A method and apparatus for testing acceleration noise induced by temperature fluctuations in a sensitive structure

Abstract

This invention discloses a method and device for testing acceleration noise introduced by temperature fluctuations in a sensitive structure. The method includes: a sensitive structure connected to a rotating frame via a horizontal bar to form a rigid rotating system; a weak force measuring torsion balance mounted on the rotating frame; periodic temperature excitation with a temperature difference applied at symmetrical positions on both sides of the sensitive structure to simulate the temperature fluctuation effect caused by a temperature gradient; an optical readout system measuring the torque change generated by the sensitive structure through changes in the optical path of a reflecting mirror to obtain the acceleration noise under periodic temperature fluctuations; and a temperature control system analyzing the acceleration noise generated by the coupling effect of temperature fluctuations, distinguishing the different effects of the radiometer effect and the thermal radiation pressure effect caused by the temperature gradient on the acceleration noise of the sensitive structure. This invention, by introducing temperature excitation and temperature distribution measurement, can accurately measure the acceleration noise caused by temperature fluctuations even under minute temperature differences.

Description

Technical Field

[0001] This invention relates to the field of acceleration measurement accuracy technology, and specifically to a method and equipment for testing acceleration noise introduced by temperature fluctuations in a sensitive structure. Background Technology

[0002] In high-precision measurement systems such as inertial sensors and electrostatic levitation accelerometers, the impact of temperature fluctuations and temperature gradients on the accuracy of acceleration measurement has always been one of the technical research challenges. If there is temperature non-uniformity in the electrode cage, residual gas molecules will reach thermal equilibrium after being adsorbed onto the electrode cage and then released again in a Knudzen distribution. The velocity distribution of gas molecules in different temperature regions is different, and the momentum transferred to the sensitive structure by collisions is different. As a result, the residual gas molecules will cause acceleration disturbances due to the coupling effect of random collisions with the sensitive structure and temperature fluctuations. In order to solve the influence of temperature on acceleration measurement, existing technologies have adopted several main implementation schemes: temperature control design, temperature compensation algorithm, and temperature isolation technology.

[0003] Existing temperature control designs attempt to maintain a uniform temperature by arranging a temperature control system around the sensitive structure, minimizing the interference of external temperature changes. This approach focuses on precisely controlling the temperature to reduce the impact of temperature gradients on the sensor, ensuring the sensitive structure is under uniform temperature. Another common approach is to use temperature compensation algorithms to correct errors caused by temperature fluctuations in real time. In this approach, a temperature sensor is installed inside the sensor to collect temperature change data in real time, and compensation is performed through data processing algorithms. These algorithms adjust the sensor output based on real-time temperature data to mitigate temperature-induced interference. Compensation algorithms are typically based on linear regression or more complex mathematical models, attempting to automatically adjust temperature-related errors during measurement. To avoid the influence of external temperature changes on the sensitive structure, existing technologies also employ thermal insulation or temperature shielding techniques. By placing a thermal insulation layer between the sensitive structure and the external environment or using a temperature-controlled enclosure, external temperature fluctuations are prevented from being transmitted to the sensor, thereby reducing interference from environmental changes.

[0004] Although existing technologies employ various methods such as temperature control design, compensation algorithms, and temperature isolation techniques to reduce the impact of temperature fluctuations on acceleration measurements, these solutions still have the following drawbacks:

[0005] 1. Temperature control design cannot completely eliminate the influence of temperature gradient;

[0006] While temperature control design ensures that the sensor operates in a relatively stable temperature environment, temperature fluctuations always exist in actual operation, making complete temperature uniformity difficult to achieve. Especially in high-precision inertial sensors, temperature non-uniformity within the electrode cage can still cause errors in acceleration measurements. Therefore, while temperature control design can alleviate some of the problems, it cannot fundamentally solve the acceleration noise caused by temperature fluctuations.

[0007] 2. Limitations of the temperature compensation algorithm;

[0008] Temperature compensation algorithms rely on the accuracy of temperature sensors and data processing systems. However, temperature changes are often very small, and the accuracy of temperature sensors and the processing delay of algorithms can lead to incomplete compensation, especially under conditions of small temperature differences, where the effectiveness of algorithmic compensation is limited. Compensation algorithms cannot directly measure complex factors such as radiometer effects and thermal radiation pressure effects caused by temperature fluctuations, making it impossible for existing algorithms to effectively address acceleration noise generated by all temperature fluctuations.

[0009] 3. Temperature isolation technology has poor adaptability;

[0010] While temperature isolation and shielding technologies can reduce the impact of external temperature fluctuations, in practical applications, the complexity of the testing environment and the limitations of sensor structure make it difficult to completely isolate temperature changes. This is especially true in high-precision applications where equipment size constraints make complete temperature shielding difficult to achieve. Furthermore, this technology typically focuses on isolating external temperatures and has no direct effect on temperature non-uniformity within the electrode cage and the resulting acceleration noise. Summary of the Invention

[0011] The purpose of this invention is to provide a method and device for testing acceleration noise introduced by temperature fluctuations in a sensitive structure, in order to solve the technical problem in the prior art that it is difficult to accurately distinguish and measure these different noise effects (such as radiometer effect and thermal radiation pressure effect) caused by temperature changes, especially when the temperature difference is small.

[0012] To solve the above-mentioned technical problems, the present invention specifically provides the following technical solution:

[0013] An acceleration noise testing device introduced by temperature fluctuations in a sensitive structure, comprising:

[0014] Two sensitive structures are placed inside a vacuum chamber and symmetrically distributed on both sides of a rotating frame. Each of the sensitive structures is connected to the rotating frame via a horizontal bar to form the same rigid rotating system. A weak force measuring torsion balance for measuring the damping received by the sensitive structure is installed on the rotating frame.

[0015] Furthermore, a temperature control system is provided at the symmetrical position on the outer periphery of the sensitive structure. The temperature control system applies periodic temperature excitation at the symmetrical positions on both sides of the outer side of the sensitive structure and controls the temperature difference between the two sides multiple times to simulate the temperature fluctuation effect generated by the temperature gradient.

