A method for extracting spacecraft interface forces and conducting force limit tests based on the least squares method.

Abstract

This invention provides a spacecraft interface force extraction and force limit testing method based on the least squares method, applicable to a spacecraft vibration testing system. The testing system includes a vibration table, an extended table surface or horizontal slide, test fixtures, a signal conditioner, a vibration controller, a power amplifier, a vibration table oil pump, a cooling unit, and an external circulating water system. The testing method comprises fourteen steps. This invention's method analyzes a wide frequency range, reduces the cost of spacecraft force limit testing, meets the engineering application requirements for quantifying interface forces, effectively mitigates overtesting in spacecraft vibration testing, and ensures the safety of spacecraft products and equipment operation.

Description

Technical Field

[0001] This invention belongs to the field of spacecraft mechanical environment testing, specifically involving a method for extracting spacecraft interface forces and conducting force limit tests based on the least squares method. Background Technology

[0002] The spacecraft force limit test method introduces force response limiting control technology on the basis of traditional acceleration control methods. During the test, the spacecraft product must simultaneously meet both acceleration test conditions and force response limiting control conditions. This dual acceleration and force control technology can realistically reproduce the spacecraft's response during system resonance at launch, greatly mitigating overtesting caused by the dynamic vibration absorption effect of interface impedance, and effectively protecting the safety of the spacecraft product.

[0003] Conducting force limit tests on spacecraft requires extracting the interface force parameters between the spacecraft and the test fixture. Existing methods for extracting interface force parameters mainly include force sensor signal synthesis, strain calibration, and acceleration modal condensation. Currently, foreign countries mainly use force sensor signal synthesis to directly extract interface forces. However, for large spacecraft test products with different interfaces, the introduction of force sensors will introduce additional mass, change the product connection boundary, and the force measurement device is difficult to design, expensive, and has poor versatility, making it particularly difficult to apply for vibration testing of large-sized spacecraft products.

[0004] The interface force extraction methods proposed in the papers "Application Research of Indirect Force Measurement Method in Force-Limited Vibration Test" (Strength and Environment, Vol. 45, No. 6, December 2018) and "Interface Force Monitoring and Force-Limited Vibration Control Test Method Based on Vibration Table Armature and Its Engineering Application" (Spacecraft Environmental Engineering, Vol. 36, No. 1, February 2019) share the same basic principle and are relatively simple. They are mainly designed for sinusoidal vibration tests of spacecraft products and are suitable for a narrow frequency range concentrated in the low-frequency range. The patent "Method for Synthesizing Force Parameters of Multiple Force Sensors in Spacecraft Force-Limited Test" (Application No. 201610156958.9) mainly describes a method for directly measuring interface force parameters using force measuring devices in spacecraft force-limited tests.

[0005] Existing testing methods cannot measure interfacial force parameters without the installation of force measuring devices, and the experimental costs are high. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention proposes a spacecraft interface force extraction and force limit test method based on the least squares method by utilizing the current and voltage information of the moving coil of the vibration table. It is mainly applicable to random vibration tests of spacecraft products and aims to solve the problem of how to indirectly extract interface force parameters of spacecraft products when no force measurement device is installed. This reduces the cost of spacecraft force limit tests, meets the engineering application requirements for quantitative interface forces, effectively alleviates the overtesting phenomenon in spacecraft vibration tests, and ensures the safety of spacecraft products and equipment operation.

[0007] To achieve the above objectives, the present invention adopts the following solution:

[0008] This invention provides a spacecraft interface force extraction and force limit test method based on the least squares method, used in a spacecraft vibration test system. The test system includes a vibration table, an extended platform or horizontal slide, a test fixture, a signal conditioner, a vibration controller, a power amplifier, a vibration table oil pump, a cooling unit, and an external circulating water system. Spacecraft products are typically mounted on the extended platform or horizontal slide using the test fixture and a pressure ring. An acceleration control sensor is installed between the product and the test fixture. The acceleration signal is filtered and amplified by the signal conditioner into a voltage signal, which is then fed back to the vibration controller. The controller performs real-time corrections based on a reference spectrum and measured signals, outputting a suitable drive signal that is provided to the vibration table via the power amplifier. The vibration controller acquires and calculates the current and voltage signals from the power amplifier. The moving coil is located inside the vibration table. The vibration table oil pump supplies oil to the bearings inside the vibration table to guide their movement. The cooling unit uses distilled water to cool the moving coil and excitation coil inside the vibration table. The external circulating water system cools the distilled water in the cooling unit. The test method includes the following steps:

[0009] Step 1: Start-up procedure for the test equipment; turn on the external circulating water system, vibration table cooling unit, vibration table oil pump, power amplifier and other equipment in sequence; after the equipment is turned on, check whether its operation is normal; at the same time, check whether the extended table and test fixture are in good condition.

