Estimation method for coupling rigidity of differential resonant sensor

Abstract

The invention discloses a method for estimating coupling rigidity of a differential resonant sensor, which adopts a set of test system and comprises a differential resonant sensor, a front-end interface circuit, a signal generation and detection device, a power supply and a computer. According to the method, the frequency sweeping range of resonators is pre-estimated, frequency sweeping under single-end driving or double-end driving is carried out on each resonator for multiple times, and a resonator detection signal amplitude-frequency curve with high accuracy is drawn, so that the resonant frequencies of the two resonators and the large and small amplitudes of the resonators are obtained, and the amplitude ratio is calculated; and finally, analyzing to obtain the coupling rigidity of the differential resonant sensor. According to the method, the coupling rigidity of the sensor can be effectively obtained through a test means, the structural design of the differential resonant sensor can be guided, and the self-locking phenomenon or related application occurring in signal analysis and processing can be helped to be processed.

Description

Technical Field

[0001] The present invention belongs to the technical field of micro-inertial sensors in MEMS systems, relates to differential resonant sensors, and specifically provides a method for estimating the coupling stiffness of differential resonant sensors. Background Art

[0002] Differential resonant sensors are micro-mechanical inertial devices developed based on MEMS (Micro-Electro-Mechanical System) technology. Compared with traditional inertial sensors, MEMS inertial devices using integrated circuit technology and micro-machining technology have the advantages of small size, low power consumption, and high precision, and are widely used in various fields such as aerospace and inertial navigation.

[0003] As a typical inertial sensor for measuring acceleration, the working principle of a differential resonant sensor is to change the resonant frequency of the resonator through the inertial force generated by the externally input acceleration, and then obtain the magnitude of the externally input acceleration by detecting the change in frequency.

[0004] A differential resonant sensor is a two-degree-of-freedom spring-mass system, which is composed of two single-degree-of-freedom micro-mechanical resonators coupled by elastic forces. No matter how weak the coupling between the two resonators is, their vibrations are not independent of each other, but form an interacting vibration system. In the structure of a differential resonant sensor, the two resonators are connected together through coupling structures such as a frame, and the frame is connected to the substrate through anchor points. The energy generated by the vibration of one resonator will be conducted through structures such as the frame, anchor points, and substrate, affecting the vibration of the other resonator. Since a differential resonant sensor obtains the magnitude of the input acceleration by sensing the vibration frequency of the resonator, the vibration coupling between the two resonators will interfere with the normal output of their respective frequencies, or a self-locking phenomenon will occur, seriously affecting the static working performance of the sensor. Currently, when designing the structure of the sensor, the influence of vibration coupling is reduced by cutting off the coupling channel, adding decoupling structures, or changing the resonator size to obtain two resonators with different resonant frequencies. Therefore, a method for analyzing the coupling stiffness of the sensor is needed to estimate the coupling stiffness of the differential resonant sensor, and then guide the structure design of the sensor to help deal with the self-locking phenomenon or related applications that occur in signal analysis and processing. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for estimating the coupling stiffness of differential resonant sensors, which helps to estimate the coupling stiffness of such resonant sensors and is beneficial to guiding the structure design of differential resonant sensors.

[0006] To achieve the above-mentioned invention object, the technical solution of the present invention is as follows:

[0007] An estimation method for the coupling stiffness of a differential resonant sensor, comprising the following steps:

[0008] Step 1: Drive the differential resonant sensor in single-ended drive or double-ended drive. When in single-ended drive, only drive one resonator and do not drive the other resonator, that is, apply a harmonic driving force to only one resonator and do not apply a harmonic driving force to the other resonator; when in double-ended drive, drive both resonators simultaneously, that is, apply a harmonic driving force to both resonators;

[0009] Step 2: Simultaneously perform open-loop frequency sweeping on the two resonators, obtain the resonant frequencies of the two resonators and the amplitude ratio of the two resonators at any resonant frequency through the amplitude-frequency curves of the two resonators. According to the results of the open-loop frequency sweeping, set the resonator with the smaller resonant frequency as resonator 1, and its resonant frequency is f 1 , and set the resonator with the larger resonant frequency as resonator 2, and its resonant frequency is f 2 ;

