Method for Extracting Sensitive Probe Parameters and Calculating Degrees of Freedom Coupling of Capacitive Displacement Sensor

Abstract

This invention discloses a method for extracting parameters and calculating degree-of-freedom coupling of a capacitive displacement sensor's sensitive probe, belonging to the field of signal analysis and detection technology. This invention applies multiple sets of charge excitations to a multi-conductor mechanical sensitive probe, uses numerical methods to obtain the electrostatic field distribution inside the sensitive probe under each set of excitation charges, and calculates the electrostatic field energy accordingly, ultimately calculating the distributed capacitance matrix of the entire sensitive probe. For the coupling between the output degrees of freedom of the multi-degree-of-freedom capacitive displacement sensor caused by the sensitive probe, an indeterminate admittance matrix of the sensitive probe is established and connected to subsequent multi-channel sensing circuits to form a complete equivalent circuit model for multi-degree-of-freedom coupling analysis. This allows for the quantitative calculation of the degree of coupling between the output signals of the multi-channel sensing circuits caused by the displacement of the test mass in the sensitive probe. This method can also be extended to the output analysis of arbitrarily complex array circuits.

Description

Technical Field

[0001] This invention belongs to the field of signal analysis and detection technology, and more specifically, relates to a method for extracting sensitive probe parameters and calculating degrees of freedom coupling of a capacitive displacement sensor. Background Technology

[0002] Signal analysis and detection technology is widely used in aerospace, communication equipment, satellite communication, space gravitational wave detection and other fields, and is one of the important research contents in communication, aerospace equipment design and other fields.

[0003] Inertial sensors, as one of the key payloads of space-based gravitational wave detection devices, provide an inertial reference for laser interferometry. For example... Figure 1 As shown, the sensitive probe consists of a centrally located inspection mass, surrounding injection plates and sensing plates, and a metal outer frame. To facilitate the illustration of the connection between the sensitive probe and the capacitive displacement sensing circuit, Figure 1 The metal outer frame structure is not described. The inspection mass inside the sensing probe is the core of the inertial sensor. The main purpose of the inertial sensor is to keep the inspection mass freely suspended at the center of the sensing probe's electrode frame, unaffected by the satellite platform and space environment. Changes in the displacement of the inspection mass will cause changes in the distributed capacitance between the sensing probe's sensing electrode and the inspection mass.

[0004] Capacitive displacement sensing circuits are key components in inertial sensors. They obtain the displacement change of the inspection mass by measuring the change in distributed capacitance between the sensing plate of the mechanical sensitive probe and the internal inspection mass. Therefore, extracting the distributed capacitance parameters between the multiple conductors in the sensitive probe structure provides crucial technical support for a comprehensive analysis of the displacement change of the inspection mass within the sensitive probe. Simultaneously, the abundant distributed capacitance within the sensitive probe causes the inspection mass, displacing only along one degree of freedom, to simultaneously induce non-zero displacement outputs in the other five degrees of freedom of the displacement sensing circuit, thus creating coupling between the output displacement degree-of-freedom signals. Analyzing and calculating the degree of coupling between the output signals of the multi-channel capacitive displacement sensing circuit caused by the displacement of the inspection mass in the sensitive probe is a significant technical challenge.

[0005] Currently, some scholars have analyzed the electrostatic coupling effect of the non-sensitive axis (i.e., Y and Z axes) of the sensitive probe to the sensitive axis (i.e., X axis) from the perspective of physical mechanics.

[0006] This invention extracts the distributed capacitance of the mechanically sensitive probe in the inertial sensor from the perspective of electromagnetic field and circuit, and analyzes the output signal of the equivalent circuit model after the sensitive probe is connected to the multi-degree-of-freedom capacitive displacement sensing circuit, thereby calculating the coupling between the multi-degree-of-freedom displacement signals. Summary of the Invention

[0007] The present invention aims to provide a method for extracting the distributed capacitance parameters of the mechanical sensing probe of a capacitive displacement sensor and for calculating the coupling between the output degrees of freedom of a multi-degree-of-freedom capacitive displacement sensor caused by the sensing probe.

