown in figure 3.
In the figure, 101 is a first resonator equivalent, 102 is a second resonator equivalent, 103 is a third resonator equivalent, 104 is a stiffness model of the first resonator, 105 is a stiffness model of the second resonator, 106 is a stiffness model of the second resonator, 107 is a mass model of the first resonator, 108 is a mass model of the second resonator, 109 is a mass model of the third resonator, 110 is a stiffness model of a mechanical coupling beam connecting the first resonator 101 and the second resonator 102, and 111 is a stiffness model of a mechanical coupling beam connecting the second resonator 102 and the third resonator 103;
301 is a first mass block, 302 is a second mass block, 303 is a first fixed anchor point, 304 is a second fixed anchor point, 305 is an elastic support beam supporting the first mass block 301, 306 is an elastic support beam supporting the second mass block 302, 307 is a mechanical coupling beam, 308 is a first resonator, 309 is a second resonator, and 310 is a third resonator; a first load applying capacitance 311 and a second load applying capacitance 312;
401 is a fixed direct current driving electrode, 402 is an outer side detection electrode of the first resonator, 403 is an outer side detection electrode of the second resonator, 404 is an inner side detection electrode of the first resonator, 405 is an inner side detection electrode of the second resonator, 406 is an alternating current driving electrode of the first resonator, 407 is an alternating current driving electrode of the second resonator, 408 is an electrostatic force application capacitor plate of the first mass, 409 is an electrostatic force application capacitor plate of the second mass, 410 is an electrostatic rigidity adjusting electrode of the first resonator, and 411 is an electrostatic rigidity adjusting electrode of the third resonator, respectively.
The specific implementation mode is as follows:
before the present invention is described in detail, the principle of mode localization based on a weakly coupled resonant system and the theoretical basis for applying the sensing mechanism to the field of acceleration detection will be described. Fig. 1 is a simplified spring-mass model diagram of a three-degree-of-freedom resonant system, which is composed of a resonator primary equivalent 101, a resonator secondary equivalent 102, a resonator tertiary equivalent 103, a coupling beam and a fixed anchor point. In the three-degree-of-freedom weak coupling resonator designed by the invention, a resonator-equivalent 101 and a resonator-equivalent 103 are completely symmetrical, and in fig. 1, a spring is used as stiffness models 110 and 111 of a mechanical coupling beam to equivalently represent the stiffness k of the coupling beamcIts mass is negligible; the stiffness k of the resonator one equivalent 101 and the stiffness k of the resonator three equivalent 103 are equivalently represented by a stiffness model 104 using a spring as the resonator one and a stiffness model 106 using a spring as the resonator three, respectively, and the stiffness k of the resonator two equivalent 102 is equivalently represented by a stiffness model 105 using a spring as the resonator two2(ii) a The masses m of the first equivalent 101, the second equivalent 102 and the third equivalent 103 are equivalently represented by the masses 107, 108 and 109, respectively. The three-degree-of-freedom resonance system has three modes, namely a resonator I equivalent 101 and a resonatorThe equidirectional motion of the first equivalent 102 and the third equivalent 103 of the resonator is the equidirectional mode, the opposite motion of the first equivalent 101 and the third equivalent 103 of the resonator is the opposite mode, the static motion of the second equivalent 102 of the resonator is the opposite mode, the opposite motion of the first equivalent 101 of the resonator and the second equivalent 102 of the resonator is the opposite mode, and the opposite motion of the second equivalent 102 of the resonator and the third equivalent 103 of the resonator is the third mode. Hereinafter x1、x2And x3 are the displacements, u, of the first resonator mass model 107, the second resonator mass model 108, and the third resonator mass model 109, respectively1And u2Indicating the amplitude ratio of the homodromous mode and the opposite mode, respectively. Obtaining a vibration equation of the three-degree-of-freedom coupling system according to Newton's second law:
writing equation (1) in matrix form:
then, assuming that the stiffness of the resonator triple equivalent 103 changes Δ k, the vibration equation of the whole resonance system changes as follows:
the expression of the amplitude ratio of the resonator-one equivalent 101 and the resonator-three equivalent 103 at this time is:
the input of acceleration causes a change in stiffness with the relationship:
where a is the acceleration causing the change in stiffness, ε is the dielectric constant, A is the area of the overlap between adjacent plates of the sense parallel plate capacitor, V is the potential difference between the mass and the resonator, i.e. the potential difference across the sense capacitor, g0Is the inter-plate spacing, m, of the parallel plate capacitorsIs the mass of the proof-mass, ksIs the stiffness of the mass elastic support beam.
