Magnetic suspension inertia actuator extremely slight vibration ground test system and application method

Abstract

The application discloses a kind of magnetic suspension inertial actuator extremely slight vibration ground test system and application method, the test system of the present application includes base assembly, force sensor, adapter, magnetic suspension inertial actuator, accelerometer, laser vibration meter and test terminal, magnetic suspension inertial actuator is installed on adapter, adapter is installed on mounting plate by force sensor, accelerometer is installed on mounting plate, force sensor, accelerometer, laser vibration meter are connected with test terminal respectively, the laser beam of laser vibration meter covers the mounting surface of magnetic suspension inertial actuator.The base assembly and adapter of the present application can flexibly simulate the test environment required by magnetic suspension inertial actuator, the output response of magnetic suspension inertial actuator during work is collected using sensor to identify the sensitive parameters of magnetic suspension inertial actuator, and then the influence law of boundary condition on extremely slight vibration transmission characteristic is analyzed.

Description

Technical Field

[0001] This invention belongs to the field of aerospace component testing technology, specifically relating to a ground testing system and application method for extremely low vibration of a magnetic levitation inertial actuator. Background Technology

[0002] Magnetic levitation inertial actuators in spacecraft (such as magnetically levitated reaction wheels and magnetically levitated control moment gyroscopes) generate unnecessary micro-amplitude vibrations and torque excitations during normal operation due to non-ideal factors, which are output to the spacecraft structure from their mounting interface. These micro-amplitude vibrations are called micro-vibrations or extremely micro-vibrations. Their direct impact is to interfere with the pointing accuracy and performance of sensitive payloads on the spacecraft. When magnetically levitated inertial actuators are applied to in-orbit spacecraft, their dynamic environment differs significantly from that on Earth. This difference is mainly reflected in three aspects: first, the mechanical environment in outer space is generally a microgravity field compared to Earth; second, the spacecraft is in a free-floating state, exhibiting rigid body motion; and third, the mounting boundary of the magnetically levitated inertial actuator is generally the spacecraft bulkhead, which is typically made of high-mass, highly elastic honeycomb sandwich panels. These three types of dynamic environments significantly affect the extremely micro-vibration characteristics of the magnetically levitated inertial actuator. Currently, ground-based testing methods for micro-vibrations of inertial actuators in spacecraft mainly involve horizontally mounting the inertial actuator on a rigid platform or on an air-floating platform. While the above methods have some feasibility, they differ significantly from the dynamic environment during on-orbit operation and cannot meet the testing requirements for the vibration characteristics of inertial actuators in future high-precision Earth observation. Summary of the Invention

[0003] The technical problem to be solved by this invention is to provide a ground testing system and application method for extremely low vibration of a magnetic levitation inertial actuator, which addresses the above-mentioned problems in the prior art. This invention utilizes a base assembly and adapter to flexibly simulate the testing environment required by the magnetic levitation inertial actuator. Force sensors, accelerometers, and laser vibration meters are used to collect the output response of the magnetic levitation inertial actuator during operation to identify the sensitive parameters of the magnetic levitation inertial actuator, and then analyze the influence of boundary conditions on the transmission characteristics of extremely low vibration.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0005] A ground testing system for extremely low vibration of a magnetically levitated inertial actuator includes a base assembly, a force sensor, an adapter, a magnetically levitated inertial actuator, an accelerometer, a laser vibrometer, and a testing terminal. The base assembly is used to simulate the mechanical boundary conditions of the magnetically levitated inertial actuator. The base assembly includes interconnected support boundaries and a mounting plate. The support boundaries define the relative relationship between the mounting foundation of the magnetically levitated inertial actuator and the ground. The mounting plate defines the installation stiffness characteristics of the magnetically levitated inertial actuator. The magnetically levitated inertial actuator is mounted on the adapter, which is mounted on the mounting plate via the force sensor. The accelerometer is mounted on the mounting plate. The force sensor, accelerometer, and laser vibrometer are all connected to the testing terminal. The laser beam of the laser vibrometer covers the mounting surface of the magnetically levitated inertial actuator.

[0006] Optionally, the adapter is a parallel fixture with a horizontally arranged mounting position. When the magnetic levitation inertial actuator is installed in the mounting position of the parallel fixture, the axis of the magnetic levitation inertial actuator coincides with the direction of gravity.

[0007] Optionally, the adapter is an inclined mounting fixture, which has an inclined mounting position. When the magnetic levitation inertial actuator is installed on the mounting position of the inclined mounting fixture, the axis of the magnetic levitation inertial actuator intersects the direction of gravity and the included angle is acute or obtuse.

[0008] Optionally, the adapter is a vertical fixture with a vertically arranged mounting position. When the magnetic levitation inertial actuator is installed in the mounting position of the vertical fixture, the axis of the magnetic levitation inertial actuator intersects the direction of gravity at a right angle.

[0009] Optionally, the support boundary is a fixed boundary, which includes multiple mounting columns, and the mounting plate is horizontally and fixedly mounted on the multiple mounting columns.