[0010] Step 3: Measure the corresponding quality factors Q 1 、Q 2 of the two resonators, limit the frequency range of the driving signals of the two resonators to

[0011]

[0012] and perform frequency sweeping on the two resonators under the first round of single-ended drive or double-ended drive within this frequency range of the driving signals, and plot the amplitude-frequency curves of the detection signals of each resonator; then narrow the frequency sweeping range and step size, and repeat the frequency sweeping process until the maximum amplitudes of the amplitude-frequency curves of the two resonators in the last two rounds of frequency sweeping coincide;

[0013] Step 4: Obtain the resonant frequencies f 1 、f 2 of the two resonators through the amplitude-frequency curves of the last round of frequency sweeping, and record the amplitude value X 1 of resonator 1 corresponding to the resonant frequency f 1 (f 1 ) and the amplitude value X 2 (f 1 ) of resonator 2, record the amplitude value X 2 of resonator 1 corresponding to the resonant frequency f 1 (f 2 ), and the amplitude value X 2 (f 2 ) of resonator 2;

[0014] Step 5: Calculate the coupling stiffness of the differential resonant sensor.

[0015] Further, in step 1, a differential resonant sensor test system is used to perform single - end drive or double - end drive on the differential resonant sensor. The differential resonant sensor test system includes a differential resonant sensor, a front - end interface circuit, a signal generator and detector, a power supply, and a computer. Among them, the differential resonant sensor includes two resonators. When an external input acts on the sensor, the resonant frequencies of its resonators change; the front - end interface circuit is used to convert the mechanical signal of the resonator vibration into an electrical signal convenient for detection; the signal generator and detector provides an AC drive voltage for the resonant sensor and detects the electrical signal output by the front - end interface circuit; the power supply powers the resonant sensor; the computer is the carrier for data processing and analysis of the estimation of the coupling stiffness of the resonant sensor.

[0016] Further, the mechanical signals in step 1 include displacement signals and velocity signals.

[0017] Further, the electrical signals in step 1 include voltage signals and current signals.

[0018] Further, in step 2, the open - loop frequency sweep of the resonator is in the order from low frequency to high frequency with a fixed step size as the frequency increment of the signal, or in the order of a simple harmonic force from high frequency to low frequency to drive the resonator. The frequency range of the frequency sweep refers to the change range of the frequency from high to low or from low to high, and the frequency sweep step size is the minimum increment of the signal frequency change.

[0019] Further, step 5 is specifically as follows:

[0020] The differential resonant sensor composed of resonator 1 and resonator 2 can be regarded as a two - degree - of - freedom spring - mass system. According to Newton's law, the free - vibration differential equation of the two - degree - of - freedom spring - mass system is obtained:

[0021]

[0022] where, m 1 、m 2 are the equivalent masses of the two resonators respectively, k m1 、k m2 are the equivalent stiffnesses of the two resonators respectively, k c is the coupling stiffness between the two resonators, x 1 、x 2 are the vibration displacements of the resonant beams of the corresponding resonators;

[0023] The simple - harmonic motion equation of the bending vibration of the resonant beam of the resonator is:

[0024] x = Xsin(2πft + θ)

[0025] Wherein, x is the vibration displacement of the resonant beam, X is the maximum vibration displacement of the resonant beam, f is the resonant frequency of the resonant beam, t is the time, and θ is the phase;

[0026] The free vibration differential equation of the two-degree-of-freedom spring-mass system and the simple harmonic motion equation of the bending vibration of the resonant beam are combined, and the equivalent masses of the two resonators are set equal, and the resonant frequency equation of the two-degree-of-freedom spring-mass system is obtained:

[0027]

[0028] Among them, f 1 and f 2 is the resonant frequency of the two resonators of the two-degree-of-freedom spring-mass system, and m is the equivalent mass of the two resonators;