[0008] By applying multiple sets of charge excitations to the mechanically sensitive probe with a multi-conductor structure, the electrostatic field distribution inside the sensitive probe under each set of excitation charges is obtained by numerical method, and the electrostatic field energy is calculated accordingly, thereby finally calculating the distributed capacitance matrix of the entire sensitive probe.

[0009] By establishing the indefinite admittance matrix of the sensitive probe and connecting it to the subsequent multi-channel sensing circuit, a complete equivalent circuit model for multi-degree-of-freedom coupling analysis is formed. This allows for the quantitative calculation of the coupling degree between the output signals of the multi-channel sensing circuit caused by the displacement of the test mass in the sensitive probe.

[0010] To achieve the above objectives, this invention provides a method for extracting sensitive probe parameters and calculating degrees of freedom coupling of a capacitive displacement sensor, comprising the following steps:

[0011] Step 1: For the multi-conductor structure of the sensitive probe, the internal inspection mass is subjected to translational or rotational displacements with different degrees of freedom. N(N+1) / 2 sets of conductor excitation charges are set. The three-dimensional electrostatic field distribution under each set of excitation charges is calculated and the electrostatic field energy is calculated accordingly. Thus, the full capacitance matrix of the sensitive probe under different translational or rotational displacements is obtained, where N is the number of conductors in the sensitive probe.

[0012] Step 2: Based on the total capacitance matrix of the sensitive probe extracted in Step 1, obtain the capacitance between any two conductors of the sensitive probe, and then calculate the indefinite admittance matrix Y of the N-port network of the sensitive probe. N×N ;

[0013] Step 3: Based on the full capacitance matrix of the sensitive probe extracted in Step 1, and combined with the specific connection method of the N external nodes of the sensitive probe and the capacitance displacement sensing circuit of each channel, establish an equivalent circuit model. Directly write the equation I = YV satisfied by the voltage and current of the N nodes from the indefinite admittance matrix. Then, substitute the VI characteristics satisfied by the external termination elements of the N nodes into the above equation to obtain the voltage and current at each node. Finally, the output complex voltage of each capacitance displacement sensing circuit channel can be obtained.

[0014] Step 4: Using the full capacitance matrix of the sensitive probe extracted in Step 1 at different translational or rotational displacements, interpolate and fit the sequence of values ​​of each distributed capacitance changing with displacement to obtain the continuous change curve of each distributed capacitance with displacement.

[0015] Step 5: Arbitrarily specify the time-varying mode of the test mass displacement in the sensitive probe, and according to the curve of the change of each distributed capacitance with displacement obtained in Step 4, obtain the value of each distributed capacitance at each displacement moment, and then use it in the complex voltage calculation of the output of each capacitor displacement sensing circuit channel in Step 3.

[0016] Step 6: Combine the time series of the output complex voltage of each capacitive displacement sensing circuit channel with displacement degrees of freedom, and then perform Fourier transform to obtain the spectrum of the output signal of each displacement degree of freedom. Calculate the coupling degree between each displacement degree of freedom caused by the sensitive probe.

[0017] Furthermore, in step 1, Q (k) The excitation charge applied to the N conductors of the k-th group of the mechanically sensitive probe is:

[0018]

[0019] in, Let Q be the excitation charge of the kth group. (k) The charge on the nth conductor in the diagram can take the values ​​of -1 coulomb, +1 coulomb, or zero coulomb, and must satisfy the following conditions: And the requirement that different groups have different excitation charges, or to meet the following conditions. And the requirement that different groups have different excitation charges.

[0020] Furthermore, in step 1, numerical methods such as the finite difference method are used to calculate and obtain the k-th group of excitation charges Q. (k) The three-dimensional electrostatic field distribution E in the internal medium region of the mechanically sensitive probe during operation (k) Then, α is calculated using the following formula. ij α ij Let be the matrix element in the i-th row and j-th column of an N×N symmetric matrix α, where i,j=1,2,…,N:

[0021]

[0022] Where ε is the dielectric constant of the medium filling the sensitive probe. To determine the electric field distribution E inside the sensitive probe (k) Calculate the electrostatic field energy in the spatial region τ; obtain α from the above formula. ij Then an N×N symmetric matrix α is constructed;

[0023] Then from β=α -1 Calculate matrix β, whose elements are β. ij , i,j=1,2,…,N;

[0024] The distributed capacitance C between the i-th conductor and the j-th conductor in the sensitive probe is calculated using the following formula. ijThe distributed capacitance C between the i-th conductor and the metal outer frame of the sensitive probe ii :

[0025] C ij =-β ij (i≠j)

[0026]

[0027] This yields the total capacitance matrix C of the sensitive probe. N×N It is a symmetric matrix.