[0010] Optionally, the support boundary is a floating boundary, which includes a support truss and a fixed hoisting plate mounted on the support truss. Multiple springs are mounted on the fixed hoisting plate, and steel wire ropes are hinged to the springs. The mounting plate is connected to the multiple springs via the steel wire ropes to suspend the mounting plate on the fixed hoisting plate, thus giving the magnetic levitation inertial actuator five degrees of freedom, including: a swing angle θ along the x-axis. x The y-angle of oscillation θ y The displacement of the reaction flywheel along the z-direction is z s The installation platform oscillates and vibrates around the x-axis at an angle α. s And the angle β of the oscillation vibration of the mounted plate around the y-axis. s .

[0011] Optionally, the mounting plate is a rigid plate or a flexible plate.

[0012] Optionally, the mounting plate is a flexible plate, and a piezoelectric ceramic sheet and a piezoelectric sensor are laid between the mounting plate and the force sensor. The piezoelectric ceramic sheet corresponding to each force sensor works independently, and the control voltage of the piezoelectric ceramic sheet is... for:

[0013]

[0014] In the above formula, G is the feedback amplification factor, which is the product of the amplification factor of the piezoelectric sensor and the piezoelectric ceramic sheet. It is the derivative of the charge Q generated by the actuating layer.

[0015] Furthermore, this invention also provides an application method for the aforementioned ground testing system for extremely low vibration of a magnetically levitated inertial actuator. The support boundary is a floating boundary, the mounting plate is a rigid plate, and the magnetically levitated inertial actuator is a reaction flywheel. The application method includes:

[0016] S101, define the coordinate system, including: o-xyz is a spatial inertial coordinate system, fixed to the supporting truss; ox e y e z e ox is a fixed coordinate system for the reaction flywheel, used to describe the rotation of the flywheel rotor; p y p z p The coordinate system is a fixed coordinate system for mounting the plate, with the origin at the centroid of the plate and the three axes parallel to the o-xyz axes respectively.

[0017] S102, the generalized degree of freedom q of the reaction flywheel is determined as follows:

[0018] q=[θ x θ y z s α s β s ],

[0019] In the above formula, θ x Let θ be the swing angle along the x-axis. y Let z be the y-angle of the swing. s For the displacement of the reaction flywheel along the z-direction, α s The angle of oscillation vibration of the mounting platform around the x-axis, β s The angle of the oscillation vibration of the installation platform around the y-axis;

[0020] S103, determine the translational velocity of the reaction flywheel and the mounting plate in the generalized coordinate system and their angular velocity in the body coordinate system:

[0021]

[0022]

[0023]

[0024] In the above formula, v r v is the average speed of the flywheel rotor. s To speed up the installation of the tablet, and , , and , respectively, are the derivatives of the displacements of the reaction flywheel along the x, y, and z directions, and represent the translational velocities along the x, y, and z directions, respectively; l is the length of the mounting plate suspension, which is the sum of the length of the wire rope and the spring. For θ x The derivative of For θ y The derivative of ω; s For the angular velocity of the mounting plate, ω r Let be the angular velocity of the flywheel rotor. For α s The derivative of For β s The derivative of Ω, where Ω is the steady rotational speed of the flywheel rotor;

[0025] S104, using the energy principle of the Lagrange equation to determine the kinetic equation:

[0026]

[0027] In the above formula, L = TV, and T, V, and D represent the total kinetic energy, total potential energy, and total dissipated energy of the system, respectively. The generalized degree of freedom q of the reaction flywheel i The derivative; based on the dynamic equations, the kinetic energy equation of the system is determined as:

[0028]

[0029]

[0030] In the above formula, m is the sum of the masses of the mounting plate and the reaction flywheel, and k sz Let be the spring constant along the z-direction. For θ x The second derivative, For θ y The second derivative, I x I y and I r These are the x-direction moment of inertia, y-direction moment of inertia of the mounting plate, and the x-direction moment of inertia of the reaction flywheel, respectively. For α s The second derivative, For β s The second derivative, For α s The derivative of For β s The derivative of I p Let d be the y-direction moment of inertia of the reaction flywheel, and d be the distance between the suspension points of the two wire ropes.

[0031] S105, Determine the system parameters of the reaction flywheel based on the system's kinetic energy equation:

[0032]

[0033]

[0034]

[0035] In the above formula, and These are the natural frequencies of the system's oscillation along the x-axis, oscillation along the y-axis, and vertical motion along the z-axis, respectively. Let g be the rotational frequency of the system about the x-axis and y-axis, and g be the gravitational acceleration.

[0036] Furthermore, the present invention also provides an application method for the aforementioned ground testing system for extremely low vibration of a magnetic levitation inertial actuator, wherein the support boundary is a floating boundary, the mounting plate is a flexible plate, and the application method includes:

[0037] S201, based on the hexagonal honeycomb sandwich structure constituting the flexible plate of the mounting plate, the honeycomb sandwich structure is equivalent to anisotropic material of uniform thickness, an anisotropic material layer is established, and the parameters of the anisotropic material are calculated according to the following formula:

[0038]

[0039]

[0040] Among them, E 11 and E 12 E represents the elastic modulus of the equivalent material in two directions, t is the wall thickness of the honeycomb core, and E is the elastic modulus of the material in two directions. s Let G be the elastic modulus of the isotropic material, L be the side length of the hexagon, and G be the elastic modulus of the material. 11 G 12 and G 23 G represents the shear modulus of the equivalent material in the xoy plane, xoz plane, and yoz plane, respectively, where γ is the equivalent material correction factor. s For the shear modulus of an isotropic material, ρ s For the density of isotropic materials, u sLet ρ be the Poisson's ratio of the material. c For the density of the equivalent material, u c The equivalent material's Poisson's ratio;

[0041] S202, Establish an equivalent model of the base component and perform finite element simulation to obtain simulation results.

