Scale factor testing method and system for differential capacitive displacement sensor based on torsion pendulum

Abstract

The present invention relates to the technical field of calibration of capacitance displacement sensors, and specifically provides a method and system for testing the scale factor of a differential capacitance displacement sensor based on a torsion pendulum. A detection plate is suspended by a wire to form a torsion pendulum, and the rotation angle of the detection plate is measured by a high-precision optical measuring instrument. After applying an excitation voltage to the excitation plate, an induced voltage is generated on the detection plate, and the interaction with the induction plate generates an electrostatic negative stiffness, so that the resonant frequency of the torsion pendulum is reduced. The induced voltage generated on the detection plate is calculated by the change in the resonant frequency, and the scale factor is obtained. The present invention uses a non-contact indirect method to test the induced voltage of the detection plate, and then obtains the scale factor, thereby realizing the actual measurement of the scale factor of the differential capacitance displacement sensor, avoiding the error generated by using simulation or theoretical calculation results, and also avoiding the interference introduced by the existing direct measurement of the induced voltage, and effectively improving the measurement accuracy of the scale factor.

Description

Technical Field

[0001] The present invention relates to the technical field of capacitance displacement sensor calibration, and in particular provides a method and system for testing the calibration factor of a differential capacitance displacement sensor based on a torsion pendulum. Background Art

[0002] Differential capacitive displacement sensors are widely used in aerospace and other fields, especially in the measurement of weak forces, such as inertial sensors, electrostatic accelerometers, electrostatic torsion balances, etc.

[0003] The differential capacitive displacement sensor is a non-contact sensor. Its basic principle is to use the detection plate and the sensing plate to form a multi-channel differential capacitor, apply an excitation signal to the detection plate, read the sensing plate voltage through the bridge circuit and demodulation circuit, and thus convert the capacitive signal into a voltage signal. The capacitance sensing capacitance signal to voltage signal scaling factor is proportional to the excitation voltage amplitude applied to the detection plate.

[0004] Due to special design requirements or installation conditions, sometimes the excitation signal of capacitive sensing cannot be directly applied to the detection plate, and the excitation signal needs to be indirectly applied to the detection plate through the excitation electrode. At this time, the relationship between the amplitude of the sensed voltage of the detection plate and the excitation voltage is related to the mutual capacitance matrix. The commonly used theoretical calculation method has a large deviation from the actual test value. If the voltage on the detection plate is directly measured by contact, more interference will be introduced, making the test result inaccurate.

[0005] Existing methods usually use simulation or theoretical calculation to obtain the mutual capacitance matrix of the system, and then calculate the scaling factor from the capacitance signal to the voltage signal, such as Brandt, N. and W. Fichter (2009). "Revised electrostaticmodel of the LISA Pathfinder inertial sensor." Journal of Physics: ConferenceSeries 154., but this method has a large error compared with the measured value.

[0006] If the voltage on the detection plate is directly measured by contact (for example, using a voltmeter), on the one hand, more interference will be introduced, making the test result inaccurate. On the other hand, the test plan is difficult to implement due to the structural limitations of the capacitive sensor sensitive probe. Summary of the invention

[0007] In order to solve the above problems, the present invention provides a method and system for testing the scale factor of a differential capacitive displacement sensor based on a torsion pendulum. A torsion pendulum is formed by suspending a detection electrode plate with a hanging wire, and the scale factor of the capacitive sensor is calculated by using the resonant frequency in the initial state of the torsion pendulum and the resonant frequency after applying an excitation voltage. There is no need to calculate the differential capacitance through simulation, so the actual measurement of the scale factor is realized, the error between theoretical analysis and actual test is avoided, and the technical gap in the field of scale factor measurement is filled.