[0028] Furthermore, in step 2, the N-port indefinite admittance matrix Y of the sensitive probe... N×N The calculation method is as follows:

[0029] Step 2-1: Number the nodes of the N conductors of the sensitive probe in sequence, and take the metal outer frame of the sensitive probe as the common node;

[0030] Step 2-2: Based on the extracted total capacitance matrix of the sensitive probe, calculate the indefinite admittance matrix for the distributed capacitance between any two conductors of the sensitive probe, where the distributed capacitance C between node i and node j is... i,j The corresponding indefinite admittance matrix is:

[0031]

[0032] in, ω is the angular frequency of the carrier signal, and N is the number of conductors in the sensitive probe;

[0033] Steps 2-3: Summate the indeterminate admittance matrices of all distributed capacitances to obtain the N-port indeterminate admittance matrix Y of the sensitive probe. N×N .

[0034] Furthermore, in step 3, the injection plate of the sensitive probe is connected to the carrier voltage source, and the sensing plate of the sensitive probe is connected to the capacitive displacement sensing circuit. All N conductor plates of the sensitive probe are external nodes, thus establishing an equivalent circuit model of the sensitive probe connected to the multi-channel capacitive displacement sensing circuit. The equation I = YV satisfied by the voltage and current of the N nodes is directly written from the indefinite admittance matrix, the voltage of the N nodes of the sensitive probe is calculated, and then the output complex voltage of each capacitive displacement sensing circuit channel is obtained.

[0035] Furthermore, in step 5, the time-varying displacement x(t) of the test quality in any specified sensitive probe is sampled at a frequency f. s=M1f0 is used for sampling, where f0 is the highest frequency of the time-varying displacement of the test quality, M1 is the value that the sampled value can contain all the information of the original signal, and M1≥2, the total number of sampling points is M1M2, M2 is the number of sampling periods, and t is the sampling time. m for:

[0036]

[0037] By combining the curves of the distributed capacitance as a function of displacement obtained in step 4, the sampling time t can be obtained. m The values ​​of the distributed capacitance of each sensitive probe corresponding to the quality displacement at the test point;

[0038] Then, it is used in the equivalent circuit model established in step 3 to perform AC steady-state response analysis, and t is obtained. m The complex voltage V output of each channel of the capacitive displacement sensing circuit at any time oi (t m ), i = 1, 2, ..., k, where k is the number of channels in the displacement sensing circuit;

[0039] Then, the output complex voltages of each channel at all sampling times are combined in the order of sampling times to obtain the time series of the output complex voltages of each channel.

[0040]

[0041] Further, in step 6, according to the displacement degree-of-freedom combination rule, the output complex voltage time series of each channel is combined with the displacement degrees of freedom; then, a Fourier transform is performed to obtain the output signal spectrum corresponding to each displacement degree of freedom: as well as These correspond to the output signal spectra of translational and rotational displacements along the X, Y, and Z axes, respectively.

[0042] Furthermore, in step 6, if the inspection mass in the sensitive probe only translates along the X-axis, the coupling degree between the X-axis translational displacement degree-of-freedom output signal and the other five displacement degree-of-freedom output signals is calculated using the following formula:

[0043]

[0044]

[0045] Where f0 is the highest frequency of the time-varying displacement of the test mass, |·| is the amplitude calculation on the spectrum, and C X-Y C represents the relative magnitude of the Y-axis output translational displacement signal caused by the X-axis translational displacement. X-Z The relative magnitude of the Z-axis output translational displacement signal caused by the X-axis translational displacement. The relative magnitude of the output displacement signal is the rotation around the Z-axis caused by the translational displacement along the X-axis. The relative magnitude of the output displacement signal is the rotation around the X-axis caused by the translational displacement along the X-axis. The relative magnitude of the rotation around the Y-axis caused by the translational displacement along the X-axis is output as the displacement signal. as well as The output signal spectra correspond to the translational and rotational displacements along the X, Y, and Z axes, respectively.