[0016] An optical readout system is installed on the rotating frame, and a reflective mirror is installed on the weak force measuring torsion balance. The optical readout system measures the torque change generated by the sensitive structure by changing the optical path of the reflective mirror, so as to obtain the acceleration noise under periodic temperature fluctuations.

[0017] Furthermore, the temperature control system analyzes the acceleration noise generated by the coupling effect of temperature fluctuations and distinguishes the different effects of the radiometer effect and the thermal radiation pressure effect caused by the temperature gradient on the acceleration noise of the sensitive structure.

[0018] As a preferred embodiment of the present invention, the temperature control system includes two heating elements disposed outside the sensitive structure and symmetrically distributed thereon, a heat-conducting structure being provided between the heating elements and the sensitive structure, and a temperature controller being connected to the heating elements;

[0019] The temperature controller regulates the two heating elements to apply periodic temperature excitation at symmetrical positions outside the sensitive structure, and the temperature of the heating elements is transferred to the side of the sensitive structure through the heat conduction structure;

[0020] The temperature controller and optical readout system are connected to a data processing system, which analyzes the acceleration noise generated by the coupling effect of temperature fluctuations.

[0021] In a preferred embodiment of the present invention, the heating element includes TEC semiconductor coolers symmetrically arranged on both sides of the sensitive structure, wherein the side of the TEC semiconductor cooler facing the sensitive structure is provided with a heat-conducting structure, and the temperature of the heat-conducting structure represents the temperature applied to the sensitive structure;

[0022] The TEC semiconductor cooler has a heat sink plate on the side away from the sensitive structure, and the heat sink plate is used to receive the heat dissipated by the heat dissipation end of the TEC semiconductor cooler;

[0023] The outer surface of the heat sink plate is provided with a heat-conducting pipe, which conducts heat out of the heat sink plate.

[0024] In a preferred embodiment of the present invention, the heat-conducting structure is provided with a plurality of uniformly distributed temperature sensors, the temperature sensors being used to monitor the temperature of the heat-conducting structure, and the temperature sensors being communicatively connected to the temperature controller.

[0025] As a preferred embodiment of the present invention, a suspension wire is installed at the top center position of the rotating frame via a suspension wire lower clamp, and a weak force measuring torsion balance for measuring the rotation angle of the suspension wire is assembled on the suspension wire lower clamp.

[0026] The rotation angle of the sensitive structure is transmitted through a rigid force transmission chain of a horizontal rod, a rotating frame, and a suspension wire clamp, so that the lower end of the suspension wire is synchronized with the angular displacement of the sensitive structure. The main body of the weak force measuring torsion balance is used to measure the torsion angle of the suspension wire, which is equivalent to the torque / rotation angle generated by the sensitive structure.

[0027] As a preferred embodiment of the present invention, counterweights are respectively installed on the other two sides of the rotating frame, and the counterweights and the sensitive structure form a cross-shaped symmetrical layout.

[0028] Each counterweight is connected to the rotating frame via a counterweight horizontal bar;

[0029] Furthermore, the counterweight is connected to the rotating frame via a slider mechanism, enabling continuous adjustment of the counterweight arm length and equivalent torque.

[0030] In addition, the present invention also provides a method for testing acceleration noise introduced by temperature fluctuations in a sensitive structure, comprising the following steps:

[0031] Step 100: Apply periodic temperature excitation at symmetrical positions on both sides of the outer side of the sensitive structure to simulate the formation of a non-uniform temperature field that changes with time on the inner surface of the electrode cage. Control the temperature difference between the two surfaces of the sensitive structure to simulate the temperature fluctuation effect generated by the temperature gradient. Measure the torque change of the sensitive structure to obtain the acceleration noise under periodic temperature fluctuation.

[0032] Step 200: Collect multi-point temperature data around the sensitive structure in real time, and use the data processing system to interpolate and fit these discrete temperature points to map them into an inner surface temperature distribution T(x,y,t) consistent with the geometry of the electrode cage, thereby obtaining the spatial distribution of temperature profile and temperature gradient.

[0033] Step 300: Substitute the reconstructed inner surface temperature field into the temperature noise theoretical model, and calculate the equivalent theoretical torque or acceleration contribution of the radiometer effect and thermal radiation pressure effect to the sensitive structure under the current temperature distribution.

[0034] Step 400: Change the ambient temperature and ambient air pressure of the sensitive structure, use the optical readout system to measure the first harmonic torque at the temperature modulation frequency, fit and compare the measured total temperature modulation torque with the theoretical torque calculated from the temperature field, obtain the correction factor and weight of each temperature effect through fitting, and separate the actual contribution of different temperature effects.

[0035] Step 500: Divide the separated temperature effect torques by the equivalent force arm and mass of the sensitive structure to convert them into equivalent acceleration noise, and obtain the magnitude and frequency characteristics of the temperature noise introduced by the temperature-nonuniform electrode cage under a given temperature gradient and air pressure conditions.

[0036] In a preferred embodiment of the present invention, in step 300, the temperature noise theoretical model includes acceleration noise caused by the radiometer effect and acceleration noise caused by the thermal radiation pressure effect, wherein the acceleration noise model caused by the radiometer effect is as follows:

[0037] ,in, ;

[0038] The acceleration noise model caused by thermal radiation pressure effect is as follows:

[0039] ;in, .

[0040] As a preferred embodiment of the present invention, in step 400, the ambient temperature where the sensitive structure is located is changed, and step 100 is repeated according to the step change of ambient temperature, so as to measure the effect of different average ambient temperatures on acceleration noise.

[0041] Change the ambient vacuum level of the sensitive structure and repeat step 100 above to obtain the curve of normalized torque versus vacuum level at different ambient temperatures.

[0042] As a preferred embodiment of the present invention, by adjusting the air pressure of the ambient vacuum where the sensitive structure is located, the influence of air pressure change on acceleration noise is examined, and the coupling effect between air pressure change and temperature fluctuation is analyzed. This step helps to further determine the contribution ratio of radiometer effect and thermal radiation pressure effect to acceleration noise. The specific implementation method is as follows:

[0043] By adjusting the air pressure at different ambient vacuum levels, multiple sets of data were obtained to determine the normalized torque variation with ambient vacuum level under different conditions. The curve was used to verify the radiometer effect using the normalized torque formula, and its correction factor was derived. :

[0044] ;

[0045] Utilizing the variation of normalized torque with vacuum level under different environmental vacuum conditions The curve was obtained by extrapolation to show the relationship between torque and temperature at P=0, and then the effect of thermal radiation pressure effect was analyzed.