In summary, the input acceleration value can be obtained by combining equations (4) and (5).
The sensitivity of the amplitude ratio to the stiffness change with stiffness disturbance Δ k is:
in addition, the sensitivity of the amplitude ratio of the two-degree-of-freedom resonator relative to the rigidity change is as follows:
the coupling rigidity in the invention is far less than the rigidity (k) of the resonator resonance beamc<<k) That is, the coupling mode between the three resonators is weak coupling, and it can be obtained from the formulas (6) and (7) that the sensitivity of the theoretical three-degree-of-freedom resonator with the amplitude ratio as the output is higher than the sensitivity of the amplitude ratio of the two-degree-of-freedom resonator
And (4) doubling.
Fig. 2 shows the frequency response curve and the sensitivity curve of the accelerometer designed by the embodiment. Figure 2- (a) shows the amplitude frequency response of two resonators in an accelerometer when there is no acceleration input, i.e. the resonators have no disturbance, each resonator having two peaks, each peak representing one mode of the resonator. The amplitude-frequency characteristic of two resonators in the accelerometer at-1 g acceleration input is shown in fig. 2- (b). As can be seen from comparing fig. 2- (b) with fig. 2- (a), when a disturbance is input, the amplitude of the second mode of the resonator 3 is significantly increased, the amplitude of the first mode is significantly decreased, and the amplitude ratio of the two resonators is significantly changed, that is, a mode localization phenomenon occurs.
Comparing fig. 2- (a) and fig. 2- (b) at this time, and combining the sensitivity curves of the two outputs of the accelerometer (fig. 2- (c)), it can be seen that the amplitude ratio sensitivity of the accelerometer is much greater than the resonance frequency sensitivity when there is an acceleration input. The sensitivity based on the amplitude ratio is improved by 1410 times than the sensitivity based on the resonance frequency.
Fig. 3 and 4 show structural schematic diagrams of the three-degree-of-freedom weakly coupled resonator accelerometer based on modal localization effect designed by the embodiment. Two identical sensitive masses, namely a first mass 301 and a second mass 302, are arranged in bilateral symmetry; two elastic support beams 307 supporting the first mass block 301 on the first fixed anchor points 303 at two sides thereof, and two elastic support beams 306 supporting the second mass block 302 on the second fixed anchor points 304 at two sides thereof, so that the first mass block 301 and the second mass block 302 only move in the sensitive direction of the accelerometer, namely the left-right direction; the middle of the first mass block 301 and the second mass block 302 is the core structure of the accelerometer, namely a three-degree-of-freedom weakly coupled resonator, the resonator comprises a first resonator 308, a second resonator 309 and a third resonator 310, wherein the first resonator 308 and the third resonator 310 are symmetrical left and right around the center of the second resonator 309, the first resonator 308, the second resonator 309 and the third resonator 310 are connected by a mechanical coupling beam 307 to realize weak coupling, the electrostatic force application capacitive plate 408 of the first mass connected to the first mass 301 and the capacitor outer plate connected to the first resonator 308 form a first load application capacitance 311 that applies an electrostatic negative stiffness to the first resonator 308, the electrostatic force application capacitive plate 409 of the second mass coupled to the second mass 302 and the capacitor outer plate coupled to the third resonator 310 form a second load application capacitance 312 that applies an electrostatic negative stiffness to the third resonator 310.