[0046] In the same manner, the coupling degree of each output degree of freedom displacement caused by the inspection mass along other degrees of freedom displacements is calculated.

[0047] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0048] (1) This invention solves the problem of calculating the total capacitance matrix of N conductors in a sensitive probe by setting N(N+1) / 2 sets of excitation charges on N conductors in the sensitive probe structure, calculating the electrostatic field distribution under each set of excitation charges, and then calculating the electrostatic field energy. The idea of ​​using the electrostatic field distribution under charge excitation to obtain the electrostatic field energy and then calculating the total capacitance matrix of multiple conductors can be applied to the capacitance extraction of multi-conductor structures such as the sensitive probe of an inertial sensor in space gravitational wave detection.

[0049] (2) This invention establishes the indefinite admittance matrix of the sensitive probe and connects it to the subsequent multi-channel sensing circuit to form a complete equivalent circuit model for multi-degree-of-freedom coupling analysis. This is the key technology in the multi-degree-of-freedom coupling analysis calculation method of this invention, which can effectively solve the analysis and calculation of multi-port network and circuit connection in practical engineering applications.

[0050] (3) This invention proposes a multi-degree-of-freedom coupling calculation method, which can be applied to signal processing and analysis scenarios in multiple fields. It can effectively solve the problem of degree-of-freedom coupling analysis and calculation of multi-port networks (with coupling elements such as capacitors) in practical engineering applications. This invention has high engineering application value, low computational complexity, and good versatility. Attached Figure Description

[0051] Figure 1 This is a circuit diagram of a dual-channel capacitive displacement sensing circuit with a sensitive probe (N=17) in the X direction provided by the present invention.

[0052] Figure 2 This is a flowchart of the method for extracting sensitive probe parameters and calculating degrees of freedom of a capacitive displacement sensor provided by the present invention.

[0053] Figure 3This is a diagram showing the extraction result of the full capacitance matrix of the sensitive probe (N=17) provided in the embodiment of the present invention.

[0054] Figure 4 This is a graph showing the change in capacitance between a pair of sensing plates and the inspection mass as the sensitive probe (N=17) provided in this embodiment of the invention is moved along the X-axis direction by [-1,1] mm. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0056] like Figure 2 As shown, this invention provides a method for extracting sensitive probe parameters and calculating degrees of freedom coupling of a capacitive displacement sensor, including the following steps:

[0057] Step 1: For the multi-conductor structure (Nth conductor) of the sensitive probe, perform translational or rotational displacements of the internal inspection mass with different degrees of freedom, set N(N+1) / 2 sets of conductor excitation charges, and calculate the three-dimensional electrostatic field distribution function E under each set of excitation charges. (k) The electrostatic field energy is then calculated based on this, thereby obtaining the total capacitance matrix C for different translational or rotational displacements of the sensitive probe. N×N ;

[0058] Step 2: Based on the total capacitance matrix of the sensitive probe extracted in Step 1, obtain the capacitance between any two conductors of the sensitive probe, and then calculate the indefinite admittance matrix Y of the N-port network of the sensitive probe. N×N ;

[0059] Step 3: Based on the full capacitance matrix of the sensitive probe extracted in Step 1, and combined with the specific connection method of the N external nodes of the sensitive probe and the capacitive displacement sensing circuit of the k channels, establish an equivalent circuit model. Directly write the equation I = YV satisfied by the voltage and current of the N nodes from the indefinite admittance matrix. Then, substitute the VI characteristics satisfied by the external termination elements of the N nodes into the above equation to obtain the voltage and current at each node. Finally, the output complex voltage of each capacitive displacement sensing circuit channel can be obtained.

[0060] Step 4: Using the full capacitance matrix of the sensitive probe extracted in Step 1 at different translational or rotational displacements, interpolate and fit the sequence of values ​​of each distributed capacitance as a function of displacement to obtain the continuous variation curve of each distributed capacitance as a function of displacement.