[0029] According to Newton's law, the forced vibration differential equation of the two-degree-of-freedom spring-mass system is obtained:

[0030]

[0031] Among them, F 1 、F 2 are the simple harmonic forces applied to the two resonators respectively;

[0032] By combining the forced vibration differential equation of the two-degree-of-freedom spring-mass system and the simple harmonic motion equation of the resonant beam bending vibration, the relationship between the vibration displacement of the resonant beams of the two resonators in the two-degree-of-freedom spring-mass system and the simple harmonic force is obtained:

[0033] X=[K] -1 F

[0034] in,

[0035] The expression for the maximum amplitude of the resonant beam of the two resonators in the two-degree-of-freedom spring-mass system is obtained as:

[0036]

[0037] Assuming the equivalent masses of the two resonators are equal, both are m, the amplitude ratio of the two resonators at the two resonant frequencies of the two-degree-of-freedom spring-mass system is obtained:

[0038]

[0039] Among them, X 1 (f 1 ) and X 1 (f 2 ) represent the resonator 1 at f 1and f 2 The amplitude value at X 2 (f 1 ) and X 2 (f 2 ) represent the resonator 2 at f 1 and f 2 The amplitude value at u 1 For resonator 1 at f 1 The amplitude at f is the same as that of resonator 2 1 The ratio of the amplitudes at 2 For resonator 2 at f 2 The amplitude at f is the same as that of resonator 1 2 The ratio of the amplitudes at ;

[0040] When the sensor is driven by a single end, resonator 1 is driven alone, that is, no harmonic force is applied to resonator 2, and only harmonic force is applied to resonator 1, F 1 ≠0, F 2 = 0, the amplitude ratio equation of the two resonators at the resonant frequency of resonator 1 is obtained:

[0041]

[0042] The resonant frequency equation of the two-degree-of-freedom spring-mass system and the amplitude ratio equation of the two resonators at the resonant frequency of resonator 1 are combined to obtain the coupling stiffness of the differential resonant sensor:

[0043]

[0044] When the sensor is driven by a single end, resonator 2 is driven alone, that is, no harmonic force is applied to resonator 1, and only harmonic force is applied to resonator 2, F 1 =0, F 2 ≠0, the amplitude ratio equation of the two resonators at the resonant frequency of resonator 2 is obtained:

[0045]

[0046] The resonant frequency equation of the two-degree-of-freedom spring-mass system and the amplitude ratio equation of the two resonators at the resonant frequency of resonator 2 are combined to obtain the coupling stiffness of the differential resonant sensor:

[0047]

[0048] When the sensor is driven at both ends, the two resonators are driven at the same time, that is, a simple harmonic force is applied to the two resonators at the same time, F 1 =F 2 ≠0, the amplitude ratio equation of the two resonators at the resonant frequency of resonator 1 is obtained:

[0049]

[0050] By simultaneously solving the resonance frequency equation of the two-degree-of-freedom spring-mass system and the amplitude ratio equation of the two resonators at the resonance frequency of resonator 1, the coupling stiffness of the differential-mode resonant sensor is obtained:

[0051]

[0052] When the sensor is driven at both ends, the two resonators are driven simultaneously, that is, a harmonic force F 1 = F 2 ≠ 0, and the amplitude ratio equation of the two resonators at the resonance frequency of resonator 2 is obtained:

[0053]

[0054] By simultaneously solving the resonance frequency equation of the two-degree-of-freedom spring-mass system and the amplitude ratio equation of the two resonators at the resonance frequency of resonator 2, the coupling stiffness of the differential-mode resonant sensor is obtained:

[0055]

[0056] When only resonator 1 is driven, the amplitude ratio u = X 1 (f 1 ) / X 2 (f 1 ) is calculated. When only resonator 2 is driven, the amplitude ratio u = X 2 (f 2 ) / X 1 (f 2 ) is calculated. When resonator 1 and resonator 2 are driven simultaneously, the amplitude ratio u = X 1 (f 1 ) / X 2 (f 1 ) or u = X 2 (f 2 ) / X 1 (f 2 ) is calculated. Substituting it into the following formula, the coupling stiffness k c of the differential-mode resonant sensor is obtained:

[0057]

[0058] Advantages of the present invention: By establishing a mathematical model of the differential resonant sensor system, constructing an expression for the coupling stiffness of the sensor system, and relying on a test system composed of a differential resonant sensor, a front-end interface circuit, a signal generator and detector, a power supply, and a computer, the proposed analysis method can effectively perform data analysis and processing on the coupling stiffness of the differential resonant sensor, and can accurately obtain the coupling stiffness of the sensor, which is beneficial for guiding the structural design of the differential resonant sensor. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flowchart of the estimation method of the present invention.

[0060] Figure 2 It is a schematic diagram of the test system of the present invention.

[0061] Figure 3 It is a schematic diagram of the force on the resonator when the differential resonant sensor is driven by a single end.

[0062] Figure 4 It is a schematic diagram of the force on the resonator when the differential resonant sensor is driven by both ends.

[0063] Figure 5 It is a schematic diagram of the amplitude of the resonator when resonator 1 is driven alone.

[0064] Figure 6 It is a schematic diagram of the amplitude of the resonator when resonator 2 is driven alone.

[0065] Figure 7 It is a schematic diagram of the amplitude of the resonator when both resonators are driven simultaneously.

[0066] DESCRIPTION OF THE REFERENCE NUMERALS

[0067] Figure 2 In the figure, 201 is a differential resonant sensor, 202 is a front-end interface circuit, 203 is a signal generator and detector (or an instrument with similar functions such as a lock-in amplifier), 204 is a power supply, and 205 is a computer.

[0068] Figure 3 In the figure, 301 is resonator 1, 302 is resonator 2, 303 are the two resonant beams of resonator 1, 304 are the two resonant beams of resonator 2, 305 is a coupling structure such as a frame, substrate, and anchor point, 306 is a connecting beam connecting resonator 1 and the coupling structure, and 307 is a connecting beam connecting resonator 2 and the coupling structure. DETAILED DESCRIPTION OF THE INVENTION

[0069] The present invention will be further described below in conjunction with the drawings and specific embodiments.

[0070] The present invention discloses a method for estimating the coupling stiffness of a differential resonant sensor, and the method flow is as follows Figure 1 as shown, and specifically includes the following steps:

[0071] Step 1: Through a differential resonant sensor test system as shown in Figure 2 , the differential resonant sensor is driven in single-ended or double-ended mode. The differential resonant sensor test system includes a differential resonant sensor 201, a front-end interface circuit 202, a signal generation and detector 203, a power supply 204, and a computer 205. Among them, the differential resonant sensor 201 includes two resonators. When an external input acts on the sensor 201, the resonant frequencies of its resonators change; the front-end interface circuit 202 is used to convert the mechanical signal of the resonator vibration into an electrical signal convenient for detection; the signal generation and detector 203 provides an AC drive voltage for the resonant sensor 201 and detects the electrical signal output by the front-end interface circuit 202; the power supply 204 supplies power to the resonant sensor 201; the computer 205 is a carrier for data processing and analysis of the coupling stiffness estimation of the resonant sensor. In single-ended drive, the signal generation and detector only drives one resonator and does not drive the other resonator, that is, only a harmonic driving force is applied to one resonator, and no harmonic driving force is applied to the other resonator, as shown in Figure 3 ; in double-ended drive, the signal generation and detector drives both resonators at the same time, that is, a harmonic driving force is applied to both resonators, as shown in Figure 4 .

[0072] Step 2: Simultaneously perform open-loop frequency sweeping on both resonators, and obtain the resonant frequencies of the two resonators and the amplitude ratio of the two resonators at any resonant frequency through the amplitude-frequency curves of the two resonators. According to the results of the open-loop frequency sweeping, due to process errors, usually the frequencies of the two differential resonators are not exactly the same. The resonator with the smaller resonant frequency is set as resonator 1, and its resonant frequency is f 1 , and the resonator with the larger resonant frequency is set as resonator 2, and its resonant frequency is f 2 .