[0008] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0009] On the one hand, the present invention provides a differential capacitive displacement sensor scale factor test method based on torsion pendulum, the differential capacitive displacement sensor includes a detection plate, a sensing plate, an excitation plate and an electrode cage, the sensing plate and the excitation plate are arranged on the electrode cage, and the test method includes:

[0010] S1: The detection plate is suspended by a wire to form a torsion pendulum;

[0011] S2: driving the center of the electrode cage to coincide with the center of the detection electrode plate, measuring a first rotation angle of the detection electrode plate, and obtaining a first resonant frequency of the torsion pendulum according to the first rotation angle;

[0012] S3: applying an excitation voltage to the excitation plate, measuring the second rotation angle of the detection plate again, and obtaining a second resonant frequency of the torsion pendulum according to the second rotation angle;

[0013] S4: Calculate a capacitance signal to voltage signal scaling factor of the differential capacitance displacement sensor based on the first resonant frequency and the second resonant frequency.

[0014] Preferably, the differential capacitive displacement sensor is arranged in a vacuum tank to perform a scale factor test.

[0015] Preferably, one end of the suspension wire is suspended at the inner top of the vacuum tank, and the other end of the suspension wire is connected to the detection electrode plate.

[0016] Preferably, the electrode cage is arranged on a six-legged adjustment platform, and the six-legged adjustment platform is used to drive the electrode cage to move.

[0017] Preferably, the first resonant frequency The expression is:

[0018] ;

[0019] in, is the torsional stiffness of the suspension wire, To detect the rotational inertia of the plate.

[0020] Preferably, in S3, an excitation voltage is applied to the excitation plate After that, an induced voltage will be generated on the detection plate. , whose expression is:

[0021] ;

[0022] in, To detect the voltage division coefficient of the electrode plate;

[0023] Induced voltage Interaction with the sensing plate generates electrostatic negative stiffness , whose expression is:

[0024] ;

[0025] in, is a known quantity determined by the positional relationship between the detection plate, the induction plate and the excitation plate;

[0026] Output signal of differential capacitive displacement sensor The expression is:

[0027] ;

[0028] in, is the capacitance sensing electronics gain, is the differential capacitance signal generated after applying the excitation voltage, is the scaling factor from the capacitance signal to the voltage signal to be solved.

[0029] Preferably, the second resonant frequency The expression is:

[0030] .

[0031] Preferably, the capacitance signal to voltage signal scaling factor of the differential capacitance displacement sensor is calculated based on the first resonant frequency and the second resonant frequency as follows:

[0032] .

[0033] Preferably, in S3, different excitation voltages are applied multiple times, and multiple scale factors are calculated through S4, and data fitting is performed on all scale factors to obtain high-precision scale factors.

[0034] On the other hand, a differential capacitance displacement sensor scale factor test system based on a torsion pendulum is provided, which uses a differential capacitance displacement sensor scale factor test method based on a torsion pendulum to obtain a capacitance signal to voltage signal scale factor of the differential capacitance displacement sensor, and the system includes:

[0035] A differential capacitance displacement sensor is arranged in the vacuum tank, and a detection electrode of the differential capacitance displacement sensor is suspended on the vacuum tank through a suspension wire to form a torsion pendulum;

[0036] A six-legged adjustment platform for driving the displacement of an electrode cage of a differential capacitive displacement sensor;

[0037] An optical measuring instrument for measuring the rotation angle of the detection plate;

[0038] Capacitive sensing circuit;

[0039] and, a data processing device for calculating a scaling factor of a capacitance signal to a voltage signal.

[0040] Compared with the prior art, the invention can achieve the following beneficial effects:

[0041] The present invention provides a method for measuring a scale factor. A detection plate is suspended by a wire to form a torsion pendulum with extremely low thermal noise, extremely small interference and extremely high sensitivity. The resonant frequency of the torsion pendulum in different states is used to design and calculate the scale factor of capacitive sensing.

[0042] The present invention adopts a non-contact structure, and indirectly measures the induced voltage on the detection plate based on the electrostatic negative stiffness, thereby obtaining a scale factor, avoiding interference introduced by directly using a voltmeter to measure the induced voltage on the detection plate, and improving the test accuracy. In addition, the measurement data in the scale factor calculation process of the present invention are all obtained based on actual measurement and calculation, avoiding errors caused by obtaining data using simulation or theoretical calculation, and there is no need to change the structure of the differential capacitance displacement sensor during the test process, avoiding the change of parasitic capacitance affecting the accuracy of the calibration result.