[0046] Compared with the prior art, the present invention has the following advantages:

[0047] This invention introduces temperature excitation and temperature distribution measurement, which can accurately measure acceleration noise caused by temperature fluctuations under small temperature differences, solve the noise problem that existing temperature control and compensation algorithms cannot completely eliminate, and provide accurate noise assessment for inertial sensor design.

[0048] It can accurately separate the effects of radiometer effect and thermal radiation pressure effect noise sources, and provide correction factors for each noise source, thereby quantitatively analyzing the contribution of temperature fluctuation to acceleration noise. Attached Figure Description

[0049] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0050] Figure 1 This is a schematic diagram of the overall structure of the acceleration noise testing device according to an embodiment of the present invention;

[0051] Figure 2 This is a schematic diagram of the structure of the heating element according to an embodiment of the present invention;

[0052] Figure 3 This is a structural block diagram of the heating control system of the test equipment according to an embodiment of the present invention;

[0053] Figure 4 A schematic diagram of the structure of the heating element of this invention subjected to periodic temperature excitation according to an embodiment of the invention;

[0054] In the picture:

[0055] 1-Vacuum chamber; 2-Rotating frame; 3-Sensitive structure; 4-Horizontal bar; 5-Weak force measuring torsion balance; 6-Temperature control system; 7-Optical readout system; 8-Data processing system; 9-Suspension wire lower clamp; 10-Suspension wire; 11-Counterweight block; 12-Counterweight horizontal bar;

[0056] 61-Heating element; 62-Heat-conducting structure; 63-Temperature controller;

[0057] 611-TEC semiconductor cooler; 612-heat-conducting structure; 613-heat sink plate; 614-heat pipe. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] like Figures 1 to 3 As shown, the present invention provides an acceleration noise testing device introduced by temperature fluctuation of a sensitive structure, including two sensitive structures 3 placed in a vacuum chamber 1 and symmetrically distributed on both sides of a rotating frame 2, and each sensitive structure 3 is connected to the rotating frame 2 through a horizontal rod 4 to form the same rigid rotation system. A weak force measuring torsion balance 5 for measuring the damping received by the sensitive structure 3 is installed on the rotating frame 2.

[0060] Furthermore, a temperature control system 6 is provided on the outer periphery of the sensitive structure 3. The temperature control system 6 applies periodic temperature excitation at symmetrical positions on both sides of the outer periphery of the sensitive structure 3 and controls the temperature difference between the two surfaces multiple times to simulate the temperature fluctuation effect generated by the temperature gradient.

[0061] A light readout system 7 is installed on the rotating frame 2, and a reflective mirror is installed on the weak force measuring torsion balance 5. The light readout system 7 measures the torque change generated by the sensitive structure 3 by changing the light path of the reflective mirror, so as to obtain the acceleration noise under periodic temperature fluctuations.

[0062] Furthermore, the temperature control system 6 analyzes the acceleration noise generated by the coupling effect of temperature fluctuations, and distinguishes the different effects of the radiometer effect and thermal radiation pressure effect caused by the temperature gradient on the acceleration noise of the sensitive structure 3.

[0063] Because the metallic material of sensitive structure 3 has good thermal conductivity and has no mechanical contact with the outside, the vacuum level of the space between it and the electrode cage is within... The temperature is relatively uniform, so the sensitive structure 3 is minimally affected by external temperature fluctuations and can be considered to be in a uniform temperature state.

[0064] Therefore, the temperature-related acceleration noise is essentially caused by the uneven temperature distribution inside the electrode cage (sensitive structure 3 outer shell), especially the temperature gradient on both sides and the asymmetry of the temperature field on the inner surface.

[0065] In order to obtain the temperature non-uniformity of the electrode cage and the torque effect corresponding to its fluctuation, heating points need to be symmetrically arranged on two opposite sides of the sensitive structure 3 and temperature excitation is performed. Temperature sensing probes in the temperature control system 6 on the periphery of the sensitive structure 3 are used to monitor the temperature at different positions. The spatial distribution of surface temperature of the sensitive structure 3 is obtained through interpolation algorithm, the temperature profile data is reconstructed, the test data is processed and evaluated, and finally the temperature noise is evaluated.

[0066] Among them, the top center of the rotating frame 2 is equipped with a suspension wire 10 through the suspension wire lower clamp 9, and the main body of the weak force measuring torsion scale 5 is assembled on the suspension wire lower clamp 9.

[0067] The rotation angle of the sensitive structure 3 is transmitted through the rigid force transmission chain of the horizontal rod 4, the rotating frame 2 and the lower clamp of the suspension wire 9, so that the lower end of the suspension wire 10 and the sensitive structure 3 achieve angular displacement synchronization. The main body of the weak force measuring torsion balance 5 is used to measure the torsion angle of the suspension wire 10, which is equivalent to the torque / rotation angle generated by the sensitive structure 3.

[0068] The torsion generated by the sensitive structure 3 acts on the same rigid rotating component connected to the lower end of the suspension wire 10, i.e.: sensitive structure 3 → rigid connecting rod → rotating frame 2 → suspension wire lower clamp 9 / torsion balance. Thus, the suspension wire 10 only plays the role of "torsional elastic element", with the upper end fixed and the lower end rotating with the rotating component.

[0069] 1. Fix the vertical column to the base of the vacuum chamber 1;

[0070] 2. Install the rotating frame 2 / turntable and complete coaxial positioning. At this time, external displacement table / leveling screws can be used for assembly and adjustment.

[0071] 3. Fix the two sensitive structures 3 in symmetrical positions on the left and right sides respectively;

[0072] 4. Two sensitive structures 3 are connected to the rotating frame 2 by two horizontal rods 4 to form a rigid rotation system;

[0073] 5. Install the lower clamp 9 of the suspension wire at the center of the rotating frame 2; install the upper clamp of the suspension wire 10 at the top of the cavity and tension the suspension wire 10;

[0074] 6. Assemble the main body of the weak force measuring torsion balance 5 / reflector mount autocollimator at the lower end of the suspension wire 10;

[0075] 7. Finally, assemble the counterweight mechanism and fine-tune the center of mass and static balance.