[0061] Step 5: Arbitrarily specify the time-varying mode of the test mass displacement in the sensitive probe, and according to the curve of the change of each distributed capacitance with displacement obtained in Step 4 above, obtain the value of each distributed capacitance at each displacement moment, and then use it in the complex voltage calculation of the output of each capacitor displacement sensing circuit channel in Step 3 above.

[0062] Step 6: Combine the time series of the output complex voltage of each capacitive displacement sensing circuit channel with displacement degrees of freedom, and then perform Fourier transform to obtain the spectrum of the output signal of each displacement degree of freedom. From this, the coupling degree between each displacement degree of freedom caused by the sensitive probe can be calculated.

[0063] In this invention, the multi-channel configuration includes two channels along the X-axis, two channels along the Y-axis, and two channels along the Z-axis. The multiple degrees of freedom include: X-axis translational and rotational degrees of freedom, Y-axis translational and rotational degrees of freedom, and Z-axis translational and rotational degrees of freedom.

[0064] Example

[0065] This embodiment takes the extraction of sensitive probe parameters and the calculation of degree-of-freedom coupling of a capacitive displacement sensor containing 17 conductors in a six-degree-of-freedom capacitive displacement sensor as an example. The specific calculation steps are as follows:

[0066] Step 1: For a sensitive probe structure containing 17 conductors, including: 4 injection plates, 12 sensing plates, and 1 inspection mass, the internal inspection mass is subjected to translational or rotational displacements with different degrees of freedom, and 153 sets of conductor excitation charges are set: Q (k) The excitation charge applied to the N conductors of the k-th group of the mechanically sensitive probe is:

[0067]

[0068] in, Let Q be the excitation charge of the kth group. (k) The charge on the nth conductor in the diagram can take the values ​​of -1 coulomb, +1 coulomb, or zero coulomb, and must satisfy the following conditions: And the requirement that different groups have different excitation charges, or to meet the following conditions. And the requirement that different groups have different excitation charges.

[0069] The k-th excitation charge Q was calculated using numerical methods such as the finite difference method. (k) The three-dimensional electrostatic field distribution E in the internal medium region of the mechanically sensitive probe during operation (k) Then, α is calculated using the following formula. ij , i,j=1,2,…,17:

[0070]

[0071] Where ε is the dielectric constant of the medium filling the sensitive probe. To determine the electric field distribution E inside the sensitive probe (k) The electrostatic energy in the spatial region τ is calculated. α is obtained from the above equation. ij Then a 17×17 symmetric matrix α is constructed, and then β=α -1 Calculate matrix β, whose elements are β. ij Let i,j = 1,2,…,17. Then, the distributed capacitance C between the i-th conductor and the j-th conductor in the sensitive probe can be calculated using the following formula. ij The distributed capacitance C between the i-th conductor and the metal outer frame of the sensitive probe ii :

[0072]

[0073] Thus, the total capacitance matrix C of the sensitive probe is obtained. 17×17 It is a symmetric matrix.

[0074] Figure 3 The table presents the full capacitance matrix extraction results when the sensitive probe is in the equilibrium position. The leftmost and bottommost rows of numbers in the table represent the numbers of the 17 conductors of the sensitive probe. The dark gray squares mark the distributed capacitance between each plate of the sensitive probe and the metal outer frame, the light gray squares mark the distributed capacitance between adjacent plates, and the rest are the distributed capacitance between non-adjacent plates. The small text at the top of the 17th row, 17th column, and each diagonal cell represents the calculated value obtained according to the formula for calculating the mutual capacitance of parallel plate capacitors, and is shown in the figure for reference.