When acceleration is input, the first mass block 301 and the second mass block 302 will displace towards the same direction under the action of the acceleration. The capacitor plates connected to the mass are displaced relative to the equilibrium position of the resonator sensing plates. The displacement amount (Δ g) can be expressed as:
where E is the Young's modulus of silicon, b is the width of the elastic support beam, l is the length of the support beam, and h is the thickness of the support beam. Because the potential difference exists between the mass block and the resonator, the potential difference can apply electrostatic negative rigidity to the adjacent resonance beam, namely, the electrostatic negative rigidity plays a role in reducing the equivalent rigidity of the resonance beam, and the electrostatic rigidity expression is as follows:
in the above formula, V is the potential difference between the mass block and the resonator, epsilon 0 is the vacuum dielectric coefficient, and a is the overlapping area between the detection capacitor plates. Assuming both masses move to the right in FIG. 2, i.e., the spacing between mass one 301 and resonator one 308 decreases, the spacing between mass two 302 and resonator three 310 increases. Thus, the stiffness of resonator one 308 is reduced by Δ keleAnd the stiffness of resonator three 310 is increased by akele. The difference in stiffness of the two resonators is 2 akeleThen the equivalent stiffness mismatch occurs for the two originally fully symmetric resonators. Not only is the modal localization effect induced, but also the effect is enhanced, so that a signal with a higher signal-to-noise ratio is obtained. Since the output signal of the accelerometer is amplitude ratio, the amplitude of the two resonators needs to be divided, and the influence of environmental factors on the output signal can be eliminated.
Fig. 4 shows a structural schematic diagram of a core part weak coupling resonator of the accelerometer designed by the invention. The first resonator 308 and the third resonator 310 are symmetrically arranged left and right, the second resonator 309 is located between the resonators 308 and 310, the three resonators are connected through a mechanical coupling beam 307 to achieve weak coupling, the lower end of each resonator is connected and fixed with an anchor point, the upper end of each resonator is connected and fixed with a direct current driving electrode 401, and capacitor plates are arranged on the inner side and the outer side of each resonator 308 and 309 respectively and used for detecting amplitude. An alternating current driving electrode 406 is arranged at the leftmost side in the first resonator 308, and an alternating current driving electrode 407 is arranged at the rightmost side in the third resonator 310; an inner detection electrode 404 of the first resonator is arranged at the rightmost side in the first resonator 308, and an outer detection electrode 402 of the first resonator is arranged between the first resonator 308 and the second resonator 309; an inner detection electrode 405 of the second resonator is arranged at the leftmost side in the third resonator 310, and an outer detection electrode 403 of the second resonator is arranged between the second resonator 309 and the third resonator 310; an electrostatic stiffness adjusting electrode 410 is arranged on the right side of the alternating current driving electrode 406 of the first resonator 308, and an electrostatic stiffness adjusting electrode 411 is arranged on the left side of the alternating current driving electrode 407 of the third resonator 310; the electrostatic force application capacitance plate 408 of the first mass connected to the first mass 301 and the outer side of the capacitor outer plate connected to the first resonator 308 form a first load application capacitance 311 for applying electrostatic negative stiffness to the first resonator 308, and the electrostatic force application capacitance plate 409 of the second mass connected to the second mass 302 and the outer side of the capacitor outer plate connected to the third resonator 310 form a second load application capacitance 312 for applying electrostatic negative stiffness to the third resonator 310.