[0076] The rotation angle of the sensitive structure 3 is transmitted through the rigid force transmission chain of "sensitive structure 3 mounting base - horizontal rod 4 - rotating frame 2 - suspension wire lower clamp 9", so that the lower end of the suspension wire 10 and the sensitive structure 3 achieve angular displacement synchronization, thereby the torque / rotation angle generated by the sensitive structure 3 is equivalent to the torsion angle of the suspension wire 10 for measurement.

[0077] In addition, counterweights 11 are installed on the other two sides of the rotating frame 2, and the counterweights 11 and the sensitive structure 3 form a cross-shaped symmetrical layout; each counterweight 11 is connected to the rotating frame 2 through a counterweight horizontal rod 12; furthermore, the counterweights 11 are connected to the rotating frame 2 by means of sliding blocks, so that the counterweight arm length and equivalent torque of the counterweights 11 can be continuously adjusted.

[0078] The counterweights 11 are installed at the front and rear (or on the other two sides) of the column, forming a symmetrical "cross / four-quadrant" layout with the left and right sensitive structures 3. Each counterweight (11) is connected to the rotating frame 2 through a counterweight horizontal rod 12. The connection method is also "screw fastening + positioning pin / stop", and a long oval hole is reserved for fine adjustment. The counterweights 11 can adopt a "slider type (moving along the rod) + locking screw" structure for continuous adjustment of the counterweight arm length and equivalent torque.

[0079] The specific function of the counterweight 11 in this embodiment is as follows:

[0080] Static balance / center of mass alignment: Align the combined center of mass of the entire rotating assembly (two sensitive structures 3 + connecting rod + torsion balance) with the axis of suspension wire 10 to reduce the parasitic restoring torque and bending of suspension wire 10 caused by gravity.

[0081] Suppressing translational / oscillating coupling: Center of mass deviation can couple minute tilting and vertical oscillations into torsional noise; counterweights can significantly reduce this coupling.

[0082] Adjusting the moment of inertia and natural period: By changing the counterweight mass and lever arm, the system's moment of inertia is adjusted, thereby adjusting the natural period of the torsion balance to a range more suitable for temperature modulation frequency band measurement.

[0083] This embodiment uses two symmetrically distributed sensitive structures 3. Compared with the method of measuring the rotation angle corresponding to a single sensitive structure 3, the specific advantages of this embodiment are as follows:

[0084] 1. Signal enhancement (torque superposition)

[0085] When the two sensitive structures 3 are subjected to temperature modulation (or equivalent disturbance) of equal amplitude and phase, if the structure is designed to generate torque in the same direction on the suspension wire 10 axis, the torques on both sides are superimposed at the suspension wire 10, the effective signal amplitude is increased (approximately doubled in ideal case), and the signal-to-noise ratio is improved.

[0086] 2. Common-mode disturbance suppression (differential / symmetric denoising)

[0087] The micro-vibrations of the vacuum cavity 1, the slow drift of the platform, the slow change of the residual gas pressure, and the gradual change of the ambient magnetic / electric field often manifest as an approximate common mode on the left and right sides; the symmetrical structure makes the equivalent contribution of these disturbances to the torsion angle cancel each other out or significantly reduce them, thereby reducing the background noise.

[0088] 3. Reduce the coupling of "eccentricity-tilt-torsion" (mechanical self-alignment)

[0089] The single-sensitive structure 3 is more likely to cause center of mass offset and imbalance; the double-symmetric structure is naturally more likely to achieve the center of mass on the axis of the suspension wire 10, which reduces the gravitational parasitic torque and oscillation coupling, and also echoes the counterweight leveling in question 2.

[0090] 4. Enables internal cross-validation / consistency testing

[0091] The two sensitive structures 3 can work simultaneously and acquire data under the same conditions to identify "asymmetric responses caused by assembly and adjustment errors" and improve the reliability of measurement results.

[0092] The temperature control system 6 includes two heating elements 61 that are symmetrically distributed outside the sensitive structure 3. A heat-conducting structure 62 is provided between the heating elements 61 and the sensitive structure 3. The heating elements 61 are connected to a temperature controller 63.

[0093] The temperature controller 63 regulates two heating elements 61 to apply periodic temperature excitation at symmetrical positions outside the sensitive structure 3, and the temperature of the heating elements 61 is transferred to the side of the sensitive structure 3 through the heat conduction structure 62. The heating elements 61 include TEC semiconductor coolers 611 symmetrically arranged on both sides of the sensitive structure 3. The side of the TEC semiconductor cooler 611 facing the sensitive structure 3 is provided with the heat conduction structure 62. The surface temperature of the heat conduction structure 62 near the sensitive structure 3 represents the temperature applied to the sensitive structure 3. The heat conduction structure 62 is provided with multiple uniformly distributed temperature sensors. The temperature sensors are used to monitor the temperature of the heat conduction structure 62, and the temperature sensors are communicatively connected to the temperature controller 63.

[0094] A heat sink plate 613 is provided on the side of the TEC semiconductor cooler 611 away from the sensitive structure 3. The heat sink plate 613 is used to receive the heat dissipated from the heat dissipation end of the TEC semiconductor cooler 611.

[0095] The outer surface of the heat sink plate 613 is provided with a heat pipe 612, which conducts heat from the heat sink plate 613 through the heat pipe 612.

[0096] The temperature controller 63 and the optical readout system 7 are connected to a data processing system 8, which analyzes the acceleration noise generated by the coupling effect of temperature fluctuations.

[0097] In this embodiment, a TEC semiconductor cooler 611 is used to heat the sensitive structure 3. The semiconductor cooler is made using the Peltier effect of semiconductor materials, which refers to the phenomenon that when a direct current passes through a thermocouple composed of two semiconductor materials, one end absorbs heat and the other end releases heat. The heating end of the TEC faces the sensitive structure 3. The amplitude of the driving current changes with time according to a set period, such as an approximate sine wave or square wave, so that the heat absorption / release power corresponding to each TEC changes periodically with time. On the other hand, the current direction of the left and right TECs can be set to be opposite or have a phase difference, so that one side is in a "heating" state and the other side is in a "cooling" state at a certain moment. As the current direction or magnitude is periodically reversed, the heat flow direction on both sides also alternates, thereby forming a temperature difference ΔT(t) that changes periodically with time on the left and right sides of the sensitive structure 3.