[0010] Step 2: Conduct the first random vibration test before the experiment; specifically, install four control sensors evenly on the moving coil of the vibration table body and conduct the first random vibration test before the experiment; record the total mass of the moving parts of the vibration table system, and calculate the frequency response function of the power amplifier current and the average control acceleration, and the frequency response function of the power amplifier voltage and the average control acceleration by dividing the cross power spectral density and the self power spectral density, respectively.

[0011] Step 3: Conduct the second random vibration test before the actual test; specifically, fix the extended platform on the moving coil and confirm that the extended platform is in good motion state; then, evenly distribute four control sensors on the extended platform and conduct the second random vibration test before the actual test; record the total mass of the moving parts of the vibration table system, the frequency response function of the power amplifier current and the average control acceleration, and the frequency response function of the power amplifier voltage and the average control acceleration.

[0012] Step 4: Conduct the third random vibration test before the actual test; specifically, fix the test fixture on the extended platform; then, evenly distribute four control sensors on the upper surface of the test fixture and conduct the third random vibration test before the actual test; record the total mass of the moving parts of the vibration table system, the frequency response function of the power amplifier current and the average control acceleration, and the frequency response function of the power amplifier voltage and the average control acceleration.

[0013] Step 5: Determine the load force / load current ratio and key coefficients of the moving coil admittance; Specifically, using the random vibration test data obtained in steps 2, 3, and 4 before the test, the load force and load current ratio coefficients and the moving coil admittance coefficients are calculated according to formula (11) using the least squares method and the pseudo-inverse method.

[0014] Step Six: Vertical Positioning and Installation of Spacecraft Products; Specifically, install a lifting device on top of the spacecraft product, slowly lift the spacecraft product above the test fixture, and slowly lower it onto the test fixture under the guidance of the positioning pins; then, install the pressure ring on the docking frame, connect it with screws, and tighten it with a torque wrench; finally, disassemble the spacecraft lifting device;

[0015] Step 7: Conduct the first small-scale vertical vibration test of the spacecraft product; specifically, four control sensors are evenly distributed on the pressure ring, and a four-point averaging control method is used to conduct the first small-scale random vertical vibration test of the spacecraft product; record the power amplifier current, voltage, and response curves of key measuring points on the spacecraft of the vibration table system; then calculate the low-level interface force;

[0016] Step 8: Determine the current limiting spectrum for vertical force limit test of spacecraft products; specifically, use three parameters—force limit limiting spectrum, small-scale test current, and calculated low-scale interface force—to calculate the current spectrum that needs to be limited when the formal scale is reached.

[0017] Step Nine: Conduct vertical formal-scale vibration tests on spacecraft products; specifically, connect the current of the vibration table power amplifier to the vibration controller limiting channel, and use the limited current spectrum as the response limiting condition; subsequently, conduct large-scale vibration tests according to the established formal test conditions, and record the acceleration control spectrum, current spectrum, voltage spectrum, and response curves of key measurement points on the spacecraft.

[0018] Step 10: Conduct the second small-scale vertical vibration test of the spacecraft product; specifically, use the four-point averaging control method to conduct the second small-scale random vertical vibration test of the spacecraft product; record the power amplifier current, voltage, and response curves of key measuring points on the spacecraft in the vibration table system.

[0019] Step 11: Evaluation steps for vertical force limit test of spacecraft products; Specifically, the force limit test of spacecraft is evaluated based on factors such as whether the response curves of key measuring points on the spacecraft in the two small-scale vibration tests are consistent, whether the current limiting spectrum of the formal force limit test meets the requirements, whether the spacecraft functions normally, and whether its performance is intact, to evaluate the effectiveness of the force limit test.