[0043] The present invention calculates the electrostatic negative stiffness by frequency domain analysis. The measurement accuracy depends on the frequency resolution. The frequency resolution is only related to the test duration. Therefore, using this method to calculate the electrostatic negative stiffness also further improves the test accuracy.

[0044] The present invention also proposes taking different excitation voltages into consideration and performing repeated tests, and adopting a data fitting method to improve the accuracy of the test results.

[0045] In addition, the system structure of the present invention is simple, there is no need to adjust the structure of the differential capacitance displacement sensor, and the calibration process is simple and easy to operate. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The drawings constituting part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation on the present invention. In the drawings:

[0047] Figure 1is a flow chart of a scale factor testing method provided according to an embodiment of the present invention;

[0048] Figure 2 is a framework diagram of a scale factor testing system provided according to an embodiment of the present invention;

[0049] Figure 3 is a schematic diagram of the distribution of the cubic sensitive probe electrode plates provided according to an embodiment of the present invention;

[0050] Figure 4 4 is a schematic diagram of frequency domain analysis of a rotation angle provided according to an embodiment of the present invention.

[0051] Reference numerals include:

[0052] Detection plate A, induction plate B, excitation plate C;

[0053] Suspension wire 1, electrode cage 2, hexapod adjustment platform 3, vacuum tank 4, optical measuring instrument 5, capacitive sensing circuit 6, data processing equipment 7. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical scheme and advantages of the invention clearer, the invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the invention and do not constitute a limitation to the invention. Similar components in different embodiments use associated similar component numbers. In the following embodiments, many detailed descriptions are to enable the invention to be better understood. However, those skilled in the art can easily recognize that some of the features can be omitted in different situations, or can be replaced by other components, materials, and methods. In some cases, some operations related to the invention are not shown or described in the specification, in order to avoid the core part of the invention being overwhelmed by too much description, and for those skilled in the art, it is not necessary to describe these related operations in detail, and they can fully understand the related operations according to the description in the specification and the general technical knowledge in the art.

[0055] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other to form various implementation methods. At the same time, the steps or actions in the method description can also be interchanged or adjusted in a manner that is obvious to those skilled in the art. Therefore, the various sequences in the specification and the drawings are only for the purpose of clearly describing a certain embodiment and are not meant to be a necessary sequence, unless otherwise specified that a certain sequence must be followed.

[0056] In the description of the invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the drawings, and are only for the convenience of describing the invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the invention, unless otherwise specified, the meaning of "multiple" is two or more.

[0057] In the description of the invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the invention can be understood according to specific circumstances.

[0058] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0059] See also Figure 1 In one embodiment of the present invention, a method for testing the scale factor of a differential capacitance displacement sensor based on a torsion pendulum is provided. The specific testing process is as follows:

[0060] S1: Please refer to Figure 2 First, it is necessary to build a differential capacitance displacement sensor scale factor test system based on torsion pendulum. The test system includes: differential capacitance displacement sensor, suspension wire 1, hexapod adjustment platform 3, vacuum tank 4, optical measuring instrument 5, capacitance sensing circuit 6 and data processing equipment 7. Among them, vacuum tank 4 is mainly used to provide a highly vacuum test environment to avoid air resistance or external disturbances affecting the test accuracy of the scale factor. Therefore, during the test, the differential capacitance displacement sensor, suspension wire 1 and hexapod adjustment platform 3 all need to be set in the vacuum tank 4.

[0061] The sensitive probe of the differential capacitance displacement sensor is mainly composed of a detection plate A, an induction plate B, an excitation plate C and an electrode cage 2. The detection plate A is suspended on the inner wall of the top of the vacuum tank 4 by a suspension wire 1 to form a torsion pendulum structure. The suspension wire 1 has the advantages of extremely low thermal noise and very little interference, so the torsion pendulum formed has high sensitivity. In order to improve the accuracy of the test results, in the embodiment of the present invention, a suspension wire 1 with a diameter of 25 microns is selected. The induction plate B and the excitation plate C are fixed on the electrode cage 2 in an insulated manner, and the electrode cage 2 is fixed on the six-legged adjustment platform 3. By driving the six-legged adjustment platform 3, the electrode cage 2 and the induction plate B and the excitation plate C connected thereto can be driven to displace, so as to adjust the relative positions of the induction plate B, the excitation plate C and the detection plate A. In addition, during the test process, it is necessary to obtain the rotation angle of the detection plate A, so an optical measuring instrument 5 facing the detection plate A is designed, and the rear end of the optical measuring instrument 5 is connected to the data processing device 7, and the information data measured by the optical measuring instrument 5 is transmitted to the data processing device 7 for data processing. In addition, the sensing plate B and the exciting plate C are connected to the capacitive sensing circuit 6 through cables for inputting and outputting signals. The back end of the capacitive sensing circuit 6 is also connected to the data processing device 7 to realize data processing.

