Dynamic modeling and mass balancing method for spacecraft ground microgravity simulation platform

Abstract

The application discloses a kind of spacecraft ground microgravity simulation platform dynamics modeling and mass balancing method, belong to the technical field of space technology.The application includes the following steps: according to the component assembly relationship of spacecraft ground microgravity semi-physical simulation platform, distinguish each component and component group;According to the condition of each component and component group and whole, respectively, each component and component group are established coordinate system;Dynamics derivation is carried out based on coordinate system, and dynamics model is obtained;The complete dynamics model of ground simulation platform is obtained by analyzing dynamics model by Lagrange method;The complete dynamics model of ground simulation platform is simplified by hypothesis, and simplified dynamics model is obtained;Mass balancing is carried out to simplified dynamics model, and the spacecraft ground microgravity semi-physical simulation platform of approximate quasi-zero stiffness is obtained.The introduction of pivot system makes the system reach approximate quasi-zero stiffness, and then reconstructs microgravity environment on the ground.

Description

Technical Field

[0001] This invention belongs to the field of aerospace technology and relates to a method for dynamic modeling and mass balancing of a microgravity simulation platform for spacecraft. Background Technology

[0002] With the deepening and expansion of human space activities, spacecraft to meet various applications have emerged, including spacecraft of various uses and functions, space shuttles, space stations, and new concept spacecraft developed in recent years. The development of each spacecraft involves processes such as concept research, overall design, key technology verification, and ground testing. Conducting key technology experiments on the ground is an indispensable step. Considering the unique characteristics of the space environment during ground testing, it is necessary to simulate the on-orbit environment for performance testing and operational verification.

[0003] The construction and simulation of microgravity environments on Earth has a long history. Traditional microgravity simulation equipment includes drop tower systems, wire suspension systems, air-bearing platform systems, and neutral buoyancy pool systems. However, the microgravity levels provided by these traditional methods are insufficient to achieve the levels required for gravitational wave detection. Furthermore, the traditional device for simulating the six degrees of freedom motion of a spacecraft platform on Earth is the Stewart platform. When the spacecraft moves, its motion information is transmitted through the Stewart platform's controller, thus inducing motion on the Stewart platform itself. Therefore, this platform is an active platform, and its motion exhibits lag, while control introduces additional interference. Summary of the Invention

[0004] The purpose of this invention is to solve the technical problem that the microgravity levels provided in existing technologies are insufficient to achieve the microgravity levels required for gravitational wave detection, and to provide a method for dynamic modeling and mass balancing of a spacecraft ground-based microgravity simulation platform. Dynamic modeling and mass balancing are performed on the ground-based microgravity semi-physical simulation platform to approximate an extremely high microgravity environment.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] In a first aspect, the present invention provides a method for dynamic modeling and mass balancing of a spacecraft ground microgravity simulation platform, comprising the following steps:

[0007] Based on the component assembly relationship of the spacecraft ground microgravity semi-physical simulation platform, distinguish individual components and component groups;

[0008] Based on the individual components, component groups, and the overall situation, coordinate systems are established for each component and component group; dynamic derivation is performed based on the coordinate systems to obtain the dynamic model.

[0009] The dynamic model was analyzed using the Lagrange method, resulting in a complete dynamic model of the ground simulation platform.

[0010] By simplifying the complete dynamic model of the ground simulation platform through assumptions, a simplified dynamic model is obtained;

[0011] Mass balancing of the simplified dynamic model yields a near-zero stiffness spacecraft ground microgravity semi-physical simulation platform.

[0012] A further improvement of the present invention is that:

[0013] The process of distinguishing individual components and component groups based on the component assembly relationship of the spacecraft ground microgravity semi-physical simulation platform includes the following steps:

[0014] The spacecraft ground microgravity simulation platform includes a base, a platform top plate, four equal-length connecting rods, two types of pivots, an outer frame, a middle frame, and an inner frame. The base is fixed to the ground. The platform top plate is connected to the base via the four equal-length connecting rods and pivots. The outer frame is connected to the platform top plate via pivots. The middle frame is connected to the outer frame via pivots. The inner frame is connected to the middle frame via pivots.

[0015] The process of establishing coordinate systems for each component and component group based on the individual components, component groups, and the overall situation includes the following steps:

[0016] Establish an inertial coordinate system: the origin is located at the center of the bottom surface of the platform; the direction of the bisector of the angle between the telescopes is the x-axis, the direction opposite to the local gravity direction is the z-axis, and the relationship between the y-axis and the x and z axes is determined by the right-hand coordinate system;

[0017] Establish a platform coordinate system for the platform: the origin is located at the three-axis rotation center of the rotating part; the three coordinate axes point in the same direction as the three coordinate axes of the inertial coordinate system.