[0073] Step 3: Measure the quality factors Q 1 and Q 2 of the two resonators by the ringdown method, and limit the frequency range of the driving signals of the two resonators to

[0074]

[0075] Perform a first-round sweep frequency for the two resonators under single-ended drive or differential drive within the frequency range of the drive signal, and plot the amplitude-frequency curve of the detection signal for each resonator. Secondly, narrow the sweep frequency range and step size, and repeat the above sweep frequency process until the maximum amplitudes of the curves in the last two rounds of sweep frequencies coincide.

[0076] Step 4: Obtain the resonance frequencies f 1 、f 2 of the two resonators through the amplitude-frequency curve of the last round, and record the amplitude X 1 of resonator 1 corresponding to the resonance frequency f 1 (f 1 ) and the amplitude X 2 (f 1 ) of resonator 2. Record the amplitude X 2 of resonator 1 corresponding to the resonance frequency f 1 (f 2 ) of resonator 2, and the amplitude X 2 (f 2 ) of resonator 2. Among them, when resonator 1 is driven alone, the amplitude-frequency curves of the two resonators are as shown in Figure 5 , when resonator 2 is driven alone, the amplitude-frequency curves of the two resonators are as shown in Figure 6 , and when the two resonators are driven simultaneously, the amplitude-frequency curves of the two resonators are as shown in Figure 7 .

[0077] Step 5: Calculate the coupling stiffness of the differential resonant sensor. The specific solution formula is derived from the following derivation process:

[0078] As shown in Figure 3 , the differential resonant sensor composed of resonator 301 and resonator 302 can be regarded as a two-degree-of-freedom spring-mass system. According to Newton's law, the free vibration differential equation of the two-degree-of-freedom spring-mass system is obtained:

[0079]

[0080] Among them, m 1 、m 2 are the equivalent masses of the two resonators respectively, k m1 、k m2 are the equivalent stiffnesses of the two resonators respectively, k c is the coupling stiffness between the two resonators, and x 1 、x 2 are the vibration displacements of the resonant beams of the corresponding resonators.

[0081] The simple harmonic motion equation of the bending vibration of the resonant beam of the resonator is:

[0082] x = Xsin(2πft + θ)

[0083] Wherein, x is the vibration displacement of the resonant beam, X is the maximum vibration displacement of the resonant beam, f is the resonant frequency of the resonant beam, t is the time, and θ is the phase.

[0084] The free vibration differential equation of the two-degree-of-freedom spring-mass system and the simple harmonic motion equation of the resonant beam are combined, and the equivalent masses of the two resonators are set equal, and the resonant frequency equation of the two-degree-of-freedom spring-mass system is obtained:

[0085]

[0086] Among them, f 1 and f 2 is the resonant frequency of the two resonators of the two-degree-of-freedom spring-mass system, and m is the equivalent mass of the two resonators.

[0087] According to Newton's law, the forced vibration differential equation of the two-degree-of-freedom spring-mass system is obtained:

[0088]

[0089] Among them, F 1 、F 2 are the simple harmonic forces applied to the two resonators respectively.

[0090] By combining the forced vibration differential equation of the two-degree-of-freedom spring-mass system with the simple harmonic motion equation of the resonant beam, we can obtain the relationship between the vibration displacement of the resonant beams of the two resonators in the two-degree-of-freedom spring-mass system and the simple harmonic force:

[0091] X=[K] -1 F

[0092] in,

[0093] The expression for the maximum amplitude of the resonant beam of the two resonators in the two-degree-of-freedom spring-mass system is obtained as:

[0094]

[0095] Assuming the equivalent masses of the two resonators are equal, both are m, the amplitude ratio of the two resonators at the two resonant frequencies of the two-degree-of-freedom spring-mass system is obtained:

[0096]

[0097] Among them, X 1 (f 1 ) and X 1 (f 2 ) represent the resonator 1 at f 1 and f2 The amplitude value at X 2 (f 1 ) and X 2 (f 2 ) represent the resonator 2 at f 1 and f 2 The amplitude value at u 1 For resonator 1 at f 1 The amplitude at f is the same as that of resonator 2 1 The ratio of the amplitudes at 2 For resonator 2 at f 2 The amplitude at f is similar to that of resonator 1 2 The ratio of the amplitudes at .