[0098] The purpose of obtaining the spatial distribution of the surface temperature of the sensitive structure 3 through the interpolation algorithm is to transform the finite number of temperature points measured by the discrete temperature probe into a continuous temperature field consistent with the geometry of the sensitive structure 3. This provides input conditions for theoretical modeling of temperature-related noise and comparison of experimental data.

[0099] Since the temperature noise generated by the radiometer effect and the thermal radiation pressure effect is directly related to the local temperature and spatial gradient of the inner surface of the electrode cage, its acceleration noise term is essentially the area integral or volume integral of the temperature distribution on the inner surface. If we rely only on the point measurements of a few temperature sensors, we cannot accurately describe the true temperature field shape and temperature gradient, and therefore cannot accurately calculate the corresponding theoretical torque and acceleration noise.

[0100] The temperature distribution on the inner surface of the electrode cage reconstructed by the interpolation algorithm can be used to numerically calculate the temperature field integral of the inner wall of the sensitive structure 3, thereby achieving quantitative calibration and correction of the temperature noise model under a given temperature difference modulation condition.

[0101] The process of reconstructing temperature profile data, processing and evaluating the tested data, and finally assessing the implementation of temperature noise can be summarized in the following steps:

[0102] (1) TEC heating / cooling components are symmetrically arranged on two opposite sides of the sensitive structure 3. By periodically changing the magnitude and direction of the current of the TECs on both sides, a periodically changing temperature gradient is applied to both sides of the sensitive structure 3 to simulate the non-uniform temperature field formed on the inner surface of the electrode cage that changes with time.

[0103] (2) Several temperature probes are arranged on the outer periphery of the sensitive structure 3 to collect multi-point temperature data in real time; the data processing system 8 interpolates and fits these discrete temperature points and maps them to the inner surface temperature distribution T(x,y,t) consistent with the geometry of the electrode cage, thereby obtaining the spatial distribution of temperature profile and temperature gradient.

[0104] (3) Substitute the reconstructed inner surface temperature field into the temperature noise theoretical model, and calculate the equivalent torque or acceleration contribution of the radiometer effect and the thermal radiation pressure effect to the sensitive structure 3 under the current temperature distribution; among which the radiometer effect mainly changes with air pressure and temperature gradient, and the thermal radiation pressure effect mainly changes with surface temperature and emissivity.

[0105] (4) At the same time, the first harmonic torque of the torsion balance at the temperature modulation frequency is measured using an optical readout system. The measured total temperature modulation torque is fitted and compared with the theoretical torque calculated from the temperature field. The correction factors and weights of each temperature effect (radiometer effect and thermal radiation pressure effect) are obtained through fitting, thereby separating the actual contributions of different temperature effects (radiometer effect and thermal radiation pressure effect).

[0106] (5) Finally, divide the separated effect torques by the equivalent force arm and mass of the sensitive structure 3 to convert them into equivalent acceleration noise (the spectral density form can be further given) to obtain the magnitude and frequency characteristics of the temperature noise introduced by the temperature non-uniformity of the electrode cage under a given temperature gradient and air pressure conditions.

[0107] In addition, the present invention also provides a method for testing acceleration noise introduced by temperature fluctuations in a sensitive structure, comprising the following steps:

[0108] Step 100: Apply periodic temperature excitation at symmetrical positions on both sides of the outside of each sensitive structure to simulate the formation of a non-uniform temperature field that changes with time on the inner surface of the electrode cage. Control the temperature difference between the two surfaces of the sensitive structure to simulate the temperature fluctuation effect generated by the temperature gradient. Use the optical readout system 7 to measure the torque change of the sensitive structure to obtain the acceleration noise under periodic temperature fluctuation.

[0109] During the experiment, such as Figure 4 As shown, the two heating modules on opposite sides of the outer sides of each sensitive structure are... The heating is provided in alternating cycles. Temperature stability is better than Temperature difference distribution.

[0110] Step 200: Real-time acquisition of multi-point temperature data around the sensitive structure, and interpolation and fitting of these discrete temperature points using the data processing system 8, mapping them to an inner surface temperature distribution T(x,y,t) consistent with the geometry of the electrode cage, thereby obtaining the spatial distribution of temperature profile and temperature gradient.

[0111] Step 300: Substitute the reconstructed inner surface temperature field into the temperature noise theoretical model, and calculate the equivalent theoretical torque or acceleration contribution of the radiometer effect and the thermal radiation pressure effect to the sensitive structure under the current temperature distribution; wherein the radiometer effect mainly varies with air pressure and temperature gradient, and the thermal radiation pressure effect mainly varies with surface temperature and emissivity.

[0112] The process of constructing the temperature noise theoretical model is as follows:

[0113] In the geometric model, when the sensitive structure is stationary relative to the electrode cage, Within the included solid angle, the number of particles hitting the sensitive structural surface per unit time Above, speed The number of molecules between them is:

[0114]

[0115] in The velocity per unit volume of gas molecules escaping from the lower surface of the upper electrode plate is The number of molecules between them, and have

[0116]

[0117] Let be the Maxwell velocity distribution function. According to the law of conservation of momentum, For the meta-surface of the upper surface of the sensitive structure The force is:

[0118]

[0119] In the formula, Let be the unit normal vector of the upper surface of the sensitive structure. Substitution The solution is:

[0120]

[0121] make ,Depend on The sum of the force vectors exerted by all molecules on the upper and lower surfaces on the sensitive structure is:

[0122]

[0123] in Let the temperature difference between the two symmetrical electrode plates be represented. Expanding it and ignoring higher-order terms, we can finally obtain:

[0124]

[0125] The acceleration noise is caused by the radiometer effect, where, The average gas pressure inside the vacuum chamber. The effective force-bearing area participating in the radiometer effect is the lateral surface area of ​​the sensitive structure. The average temperature. For the quality of sensitive structures, This represents the effective amplitude of the periodic temperature fluctuation.