[0020] Step 12: Horizontal positioning and installation of the spacecraft product; specifically, rotate the vibration table system to a horizontal position, and connect and secure the moving coil to the horizontal slide using a buckle; install the test fixture above the horizontal slide; then install the lifting device on top of the spacecraft product, lift the spacecraft product above the test fixture, and position it; subsequently, install the pressure ring on the docking frame, connect it with screws, and tighten it with a torque wrench; finally, disassemble the spacecraft lifting device.

[0021] Step Thirteen: Horizontal Force Limit Test and Evaluation Procedures for Spacecraft Products; Specifically, the following steps are performed: First small-scale horizontal vibration test of the spacecraft product; determination of the current limiting spectrum for the horizontal force limit test of the spacecraft product; formal-scale horizontal vibration test of the spacecraft product; second small-scale horizontal vibration test of the spacecraft product; followed by evaluation of the horizontal force limit test to assess its effectiveness.

[0022] Step Fourteen: Test Equipment Shutdown and Removal Procedures; Specifically, install a lifting device on top of the spacecraft product, remove the pressure ring connecting screws and take off the pressure ring, slowly lift the spacecraft product, and then lower it onto the support vehicle; sequentially shut down the power amplifier, vibration table oil pump, vibration table cooling unit, external circulating water system, and other equipment, and the force limit test of the spacecraft product is completed.

[0023] In some embodiments, the present invention further includes the following technical features:

[0024] No fewer than three low-level random vibration tests shall be conducted before the vertical and horizontal tests.

[0025] For low-level random vibration tests conducted before the vertical test: the first test requires the vibration table itself; the second test requires the vibration table itself plus the extended platform; and the third test requires the vibration table itself plus the extended platform plus the test fixture itself.

[0026] For low-level random vibration tests conducted before the horizontal test: the first test requires the vibration table itself; the second test requires the vibration table plus the horizontal slide itself; the third test requires the vibration table plus the horizontal slide plus the test fixture itself.

[0027] The test conditions for small-scale random vibration tests in the vertical and horizontal directions are generally 1 / 4 of the full-scale random test conditions in the outline.

[0028] The load force to load current ratio coefficient and the moving coil admittance coefficient need to be calculated using the least squares method to obtain a pseudo-inverse.

[0029] The beneficial effects of this invention are:

[0030] This invention proposes a least-squares-based method for extracting interfacial forces and conducting force limit tests on spacecraft, utilizing the current and voltage information of the moving coils in a vibration table. It aims to address the problem of being unable to measure interfacial force parameters using existing technologies in random vibration tests of spacecraft products when no force measurement device is installed. This method offers a wide analytical frequency range, reduces the cost of spacecraft force limit tests, meets the engineering application requirements for quantifying interfacial forces, effectively mitigates overtesting in spacecraft vibration testing, and ensures the safety of spacecraft products and equipment operation. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the equivalent circuit of the vibration table and load system.

[0032] Figure 2 A schematic diagram of the vertical force limit test for spacecraft products;

[0033] Figure 3 This is a schematic diagram of a horizontal force limit test for a spacecraft product.

[0034] Figure 4 Schematic diagram of a pressure ring used in spacecraft force limit tests;

[0035] In the figure, 1-moving coil admittance, 2-load admittance, 3-vibration table current source, 4-vibration table body, 5-power amplifier, 6-extension table surface, 7-test fixture, 8-spacecraft product, 9-control sensor, 10-signal conditioner, 11-vibration controller, 12-horizontal slide, 13-bullhead. Detailed Implementation

[0036] To make the technical solutions and advantages of the present invention clearer, the technical solutions of the embodiments of the present invention will be fully described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0037] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0038] First, the basic principles of the spacecraft interface force extraction method based on the least squares method are explained in detail. (See also...) Figure 1 , Figure 1 The equivalent circuit diagram of the vibration table and load system in the frequency domain is shown. The total current of the vibration table is equivalent to the vibration table current source 3, and the current flows to two equivalent admittances, namely the moving coil admittance 1 and the load admittance 2. The equivalent voltage across the moving coil and the load is E.