[0098] When the sensor is driven at a single end, resonator 1 is driven alone, that is, no harmonic force is applied to resonator 2, and only harmonic force (F 1 ≠0, F 2 =0), the amplitude ratio of the two resonators at the resonant frequency of resonator 1 is obtained:

[0099]

[0100] The resonant frequency equation of the two-degree-of-freedom spring-mass system and the amplitude ratio equation of the two resonators at the resonant frequency of resonator 1 are combined to obtain the coupling stiffness of the differential resonant sensor:

[0101]

[0102] When the sensor is driven at a single end, resonator 2 is driven alone, that is, no harmonic force is applied to resonator 1, and only harmonic force (F 1 =0, F 2 ≠0), the amplitude ratio of the two resonators at the resonant frequency of resonator 2 is obtained:

[0103]

[0104] The resonant frequency equation of the two-degree-of-freedom spring-mass system and the amplitude ratio equation of the two resonators at the resonant frequency of resonator 2 are combined to obtain the coupling stiffness of the differential resonant sensor:

[0105]

[0106] When the sensor is driven at both ends, the two resonators are driven at the same time, that is, a simple harmonic force (F 1 =F 2 ≠0), the amplitude ratio of the two resonators at the resonant frequency of resonator 1 is obtained:

[0107]

[0108] By simultaneously solving the resonance frequency equation of the two-degree-of-freedom spring-mass system and the amplitude ratio equation of the two resonators at the resonance frequency of resonator 1, the coupling stiffness of the differential-type resonant sensor is obtained:

[0109]

[0110] When the sensor is driven at both ends, the two resonators are driven simultaneously, that is, a harmonic force (F 1 = F 2 ≠0) is applied to the two resonators simultaneously, and the amplitude ratio of the two resonators at the resonance frequency of resonator 2 is obtained:

[0111]

[0112] By simultaneously solving the resonance frequency equation of the two-degree-of-freedom spring-mass system and the amplitude ratio equation of the two resonators at the resonance frequency of resonator 2, the coupling stiffness of the differential-type resonant sensor is obtained:

[0113]

[0114] It is assumed that the equivalent masses of the two resonators are equal, both being m, and its value can be calculated according to the structural design parameters of the resonator. When only resonator 1 is driven, the amplitude ratio u = X 1 (f 1 ) / X 2 (f 1 ) is calculated. When only resonator 2 is driven, the amplitude ratio u = X 2 (f 2 ) / X 1 (f 2 ) is calculated. When resonator 1 and resonator 2 are driven simultaneously, the amplitude ratio u = X 1 (f 1 ) / X 2 (f 1 ) or u = X 2 (f 2 ) / X 1 (f 2 ) is calculated. Substituting it into the following formula, the coupling stiffness k c of the differential-type resonant sensor can be obtained:

[0115]

[0116] In summary, the present invention provides a method for estimating the coupling stiffness of a differential-type resonant sensor. This method can effectively obtain the coupling stiffness of the sensor through testing means, which is beneficial to guiding the structural design of the differential-type resonant sensor and helping to handle the self-locking phenomenon or related applications in signal analysis and processing.