[0126] To compare the impact of different sensitive structural dimensions on radiometer noise, we substituted the design parameters of general electrostatic levitation accelerometers and inertial sensors into the formula, and further illustrated the applicability of the formula by combining the results of existing literature.

[0127] Substitute the design parameters of the inertial sensor: , Maximum temperature difference within the sensitive structure , , :

[0128]

[0129] It is worth noting that the above theoretical derivation is based on the assumption that the distance between the electrode cage and the sensitive structure is negligible compared to the size of the sensitive structure. This conclusion applies to electrostatic levitation accelerometers with small gaps, but not to inertial sensors with significantly large gaps. When the gap between the electrode plate and the sensitive structure increases, gas molecules at the corners of the sensitive structure no longer only collide between two opposing surfaces, but may also collide with other surfaces. Based on simulations and experiments in existing literature, under the corresponding LISA inertial sensor parameters, the results are consistent with the conclusion drawn under the infinite plate assumption. times, that is:

[0130]

[0131] Due to the presence of temperature and temperature gradients, thermal radiation is generated within the sensitive structure. This thermal radiation produces radiation pressure on the surface of the sensitive structure, which in turn generates acceleration noise. This problem can be transformed into a problem of momentum and energy transfer of thermal photons. Photons undergo absorption and emission, and the photon number is not conserved. Based on existing statistical physics theories, we can obtain the conclusion experimentally verified by Lebedev in 1901:

[0132] , ,

[0133] After sorting, we obtained:

[0134]

[0135] in, Radiation pressure, The internal energy density of radiation, At the speed of light, For temperature, This is the Stefanian constant. For ease of representation, the thermodynamic Stefanian constant is used instead of the fundamental physical constant.

[0136] We now use the infinite parallel plate assumption: all thermal photons are absorbed on opposite parallel planes near the emission point or on the plane containing the emission point itself. We assume all surfaces within the sensitive structure have the same radiation intensity per unit area; according to Kirchhoff's laws and the above assumptions, all surfaces have the same radiation absorptivity per unit area. Assuming the sensitive structure is isothermal, due to the symmetry of its geometry, the momentum of the emitted photons cancels out, exerting no force on the sensitive structure itself. Therefore, we only consider the effect of photons emitted from the electrode cage. Considering the small temperature difference between the sensitive structure and the electrode cage, and the roughly similar geometric area compared to the inner surface of the electrode cage, we can approximate that the cavity within the sensitive structure has reached equilibrium radiation. Thus, excluding the radiation pressure generated by the sensitive structure, we can approximate the pressure exerted on the sensitive structure by the photons emitted from the electrode cage as half of the total pressure, i.e.:

[0137]

[0138] set up and If we approximate the expression, expanding the above equation in its vicinity yields a linear approximation:

[0139]

[0140] From the above equation, the total force exerted by the two opposing surfaces of the electrode cage on the sensitive structure can be obtained as follows:

[0141]

[0142] in, To and The surface area of ​​the sensitive structure perpendicular to the sensitive axis. , and These represent the average temperatures of the electrode plates on both sides of the electrode cage along the sensitive axis.

[0143] To compare the effects of different sensitive structural dimensions on thermal radiation pressure, we substitute the design parameters of general electrostatic levitation accelerometers and inertial sensors into the formulas, and further illustrate the applicability of the formulas by referring to results from existing literature. Substituting the design parameters of the inertial sensor: , Maximum temperature difference within the sensitive structure , , , Then the acceleration noise is:

[0144]

[0145] The gap between the electrode plate and the sensing structure of a typical electrostatic levitation accelerometer is approximately... The gap of the inertial sensor is approximately The two differ by two orders of magnitude. According to simulation data from existing literature, the infinite parallel plate assumption has flaws. In the simulation results, the pressure on the surface of the sensitive structure tends to a constant value as the gap between the sensitive structure and the electrode cage decreases. Generally, the design gap of an electrostatic levitation accelerometer is much smaller than the minimum gap simulated in the literature. Therefore, the infinite electrode plate model is well-suited for accelerometer noise estimation. However, the gap of the inertial sensor cannot be ignored compared to the size of the sensitive structure. According to simulations in existing literature, under the aforementioned inertial sensor parameters, the results are less than the theoretical results. Increasing the gap by a factor of two reduces thermal radiation pressure noise.

[0146]

[0147] In summary, the theoretical model of temperature noise includes acceleration noise caused by the radiometer effect and acceleration noise caused by the thermal radiation pressure effect. The model for acceleration noise caused by the radiometer effect is as follows:

[0148] ,in, ;

[0149] The acceleration noise model caused by thermal radiation pressure effect is as follows:

[0150] ;in, .

[0151] Step 400: Change the ambient temperature and ambient air pressure of the sensitive structure, use the optical readout system to measure the first harmonic torque at the temperature modulation frequency, fit and compare the measured total temperature modulation torque with the theoretical torque calculated from the temperature field, obtain the correction factor and weight of each temperature effect through fitting, and separate the actual contribution of different temperature effects.

[0152] In step 400, the ambient temperature of the sensitive structure is changed, and step 100 is repeated according to the step changes of the ambient temperature to measure the effect of different average ambient temperatures on acceleration noise.

[0153] Specifically, the shielded room was set at different temperatures, from 10℃ to 45℃, and five sets of data were collected. The temperature gradient and temperature distribution remained constant to investigate the final measurement desired. Whether it is affected by the average ambient temperature level.

[0154] Change the ambient vacuum level of the sensitive structure and repeat step 100 above to obtain the curves of normalized torque versus vacuum level at different ambient temperatures.

