Hemispherical harmonic oscillator quality factor estimation method based on vibration pickup circuit

Abstract

The invention discloses a hemispherical harmonic oscillator quality factor estimation method based on a vibration pickup circuit, and belongs to the technical field of inertia. According to the invention, the problem of low test precision of the quality factor of the hemispherical resonator based on a vibration pickup circuit in the prior art is solved. According to the method, a vibration pick-up circuit model with a trans-impedance amplifier as a core is analyzed, the mechanism that the vibration pick-up circuit causes extra energy dissipation of the hemispherical resonator is obtained, and the quantitative relation between the total quality factor of the circuit and the direct-current high voltage under a double-channel synchronous detection scheme is given. Aiming at the scenes that the mechanical property change is relatively large and the quality factor of a vibration pickup circuit is reduced in the manufacturing process of the hemispherical resonator gyroscope, the least square method disclosed by the invention can be used for effectively reducing the misjudgment on the quality factor caused by errors in the gyroscope manufacturing process through data processing, and the testing precision of the quality factor of the hemispherical resonator is improved. The method can be applied to hemispherical harmonic oscillator quality factor estimation.

Description

Technical Field

[0001] The invention belongs to the field of inertial technology, and in particular relates to a method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit. Background Art

[0002] The hemispherical resonator gyroscope (HRG) is a rate-integrating gyroscope based on the Coriolis effect. It senses the angular velocity of the gyroscope by detecting the vibration signal of the hemispherical resonator. It has the advantages of simple structure, wide detection range, and strong anti-interference ability.

[0003] When evaluating the mechanical properties of a hemispherical resonator gyroscope (HRG), especially estimating its quality factor, a vibration pickup circuit is often used to detect the HRG's vibration signal in a non-contact manner. However, when sampling the weak current signal caused by the resonator's vibration, the vibration pickup circuit causes excessive energy dissipation, which affects the accuracy of the HRG's quality factor measurement. Therefore, it is necessary to analyze the impact of the HRG's energy dissipation characteristics on the vibration pickup circuit so that compensation can be used to improve the accuracy of the HRG's quality factor estimation. Summary of the Invention

[0004] The purpose of the present invention is to solve the problem of low testing accuracy of the quality factor of a hemispherical resonator by the existing method based on a vibration pickup circuit, and to propose a method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit, the method specifically comprising the following steps:

[0006] Step 1: Use the end face of the hemispherical resonator and the detection electrode to form the detection capacitor of the vibration pickup circuit, and establish the quality factor Q of the hemispherical resonator gyroscope as a whole and the quality factor Q of the hemispherical resonator. r and the overall quality factor Q of the vibration pickup circuit T relationship;

[0007] Step 2: In the DC high voltage range [U s (1),U s (N)], and the sequence of N DC high voltage sample points is recorded as {U s (1),U s (2),…U s (N)};

[0008] Step 3: Drive the hemispherical resonator of the hemispherical resonator gyroscope to vibrate, and obtain the overall quality factor {Q(1), Q(2), ..., Q(N)} of the hemispherical resonator gyroscope corresponding to each DC high-voltage sample point. Perform the least square method on the obtained N groups of data to solve the quality factor Q of the hemispherical resonator. r .

[0009] The beneficial effects of the present invention are:

[0010] This paper first analyzes a vibration pickup circuit model centered on a transimpedance amplifier, deriving the mechanism by which the vibration pickup circuit causes additional energy dissipation in the hemispherical resonator. It also presents a quantitative relationship between the circuit's total quality factor and the DC high voltage under a dual-channel synchronous detection scheme. Next, a least-squares-based method for estimating the quality factor of a hemispherical resonator is proposed, addressing scenarios where mechanical properties vary significantly during the manufacturing process of a hemispherical resonator gyroscope and the quality factor of the vibration pickup circuit decreases. Data processing can effectively reduce misjudgments of the quality factor caused by errors in the gyroscope manufacturing process, improve the test accuracy of the hemispherical resonator's quality factor, and replace complex quality factor measurement methods such as laser vibrometers. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a flow chart of a method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit of the present invention;

[0012] Figure 2 This is a schematic diagram of a typical resonator vibration pickup circuit with a transimpedance amplifier as its core;

[0013] Figure 3 This is the schematic diagram of the circuit after the first equivalent transformation;