[0042] Compared with the prior art, the present invention has the following main advantages:

[0043] This invention focuses on magnetic levitation inertial actuators, considering external conditions (space dynamic environment), gravity conditions caused by differences between Earth and space, and the influence mechanism and laws of dynamic boundaries such as simulated rigid body motion and flexible vibration of spacecraft on micro-vibration output characteristics. It studies the influence of intelligent boundaries (such as piezoelectric flexible boundaries) on the vibration output of the actuator. A base assembly is used to simulate the mechanical boundary conditions of the magnetic levitation inertial actuator. Force sensors, accelerometers, and laser vibrometers are used to collect the output response of the magnetic levitation inertial actuator during operation to identify its sensitive parameters. Furthermore, the influence of boundary conditions on the transmission characteristics of extremely small vibrations is analyzed. This invention can be used to study the influence of ground gravity on the dynamic characteristics of magnetic levitation inertial actuators, the influence of dynamic boundaries on the dynamic characteristics of magnetic levitation inertial actuators, and the influence of controllable intelligent dynamic boundaries on the dynamic characteristics of magnetic levitation inertial actuators. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the test system in Embodiment 1 of the present invention.

[0045] Figure 2 This is a schematic diagram of the installation structure of the adapter in Embodiment 1 of the present invention.

[0046] Figure 3 This is a schematic diagram of the installation structure of the adapter in Embodiment 2 of the present invention.

[0047] Figure 4 This is a schematic diagram of the installation structure of the adapter in Embodiment 3 of the present invention.

[0048] Figure 5 This is a schematic diagram of the installation structure of the supporting boundary in Embodiment 4 of the present invention.

[0049] Figure 6 This is a schematic diagram of the coordinate system definition in Embodiment Six of the present invention. Detailed Implementation

[0050] Example 1:

[0051] like Figure 1 and Figure 2As shown, the ground testing system for the extremely low vibration of the magnetic levitation inertial actuator in this embodiment includes a base assembly 1, a force sensor 2, an adapter 3, a magnetic levitation inertial actuator 4, an accelerometer 5, a laser vibrometer 6, and a testing terminal 7. The base assembly 1 is the core component of the design of the extremely low vibration testing system for the magnetic levitation inertial actuator 4. The base assembly 1 is used to simulate the mechanical boundary conditions of the magnetic levitation inertial actuator 4. The base assembly 1 includes an interconnected support boundary 11 and a mounting plate 12. The support boundary 11 is used to define the relative relationship between the mounting foundation of the magnetic levitation inertial actuator 4 and the ground. The mounting plate 12 is used to define the installation stiffness characteristics of the magnetic levitation inertial actuator 4. The magnetic levitation inertial actuator 4 is mounted on the adapter 3. The adapter 3 is mounted on the mounting plate 12 via the force sensor 2. The accelerometer 5 is mounted on the mounting plate 12. The force sensor 2, the accelerometer 5, and the laser vibrometer 6 are respectively connected to the testing terminal 7. The laser beam of the laser vibrometer 6 covers the mounting surface of the magnetic levitation inertial actuator 4.

[0052] Depending on whether the rigid body motion of a spacecraft is being simulated, the support boundary 11 can be either a fixed boundary or a floating boundary. See also Figure 2 In this embodiment, the support boundary 11 is a fixed boundary, which includes multiple mounting columns (specifically four in this embodiment, but the number can be designed as needed). The mounting plate 12 is horizontally fixed on the multiple mounting columns. The fixed boundary is used to provide boundary conditions where the magnetic levitation inertial actuator 4 has no rigid body motion when working on the ground. At this time, it is assumed that the mounting foundation of the stator inside the magnetic levitation inertial actuator 4 is absolutely stationary, and the rigid support boundary 11 is achieved through rigid supports (mounting columns) fixed to the ground.

[0053] Depending on whether the mounting interface of the magnetic levitation inertial actuator 4 deforms, the mounting plate 12 can be a rigid plate or a flexible plate as needed. As an optional implementation, the mounting plate 12 in this embodiment is a rigid plate. The rigid plate is used to ensure that the mounting interface of the magnetic levitation inertial actuator 4 does not undergo elastic deformation or elastic vibration. In this embodiment, the rigid plate is a rigid metal block (such as hard aluminum alloy), and its mass is approximately n times that of the magnetic levitation inertial actuator 4 under test, where n is generally 5-8.