[0062] The above is the system construction process for the differential capacitance displacement sensor to test the scale factor. The following is specifically for a certain type of inertial sensor, such as Figure 3 Taking the cubic sensitive probe shown in FIG. 1 as an example, the positional relationship among the detection plate A, the induction plate B and the excitation plate C is described in detail. Specifically, Figure 3 It can be seen that the detection electrode A of the sensitive probe is a cube structure and is located in the center of the sensitive probe. The induction electrode B is symmetrically distributed around the detection electrode A. Specifically, four induction electrodes B are arranged in an equidistant distribution manner along the positive and negative directions of the X-axis. For the convenience of distinction, they are respectively recorded as , , and ; Four sensing plates B are arranged in an evenly spaced distribution along the positive and negative directions of the Y axis, respectively denoted as , , and ; Four sensing plates B are arranged in an evenly spaced distribution along the positive and negative directions of the Z axis, respectively denoted as , , and The excitation plates C are also symmetrically distributed around the detection plate A. Specifically, two excitation plates C are arranged at equal intervals along the positive and negative directions of the Y axis, and are respectively denoted as , ; Four excitation plates C are arranged in an equidistant manner along the positive and negative directions of the Z axis, respectively, and are denoted as , , and Since the detection electrode A is fixed on the suspension wire 1 in the positive direction of the Z axis, the degree of freedom of rotation around the suspension wire 1 The stiffness of the X-axis sensing plate B (i.e. , , and ) and the relative position relationship between the detection electrode A and the voltage difference. Therefore, by obtaining the change in the rotation angle of the detection electrode A around the suspension wire 1 under different voltages, the induced voltage generated on the detection electrode A can be obtained, and then the capacitance signal to voltage signal scaling factor of the capacitive sensing can be obtained.

[0063] S2: First, start the vacuum tank 4 to put the entire test system in a high vacuum state, so that the free oscillation of the detection plate A gradually decays. At the same time, start the temperature control and environmental monitoring to avoid the interference of environmental factors on the test results and improve the accuracy of the actual measurement.

[0064] The electrode cage 2 is controlled to move by the six-legged adjustment platform 3, so that the center of the electrode cage 2 coincides with the center of the detection electrode plate A, and then the detection electrode plate A is allowed to oscillate freely within a smaller range inside the electrode cage 2, and the rotation angle of the detection electrode plate A is continuously measured for a long time by the optical measuring instrument 5. In the state of no voltage excitation, through long-term testing and recording, the rotation angle data of the detection plate A during this period of time can be obtained. , see Figure 4 , the rotation angle data is transformed by short-time Fourier transform By performing frequency domain analysis, the resonant frequency of the torsion pendulum under no voltage excitation conditions can be calculated. (i.e. the first resonant frequency). Since the entire test environment is a high vacuum environment, the dissipation coefficient of the high vacuum environment is very small, so the resonant frequency It can be expressed as an equation:

[0065] ;

[0066] in, is the torsional stiffness of suspension wire 1, To detect the moment of inertia of plate A.

[0067] S3: Generate excitation voltage through capacitive sensing circuit 6 and applied to the excitation plate through the cable , , and At this time, a corresponding induced voltage will be generated on the detection plate A. , and the differential capacitance signal generated by the capacitance sensing circuit 6 and Converted into the output signal of differential capacitance displacement sensor and , , and The relationship between satisfies the following equation:

[0068] ;

[0069] in, is the capacitance sensing electronics gain, is the scaling factor from capacitance signal to voltage signal to be solved, It is the voltage division coefficient of the detection plate A.