[0014] Figure 4 This is the schematic diagram of the circuit after the second equivalent transformation;

[0015] Figure 5 This is the schematic diagram of the circuit after the third equivalent transformation;

[0016] Figure 6 This is a schematic diagram of a typical dual-channel synchronous drive detection circuit. DETAILED DESCRIPTION

[0017] Specific implementation method 1: Combination Figure 1 This embodiment describes a method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit, the method specifically comprising the following steps:

[0018] Step 1: Use the end face of the hemispherical resonator and the detection electrode to form the detection capacitor of the vibration pickup circuit, and establish the quality factor Q of the hemispherical resonator gyroscope as a whole and the quality factor Q of the hemispherical resonator. r and the overall quality factor Q of the vibration pickup circuit T relationship;

[0019] Step 2: In the DC high voltage range [U s (1),U s (N)], and the sequence of N DC high voltage sample points is recorded as {U s (1),U s (2),…U s (N)};

[0020] Step 3: Figure 6 As shown in the figure, the hemispherical resonator of the hemispherical resonator gyroscope is driven to vibrate, and N quality factor measurement experiments are performed to obtain the overall quality factor {Q(1), Q(2), ..., Q(N)} of the hemispherical resonator gyroscope corresponding to each DC high voltage sample point. The quality factor Q of the hemispherical resonator is solved by the least square method for the N sets of data obtained. r .

[0021] The present invention establishes a hemispherical resonator vibration pickup circuit model with a transimpedance amplifier as the main component, analyzes the influence of the vibration pickup circuit on the energy dissipation characteristics and quality factor of the gyroscope, and proposes an estimation method based on the least squares method. By applying different DC voltages, a more accurate quality factor estimation value is obtained.

[0022] Specific embodiment 2: This embodiment differs from the specific embodiment 1 in that the quality factor Q of the hemispherical resonator gyroscope as a whole and the quality factor Q of the hemispherical resonator are r and the overall quality factor Q of the vibration pickup circuit T The relationship is:

[0023] Q=(Q r -1 +Q T -1 ) -1

[0024] The superscript -1 indicates the reciprocal.

[0025] Other steps and parameters are the same as those in the first embodiment.

[0026] Specific embodiment three: This embodiment differs from specific embodiment one or two in that the resonator end surface of the hemispherical resonator and the 0° detection electrode, and the resonator end surface and the 45° detection electrode respectively constitute detection capacitors of the vibration pickup circuit.

[0027] Other steps and parameters are the same as those in the first or second embodiment.

[0028] In the present invention, data when the end face of the resonator and the 0° detection electrode form a detection capacitor and data when the end face of the resonator and the 45° detection electrode form a detection capacitor are collected respectively.

[0029] Specific embodiment 4: This embodiment differs from any one of specific embodiments 1 to 3 in that the total quality factor Q of the vibration pickup circuit is T The calculation method is:

[0030] When the resonator end face of the hemispherical resonator and the detection electrode form the detection capacitor of the vibration pickup circuit, the total quality factor of the vibration pickup circuit is:

[0031]

[0032] Where k is the Coulomb constant, m0 is the equivalent modal mass of the resonator, d0 is the average distance between the end face of the resonator and the detection electrode, ω0 is the natural frequency of the resonator vibration, S is the area of ​​the capacitance formed by the end face of the resonator and the detection electrode, and U s is DC high voltage, R i is the resistance of the film layer, θ is the azimuth angle of the resonator standing wave, θ e To detect the electrode azimuth;

[0033] θ e =0° and θ e =45° and substitute into Q t (2θ,2θ e ), the total quality factor Q of the vibration pickup circuit is obtained T .

[0034] The other steps and parameters are the same as those in the first to third embodiments.

[0035] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the total quality factor Q of the vibration pickup circuit is T for:

[0036]

[0037] The other steps and parameters are the same as those in the first to fourth embodiments.

[0038] make Then K can be regarded as a parameter related to the resonator and the vibration pickup circuit itself, and will remain unchanged after the hemispherical resonator gyroscope is assembled.