[0039] The total current during the vibration table and load tests is I. The current driving the moving coil of the vibration table is I0. O The driving load current is I L The equivalent voltage across the vibration table and the load is E. Then the driving load current I... L It can be represented as follows:

[0040] I L =I-EY O (1)

[0041] Assume the interface force between the shaking table and the load is proportional to the acceleration at the interface. Assume the interface motion can be described with a single degree of freedom. The relationship between the force and acceleration at the interface is as follows:

[0042] F L =ZA L (2)

[0043] Where Z represents the apparent mass. The load here can be the spacecraft product itself, the product and its fixture, or the product, fixture, and moving coil assembly, depending on the user's assumptions. Note that Z is not a constant. Furthermore, it is assumed that the equivalent current driving the load is proportional to the force at the interface.

[0044] F L =I L K (3)

[0045] Here, the coefficient K is the ratio of the force on the load to the current. Substituting equations (1) and (2) into the right and left sides of equation (3) respectively, we get:

[0046] ZA L =(I-EY) O )K (4)

[0047] Multiplying both sides by the conjugate transpose of the acceleration and taking the expected value, we get:

[0048] ZG AA =(G IA -G EA Y O )K (5)

[0049] Among them G AA G represents the acceleration power spectral density at the interface. IA G represents the cross-power spectral density between the total current and acceleration of the shaking table. EA Let G be the cross-power spectral density between the shaking table voltage and acceleration. Divide both sides by G. AA K, and rearranged, we get:

[0050]

[0051] The frequency response function is defined as follows:

[0052]

[0053]

[0054] Then formula (6) can be transformed into

[0055]

[0056] The above formula contains two unknowns: the load force to load current ratio coefficient K and the moving coil admittance coefficient Y. o If N groups of experiments are conducted, and N is required to be ≥3, then the above formula can be rewritten in matrix form:

[0057]

[0058] coefficients K and Y o The least squares method can be used to calculate the pseudo-inverse of the above equation. The calculation formula is as follows:

[0059]

[0060] Finally, during the formal testing of the spacecraft, the coefficients K and Y were used... o By measuring the voltage and current of the vibration table, the interfacial forces of the spacecraft can be calculated.

[0061] F L =(I-EY) o K (12)

[0062] Force limit tests using a spacecraft interface force extraction method based on the least squares approach first require obtaining the load force to load current ratio and key coefficients of the moving coil admittance through at least three tests with different configurations. For vertical vibration tests, according to the attached... Figure 2 The process involves installing spacecraft components and conducting three vertical vibration tests, followed by a vertical force limit test evaluation. Figure 2 In the process, the extended platform 6 and the vibration table body 4 are fixedly connected by screws. The test fixture 7 is installed on the extended platform 6. The spacecraft product 8 is fixedly connected to the test fixture 7 by a pressure ring. Four acceleration control sensors 9 are generally installed on the pressure ring. An averaging control method is adopted. The acceleration signal is filtered and amplified by the signal conditioner 10 and converted into a voltage signal before being fed back to the vibration controller 11. The current and voltage signals of the power amplifier 5 are fed back to the vibration controller 11 for acquisition and calculation. For horizontal vibration tests, according to the attached... Figure 3 The process involves installing spacecraft components and conducting three horizontal vibration tests, followed by a horizontal force limit test evaluation. Figure 3 In this process, the horizontal slide 12 is connected to the vibration table body 4 via the bullhead 13. The test fixture 7 is mounted on the horizontal slide 12. The spacecraft product 8 is fixedly connected to the test fixture 7 via a pressure ring. Four acceleration control sensors 9 are generally installed on the pressure ring. An averaging control method is adopted. The acceleration signal is filtered and amplified by the signal conditioner 10 and converted into a voltage signal before being fed back to the vibration controller 11. The current and voltage signals of the power amplifier 5 are also fed back to the vibration controller 11 for acquisition and calculation. The detailed steps are as follows:

[0063] (1) Start the test equipment. Specifically, turn on the external circulating water system, vibration table cooling unit, vibration table oil pump, power amplifier, and other equipment in sequence. After starting the equipment, check whether its operating status is normal. At the same time, check whether the extended table and test fixtures are in good condition.