[0075] Step 2: Based on the extracted sensitive probe full capacitance matrix C 17×17 The distributed capacitance between the multiple conductors of the sensitive probe can be obtained, and then the indeterminate admittance matrix Y of the 17-port network of the sensitive probe can be calculated. 17×17 The calculation process is as follows:

[0076] 1) Number the 17 conductors in the sensitive probe structure sequentially, using the metal outer frame as a common reference point. The specific node numbers are as follows: 1: Front injection electrode (Y-); 2: Rear injection electrode (Y+); 3: Lower injection electrode (Z-); 4: Upper injection electrode (Z+); 5: Front sensing electrode 2 (Z-); 6: Rear sensing electrode 2 (Z-); 7: Front sensing electrode 1 (Z+); 8: Rear sensing electrode 1 (Z+); 9: Lower sensing electrode 1 (X-); 10: Upper sensing electrode 1 (X-); 11: Lower sensing electrode 2 (X+); 12: Upper sensing electrode 2 (X+); 13: Left sensing electrode 2 (Y-); 14: Right sensing electrode 2 (Y-); 15: Left sensing electrode 1 (Y+); 16: Right sensing electrode 1 (Y+); 17: Quality inspection.

[0077] 2) Only distributed capacitance exists between the nodes of the sensitive probe, where the distributed capacitance C between node i and node j is... i,j The corresponding indefinite admittance matrix is:

[0078]

[0079] in, ω is the angular frequency of the carrier signal, and the carrier signal frequency is 100kHz.

[0080] 3) All distributed capacitances C i,j Summing the indefinite admittance matrices yields the indefinite admittance matrix Y of the 17-port network of the sensitive probe. 17×17 .

[0081] Step 3: The four injection plates of the sensitive probe are connected to the carrier voltage source, and the twelve sensing plates are connected to the capacitive displacement sensing circuit. Furthermore, a distributed capacitance C exists between all sixteen plates, the inspection mass, and the metal outer frame. i,i The 17 conductors of the sensitive probe are all external nodes, thus establishing an equivalent circuit model of the sensitive probe connected to the six-channel capacitive displacement sensing circuit. The equation I = YV satisfied by the voltage and current of the 17 nodes can be directly written from the indefinite admittance matrix. Then, the VI characteristics satisfied by the external terminal components of the N nodes can be substituted into the above to obtain the voltage and current at each node. Finally, the output complex voltage of each capacitive displacement sensing circuit channel can be obtained.

[0082] Step 4: Using the full capacitance matrix of the sensitive probe extracted in Step 1 at different translational or rotational displacements, interpolate and fit the sequence of values ​​of each distributed capacitance with displacement to obtain the continuous variation curve of each distributed capacitance with displacement. Figure 4 The curves showing the capacitance change with displacement between a pair of sensing plates and the test mass when the sensitive probe is translated along the X-axis direction by [-1,1] mm are presented.

[0083] Step 5: The time-varying displacement of the inspection mass in the sensitive probe is x(t) = x m cos(2πf0t), the displacement signal frequency f0 is 9.765mHz, and the sampling frequency f for sampling the time-varying displacement is... s The frequency is 0.1Hz, the total number of sampling points m is 1024, and the sampling time t is... m :

[0084]

[0085] By combining the curves of the distributed capacitance as a function of displacement obtained in step 4 above, the sampling time t can be obtained. m The values ​​of the distributed capacitances of each sensitive probe corresponding to the mass displacement at the test point are then used in the equivalent circuit model established in step 3 above to perform AC steady-state response analysis, and t is obtained. m The complex voltage V output of each channel of the capacitive displacement sensing circuit at any time oi (t m ), i = 1, 2, ..., 6, where the displacement sensing circuit has 6 channels; then, the output complex voltages of each channel at all sampling times are sequentially combined to obtain the time series of the output complex voltages of each channel.

[0086]

[0087] Step 6: Compare the output complex voltage time series of each channel. Perform a Fourier transform to obtain the output voltage spectrum of each channel:

[0088]

[0089] The output complex voltage time series of the two channels of the sensitive probe in the X, Y, and Z axes respectively (the output complex voltage time series of the two channels in the X direction corresponds to...) and The output complex voltage time series of the two channels in the Y direction corresponds to and The output complex voltage time series of the two channels in the Z direction corresponds to and

[0090] The methods for constructing each displacement degree of freedom in this invention include, but are not limited to, linear combinations and polynomial combinations. This embodiment uses a linear combination method to construct each displacement degree of freedom:

[0091]

[0092] By performing a Fourier transform, the spectrum of the output signal for each displacement degree of freedom is obtained:

[0093]