[0039] Specific embodiment 6: This embodiment differs from the specific embodiments 1 to 5 in that the quality factor Q of the hemispherical resonator is solved by the least square method on the obtained N sets of data. r The specific process is:

[0040] According to the overall quality factor Q of the hemispherical resonator gyroscope and the quality factor Q of the hemispherical resonator r and the total quality factor Q of the vibration pickup circuit T The relationship is:

[0041] HX=Y

[0042] Among them, the intermediate variable matrix K is an intermediate variable, Q(1), Q(2), ..., Q(N) represent the DC high voltage sample points U s (1),U s (2),…U s (N) The corresponding overall quality factor of the hemispherical resonant gyroscope;

[0043] The estimate of X is obtained by the least squares method

[0044] The other steps and parameters are the same as those in the first to fifth embodiments.

[0045] Specific embodiment seven: This embodiment differs from any one of the specific embodiments one to six in that the estimation for:

[0046]

[0047] Among them, the superscript T represents transposition;

[0048] according to in Get Q r -1 , and then get Q r ,in, for The first element in .

[0049] The other steps and parameters are the same as those in the first to sixth embodiments.

[0050] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the intermediate variable K is:

[0051]

[0052] The other steps and parameters are the same as those in the first to seventh embodiments.

[0053] Specific embodiment 9: This embodiment differs from any one of the specific embodiments 1 to 8 in that in the DC high voltage range [U s (1),U s (N)], select N DC high voltage sample points, specifically:

[0054] For DC high voltage section [U s (1),U s (N)] is divided into equal intervals to obtain N DC high-voltage sample points including the two interval endpoints and all equally divided points.

[0055] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0056] Aiming at the problem that the quality factor of the vibration pickup circuit decreases after increasing the DC high voltage, the present invention adopts the least squares method to batch process the quality factor Q of the hemispherical resonator. r Make a more precise estimate.

[0057] The DC high voltage U selected by the present invention s The voltage sampling sequence {U s (1),U s (2),…U s (N)}. Perform N quality factor measurement experiments to obtain the Q value test sequence {Q(1), Q(2), ..., Q(N)}. Based on the relationship of the fifth embodiment, the standard form of the least square method as shown in the sixth and seventh embodiments is constructed, and the quality factor estimate of the hemispherical resonator can be finally solved as

[0058] The specific process of the method of the present invention is shown in Table 1:

[0059] Table 1

[0060]

[0061] In addition, if the area S and equivalent modal mass m0 are obtained by finite element analysis of the hemispherical resonator, it can also be used Obtaining an estimate of the oscillator assembly spacing d0 will help other analyses of the hemispherical oscillator.

[0062] The overall quality factor of the vibration pickup circuit is calculated as follows:

[0063] The core component of the hemispherical resonator gyroscope is the hemispherical resonator, which is made of high-purity fused quartz. A layer of metal film with good conductivity is plated on the surface of the end face of the resonator and the surface of the flat electrode substrate to form 8 excitation and detection electrodes. The detection electrode converts the vibration signal of the resonator into a change in capacitance value, and introduces the capacitance value change signal into the vibration pickup circuit to detect the vibration of the hemispherical resonator. Figure 2 As shown, the DC high voltage U s , R f1 、R f2 、C f1 、C f2 Constructing a second-order low-pass filter, R i is the resistance of the film layer, C d is the detection capacitor formed by the end face of the resonator and the detection electrode, R f 、C f Together with the operational amplifier, it forms a transimpedance amplifier.

[0064] A transimpedance amplifier is a circuit that converts and amplifies the weak output current of a sensor into a volt-level voltage. i is the resistance of the film layer, C d It is the detection capacitor formed by the end face of the resonator and the detection electrode. s After passing through the second-order low-pass filter circuit, it is transmitted to the end face of the resonator through the membrane layer. The detection electrode is connected to the input end of the transimpedance amplifier, and the output voltage signal can represent the vibration of the resonator and detect the capacitance C. d for:

[0065]

[0066] Among them, ω0 and are the natural frequency and initial phase of the oscillator, d Δ is the vibration amplitude of the end face at the position of the detection electrode, d0 is the average distance between the end face of the resonator and the detection electrode, S is the facing area of ​​the capacitance formed by the end face of the resonator and the detection electrode, and k is the Coulomb constant.