[0064] (2) Conduct the first random vibration test before the actual test. Specifically, four control sensors are evenly distributed on the moving coil of the vibration table. Using a four-point averaging control method and a flat reference spectrum random test condition, the first random vibration test before the actual test is conducted. Record the frequency response function H of the total mass Z1 of the moving parts of the vibration table system, the power amplifier current, and the average control acceleration. IA1 The frequency response function H of power amplifier voltage and average control acceleration EA1 .

[0065] (3) Conduct a second random vibration test before the actual test. Specifically, place the vibration table itself in a vertical position, then hoist the extended platform above the table and connect it to the moving coil, securing it with screws to confirm that the vertical movement of the extended platform is good. Subsequently, evenly distribute four control sensors on the extended platform, and use a four-point averaging control method and a flat reference spectrum random test condition to conduct the second random vibration test before the actual test. Record the total mass Z2 of the moving parts of the vibration table system, the frequency response function H of the power amplifier current and the average control acceleration. IA2 The frequency response function H of power amplifier voltage and average control acceleration EA2 .

[0066] (4) Conduct the third random vibration test before the actual test. Specifically, the spacecraft test fixture is hoisted above the extended platform, then lowered onto the extended platform and secured with screws. Subsequently, four control sensors are evenly distributed on the upper surface of the test fixture. Using a four-point averaging control method and a flat reference spectrum random test condition, the third random vibration test before the actual test is conducted. Record the frequency response function H of the total mass Z3 of the moving parts of the vibration table system, the power amplifier current, and the average control acceleration. IA3 The frequency response function H of power amplifier voltage and average control acceleration EA3 .

[0067] (5) Determine the load force to load current ratio and the key coefficients of the moving coil admittance. Specifically, using random vibration test data before the test, the force to load current ratio coefficient K and the moving coil admittance coefficient Y are calculated using the least squares method in a pseudo-inverse manner. o .

[0068] (6) Vertical positioning and installation of spacecraft products. For details, please refer to the appendix. Figure 2 A lifting device is installed on top of the spacecraft product, and the product is slowly lifted above the test fixture. Guided by the positioning pins, it is then slowly lowered onto the test fixture. Subsequently, a pressure ring is installed on the docking frame (see attached diagram). Figure 4 The spacecraft lifting gear is then connected with screws and tightened using a torque wrench. Finally, the lifting gear is disassembled.

[0069] The pressure ring is made of steel and is generally shaped as two semicircles with a sloping surface in its cross-section. The sloping surface is pressed against the spacecraft docking frame by the screw in the center hole of the pressure ring, thereby achieving a fixed connection between the product and the test fixture.

[0070] (7) Conduct the first small-scale vertical vibration test of the spacecraft product. Specifically, four control sensors are evenly distributed on the pressure ring. Using the four-point averaging control method and the full-scale 1 / 4 random test conditions, the first small-scale random vertical vibration test of the spacecraft product is conducted. Record the power amplifier current I, voltage E, and response curves of key measuring points on the spacecraft in the vibration table system. Calculate the low-scale interface force F using formula (12). Low .

[0071] (8) Determine the vertical force-limiting test current limiting spectrum for spacecraft products. Specifically, use the force-limiting limiting spectrum F. High Small-scale test current I Low Calculation of low-order interfacial forces F Low Three parameters, the current spectrum I that needs to be limited when calculating the formal magnitude. High The calculation formula is as follows:

[0072]

[0073] (9) Conduct vertical vibration tests on the spacecraft product. Specifically, the current of the vibration table power amplifier is connected to the vibration controller limiting channel, and the current limiting spectrum calculated in step (8) is used as the response limiting condition. Subsequently, a large-scale vibration test is carried out according to the established formal test conditions, and the acceleration control spectrum, current spectrum, voltage spectrum, and response curves of key measuring points on the spacecraft are recorded.

[0074] (10) Conduct the second small-scale vertical vibration test on the spacecraft product. Specifically, referring to step (7), adopt the four-point averaging control method and the full-scale 1 / 4 random test conditions of the outline to conduct the second small-scale random vertical vibration test on the spacecraft product. Record the power amplifier current I, voltage E, and response curves of key measuring points on the spacecraft in the vibration table system.