[0155] By adjusting the atmospheric pressure of the environment where the sensitive structure is located, the influence of atmospheric pressure changes on acceleration noise is examined, and the coupling effect between atmospheric pressure changes and temperature fluctuations is analyzed. This step helps to further determine the contribution ratio of radiometer effect and thermal radiation pressure effect to acceleration noise. The specific implementation method is as follows:

[0156] Adjust the ambient vacuum pressure and obtain multiple sets of data from different vacuum pressures, specifically from 5 × 10 -5 Pa to 2×10 -3 Pa collected three sets of data to obtain the normalized torque as a function of the ambient vacuum level under different environmental vacuum conditions. The curve was used to verify the radiometer effect using the normalized torque formula, and its correction factor was derived. :

[0157] ;

[0158] Utilizing the variation of normalized torque with vacuum level under different environmental vacuum conditions The curve can be extrapolated to obtain the relationship between torque and temperature at P=0, and then the effect of thermal radiation pressure can be analyzed.

[0159] Step 500: Divide the separated temperature effect torques by the equivalent force arm and mass of the sensitive structure to convert them into equivalent acceleration noise, and obtain the magnitude and frequency characteristics of the temperature noise introduced by the temperature-nonuniform electrode cage under a given temperature gradient and air pressure conditions.

[0160] A periodic temperature difference excitation is applied to the heating components on both sides, for example, with a period of approximately 2500 s and a temperature difference amplitude of approximately 400 mK, for each set pressure. After the temperature reaches a stable period, the torsion balance is measured at the excitation frequency using the optical readout system 7. First harmonic torque amplitude at the location Simultaneously record the corresponding temperature difference amplitude. To facilitate comparison with the theoretical model, the measured torque is normalized, and the normalized torque is defined. for:

[0161]

[0162] in The effective area of ​​the sensing structure perpendicular to the sensing axis can be equivalently represented by the effective projected area of ​​the sensing structure "seen" by the upper and lower electrode plates. The purpose of this normalization is to isolate factors such as geometric dimensions and temperature difference amplitude, allowing the theoretical radiometer model to be written in a form linear with pressure. For all... calculate With pressure as the x-axis, Using the vertical axis as the ordinate, while keeping the temperature modulation conditions essentially constant, the pressure inside the vacuum chamber is adjusted. By repeating the above measurements under multiple different ambient vacuum levels, the results for different vacuum levels can be obtained. curve.

[0163] Theoretically, under molecular flow conditions, the acceleration or torque generated by the radiometer effect is proportional to the air pressure and temperature difference, and the acceleration can be written as...

[0164]

[0165] in The residual gas static pressure, The average temperature. For the effective amplitude of the excitation signal, corresponding to the normalized torque, we have: and The relationship is linear. Within this pressure range, the thermal radiation pressure effect... The dependence of the curve on the radiometer effect is negligible or much weaker than that on the radiometer effect, so the slope of the curve can be considered to be mainly contributed by the radiometer effect, and the correction factor can be obtained from the slope. .

[0166] The torque caused by thermal radiation pressure effect is mainly related to temperature and temperature gradient. The dependence is much weaker; firstly, the effect of the thermometer effect is eliminated, and the acceleration noise is compared with the theoretical thermoradiative pressure model. , Once a definite scaling relationship is established, the torque after deducting the thermometer effect is fitted to obtain the coefficient of the thermal radiation pressure effect.

[0167] This solution introduces periodic temperature excitation into the testing system, combined with temperature distribution reconstruction technology, to accurately measure acceleration noise caused by temperature fluctuations, precisely control the temperature gradient, and collect surface temperature data of sensitive structures. It can accurately measure acceleration noise caused by temperature fluctuations, especially in noise source identification and separation under conditions of minute temperature differences.

[0168] Through multiple theoretical calculations, the effects of radiometer effects and thermal radiation pressure effects on acceleration noise can be effectively separated and quantified under different temperature excitation and vacuum conditions. Using multiple sets of experimental data and normalized torque curves, this method can quantitatively assess the impact of temperature fluctuations on acceleration measurements, providing a more accurate noise correction factor for inertial sensor design. In experiments on inertial sensor design, theoretical calculations show that the radiometer effect contributes up to 60% of the total acceleration noise caused by temperature fluctuations, while the thermal radiation pressure effect contributes 40%. These data help designers better understand the impact of different noise sources, enabling them to make targeted adjustments in their designs.

[0169] The above embodiments are merely exemplary embodiments of this application and are not intended to limit this application. The scope of protection of this application is defined by the claims. Those skilled in the art can make various modifications or equivalent substitutions to this application within its substance and scope of protection, and such modifications or equivalent substitutions should also be considered to fall within the scope of protection of this application.

Claims

1. A testing device for acceleration noise introduced by temperature fluctuations in a sensitive structure, characterized in that, include: Two sensitive structures (3) are placed inside the vacuum cavity (1) and symmetrically distributed on both sides of the rotating frame (2). Each of the sensitive structures (3) is connected to the rotating frame (2) through a horizontal rod (4) to form the same rigid rotating system. A weak force measuring torsion balance (5) for measuring the damping received by the sensitive structure (3) is installed on the rotating frame (2). Furthermore, a temperature control system (6) is provided at the symmetrical position on the outer periphery of the sensitive structure (3). The temperature control system (6) applies periodic temperature excitation at the symmetrical positions on both sides of the outer periphery of the sensitive structure (3) and controls the temperature difference between the two sides multiple times to simulate the temperature fluctuation effect generated by the temperature gradient. The rotating frame (2) is equipped with an optical readout system (7), and the weak force measuring torsion balance (5) is equipped with a reflective mirror. The optical readout system (7) measures the torque change generated by the sensitive structure (3) by changing the optical path of the reflective mirror in order to obtain the acceleration noise under periodic temperature fluctuations. Furthermore, the temperature control system (6) analyzes the acceleration noise generated by the temperature fluctuation coupling effect and distinguishes the different effects of the radiometer effect and thermal radiation pressure effect caused by the temperature gradient on the acceleration noise of the sensitive structure (3).

2. The acceleration noise testing device introduced by temperature fluctuations of a sensitive structure according to claim 1, characterized in that, The temperature control system (6) includes two heating elements (61) disposed outside the sensitive structure (3) and symmetrically distributed. A heat-conducting structure (62) is provided between the heating elements (61) and the sensitive structure (3). The heating elements (61) are connected to a temperature controller (63). The temperature controller (63) regulates the two heating elements (61) to apply periodic temperature excitation at the external symmetrical position of the sensitive structure (3), and the temperature of the heating elements (61) is transferred to the side of the sensitive structure (3) through the heat conduction structure (62). The temperature controller (63) and the optical readout system (7) are connected to a data processing system (8), which analyzes the acceleration noise generated by the coupling effect of temperature fluctuations.