[0018] Establish an outer frame coordinate system: the origin is located at the three-axis rotation center of the rotating part; it coincides with the platform system in the nominal state; the pivot connecting the outer frame and the platform plate is arranged along the y-axis of the outer frame coordinate system.

[0019] Establish a coordinate system for the middle frame: the origin is located at the three-axis rotation center of the rotating part; under nominal conditions, it coincides with the platform system and rotates around the x-axis; the pivot connecting the middle frame and the outer frame is arranged along the x-axis direction of the middle frame coordinate system.

[0020] Establish an inner frame coordinate system: the origin is located at the three-axis rotation center of the rotating part; under nominal conditions, it coincides with the platform system and rotates around the z-axis; the pivot connecting the inner frame and the middle frame is arranged along the z-axis direction of the inner frame coordinate system.

[0021] The inertial coordinate system is denoted by I; the platform coordinate system is denoted by P; the outer frame coordinate system is denoted by O; the middle frame coordinate system is denoted by M; and the inner frame coordinate system is denoted by N.

[0022] The dynamic derivation based on the coordinate system to obtain the dynamic model includes the following steps:

[0023] Five generalized coordinate systems are selected. For four connecting rods of equal length, it is assumed that the generalized coordinate system is first rotated around the negative x-axis by θ2, and then around the positive y-axis by θ1. All angles are based on the vertical direction. The outer frame coordinate system rotates around the platform coordinate system by the generalized coordinate system θ4, the middle frame coordinate system rotates around the outer frame coordinate system by the generalized coordinate system θ3, and the inner frame coordinate system rotates around the middle frame coordinate system by the generalized coordinate system θ5. The coordinates of the center of the inertial frame are defined as (0,0,0). I The center of the four pivots on the upper platform is (0,0,l). I , or represented as (0,0,-h1) P The center of gravity of the platform is (x4, y4, z4). P The centroid coordinates of the outer frame are (x1, y1, z1). O The centroid coordinates of the middle frame are (x2, y2, z2). M The centroid coordinates of the inner frame are (x3, y3, z3). N The masses of the platform's top plate, outer frame, middle frame, and inner frame are respectively m P ,m O ,m M and m N ;

[0024] Wherein, the superscript I represents the coordinate in the I coordinate system; the superscript P represents the coordinate in the P coordinate system; the superscript O represents the coordinate in the O coordinate system; the superscript M represents the coordinate in the M coordinate system; the superscript N represents the coordinate in the N coordinate system; l is the length of the connecting rod; h1 is the distance from the center of the four pivots on the upper platform to the center of rotation of the three axes of the rotating part;

[0025] For the outer frame, assume its rotation about the y-axis is θ₄, and the principal axes of inertia of the frame coincide with those of the outer frame system. Its inertia matrix at its center of mass is I. O =diag(I 11,O ,I 22,O ,I 33,O Its rotational angular velocity relative to the inertial frame is:

[0026]

[0027] For the middle frame, assume its rotation about the x-axis is θ3, and the principal axes of inertia of the frame coincide with those of the middle frame system, with its inertia matrix being I. M =diag(I 11,M ,I22,M ,I 33,M Its rotational angular velocity relative to the inertial frame is:

[0028]

[0029] For the inner frame, assuming the outer frame rotates about the z-axis by θ5, its inertia matrix is:

[0030]

[0031] Its rotational angular velocity relative to the inertial frame is:

[0032]

[0033] The transition matrix mentioned above is:

[0034]

[0035] Unifying the parameters of the five selected generalized coordinate systems into the inertial coordinate system yields the following coordinates: platform upper plate four-axis pivot center (lsinθ1cosθ2,lsinθ2,lcosθ1cosθ2), platform three-axis rotation center (lsinθ1cosθ2,lsinθ2,lcosθ1cosθ2+h1), platform upper plate centroid (lsinθ1cosθ2+z4,lsinθ4+z4,lcosθ1cosθ2+h1+z4), outer frame centroid. Mid-frame center of gravity Inner frame center of gravity

[0036] Kinetic energy is divided into rotational kinetic energy about the center of mass and translational kinetic energy about the center of mass:

[0037]

[0038] Among them, V O V is the speed of the outer frame. M V is the speed of the middle frame. N V is the speed of the inner frame. P The velocity of the platform is T; T is the kinetic energy.