[0094] The abundant distributed capacitance in the sensitive probe causes the inspection mass, moving only along one degree of freedom, to simultaneously induce non-zero displacement outputs in the other five degrees of freedom of the displacement sensing circuit. This creates coupling between the output displacement degree-of-freedom signals, which can be quantitatively characterized by the degree of coupling. Taking the inspection mass in the sensitive probe moving only along the X-axis as an example, the coupling degree between the X-axis translational displacement degree-of-freedom output signal and the output signals of the other five displacement degrees of freedom is defined as follows:

[0095]

[0096]

[0097] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for extracting parameters of a capacitive displacement sensor's sensitive probe and calculating its degrees of freedom coupling, characterized in that, Includes the following steps: Step 1: For the multi-conductor structure of the sensitive probe, the internal inspection mass is subjected to translational or rotational displacements with different degrees of freedom. N(N+1) / 2 sets of conductor excitation charges are set. The three-dimensional electrostatic field distribution under each set of excitation charges is calculated and the electrostatic field energy is calculated accordingly. Thus, the full capacitance matrix of the sensitive probe under different translational or rotational displacements is obtained, where N is the number of conductors in the sensitive probe. Step 2, based on the sensitive probe full capacitance matrix extracted in step 1, the capacitance between any two conductors of the sensitive probe is obtained, and thus the N-port network indefinite admittance matrix Y of the sensitive probe is calculated N×N ; Step 3: Based on the full capacitance matrix of the sensitive probe extracted in Step 1, and combined with the specific connection method of the N external nodes of the sensitive probe and the capacitance displacement sensing circuit of each channel, establish an equivalent circuit model. Directly write the equation I = YV satisfied by the voltage and current of the N nodes from the indefinite admittance matrix. Then, substitute the VI characteristics satisfied by the external termination elements of the N nodes into the above equation to obtain the voltage and current at each node. Finally, the output complex voltage of each capacitance displacement sensing circuit channel can be obtained. Step 4: Using the full capacitance matrix of the sensitive probe extracted in Step 1 at different translational or rotational displacements, interpolate and fit the sequence of values ​​of each distributed capacitance changing with displacement to obtain the continuous change curve of each distributed capacitance with displacement. Step 5: Arbitrarily specify the time-varying mode of the test mass displacement in the sensitive probe, and according to the curve of the change of each distributed capacitance with displacement obtained in Step 4, obtain the value of each distributed capacitance at each displacement moment, and then use it in the complex voltage calculation of the output of each capacitor displacement sensing circuit channel in Step 3. Step 6: Combine the time series of the output complex voltage of each capacitive displacement sensing circuit channel with displacement degrees of freedom, and then perform Fourier transform to obtain the spectrum of the output signal of each displacement degree of freedom. Calculate the coupling degree between each displacement degree of freedom caused by the sensitive probe.

2. The method according to claim 1, characterized in that, In step 1, Q (k) The excitation charge applied on the N conductors of the mechanically sensitive probe for the kth group: in, Let Q be the excitation charge of the kth group. (k) The charge on the nth conductor in the diagram can take the values ​​of -1 coulomb, +1 coulomb, or zero coulomb, and must satisfy the following conditions: And the requirement that different groups have different excitation charges, or to meet the following conditions. And the requirement that different groups have different excitation charges.

3. The method according to claim 1, characterized in that, In step 1, the finite difference method or other numerical method is used to calculate the kth group of excitation charges Q (k) The three-dimensional electrostatic field distribution E of the medium region inside the mechanical sensitive probe when in action (k) Then, α is calculated using the following formula ij , α ij The matrix element of the ith row and jth column in the N×N symmetric matrix α, i, j = 1, 2,..., N: Where ε is the dielectric constant of the medium filling the sensitive probe. To determine the electric field distribution E inside the sensitive probe (k) Calculate the electrostatic field energy in the spatial region τ; obtain α from the above formula. ij Then an N×N symmetric matrix α is constructed; Again, β = α -1 The matrix β is computed, whose elements are β ij , i,j = 1,2,...,N; The distributed capacitance C between the i-th conductor and the j-th conductor in the sensitive probe is calculated using the following formula. ij The distributed capacitance C between the i-th conductor and the metal outer frame of the sensitive probe ii : C ij =-β ij ,(i≠j) This yields the total capacitance matrix C of the sensitive probe. N×N It is a symmetric matrix.