[0075] (11) Evaluation of vertical force limit test of spacecraft products. Specifically, the effectiveness of the force limit test is evaluated based on factors such as whether the response curves of key measuring points on the spacecraft in two small-scale vibration tests are consistent, whether the current limiting spectrum of the formal force limit test meets the requirements, whether the spacecraft functions normally, and whether its performance is intact.

[0076] (12) Horizontal installation of spacecraft products. For details, refer to the appendix. Figure 3 The vibration table system was rotated to a horizontal position, and the moving coil was connected and secured to the horizontal slide using the buckle. The test fixture was installed above the horizontal slide, and the smooth movement of the slide was confirmed. Then, a lifting device was installed on top of the spacecraft product, and the product was slowly lifted onto the test fixture, guided by the positioning pins, and then slowly lowered onto the fixture. Finally, the pressure ring was installed on the docking frame (see attached diagram). Figure 4The components are connected with screws and tightened with a torque wrench. Finally, the spacecraft lifting gear is disassembled.

[0077] (13) Horizontal force limit test and evaluation of spacecraft products. Specifically, referring to steps (7) to (10), the first small-scale horizontal vibration test of the spacecraft product, the determination of the current limiting spectrum for the horizontal force limit test of the spacecraft product, the formal horizontal vibration test of the spacecraft product, and the second small-scale horizontal vibration test of the spacecraft product are carried out respectively. Subsequently, the horizontal force limit test is evaluated to assess its effectiveness.

[0078] (14) Shutdown and Removal of Test Equipment. Specifically, a lifting device is installed on top of the spacecraft product, the pressure ring connecting screws are removed and the pressure ring is taken off, the spacecraft product is slowly lifted up and then lowered onto the support vehicle. The power amplifier, vibration table oil pump, vibration table cooling unit, external circulating water system and other equipment are shut down in sequence, and the force limit test of the spacecraft product is completed.

[0079] In the description of this specification, references to terms such as "an embodiment" and "example" refer to specific features, structures, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms are not necessarily intended to refer to corresponding embodiments or examples in a suitable manner.

[0080] It must be pointed out that the above description of the embodiments is not intended to limit the invention but only to help understand the core idea of ​​the invention. For those skilled in the art, any improvements to the invention and equivalent alternatives made to the invention without departing from the principle of the invention are also within the scope of protection of the claims of the invention.