[0054] The magnetic levitation inertial actuator is fixedly connected to the base system via adapter 3. To study the effect of gravity on the magnetic bearing, based on the support direction of the magnetic levitation bearing on the rotor, adapter 3 can be designed to form a certain angle with the direction of gravity on the ground. For example... Figure 1 and Figure 2As shown, in this embodiment, the adapter 3 is an inclined mounting fixture with an inclined mounting position. When the magnetic levitation inertial actuator 4 is mounted on the mounting position of the inclined fixture, the axis of the magnetic levitation inertial actuator 4 intersects the direction of gravity at an acute or obtuse angle. By using different inclination angles of the inclined fixture, the influence of different gravity components on the magnetic levitation bearing can be tested, such as a 45° inclination.

[0055] Example 2:

[0056] This embodiment is basically the same as Embodiment 1, the main difference being the shape of the adapter 3. For example... Figure 3 As shown, the adapter 3 can be a parallel fixture with a horizontally arranged mounting position. When the magnetic levitation inertial actuator 4 is installed on the mounting position of the parallel fixture, the axis of the magnetic levitation inertial actuator 4 is aligned with the direction of gravity.

[0057] Example 3:

[0058] This embodiment is basically the same as Embodiment 1, the main difference being the shape of the adapter 3. For example... Figure 4 As shown, the adapter 3 can be a vertical fixture with a vertically arranged mounting position. When the magnetic levitation inertial actuator 4 is installed in the mounting position of the vertical fixture, the axis of the magnetic levitation inertial actuator 4 intersects the direction of gravity and the included angle is a right angle.

[0059] Example 4:

[0060] This embodiment is basically the same as Embodiment 1, with the main difference being the implementation method of the support boundary 11. The support boundary 11 used in this embodiment is a floating boundary. A floating boundary is used to simulate the rigid body motion of a spacecraft under microgravity conditions during its orbital flight. The space microgravity environment simulation method uses environmental effect simulation, meaning the test piece is continuously subjected to external forces that can balance or approximately balance gravity, making the apparent weight zero. Considering factors such as cost and experimental duration, a floating boundary with a vertical suspension structure is selected to simulate the microgravity environment. Specifically, as shown... Figure 5 As shown, the floating boundary includes a support truss 111 and a fixed suspension plate 112 mounted on the support truss 111. Multiple springs 113 are mounted on the fixed suspension plate 112, and steel wire ropes 114 are hinged to the springs 113. The mounting plate 12 is connected to the multiple springs 113 via the steel wire ropes 114 to suspend the mounting plate 12 on the fixed suspension plate 112, thus giving the magnetic levitation inertial actuator 4 five degrees of freedom, including: a swing angle θ along the x-axis. x The y-angle of oscillation θ y The displacement of the reaction flywheel along the z-direction is z s The installation platform 12 oscillates and vibrates around the x-axis at an angle α. sAnd the angle β of the oscillation vibration of the mounted plate 12 around the y-axis. s .

[0061] Example 5:

[0062] This embodiment is basically the same as Embodiment 1, the main difference being that the mounting plate 12 uses a flexible plate. As an optional implementation method, the flexible plate can be a commonly used substrate in satellite structures as needed. Considering that it should be consistent with the actual situation, this embodiment uses an aluminum honeycomb plate. The aluminum honeycomb plate consists of two panels and a honeycomb plate sandwiched between the panels. The honeycomb plate is a hexagonal array structure similar to a honeycomb, and its axis is perpendicular to the two panels. It has the advantages of lightweight structure, high strength and large deformation coefficient, which can realistically simulate the satellite installation environment of the magnetic levitation inertial actuator 4.

[0063] As a preferred embodiment, for studying the influence of controllable intelligent dynamic boundaries on the dynamic characteristics of a magnetic levitation inertial actuator, in this embodiment, piezoelectric ceramic sheets and piezoelectric sensors are laid between the mounting plate 12 (flexible plate) and the force sensor 2. Each force sensor 2 has a corresponding piezoelectric ceramic sheet that operates independently, and the control voltage of the piezoelectric ceramic sheet... for:

[0064]

[0065] In the above formula, G is the feedback amplification factor, which is the product of the amplification factor of the piezoelectric sensor and the piezoelectric ceramic sheet. This is the derivative of the charge Q generated by the actuating layer. Existing technologies have significant limitations in testing different mounting surfaces. For example, a honeycomb panel needs to be fabricated for each mounting surface, and a new mounting plate needs to be fabricated for each different mounting surface. Furthermore, existing technologies can only be tested on a few fixed mounting surfaces. This embodiment uses piezoelectric sensors and piezoelectric actuating layers to intelligently control the vibration of the mounting plate, thus enabling the same mounting plate 12 to simulate multiple different mounting interfaces. This embodiment employs a local vibration information feedback control scheme, where each piezoelectric layer works independently. The piezoelectric sensing layer measures its own vibration signal. When the flywheel generates micro-vibrations, the force sensor 2 feeds the force signal back to the control system. Since the piezoelectric material generates an electrical signal when compressed, this signal is synchronously transmitted to the actuating layer, synchronously controlling the vibration of the piezoelectric material to counteract the disturbances caused by the flywheel, enabling the system to simulate intelligent boundary conditions. The mounting plate 12 (rigid plate) can simulate the situation where the flywheel mounting surface does not undergo elastic deformation or elastic vibration, while the mounting plate 12 (flexible plate) can simulate the situation where the flywheel is mounted on a mounting surface with a specific vibration frequency. By placing a piezoelectric sensor and actuator between the mounting plate 12 (flexible plate) and the force sensor 2, the frequency of the mounting surface can be actively changed to simulate the vibration of the flywheel on different mounting surfaces. Specifically, when the flywheel vibrates during operation, the piezoelectric sensor measures the vibration signal of the system. After processing by the control system, the control information is transmitted to the piezoelectric actuation layer, which vibrates to actively control the vibration of the mounting surface, thereby simulating the vibration of the flywheel on different mounting surfaces and enabling the system to simulate intelligent boundary conditions.