4. The method according to claim 1, characterized in that, In step 2, the N-port indefinite admittance matrix Y of the sensitive probe N×N The calculation method is as follows: Step 2-1: Number the nodes of the N conductors of the sensitive probe in sequence, and take the metal outer frame of the sensitive probe as the common node; Step 2-2: Based on the extracted total capacitance matrix of the sensitive probe, calculate the indefinite admittance matrix for the distributed capacitance between any two conductors of the sensitive probe, where the distributed capacitance C between node i and node j is... i,j The corresponding indefinite admittance matrix is: in, ω is the angular frequency of the carrier signal, and N is the number of conductors in the sensitive probe; Steps 2-3: Summate the indeterminate admittance matrices of all distributed capacitances to obtain the N-port indeterminate admittance matrix Y of the sensitive probe. N×N .

5. The method according to claim 1, characterized in that, In step 3, the injection plate of the sensitive probe is connected to the carrier voltage source, and the sensing plate of the sensitive probe is connected to the capacitive displacement sensing circuit. All N conductor plates of the sensitive probe are external nodes, thus establishing an equivalent circuit model of the sensitive probe connected to the multi-channel capacitive displacement sensing circuit. The equation I = YV satisfied by the voltage and current of the N nodes is directly written from the indefinite admittance matrix. Then, the VI characteristics satisfied by the external termination elements of the N nodes are substituted into the above equation to obtain the voltage and current at each node. Finally, the output complex voltage of each capacitive displacement sensing circuit channel can be obtained.

6. The method according to claim 1, characterized in that, In step 5, the time-varying displacement x(t) of the test quality in any specified sensitive probe is sampled at a frequency f. s =M1f0 is used for sampling, where f0 is the highest frequency of the time-varying displacement of the test quality, M1 is the value that the sampled value can contain all the information of the original signal, and M1≥2, the total number of sampling points is M1M2, M2 is the number of sampling periods, and t is the sampling time. m for: By combining the curves of the distributed capacitance as a function of displacement obtained in step 4, the sampling time t can be obtained. m The values ​​of the distributed capacitance of each sensitive probe corresponding to the quality displacement at the test point; Then, it is used in the equivalent circuit model established in step 3 to perform AC steady-state response analysis, and t is obtained. m The complex voltage V output of each channel of the capacitive displacement sensing circuit at any time oi (t m ), i = 1, 2, ..., k, where k is the number of channels in the displacement sensing circuit; Then, the output complex voltages of each channel at all sampling times are combined in the order of sampling times to obtain the time series of the output complex voltages of each channel.

7. The method according to claim 1, characterized in that, In step 6, according to the displacement degree-of-freedom combination rule, the output complex voltage time series of each channel is combined with the displacement degrees of freedom; then, a Fourier transform is performed to obtain the output signal spectrum corresponding to each displacement degree of freedom: as well as These correspond to the output signal spectra of translational and rotational displacements along the X, Y, and Z axes, respectively.

8. The method according to claim 1, characterized in that, In step 6, if the inspection mass in the sensitive probe only translates along the X-axis, the coupling degree between the X-axis translational displacement degree-of-freedom output signal and the other five displacement degree-of-freedom output signals is calculated using the following formula: Where f0 is the highest frequency of the time-varying displacement of the test mass, |·| is the amplitude calculation on the spectrum, and C X-Y C represents the relative magnitude of the Y-axis output translational displacement signal caused by the X-axis translational displacement. X-Z The relative magnitude of the Z-axis output translational displacement signal caused by the X-axis translational displacement. C represents the relative magnitude of the rotation around the Z-axis caused by the translational displacement along the X-axis. X-θ C represents the relative magnitude of the rotation around the X-axis caused by the translational displacement along the X-axis. X-η The relative magnitude of the rotation around the Y-axis caused by the translational displacement along the X-axis is output as the displacement signal. as well as The output signal spectra correspond to the translational and rotational displacements along the X, Y, and Z axes, respectively. In the same manner, the coupling degree of each output degree of freedom displacement caused by the inspection mass along other degrees of freedom displacements is calculated.

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