Claims

1. A method for extracting interface forces and conducting force limit tests on spacecraft based on the least squares method, used in spacecraft vibration testing systems, characterized in that, The test system includes a vibration table body, an extended table surface or a horizontal slide, test fixtures, a signal conditioner, a vibration controller, a power amplifier, a vibration table oil pump, a cooling unit, and an external circulating water system. The test method includes the following steps: Step 1: Start-up procedure for the test equipment; turn on the external circulating water system, vibration table cooling unit, vibration table oil pump, and power amplifier equipment in sequence; after the equipment is turned on, check whether its operating status is normal; at the same time, check whether the extended table and test fixtures are in good condition. Step 2: Conduct the first low-level random vibration test before the actual test; specifically, install four control sensors evenly on the moving coil of the vibration table body and conduct the first low-level random vibration test before the actual test; record the total mass of the moving parts of the vibration table system, and calculate the frequency response function of the power amplifier current and the average control acceleration, and the frequency response function of the power amplifier voltage and the average control acceleration by dividing the cross power spectral density by the self power spectral density; Step 3: Conduct the second low-level random vibration test before the actual test; specifically, fix the extended platform on the moving coil and confirm that the extended platform is in good motion state; then, evenly distribute four control sensors on the extended platform and conduct the second low-level random vibration test before the actual test; record the total mass of the moving parts of the vibration table system, the frequency response function of the power amplifier current and the average control acceleration, and the frequency response function of the power amplifier voltage and the average control acceleration. Step 4: Conduct the third low-level random vibration test before the actual test; specifically, fix the test fixture on the extended platform; then, evenly distribute four control sensors on the upper surface of the test fixture and conduct the third low-level random vibration test before the actual test; record the total mass of the moving parts of the vibration table system, the frequency response function of the power amplifier current and the average control acceleration, and the frequency response function of the power amplifier voltage and the average control acceleration. Step 5: Determine the load force / load current ratio and key coefficients of the moving coil admittance; specifically, using the random vibration test data obtained in steps 2, 3, and 4 before the test, calculate the load force and load current ratio coefficients based on the least squares method using a pseudo-inverse approach. 、 Dynamic admittance coefficient; Step Six: Vertical Positioning and Installation of Spacecraft Products; Specifically, install a lifting device on top of the spacecraft product, slowly lift the spacecraft product above the test fixture, and slowly lower it onto the test fixture under the guidance of the positioning pins; then, install the pressure ring on the docking frame, connect it with screws, and tighten it with a torque wrench; finally, disassemble the spacecraft lifting device; Step 7: Conduct the first small-scale vertical vibration test of the spacecraft product; specifically, four control sensors are evenly distributed on the pressure ring, and a four-point averaging control method is used to conduct the first small-scale random vertical vibration test of the spacecraft product; record the power amplifier current, power amplifier voltage, and response curves of key measuring points on the spacecraft in the vibration table system; then calculate the low-level interface force; Step 8: Determine the current limiting spectrum for the vertical force limit test of the spacecraft product; Specifically, the force-limited amplitude spectrum, small-scale test current, and calculated low-scale interface force are used to calculate the current spectrum that needs to be limited when calculating the formal magnitude. Step Nine: Conduct vertical formal-scale vibration tests on spacecraft products; specifically, connect the current of the vibration table power amplifier to the vibration controller limiting channel, and use the limited current spectrum as the response limiting condition; subsequently, conduct large-scale vibration tests according to the established formal test conditions, and record the acceleration control spectrum, current spectrum, voltage spectrum, and response curves of key measurement points on the spacecraft. Step 10: Conduct the second small-scale vertical vibration test of the spacecraft product; specifically, use the four-point averaging control method to conduct the second small-scale random vertical vibration test of the spacecraft product; record the power amplifier current, power amplifier voltage, and response curves of key measuring points on the spacecraft in the vibration table system; Step 11: Evaluation steps for vertical force limit test of spacecraft products; Specifically, the force limit test of spacecraft is evaluated based on factors such as whether the response curves of key measuring points on the spacecraft in the two small-scale vibration tests are consistent, whether the current limiting spectrum of the formal force limit test meets the requirements, whether the spacecraft functions normally, and whether its performance is intact, to evaluate the effectiveness of the force limit test. Step 12: Horizontal positioning and installation of the spacecraft product; specifically, rotate the vibration table system to a horizontal position, and connect and secure the moving coil to the horizontal slide using a buckle; install the test fixture above the horizontal slide; then install the lifting device on top of the spacecraft product, lift the spacecraft product above the test fixture, and position it; subsequently, install the pressure ring on the docking frame, connect it with screws, and tighten it with a torque wrench; finally, disassemble the spacecraft lifting device. Step Thirteen: Horizontal Force Limit Test and Evaluation Procedures for Spacecraft Products; Specifically, the following steps are performed: First small-scale horizontal vibration test of the spacecraft product; determination of the current limiting spectrum for the horizontal force limit test of the spacecraft product; formal-scale horizontal vibration test of the spacecraft product; second small-scale horizontal vibration test of the spacecraft product; followed by evaluation of the horizontal force limit test to assess its effectiveness. Step Fourteen: Test Equipment Shutdown and Removal Procedures; Specifically, install a lifting device on top of the spacecraft product, remove the pressure ring connecting screws and take off the pressure ring, slowly lift the spacecraft product, and then lower it onto the support vehicle; sequentially shut down the power amplifier, vibration table oil pump, vibration table cooling unit, and external circulating water system equipment, and the force limit test of the spacecraft product is completed.

2. The spacecraft interface force extraction and force limit test method based on the least squares method as described in claim 1, characterized in that, For low-level random vibration tests conducted before vertical tests: the first test requires the vibration table itself; the second test requires the vibration table itself plus the extended platform; and the third test requires the vibration table itself plus the extended platform plus the test fixture itself.

3. The spacecraft interface force extraction and force limit test method based on the least squares method as described in claim 1, characterized in that, The test conditions for small-scale random vibration tests in the vertical and horizontal directions are 1 / 4 of the full-scale random test conditions in the outline.

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