[0066] As can be seen from Embodiments 1 to 5, since the support boundary 11 can be a fixed boundary or a floating boundary as needed, and the mounting plate 12 can be a rigid plate or a flexible plate as needed, the ground testing system for the magnetic levitation inertial actuator with minimal vibration can use the combination of the support boundary 11 and the mounting plate 12 to simulate different boundary conditions, such as type I to IV bases:

[0067] Type I scheme for base component 1: the support boundary 11 adopts a fixed boundary, and the mounting plate 12 adopts a rigid plate.

[0068] Type II scheme for base component 1: the support boundary 11 adopts a fixed boundary, and the mounting plate 12 adopts a flexible plate.

[0069] Type III scheme for base component 1: the support boundary 11 adopts a floating boundary, and the mounting plate 12 adopts a rigid plate.

[0070] Type IV scheme for base component 1: the support boundary 11 adopts a floating boundary, and the mounting plate 12 adopts a flexible plate.

[0071] Based on the actual situation and the specific type of the base assembly 1, different measurement methods are adopted to measure the response of physical quantities such as force, acceleration and displacement generated when the magnetic levitation inertial actuator 4 is working, and then evaluate its micro-vibration characteristics to meet different test purposes and requirements. For example: (1) Acceleration measurement scheme: Accelerometer 5 is used for measurement, mainly to measure the acceleration response of the mounting surface of the base system where the magnetic levitation actuator 4 is located. At this time, the accelerometer 5 is installed on the base assembly 1, which requires the base assembly 1 to have a large mass and rigidity. (2) Doppler optical measurement scheme: Non-contact laser vibrometer 6 is used for measurement, mainly to measure the deformation or displacement response of the mounting surface of the base assembly 1 where the magnetic levitation actuator 4 is located. At this time, the laser beam of the laser vibrometer 6 can cover the mounting surface of the magnetic levitation inertial actuator 4, which requires the base assembly 1 to have a large test reflection surface, mainly for flexible mounting surfaces with elastic deformation. (3) Force sensor measurement scheme: Force sensor 2 is used for measurement, mainly to measure the interaction force and torque between the magnetic levitation actuator 4 and the base assembly 1. At this point, force sensor 2 is installed between the magnetic levitation actuator 4 and the base assembly 1, requiring the base assembly 1 to have high rigidity. In summary, Examples 1 to 5, which focus on the magnetic levitation inertial actuator, consider external conditions (space dynamic environment), gravity conditions caused by differences between Earth and space, and the influence mechanism and laws of dynamic boundaries such as simulated rigid body motion and flexible vibration of spacecraft on the micro-vibration output characteristics. They study the influence of intelligent boundaries (such as piezoelectric flexible boundaries) on the vibration output of the actuator, using the base assembly to simulate the mechanical boundary conditions of the magnetic levitation inertial actuator 4. Force sensors, accelerometers, and laser vibrometers are used to collect the output response of the magnetic levitation inertial actuator 4 during operation to identify its sensitive parameters. This allows for the analysis of the influence of boundary conditions on the transmission characteristics of extremely small vibrations. This can be used to study the influence of ground gravity on the dynamic characteristics of the magnetic levitation inertial actuator, the influence of dynamic boundaries on the dynamic characteristics of the magnetic levitation inertial actuator, and the influence of controllable intelligent dynamic boundaries on the dynamic characteristics of the magnetic levitation inertial actuator.

[0072] Example 6:

[0073] This embodiment further provides an application method for a ground testing system of a magnetic levitation inertial actuator for the Type III scheme of base assembly 1 (where the support boundary 11 is a floating boundary and the mounting plate 12 is a rigid plate). The magnetic levitation inertial actuator 4 is a reaction flywheel. In this embodiment, the following assumptions are made for the Type III scheme of base assembly 1: the fundamental frequency of the extremely low vibration system mentioned in this invention is set to be less than 0.5Hz. It is assumed that the rotor of the reaction flywheel rotates steadily, and the elastic vibration of the internal structure of the reaction flywheel is not considered. It is assumed to be a rigid component, and only its mass and inertia characteristics are considered. The vibration generated by the reaction flywheel during operation is a micro-vibration. When performing dynamic modeling of the experimental test system, the assumptions of small angle and small displacement are satisfied. It is assumed that the mounting platform has a large stiffness, and its own elastic vibration is not considered. It is a cuboid configuration with uniform internal material distribution, and only its mass and inertia characteristics are considered. It is assumed that the stiffness coefficient of each individual spring is the same and works within the linear range. At this time, the stiffness coefficient of the linear spring can be used to describe its stiffness characteristics. It is assumed that the vibration deformation of the spring at the static equilibrium position is small, and the influence on the change of rope length can be ignored. Specifically, the application method of this embodiment includes:

[0074] S101, define the coordinate system, including: o-xyz is a spatial inertial coordinate system, fixed to the supporting truss 111; ox e y e z e ox is a fixed coordinate system for the reaction flywheel, used to describe the rotation of the flywheel rotor; p y p z p The fixed coordinate system for mounting plate 12 has its origin at the centroid of mounting plate 12, and its three axes are parallel to the o-xyz axes, respectively. Figure 6 As shown, l is the length of the mounting plate 12 suspension, which is the sum of the length of the wire rope 114 and the length of the spring 113, and d is the side length of the mounting plate 12. In this system, the length and width of the mounting plate are equal.

[0075] S102, the generalized degree of freedom q of the reaction flywheel is determined as follows:

[0076] q=[θ x θ y z s α s β s ],

[0077] In the above formula, θ x Let θ be the swing angle along the x-axis. y Let z be the y-angle of the swing. s For the displacement of the reaction flywheel along the z-direction, α s The angle of oscillation vibration of the mounting platform around the x-axis, β sThe angle of the oscillation vibration of the installation platform around the y-axis;

[0078] S103, Based on the small deformation assumption and coordinate transformation relationship, determine the translational velocity of the reaction flywheel and the mounting plate 12 in the generalized coordinate system and their angular velocity in the body coordinate system:

[0079]

[0080]

[0081]

[0082] In the above formula, v r v is the average speed of the flywheel rotor. s To install the tablet 12 at a faster speed, and , are the derivatives of the displacements of the reaction flywheel along the x, y, and z directions, respectively; represent the translational velocities along the x, y, and z directions, respectively; l is the length of the suspension plate 12, which is the sum of the lengths of the wire rope 114 and the spring 113; For θ x The derivative of For θ y The derivative of ω; s For the angular velocity of the mounting plate 12, ω r Let be the angular velocity of the flywheel rotor. For α s The derivative of For β s The derivative of Ω, where Ω is the steady rotational speed of the flywheel rotor;

[0083] S104, using the energy principle of the Lagrange equation to determine the kinetic equation:

[0084]

[0085] In the above formula, L = TV, and T, V, and D represent the total kinetic energy, total potential energy, and total dissipated energy of the system, respectively. The generalized degree of freedom q of the reaction flywheel i The derivative; based on the dynamic equations, the kinetic energy equation of the system is determined as:

[0086]

[0087]

[0088] In the above formula, m is the sum of the masses of the mounting plate 12 and the reaction flywheel, and k sz Let be the spring constant of spring 113 along the z-direction. For θx The second derivative, For θ y The second derivative, I x I y and I r These are the x-direction moment of inertia, y-direction moment of inertia of the mounting plate 12, and the x-direction moment of inertia of the reaction flywheel, respectively. For α s The second derivative, For β s The second derivative, For α s The derivative of For β s The derivative of I p Let d be the y-direction moment of inertia of the reaction flywheel, and d be the distance between the suspension points of the two steel wire ropes 114. Currently, the most common design method for spring suspension systems is to design solely by changing the spring stiffness. However, this method is cumbersome, and it's difficult to satisfy a five-degree-of-freedom system by simply changing the spring stiffness. This method, building upon traditional design methods, designs the translational degrees of freedom of the system by changing the length l of the suspension plate 12. This design method is simple, and during subsequent system design, the natural frequency of the system can be easily and quickly changed by altering the suspension rope length, which is difficult to achieve using traditional methods of changing spring stiffness.

[0089] S105, Determine the system parameters of the reaction flywheel based on the system's kinetic energy equation:

[0090]

[0091]

[0092]

[0093] In the above formula, and These are the natural frequencies of the system's oscillation along the x-axis, oscillation along the y-axis, and vertical motion along the z-axis, respectively. Let be the rotational frequencies of the system about the x-axis and y-axis, and g be the acceleration due to gravity. This analytical solution can guide the design of extremely small vibration systems. For those skilled in the art, this method and the analytical solution can be applied to design experimental systems without any inventive effort.