[0070] Since the excitation voltage The induced voltage on plate A is detected by applying The interaction with the induction plate B will produce electrostatic negative stiffness , whose expression is:

[0071] ;

[0072] in, is a known quantity determined by the positional relationship between the detection plate A, the sensing plate B, and the excitation plate C. When testing differential capacitive displacement sensors with different structures, the positional relationship between the detection plate A, the sensing plate B, and the excitation plate C may be different, which will change The specific calculation method is exactly the same. is the dielectric constant of vacuum, is the plate area in the X-axis direction, is the force arm from the center of the electrode plate to the center of the electrode cage 2 in the X-axis direction, i.e., the equivalent force arm. It is the distance from the electrode plate to the detection electrode A in the X-axis direction.

[0073] When applying excitation voltage After that, the optical measuring instrument 5 continuously measures the detection plate A for a long time, and records the rotation angle data of the detection plate A during this period of time. , the rotation angle data is transformed by short-time Fourier transform By performing frequency domain analysis, the excitation voltage of the torsion pendulum can be calculated. Resonant frequency under conditions (i.e. the second resonant frequency), and then the relationship between it and the electrostatic negative stiffness is obtained, and its expression is:

[0074] .

[0075] Through the frequency domain analysis method, the resonant frequency and The induced voltage on the detection plate A can be calculated , the induced voltage was obtained by non-contact testing This avoids the traditional method of directly measuring the induced voltage on plate A through a voltmeter or other equipment. , direct measurement will introduce interference and reduce the test accuracy. In addition, the accuracy of the calculation result of the electrostatic negative stiffness calculated by the frequency domain analysis method depends on the frequency resolution, and the frequency resolution is only related to the test time. The test accuracy can be improved by extending the test time.

[0076] S4: , and The relationship equation between can be used to derive the voltage division coefficient of the detection plate A. The calculation equation of the capacitance signal to voltage signal scaling factor of the differential capacitance displacement sensor is obtained based on the resonant frequency and resonant frequency Calculate the voltage divider coefficient And the scaling factor is:

[0077] ;

[0078] .

[0079] As a preferred embodiment, the excitation voltage applied in S3 can be changed , and repeat the test to calculate multiple scale factors, and use the data fitting method to fit all the scale factors, and use the fitted scale factors as the final test results to improve the test accuracy.

[0080] As a preferred embodiment, for the calculated scaling factor, the influence of the induced potential of the sensing plate B, the stray potential and the residual charge on the detection plate A on the electrostatic negative stiffness can also be comprehensively considered to compensate for the final test result.

[0081] The differential capacitance displacement sensor scale factor test system based on torsion pendulum proposed in the present invention can perform actual measurement of the scale factor for the differential capacitance displacement sensor. During the test, there is no need to adjust the structure of the differential capacitance displacement sensor, thus avoiding changes in the parasitic capacitance caused by changes in the structure of the differential capacitance displacement sensor, which in turn affects the test results. In addition, the system construction and test operation process are simplified. The process of calibrating the scale factor by using the differential capacitance displacement sensor scale factor test method based on torsion pendulum proposed in the present invention is to perform physical measurement on the differential capacitance sensor, without the need to use simulation and theoretical calculation to detect the induced voltage on the electrode plate A. Instead, the induced voltage generated on the detection plate A is actually calculated by the change of the torsion pendulum resonant frequency. , avoiding the error between the simulation value and the measured value. Compared with the results of simulation theoretical calculation, the measured results are more accurate and convincing.

[0082] In short, the above description is only a preferred embodiment of this specification and is not intended to limit the protection scope of this specification. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of this specification shall be included in the protection scope of this specification.

[0083] The systems, devices, modules or units described in one or more of the above embodiments may be implemented by a computer chip or entity, or by a product having a certain function. A typical implementation device is a computer. Specifically, the computer may be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smart phone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.

[0084] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0085] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment.