When no acceleration is input, the weakly coupled resonator resonates at a high frequency under excitation of the drive signals applied to the dc drive electrode 401 and the ac drive electrode 406, and a mode localization phenomenon does not occur. When acceleration is input, the two symmetrical first mass blocks 301 and the two symmetrical second mass blocks 302 are sensitive to the acceleration and generate equal and same-direction displacement, and the weak coupling resonance system is positioned between the two symmetrical mass blocks, so that the plate distances of the two completely symmetrical first load application capacitors 311 and the second load application capacitors 312 are increased by one and reduced by one, and the rigidity difference of 2 delta k exists between the rigidity of the first resonator 308 and the rigidity of the third resonator 310. Thus a modal localization phenomenon occurs and the weakly coupled resonant system will resonate at high frequency at the new resonant frequency. In the design, the inner and outer polar plates of one resonator are simultaneously detected for amplitude, and because the inner and outer detection electrodes are fixed, the change trend of the distance between the polar plates of the inner polar plate detection capacitor and the outer polar plate detection capacitor of the single resonator is opposite. And the output signals of the two detection electrodes are subjected to subtraction operation, so that differential detection of the single resonator is realized, and feed-through capacitance signal interference can be eliminated. The resonator structure with the feed-through signal elimination function and the detection method are designed, so that the detection of the amplitude and the frequency can be more accurate, the intensity of an output signal can be doubled, and the signal-to-noise ratio of the output signal of the sensor is greatly improved. In actual measurement, the sensitivity of the present invention is about 1410 times higher with the amplitude ratio as the output of the accelerometer than with the resonance frequency as the output.
The acceleration detection comprises the following specific steps:
in the first step, when acceleration a (g) is input, the first resonator 101 of the accelerometer outputs a dc voltage Ui1(i equals 1.2), the third resonator 103 outputs a dc voltage Ui3(i equals 1.2), and Ui1/Ui3 is the amplitude ratio u of the two weakly coupled resonatorsi。
Second, the amplitude ratio u is comparediSubstituting equation (4), since k, k2, kc are known parameters, the stiffness change Δ k of the resonator can be obtained.
And thirdly, substituting the rigidity change quantity delta k into the formula (5) to obtain the value of the acceleration a causing the rigidity change.
Claims (1)
1. A three-degree-of-freedom weak coupling resonant accelerometer based on modal localization effect is characterized in that two identical sensitive mass blocks, namely a mass block I (301) and a mass block II (302), are arranged in bilateral symmetry; two elastic supporting beams (305) supporting the first mass block support the first mass block (301) on first fixed anchor points (303) on two sides of the first mass block, and two elastic supporting beams (306) supporting the second mass block support the second mass block (302) on second fixed anchor points (304) on two sides of the second mass block, so that the first mass block (301) and the second mass block (302) only move in the sensitive direction of the accelerometer, namely the left-right direction; the middle of the first mass block (301) and the second mass block (302) is a core structure of the accelerometer, namely a three-degree-of-freedom weak coupling resonator, and the accelerometer comprises the following main components of a first resonator (308), a second resonator (309) and a third resonator (310), wherein the first resonator (308) and the third resonator (310) are symmetrical left and right around the center of the second resonator (309), and the first resonator (308), the second resonator (309) and the third resonator (310) are connected through a mechanical coupling beam (307) so as to realize weak coupling, and the specific connection mode is as follows: one ends of the first resonator (308), the second resonator (309) and the third resonator (310) are directly connected to the anchor points, the other ends of the first resonator (308) and the second resonator (309), the second resonator (309) and the third resonator (310) are respectively connected through a cross beam, and after the cross beam outwards extends for a certain distance from the connection point of the first resonator (308) and the third resonator (310), the end points of two sides of the cross beam are respectively connected to the anchor points through a longitudinal beam; the transverse beam and the longitudinal beams at two ends jointly form the mechanical coupling beam (307); the electrostatic force application capacitive plate (408) of the first mass connected to the first mass (301) and the capacitor outer plate connected to the first resonator (308) form a first load application capacitance (311) that applies electrostatic negative stiffness to the first resonator (308), and the electrostatic force application capacitive plate (409) of the second mass connected to the second mass (302) and the capacitor outer plate connected to the third resonator (310) form a second load application capacitance (312) that applies electrostatic negative stiffness to the third resonator (310).
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