[0067] Using the impedance equivalent transformation method Figure 2 The vibration pickup circuit is simplified, such as Figure 3 As shown, first, the second-order low-pass filter and the film resistance are equivalent to the impedance Z1, and the transimpedance amplifier is equivalent to Z2. The expressions of Z1 and Z2 are as follows:

[0068]

[0069] Where j is the imaginary unit and GBW is the gain-bandwidth product of the non-ideal op amp;

[0070] GBW=R′f ·f BW ·2π (4)

[0071] Where R′ f is the feedback resistor, f BW For bandwidth.

[0072] For a given op amp model, GBW is a constant within its operating frequency range, and the op amp's open-loop gain A(ω) is approximated by a single-pole model, which is:

[0073]

[0074] Based on this, we can get the current controlled voltage source U0 and the input current I d Relationship:

[0075]

[0076] Due to the stability of the natural frequency of the hemispherical resonant gyroscope, the vibration pickup circuit can be considered to operate at a single frequency point ω0, such as Figure 4 As shown in the figure, based on the impedance equivalent transformation, the impedance Z2 and the capacitance C d Exchange positions, Z1 and Z2 are connected in series to form impedance Z e ,have to:

[0077] Z e =Z1+Z2 (7)

[0078] Further, in order to facilitate the analysis of the current, such as Figure 5 As shown, the impedance Z e Decomposed into resistance R e With capacitor C e In parallel, we get:

[0079]

[0080] Where Re(·) represents the real part, and Im(·) represents the imaginary part;

[0081] The current at this time satisfies formula (9):

[0082]

[0083] Solve equation (9) to get the detection current i d :

[0084] i d =-ω0U s ·C Δ sinω0t (10)

[0085] Based on the phasor method, the detection current i is obtained d with Id The relationship is shown in formula (11):

[0086]

[0087] Among them, ∠0° means 0° is the reference;

[0088] According to formula (10) and formula (11), I d , and then I d Substituting into equation (6), we can get the output equation of the final vibration pickup circuit:

[0089]

[0090] Where φ0 is the output current i d With voltage u d The phase shift between the hemispherical resonator vibration signal and the vibration pickup circuit is φ0-90°. For formula (12), consider the resonator capacitance signal C Δ With the output voltage u d When the DC high voltage U s Or feedback impedance Z e When it increases, the gain of the vibration pickup circuit for the capacitance signal will also increase.

[0091] In the actual vibration pickup circuit, in order to improve the real-time performance of signal conversion, the feedback capacitor C f The phase shift is designed to be almost negligible, and the detection current i caused by the vibration of the resonator d Almost all of the current flows through the feedback resistor R f , in each vibration cycle of the resonator, the film resistance R i There will be additional energy dissipation, which will increase the energy required to be supplemented to the resonator and reduce the excitation efficiency of the resonator.

[0092] According to formula (10), R i The additional energy dissipation ΔE caused t :

[0093]

[0094] When the hemispherical resonator is stably oscillating, the mechanical energy of the hemispherical resonator is equal to its maximum kinetic energy. The relationship between the mechanical energy of the hemispherical resonator, the amplitude a of the resonator standing wave, and the equivalent modal mass m0 of the resonator is as follows:

[0095]

[0096] Where a is the standing wave amplitude of the resonator, and m0 is the equivalent modal mass of the resonator.

[0097] According to the calculation formula of the resonant circuit quality factor, the quality factor of the vibration pickup circuit is obtained as shown in formula (15):

[0098]

[0099] Among them, d Δ is the vibration amplitude of the end face of the hemispherical resonator, d Δ The azimuth angle 2θ of the resonator standing wave and the azimuth angle 2θ of the electrode e The relationship is:

[0100] d Δ =acos(2θ-2θ e ) (16)

[0101] Therefore, we can further obtain the quality factor expression related to the electrode position:

[0102]

[0103] like Figure 6 The figure shows a typical dual-channel detection scheme for a hemispherical resonator gyroscope. There are 8 electrodes in total, of which 4 are driving electrodes and 4 are detection electrodes. The 0° electrode and the 180° electrode are connected in parallel to form the x detection channel; the 45° electrode and the 225° electrode are connected in parallel to form the y detection channel. The end faces of the resonator form detection capacitors with the 0° and 45° detection electrodes respectively. e The quality factor of the entire detection circuit is obtained as shown in formula (18):

[0104]

[0105] According to formula (18), as the distance d0 between the resonator and the electrode substrate increases, the DC high voltage U s The reduction or resistance R i As the value of is reduced, the energy loss caused by the vibration pickup circuit will be reduced accordingly, and the quality factor will be improved. However, as can be seen from Equation (12), the efficiency of the resonator's vibration detection and excitation will be reduced. Therefore, it is necessary to balance the relationship between energy loss and detection efficiency and select appropriate resonator and circuit parameters.