[0094] Example 7:

[0095] This embodiment further provides an application method for a ground testing system for a magnetically levitated inertial actuator with minimal vibration, specifically for the Type IV scheme of the base component 1 (the support boundary 11 adopts a floating boundary, and the mounting plate 12 adopts a flexible plate). The mounting plate 12 is specifically an aluminum honeycomb plate, which is a flexible continuous structure with many degrees of freedom. Therefore, the finite element method is used for structural modeling and analysis. The system frequency is no greater than 0.5Hz, and the frequency of the flexible mounting plate is no less than 50Hz. Similarly, the experimental system of type IV base 1 is subject to the following basic assumptions: The rotor of the reaction flywheel is assumed to rotate steadily, and the elastic vibration of the internal structure of the reaction flywheel is ignored; it is assumed to be a rigid component, considering only its mass and inertia characteristics. The vibration generated by the reaction flywheel during operation is a micro-vibration, satisfying the assumptions of small angle and small displacement when modeling the dynamics of the experimental test system. The mounting plate 12 is a honeycomb panel, assuming uniform distribution within the honeycomb sandwich structure and uniform thickness distribution of the panel, ignoring the bonding between the panel and the core plate. Each individual spring is assumed to have the same stiffness coefficient and operate within the linear range, with only elongation motion in the z-direction; in this case, the stiffness coefficient of the linear spring can be used to describe its stiffness characteristics. The spring's vibration deformation at the static equilibrium position is small, and its influence on the rope length change can be ignored. Specifically, the application method of this embodiment includes:

[0096] S201, based on the hexagonal honeycomb sandwich structure constituting the flexible plate 12, the honeycomb sandwich structure is equivalent to anisotropic materials of equal thickness, and an anisotropic material layer is established. Taking the honeycomb core material as LY12 and the panel material as aluminum (L2) as an example, the parameters of the anisotropic material are calculated according to the following formula:

[0097]

[0098]

[0099] Among them, E 11 and E 12 E represents the elastic modulus of the equivalent material in two directions, t is the wall thickness of the honeycomb core, and E is the elastic modulus of the material in two directions. s Let G be the elastic modulus of the isotropic material, L be the side length of the hexagon, and G be the elastic modulus of the material. 11 G 12 and G 23 G represents the shear modulus of the equivalent material in the xoy plane, xoz plane, and yoz plane, respectively, where γ is the equivalent material correction factor. s For the shear modulus of an isotropic material, ρ s For the density of isotropic materials, u s Let ρ be the Poisson's ratio of the material. c For the density of the equivalent material, u c The equivalent material's Poisson's ratio;

[0100] S202, Establish an equivalent model of base component 1 and perform finite element simulation to obtain simulation results.

[0101] In the simulation results of this embodiment, the natural frequencies of the first six orders are less than 0.5 Hz, and the seventh order is the mode of the mounting plate 12, which is not less than 50 Hz. The first six orders of frequencies are used to simulate the free-floating state of the spacecraft, and the seventh order and above are used to simulate the floating boundary of the magnetic levitation inertial actuator 4 and the mode of the mounting plate 12 of the flexible plate. It can be seen that it is feasible to use this finite element method to analyze the Type IV scheme of the base assembly 1.

[0102] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A ground testing system for extremely low vibration of a magnetic levitation inertial actuator, characterized in that, The test setup includes a base assembly (1), a force sensor (2), a connector (3), a magnetic levitation inertial actuator (4), an accelerometer (5), a laser vibration meter (6), and a test terminal (7). The base assembly (1) is used to simulate the mechanical boundary conditions of the magnetic levitation inertial actuator (4). The base assembly (1) includes interconnected support boundaries (11) and mounting plates (12). The support boundaries (11) define the relative relationship between the mounting base of the magnetic levitation inertial actuator (4) and the ground. The mounting plates (12) define the installation stiffness characteristics of the magnetic levitation inertial actuator (4). The magnetic levitation inertial actuator (4) is mounted on the connector (3). The connector (3) is mounted on the mounting plate (12) via the force sensor (2). The accelerometer (5) is mounted on the mounting plate (7). On the plate (12), the force sensor (2), accelerometer (5), and laser vibration meter (6) are connected to the test terminal (7) respectively. The laser beam of the laser vibration meter (6) covers the mounting surface of the magnetic levitation inertial actuator (4). The support boundary (11) is a floating boundary. The floating boundary includes a support truss (111) and a fixed hoisting plate (112) mounted on the support truss (111). Multiple springs (113) are mounted on the fixed hoisting plate (112). Steel wire ropes (114) are hinged on the springs (113). The mounting plate (12) is connected to the multiple springs (113) through the steel wire ropes (114) to suspend the mounting plate (12) on the fixed hoisting plate (112), so that the magnetic levitation inertial actuator (4) has five degrees of freedom, including: along The swing angle of the shaft ,along The swing angle of the shaft , reaction flywheel along displacement in the direction Install flat plate (12) around Shaft oscillation angle And the installation of the flat plate (12) around Shaft oscillation angle .

2. The ground testing system for extremely low vibration of a magnetic levitation inertial actuator according to claim 1, characterized in that, The adapter (3) is a parallel fixture with a horizontally arranged mounting position. When the magnetic levitation inertial actuator (4) is installed on the mounting position of the parallel fixture, the axis of the magnetic levitation inertial actuator (4) coincides with the direction of gravity.

3. The ground testing system for extremely low vibration of a magnetic levitation inertial actuator according to claim 1, characterized in that, The adapter (3) is an inclined mounting fixture with an inclined mounting position. When the magnetic levitation inertial actuator (4) is installed on the mounting position of the inclined mounting fixture, the axis of the magnetic levitation inertial actuator (4) intersects the direction of gravity and the included angle is acute or obtuse.