[0039] Solve for potential energy:

[0040]

[0041] Among them, z O Let z be the component of the outer frame's centroid in the z-direction in the inertial coordinate system. M Let z be the component of the center of gravity of the middle frame in the z-direction in the inertial coordinate system. N Let z be the z-component of the inner frame's centroid in the inertial coordinate system. PLet be the z-component of the platform's center of gravity in the inertial coordinate system; U is the potential energy.

[0042] The process of analyzing the dynamic model using the Lagrange method to obtain the complete dynamic model of the ground simulation platform includes the following steps:

[0043] Calculate the Lagrange quantity L = TU;

[0044] The formula for calculating the left-hand side of the Lagrange dynamics equations is as follows:

[0045]

[0046] For the calculation of the right-hand side of the Lagrange equation, the position vector of the force under the inner frame system is (x F ,y F ,z F ) N Then for the position vector of the inertial frame, it is The force in the inner frame system is of magnitude F. N =(F x ;F y ;F z ) N In an inertial frame of reference

[0047] The formula for calculating the right-hand side of the Lagrange dynamic equations is as follows:

[0048]

[0049] The process of simplifying the complete dynamic model of the ground simulation platform by making assumptions to obtain the simplified dynamic model includes the following steps:

[0050] Reasonable assumptions are made about the quantities involved in the Lagrange dynamic equations:

[0051] The small-angle assumption applies; the rotation angles of each pivot axis of the spacecraft's ground microgravity simulation platform are extremely small during motion, satisfying the small-angle assumption, i.e.

[0052] cosθ1=1, sinθ1=θ1, cosθ2=1, sinθ2=θ2, cosθ3=1, sinθ3=θ3, cosθ4=1, sinθ4=θ4, cosθ5=1, sinθ5=θ5

[0053] The inner frame rotational inertia is leveled as follows: The inner frame of the spacecraft's ground microgravity simulation platform is leveled during the design and assembly process, therefore its rotational inertia satisfies a certain relationship, namely...

[0054] I 12,N =0, I 13,N =0, I 21,N =0, I23,N =0, I 31,N =0, I 32,N =0

[0055] Discard higher-order terms; retain first-order terms in both the left-hand and right-hand sides of the derived Lagrange dynamics equations; the first-order terms involved are generalized coordinates, and the product of the angular velocity and angular acceleration of the generalized coordinates or the square of the product of the two terms is the higher-order small quantity.

[0056] Rewriting the Lagrange dynamics equations based on the above assumptions yields the simplified left-hand side terms as follows:

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] Rewriting the Lagrange dynamics equations based on the above assumptions yields the simplified right-hand side as follows:

[0063]

[0064]

[0065]

[0066]

[0067]

[0068] The process of mass balancing the simplified dynamic model to obtain a spacecraft ground-based microgravity semi-physical simulation platform with approximately zero stiffness includes the following steps:

[0069] Based on the simplified left-hand side of the Lagrange dynamics equations, terms that do not contain pivot stiffness are processed and eliminated by adjusting the position of the centroid involved.

[0070] After elimination, the terms containing pivot stiffness are processed again. By adjusting the position of the involved centroids, a second elimination is performed to obtain the mass-balanced Lagrange dynamic equations.

[0071] The process of eliminating terms without pivot stiffness based on the simplified left-hand side of the Lagrange dynamics equations by adjusting the position of the centroid involved includes the following steps:

[0072] x1=0, y1=0, z1=0, x2=0, y2=0, z2=0, x3=0, y3=0, x4=0, y4=0, z4=0.

[0073] The process of eliminating the pivot stiffness and then processing the terms containing pivot stiffness by adjusting the position of the centroid involved includes the following steps:

[0074] The term containing pivot stiffness was processed by adjusting the position of the involved centroid for secondary elimination, and the conclusion is:

[0075]

[0076] The obtained mass-balanced Lagrange dynamic equations include the following steps:

[0077] After balancing the mass, the Lagrange dynamic equations after mass balancing are as follows:

[0078]

[0079]

[0080]

[0081]

[0082]

[0083] Compared with the prior art, the present invention has the following beneficial effects:

[0084] This invention discloses a dynamic modeling and mass balancing method for a spacecraft-based microgravity simulation platform. The method performs dynamic modeling and mass balancing on this novel ground-based microgravity semi-physical simulation platform, thereby simulating an environment approximately under extremely high microgravity. By introducing a pivot system, the spacecraft-based microgravity semi-physical simulation platform achieves near-zero stiffness, thus reconstructing a microgravity environment on the ground. Attached Figure Description