[0117] The basic principles, main features and advantages of the present invention have been shown and described above. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for estimating coupling stiffness of a differential resonant sensor, characterized in that: The following steps are involved: Step 1: The differential resonant sensor is driven single-ended or double-ended. When the sensor is driven single-ended, only one resonator is driven and the other resonator is not driven, that is, a simple harmonic driving force is applied to only one resonator and the other resonator is not driven. In double-ended driving, two resonators are driven simultaneously, that is, a simple harmonic driving force is applied to the two resonators; Step 2: Perform open-loop frequency sweep on the two resonators at the same time, and obtain the resonant frequencies of the two resonators and the amplitude ratio of the two resonators at any resonant frequency through the amplitude-frequency curves of the two resonators. According to the result of the open-loop frequency sweep, the resonator with a smaller resonant frequency is set as resonator 1, and its resonant frequency is f1, and the resonator with a larger resonant frequency is set as resonator 2, and its resonant frequency is f2; Step 3: Measure the quality factors Q1 and Q2 of the two resonators, and limit the frequency range of the driving signals of the two resonators to and performing a first round of single-end driving or double-end driving frequency sweep on the two resonators within the frequency range of the driving signal, and drawing an amplitude-frequency curve of the detection signal of each resonator; Then reduce the frequency sweep range and step size, and repeat the frequency sweep process until the maximum amplitudes of the two resonator amplitude-frequency curves in the last two sweeps coincide; Step 4: Obtain the resonant frequencies f1 and f2 of the two resonators through the amplitude-frequency curve of the last frequency sweep, and record the amplitude value X1(f1) of resonator 1 and the amplitude value X2(f1) of resonator 2 corresponding to the resonant frequency f1 of resonator 1, and record the amplitude value X1(f2) of resonator 1 and the amplitude value X2(f2) of resonator 2 corresponding to the resonant frequency f2 of resonator 2; Step 5: Calculate the coupling stiffness of the differential resonant sensor.

2. The method for estimating coupling stiffness of a differential resonant sensor according to claim 1, characterized in that: In step 1, a differential resonant sensor test system is used to perform single-end drive or double-end drive on the differential resonant sensor. The differential resonant sensor test system comprises a differential resonant sensor (201), a front-end interface circuit (202), a signal generator and detector (203), a power supply (204), and a computer (205). The differential resonant sensor (201) comprises two resonators. When an external input acts on the sensor (201), the resonant frequency of the resonator changes. The front-end interface circuit (202) is used to convert the mechanical signal of the resonator vibration into an electrical signal that is easy to detect. The signal generator and detector (203) provides an AC drive voltage for the resonant sensor (201) and detects the electrical signal output by the front-end interface circuit (202). The power supply (204) supplies power to the resonant sensor (201). The computer (205) is a carrier for data processing and analysis of coupling stiffness estimation of the resonant sensor.

3. The method for estimating coupling stiffness of a differential resonant sensor according to claim 2, characterized in that: The mechanical signal in step 1 includes a displacement signal and a speed signal.

4. The method for estimating coupling stiffness of a differential resonant sensor according to claim 2, characterized in that: The electrical signal in step 1 includes a voltage signal and a current signal.

5. The method for estimating coupling stiffness of a differential resonant sensor according to any one of claims 1 to 4, characterized in that: In step 2, the open-loop frequency sweep of the resonator is to drive the resonator in a simple harmonic force sequence from low frequency to high frequency, or from high frequency to low frequency, with a fixed step size as the frequency increment of the signal. The frequency range of the frequency sweep refers to the range of frequency change from high to low or from low to high, and the frequency sweep step size is the minimum increment of the frequency change of the signal.