4. The ground testing system for extremely low vibration of a magnetic levitation inertial actuator according to claim 1, characterized in that, The adapter (3) is a vertical fixture with a vertically arranged mounting position. When the magnetic levitation inertial actuator (4) is installed on the mounting position of the vertical fixture, the axis of the magnetic levitation inertial actuator (4) intersects the direction of gravity and the included angle is a right angle.

5. The ground testing system for extremely low vibration of a magnetic levitation inertial actuator according to claim 1, characterized in that, The mounting plate (12) is a rigid plate or a flexible plate.

6. The ground testing system for extremely low vibration of a magnetic levitation inertial actuator according to claim 1, characterized in that, The mounting plate (12) is a flexible plate. A piezoelectric ceramic sheet and a piezoelectric sensor are laid between the mounting plate (12) and the force sensor (2). The piezoelectric ceramic sheet corresponding to each force sensor (2) works independently, and the control voltage of the piezoelectric ceramic sheet is... for: ， In the above formula, The feedback amplification factor is the product of the amplification factor of the piezoelectric sensor and the piezoelectric ceramic sheet. It is the derivative of the charge Q generated by the actuating layer.

7. A method for applying the ground testing system for extremely low vibration of a magnetic levitation inertial actuator as described in any one of claims 1 to 5, characterized in that, The supporting boundary (11) is a floating boundary, the mounting plate (12) is a rigid plate, the magnetic levitation inertial actuator (4) is a reaction flywheel, and the application method includes: S101, define the coordinate system, including: o-xyz is a spatial inertial coordinate system, fixed to the supporting truss (111); ox e y e z e ox is a fixed coordinate system for the reaction flywheel, used to describe the rotation of the flywheel rotor; p y p z p The coordinate system is fixed to the mounting plate (12), with the origin being the centroid of the mounting plate (12) and the three axes being parallel to the o-xyz axes respectively. S102, Determine the generalized degrees of freedom of the reaction flywheel. for: ， In the above formula, For along The swing angle of the shaft, For along The swing angle of the shaft, For the reaction flywheel along displacement in the direction, For mounting the flat plate (12) around The axial oscillation angle For mounting the flat plate (12) around The axial oscillation angle; S103, determine the translational velocity of the reaction flywheel and the mounting plate (12) in the generalized coordinate system and the angular velocity in the body coordinate system: ， ， ， In the above formula, The average speed of the flywheel rotor. For the speed of installing the tablet (12), , and The reaction flywheel along the x, y and The derivatives of the displacements along the x, y, and y axes represent the displacements along the x, y, and Translational velocity in the direction; The length of the suspension of the mounting plate (12) is the sum of the length of the wire rope (114) and the length of the spring (113); for The derivative, for The derivative; To determine the angular velocity of the mounting plate (12), Let be the angular velocity of the flywheel rotor. for The derivative, for The derivative, This is the steady rotational speed of the flywheel rotor; S104, using the energy principle of the Lagrange equation to determine the kinetic equation: ， In the above formula, ,and , and These represent the system's total kinetic energy, total potential energy, and total dissipated energy, respectively. Generalized degrees of freedom for the reaction flywheel The derivative; based on the dynamic equations, the kinetic energy equation of the system is determined as: ， ， In the above formula, The sum of the masses of the mounting plate (12) and the reaction flywheel, Let be the spring constant of spring (113) along the z-direction. for The second derivative, for The second derivative, , and For each of the tablets (12) that are installed x Moment of inertia, y Towards the moment of inertia and reaction of the flywheel x Moment of inertia, for The second derivative, for The second derivative, for The derivative, for The derivative, The y-direction moment of inertia of the reaction flywheel, The distance between the suspension points of the two wire ropes (114); S105, Determine the system parameters of the reaction flywheel based on the system's kinetic energy equation: ， ， ， In the above formula, , and These are the natural frequencies of the system's oscillation along the x-axis, oscillation along the y-axis, and vertical motion along the z-axis, respectively. Let be the rotational frequencies of the system about the x-axis and y-axis. This is the acceleration due to gravity.

8. A method for applying the ground testing system for extremely low vibration of a magnetic levitation inertial actuator as described in any one of claims 1 to 6, characterized in that, The supporting boundary (11) is a floating boundary, the mounting plate (12) is a flexible plate, and the application method includes: S201, based on the hexagonal honeycomb sandwich structure of the flexible plate constituting the mounting plate (12), the honeycomb sandwich structure is equivalent to anisotropic material of equal thickness, anisotropic material layer is established, and the parameters of the anisotropic material are calculated according to the following formula: ， ， in, and This represents the elastic modulus of the equivalent material in two directions. The thickness is the wall thickness of the honeycomb core. For the elastic modulus of isotropic materials, The side length of the hexagon is... , and Equivalent materials xoy flat, xoz plane and yoz Shear modulus of a plane This is the equivalent material correction factor. For isotropic materials, shear modulus For the density of isotropic materials, For the material's Poisson's ratio, The density of the equivalent material, The equivalent material's Poisson's ratio; S202, establish an equivalent model of the base component (1) and perform finite element simulation to obtain simulation results.

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