[0085] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0086] Figure 1 This is a step diagram of the dynamic modeling and mass balancing method for a spacecraft ground microgravity simulation platform in this invention;

[0087] Figure 2 This is a schematic diagram of the structure of the novel spacecraft ground microgravity semi-physical simulation platform of the present invention;

[0088] Figure 3 This is a schematic diagram of the coordinate systems of the novel spacecraft ground microgravity semi-physical simulation platform of the present invention;

[0089] Figure 4 This illustrates the changes of various generalized coordinates over time in a specific embodiment of the present invention. Detailed Implementation

[0090] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0091] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0092] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0093] The present invention will now be described in further detail with reference to the accompanying drawings:

[0094] See Figure 1 This invention discloses a method for dynamic modeling and mass balancing of a spacecraft ground microgravity simulation platform, comprising the following steps:

[0095] S1, distinguish individual components and component groups based on the component assembly relationship of the spacecraft ground microgravity semi-physical simulation platform;

[0096] S2, establish coordinate systems for each component and component group based on the individual components, component groups and the overall situation; derive the dynamics model based on the coordinate systems;

[0097] S3. The dynamic model is analyzed using the Lagrange method to obtain the complete dynamic model of the ground simulation platform;

[0098] S4. By simplifying the complete dynamic model of the ground simulation platform through assumptions, a simplified dynamic model is obtained.

[0099] S5 performs mass balancing on the simplified dynamic model to obtain a near-zero stiffness spacecraft ground microgravity semi-physical simulation platform.

[0100] Dynamic modeling and mass balancing were performed on this novel ground-based microgravity semi-physical simulation platform to approximate an extremely high microgravity environment. By introducing a pivot system, the spacecraft-based ground-based microgravity semi-physical simulation platform achieves near-zero stiffness, thereby reconstructing a microgravity environment on the ground.

[0101] The present invention will be described in detail below with reference to specific embodiments:

[0102] Step 1: Differentiate individual components and component groups based on the component assembly relationship of the spacecraft ground microgravity semi-physical simulation platform;

[0103] See Figure 2 This invention relates to a spacecraft ground microgravity simulation platform, which consists of a base, a platform upper plate, four connecting rods of equal length, two types of pivots, an outer frame, a middle frame, and an inner frame. During dynamic modeling, coordinate systems are designed for the platform upper plate, outer frame, middle frame, and inner frame.

[0104] The proposed microgravity semi-physics simulation platform for spacecraft consists of a base fixed to a ground foundation. The platform's upper plate is connected to the base via four links and pivots. An outer frame is pivoted to the platform's upper plate, a middle frame is pivoted to the outer frame, and an inner frame is pivoted to the middle frame. The platform's base is fixed to a vibration-isolated foundation. The translational mechanism (or platform upper plate) is connected to the base by four support rods and 16 identical pivots. The rotational mechanism consists of an outer frame, a middle frame, and an inner frame. The inner frame is also fixed to the simulated satellite platform, while the outer frame is connected to the translational mechanism. The satellite simulation platform carries three sets of micro-thrust clusters, a telescope simulation mechanism, and optical motion measurement equipment. The translational mechanism and the outer frame, as well as the three parts within the rotational mechanism, are all connected via two pivots. When the platform is subjected to forces and torques, the four-bar linkage formed by the platform upper plate, the base, and the support rods and pivots reflects the system's translational motion. The rotational mechanism reflects the system's rotational motion. It should be noted that the stiffness of the pivot used to characterize translational motion is different from that used to characterize rotational motion. The translational and rotational motions of the system are accurately measured using optical measuring equipment to evaluate the performance of the control system and correct errors.

[0105] Step 2: Establish coordinate systems for each component and component group based on the individual components, component groups, and the overall situation.

[0106] See Figure 3Let be the inertial coordinate system, platform coordinate system, outer frame coordinate system, middle frame coordinate system, and inner frame coordinate system involved, and their definitions are as follows:

[0107] Inertial coordinate system (I): The origin is located at the center of the bottom surface of the platform. The direction of the angle bisector of the telescope is the x-axis, and the direction opposite to the local gravity is the z-axis. The relationship between the y-axis and the x and z axes is determined by the right-hand coordinate system.

[0108] Platform coordinate system (P): The origin is located at the center of rotation of the rotating part along its three axes. The three coordinate axes point in the same direction as the coordinate axes of the inertial coordinate system.