6. The method for estimating coupling stiffness of a differential resonant sensor according to any one of claims 1 to 4, characterized in that: The step 5 is specifically as follows: The differential resonant sensor composed of resonator 1 and resonator 2 can be regarded as a two-degree-of-freedom spring-mass system. According to Newton's law, the free vibration differential equation of the two-degree-of-freedom spring-mass system is obtained: Among them, m1 and m2 are the equivalent masses of the two resonators, k m1 , k m2 are the equivalent stiffness of the two resonators, k c is the coupling stiffness between the two resonators, x1 and x2 are the vibration displacements of the resonant beams of the corresponding resonators; The simple harmonic motion equation of the resonator's resonant beam bending vibration is: x=Xsin(2πft+θ) Wherein, x is the vibration displacement of the resonant beam, X is the maximum vibration displacement of the resonant beam, f is the resonant frequency of the resonant beam, t is the time, and θ is the phase; The free vibration differential equation of the two-degree-of-freedom spring-mass system and the simple harmonic motion equation of the bending vibration of the resonant beam are combined, and the equivalent masses of the two resonators are set equal, and the resonant frequency equation of the two-degree-of-freedom spring-mass system is obtained: Where f1 and f2 are the resonant frequencies of the two resonators of the two-degree-of-freedom spring-mass system, and m is the equivalent mass of the two resonators; According to Newton's law, the forced vibration differential equation of the two-degree-of-freedom spring-mass system is obtained: Among them, F1 and F2 are the simple harmonic forces applied to the two resonators respectively; By combining the forced vibration differential equation of the two-degree-of-freedom spring-mass system and the simple harmonic motion equation of the resonant beam bending vibration, the relationship between the vibration displacement of the resonant beams of the two resonators in the two-degree-of-freedom spring-mass system and the simple harmonic force is obtained: X=[K] -1 F in, The expression for the maximum amplitude of the resonant beam of the two resonators in the two-degree-of-freedom spring-mass system is obtained as: Assuming the equivalent masses of the two resonators are equal, both are m, the amplitude ratio of the two resonators at the two resonant frequencies of the two-degree-of-freedom spring-mass system is obtained: Wherein, X1(f1) and X1(f2) represent the amplitude values ​​of resonator 1 at f1 and f2, respectively, X2(f1) and X2(f2) represent the amplitude values ​​of resonator 2 at f1 and f2, respectively, u1 is the ratio of the amplitude of resonator 1 at f1 to the amplitude of resonator 2 at f1, and u2 is the ratio of the amplitude of resonator 2 at f2 to the amplitude of resonator 1 at f2; When the sensor is driven single-ended and resonator 1 is driven alone, that is, no harmonic force is applied to resonator 2, and only harmonic force is applied to resonator 1, F1≠0, F2=0, and the amplitude ratio equation of the two resonators at the resonant frequency of resonator 1 is obtained: The resonant frequency equation of the two-degree-of-freedom spring-mass system and the amplitude ratio equation of the two resonators at the resonant frequency of resonator 1 are combined to obtain the coupling stiffness of the differential resonant sensor: When the sensor is driven single-ended and resonator 2 is driven alone, that is, no harmonic force is applied to resonator 1, and only harmonic force is applied to resonator 2, F1 = 0, F2 ≠ 0, and the amplitude ratio equation of the two resonators at the resonant frequency of resonator 2 is obtained: The resonant frequency equation of the two-degree-of-freedom spring-mass system and the amplitude ratio equation of the two resonators at the resonant frequency of resonator 2 are combined to obtain the coupling stiffness of the differential resonant sensor: When the double-ended sensor is driven, the two resonators are driven at the same time, that is, simple harmonic forces are applied to the two resonators at the same time, F1 = F2 ≠ 0, and the amplitude ratio equation of the two resonators at the resonant frequency of resonator 1 is obtained: The resonant frequency equation of the two-degree-of-freedom spring-mass system and the amplitude ratio equation of the two resonators at the resonant frequency of resonator 1 are combined to obtain the coupling stiffness of the differential resonant sensor: When the double-ended sensor is driven, the two resonators are driven at the same time, that is, simple harmonic forces are applied to the two resonators at the same time, F1 = F2 ≠ 0, and the amplitude ratio equation of the two resonators at the resonant frequency of resonator 2 is obtained: The resonant frequency equation of the two-degree-of-freedom spring-mass system and the amplitude ratio equation of the two resonators at the resonant frequency of resonator 2 are combined to obtain the coupling stiffness of the differential resonant sensor: When only resonator 1 is driven, the amplitude ratio u=X1(f1) / X2(f1) is calculated. When only resonator 2 is driven, the amplitude ratio u=X2(f2) / X1(f2) is calculated. When resonator 1 and resonator 2 are driven at the same time, the amplitude ratio u=X1(f1) / X2(f1) or u=X2(f2) / X1(f2) is calculated. Substituting into the following formula, the coupling stiffness k of the differential resonant sensor is obtained. c :

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