[0086] The above is a description of a specific embodiment of the specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the embodiments and still achieve the desired results. In addition, the processes depicted in the drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

Claims

1. A method for testing the scale factor of a differential capacitance displacement sensor based on a torsion pendulum, wherein the differential capacitance displacement sensor comprises a detection plate, a sensing plate, an excitation plate and an electrode cage, wherein the sensing plate and the excitation plate are arranged on the electrode cage, and wherein: include: S1: suspending the detection electrode plate by a suspension wire to form a torsion pendulum; S2: driving the center of the electrode cage to coincide with the center of the detection electrode plate, measuring a first rotation angle of the detection electrode plate, and obtaining a first resonant frequency of the torsion pendulum according to the first rotation angle; S3: applying an excitation voltage to the excitation plate, measuring the second rotation angle of the detection plate again, and obtaining a second resonant frequency of the torsion pendulum according to the second rotation angle; S4: Calculate a capacitance signal to voltage signal scaling factor of the differential capacitance displacement sensor based on the first resonance frequency and the second resonance frequency.

2. The method for testing the scale factor of a differential capacitance displacement sensor based on a torsion pendulum according to claim 1, characterized in that: The differential capacitance displacement sensor is arranged in a vacuum tank to perform a scale factor test.

3. The method for testing the scale factor of a differential capacitance displacement sensor based on a torsion pendulum as claimed in claim 2, characterized in that: One end of the suspension wire is suspended at the inner top of the vacuum tank, and the other end of the suspension wire is connected to the detection electrode plate.

4. The method for testing the scale factor of a differential capacitance displacement sensor based on a torsion pendulum according to claim 1, characterized in that: The electrode cage is arranged on a six-legged adjustment platform, and the six-legged adjustment platform is used to drive the electrode cage to move.

5. The method for testing the scale factor of a differential capacitance displacement sensor based on a torsion pendulum according to claim 1, characterized in that: The first resonant frequency The expression is: ； in, is the torsional stiffness of the suspension wire, is the moment of inertia of the detection plate.

6. The method for testing the scale factor of a differential capacitance displacement sensor based on a torsion pendulum according to claim 5, characterized in that: In S3, an excitation voltage is applied to the excitation plate. After that, an induced voltage will be generated on the detection plate. , whose expression is: ； in, is the voltage division coefficient of the detection plate; Induced voltage Interacting with the induction plate to generate electrostatic negative stiffness , whose expression is: ； in, is a known quantity determined by the positional relationship between the detection electrode, the induction electrode and the excitation electrode; The output signal of the differential capacitance displacement sensor The expression is: ； in, is the capacitive sensing electronics gain, is the differential capacitance signal generated after applying the excitation voltage, is the scaling factor from the capacitance signal to the voltage signal to be solved.

7. The method for testing the scale factor of a differential capacitance displacement sensor based on a torsion pendulum according to claim 6, characterized in that: The second resonant frequency The expression is: 。 8. The method for testing the scale factor of a differential capacitance displacement sensor based on a torsion pendulum according to claim 7, characterized in that: The capacitance signal to voltage signal scaling factor of the differential capacitance displacement sensor is calculated according to the first resonant frequency and the second resonant frequency: 。 9. The method for testing the scale factor of a differential capacitance displacement sensor based on a torsion pendulum according to claim 1 or 8, characterized in that: In S3, different excitation voltages are applied multiple times, and multiple scale factors are calculated through S4, and data fitting is performed on all scale factors to obtain high-precision scale factors.

10. A differential capacitance displacement sensor scale factor test system based on torsion pendulum, characterized in that: The differential capacitance displacement sensor scale factor test method based on torsion pendulum according to any one of claims 1 to 9 is used to obtain the capacitance signal to voltage signal scale factor of the differential capacitance displacement sensor, and the system comprises: A differential capacitance displacement sensor is arranged in the vacuum tank, wherein the detection electrode of the differential capacitance displacement sensor is suspended on the vacuum tank through a suspension wire to form a torsion pendulum; A six-legged adjustment platform, which is used to drive the displacement of the electrode cage of the differential capacitive displacement sensor; An optical measuring instrument for measuring the rotation angle of the detection plate; Capacitive sensing circuit; and, a data processing device for calculating a scaling factor of a capacitance signal to a voltage signal.

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