3. The acceleration noise testing device introduced by temperature fluctuations of a sensitive structure according to claim 2, characterized in that, The heating element (61) includes TEC semiconductor coolers (611) symmetrically arranged on both sides of the sensitive structure (3), wherein the side of the TEC semiconductor cooler (611) facing the sensitive structure (3) is provided with a heat-conducting structure (62), and the temperature of the heat-conducting structure (62) represents the temperature applied to the sensitive structure (3). The TEC semiconductor cooler (611) has a heat sink plate (613) on the side away from the sensitive structure (3), and the heat sink plate (613) is used to receive the heat dissipated from the heat dissipation end of the TEC semiconductor cooler (611). The outer surface of the heat sink plate (613) is provided with a heat pipe (612), which conducts heat from the heat sink plate (613) through the heat pipe (612).

4. The acceleration noise testing device introduced by temperature fluctuations of a sensitive structure according to claim 3, characterized in that, The heat-conducting structure (62) is provided with a plurality of uniformly distributed temperature sensors, which are used to monitor the temperature of the heat-conducting structure (62) and are communicatively connected to the temperature controller (63).

5. The acceleration noise testing device introduced by temperature fluctuations of a sensitive structure according to claim 1, characterized in that, The top center of the rotating frame (2) is equipped with a suspension wire (10) via a suspension wire lower clamp (9), and a weak force measuring torsion balance (5) for measuring the rotation angle of the suspension wire (10) is mounted on the suspension wire lower clamp (9). The rotation angle of the sensitive structure (3) is transmitted through the rigid force transmission chain of the horizontal rod (4), the rotating frame (2) and the lower clamp of the suspension wire (9), so that the lower end of the suspension wire (10) and the sensitive structure (3) achieve angular displacement synchronization. The main body of the weak force measuring torsion balance (5) is used to measure the torsion angle of the suspension wire (10) which is equivalent to the torque / rotation angle generated by the sensitive structure (3).

6. The acceleration noise testing device introduced by temperature fluctuations of a sensitive structure according to claim 1, characterized in that, Counterweights (11) are installed on the other two sides of the rotating frame (2), and the counterweights (11) and the sensitive structure (3) form a cross-shaped symmetrical layout. Each counterweight (11) is connected to the rotating frame (2) via a counterweight horizontal bar (12); Furthermore, the counterweight (11) is connected to the rotating frame (2) by means of a slider movement, so that the counterweight arm length and equivalent torque of the counterweight (11) can be continuously adjusted.

7. A method for testing acceleration noise introduced by temperature fluctuations in a sensitive structure, characterized in that, Includes the following steps: Step 100: Apply periodic temperature excitation at symmetrical positions on both sides of the outer side of the sensitive structure to simulate the formation of a non-uniform temperature field that changes with time on the inner surface of the electrode cage. Control the temperature difference between the two surfaces of the sensitive structure to simulate the temperature fluctuation effect generated by the temperature gradient. Measure the torque change of the sensitive structure to obtain the acceleration noise under periodic temperature fluctuation. Step 200: Collect multi-point temperature data around the sensitive structure in real time, and use the data processing system to interpolate and fit these discrete temperature points to map them into an inner surface temperature distribution T(x,y,t) consistent with the geometry of the electrode cage, thereby obtaining the spatial distribution of temperature profile and temperature gradient. Step 300: Substitute the reconstructed inner surface temperature field into the temperature noise theoretical model, and calculate the equivalent theoretical torque or acceleration contribution of the radiometer effect and thermal radiation pressure effect to the sensitive structure under the current temperature distribution. Step 400: Change the ambient temperature and ambient air pressure of the sensitive structure, use the optical readout system to measure the first harmonic torque at the temperature modulation frequency, fit and compare the measured total temperature modulation torque with the theoretical torque calculated from the temperature field, obtain the correction factor and weight of each temperature effect through fitting, and separate the actual contribution of different temperature effects. Step 500: Divide the separated temperature effect torques by the equivalent force arm and mass of the sensitive structure to convert them into equivalent acceleration noise, and obtain the magnitude and frequency characteristics of the temperature noise introduced by the temperature-nonuniform electrode cage under a given temperature gradient and air pressure conditions.

8. The method for testing acceleration noise introduced by temperature fluctuations in a sensitive structure according to claim 7, characterized in that, In step 300, the temperature noise theoretical model includes acceleration noise caused by the radiometer effect and acceleration noise caused by the thermal radiation pressure effect. The acceleration noise model caused by the radiometer effect is as follows: ,in, ; The acceleration noise model caused by thermal radiation pressure effect is as follows: ;in, .

9. The method for testing acceleration noise introduced by temperature fluctuations in a sensitive structure according to claim 7, characterized in that, In step 400, the ambient temperature of the sensitive structure is changed, and step 100 is repeated according to the step changes of the ambient temperature to measure the effect of different average ambient temperatures on acceleration noise. Change the ambient vacuum level of the sensitive structure and repeat step 100 above to obtain the curve of normalized torque versus vacuum level at different ambient temperatures.

10. A method for testing acceleration noise introduced by temperature fluctuations in a sensitive structure according to claim 9, characterized in that, By adjusting the atmospheric pressure of the environment where the sensitive structure is located, the influence of atmospheric pressure changes on acceleration noise is examined, and the coupling effect between atmospheric pressure changes and temperature fluctuations is analyzed. This step helps to further determine the contribution ratio of radiometer effect and thermal radiation pressure effect to acceleration noise. The specific implementation method is as follows: By adjusting the air pressure at different ambient vacuum levels, multiple sets of data were obtained to determine the normalized torque variation with ambient vacuum level under different conditions. The curve was used to verify the radiometer effect using the normalized torque formula, and its correction factor was derived. : ； Utilizing the variation of normalized torque with vacuum level under different environmental vacuum conditions The curve was obtained by extrapolation to show the relationship between torque and temperature at P=0, and then the effect of thermal radiation pressure effect was analyzed.

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