[0106] The above examples are merely illustrative of the calculation model and process of the present invention and are not intended to limit the embodiments of the present invention. Persons skilled in the art will readily appreciate that other variations or modifications based on the above description are possible. This list of embodiments is not exhaustive; however, any obvious variations or modifications derived from the technical solution of the present invention remain within the scope of protection of the present invention.

Claims

1. A method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit, characterized in that: The method specifically comprises the following steps: Step 1: Use the end face of the hemispherical resonator and the detection electrode to form the detection capacitor of the vibration pickup circuit, and establish the quality factor Q of the hemispherical resonator gyroscope as a whole and the quality factor Q of the hemispherical resonator. r and the overall quality factor Q of the vibration pickup circuit T relationship; Step 2: In the DC high voltage range [U s (1),U s (N)], and the sequence of N DC high voltage sample points is recorded as {U s (1),U s (2),…U s (N)}; Step 3: Drive the hemispherical resonator of the hemispherical resonator gyroscope to vibrate, and obtain the overall quality factor {Q(1), Q(2), ..., Q(N)} of the hemispherical resonator gyroscope corresponding to each DC high-voltage sample point. Perform the least square method on the obtained N groups of data to solve the quality factor Q of the hemispherical resonator. r .

2. The method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit according to claim 1, wherein: The quality factor Q of the hemispherical resonator gyroscope as a whole and the quality factor Q of the hemispherical resonator are r and the overall quality factor Q of the vibration pickup circuit T The relationship is: Q=(Q r -1 +Q T -1 ) -1 The superscript -1 indicates the reciprocal.

3. The method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit according to claim 2, wherein: The resonator end surface of the hemispherical resonator and the 0° detection electrode, and the resonator end surface and the 45° detection electrode respectively constitute detection capacitors of the vibration pickup circuit.

4. The method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit according to claim 3, wherein: The overall quality factor Q of the vibration pickup circuit T The calculation method is: When the resonator end face of the hemispherical resonator and the detection electrode form the detection capacitor of the vibration pickup circuit, the total quality factor of the vibration pickup circuit is: Where k is the Coulomb constant, m0 is the equivalent modal mass of the resonator, d0 is the average distance between the end face of the resonator and the detection electrode, ω0 is the natural frequency of the resonator vibration, S is the area of ​​the capacitance formed by the end face of the resonator and the detection electrode, and U s is DC high voltage, R i is the resistance of the film layer, θ is the azimuth angle of the resonator standing wave, θ e To detect the electrode azimuth; θ e =0° and θ e =45° and substitute into Q t (2θ,2θ e ), and the total quality factor Q of the vibration pickup circuit is obtained T .

5. The method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit according to claim 4, wherein: The overall quality factor Q of the vibration pickup circuit T for:

6. The method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit according to claim 2, wherein: The quality factor Q of the hemispherical resonator is solved by the least square method on the obtained N groups of data. r The specific process is: According to the overall quality factor Q of the hemispherical resonator gyroscope and the quality factor Q of the hemispherical resonator r and the total quality factor Q of the vibration pickup circuit T The relationship is: HX=Y Among them, the intermediate variable matrix K is an intermediate variable, Q(1), Q(2), ..., Q(N) represent the DC high voltage sample points U s (1),U s (2),…U s (N) The corresponding overall quality factor of the hemispherical resonant gyroscope; The estimate of X is obtained by the least squares method 7. The method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit according to claim 6, wherein: The estimate for: Among them, the superscript T represents transposition; according to in Get Q r -1 , and then get Q r ,in, for The first element in .

8. The method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit according to claim 6, wherein: The intermediate variable K is:

9. The method for estimating the quality factor of a hemispherical resonator based on a vibration pickup circuit according to claim 1, wherein: In the DC high voltage interval [U s (1),U s (N)], select N DC high voltage sample points, specifically: For DC high voltage section [U s (1),U s (N)] is divided into equal intervals to obtain N DC high-voltage sample points including the two interval endpoints and all equally divided points.

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