[0109] Outer frame coordinate system (O): The origin is located at the three-axis rotation center of the rotating part. Under nominal conditions, it coincides with the platform system; the pivot connecting the outer frame and the platform plate is arranged along the y-axis of the outer frame coordinate system.

[0110] The middle frame coordinate system (M) has its origin located at the center of rotation of the rotating part along three axes. In its nominal state, it coincides with the platform system (rotating about the x-axis); the pivot connecting the middle frame and the outer frame is arranged along the x-axis of the middle frame coordinate system.

[0111] Inner frame coordinate system (N): The origin is located at the three-axis rotation center of the rotating part. In the nominal state, it coincides with the platform system (rotating about the z-axis); the pivot connecting the inner frame and the middle frame is arranged along the z-axis direction of the inner frame coordinate system.

[0112] Step 3: Select generalized coordinates. For four equal-length elements, we assume that the generalized coordinates are first rotated around the negative x-axis by θ2, and then around the positive y-axis by θ1. All angles here are based on the vertical direction. The outer frame coordinate system rotates around the platform coordinate system by the generalized coordinate θ4, the middle frame coordinate system rotates around the outer frame coordinate system by the generalized coordinate θ3, and the inner frame coordinate system rotates around the middle frame coordinate system by the generalized coordinate θ5.

[0113] The coordinates of the center of the inertial frame are defined as (0,0,0). I (The superscript 'I' indicates the coordinate system in which the coordinates are represented, and the same applies below). The center of the four pivots on the upper platform is (0,0,l). I Where l is the length of the connecting rod, or it can be represented as (0,0,-h1). P h1 is the distance from the center of the four pivots on the platform's upper plate to the center of rotation of the three axes of the rotating part. The center of gravity of the platform's upper plate is (x4, y4, z4). P The centroid coordinates of the outer frame are (x1, y1, z1). O The centroid coordinates of the middle frame are (x2, y2, z2). M The centroid coordinates of the inner frame are (x3, y3, z3). N The masses of the platform's top plate, outer frame, middle frame, and inner frame are respectively m. P ,m O ,mM and m N The sum of the masses of these four parts is m = m P +m O +m M +m N .

[0114] For the outer frame, assume its rotation about the y-axis is θ₄, and the principal axes of inertia of the frame coincide with those of the outer frame system. Its inertia matrix at its center of mass is I. O =diag(I 11,O ,I 22,O ,I 33,O Its rotational angular velocity relative to the inertial frame is...

[0115]

[0116] For the middle frame, assume its rotation about the x-axis is θ3, and the principal axes of inertia of the frame coincide with those of the middle frame system, with its inertia matrix being I. M =diag(I 11,M ,I 22,M ,I 33,M Its rotational angular velocity relative to the inertial frame is...

[0117]

[0118] For the inner frame, assuming the outer frame rotates about the z-axis by θ5, its inertia matrix is...

[0119]

[0120] Its rotational angular velocity relative to the inertial frame is

[0121]

[0122] The above transition matrix is

[0123]

[0124] Subsequently, the above parameters were unified in the inertial coordinate system, resulting in the following coordinates: Platform plate four-axis pivot center (lsinθ1cosθ2,lsinθ2,lcosθ1cosθ2), platform three-axis rotation center (lsinθ1cosθ2,lsinθ2,lcosθ1cosθ2+h1), platform plate center of gravity (lsinθ1cosθ2+z4,lsinθ4+z4,lcosθ1cosθ2+h1+z4), outer frame center of gravity. Mid-frame center of gravity Inner frame center of gravity

[0125] Kinetic energy is divided into rotational kinetic energy about the center of mass and translational kinetic energy about the center of mass.

[0126]

[0127] Among them, V O V is the speed of the outer frame. M V is the speed of the middle frame. N V is the speed of the inner frame. P The speed at which the platform is loaded onto the board.

[0128] Then, solving for the potential energy yields...

[0129]

[0130] Among them, z O Let z be the component of the outer frame's centroid in the z-direction in the inertial coordinate system. M Let z be the component of the center of gravity of the middle frame in the z-direction in the inertial coordinate system. N Let z be the z-component of the inner frame's centroid in the inertial coordinate system. P Let k1 be the component of the center of gravity of the platform plate in the z-direction in the inertial coordinate system, k2 be the pivot stiffness of the support rod connection part, and k2 be the pivot stiffness of the rotating part.

[0131] Step four: Analyze the dynamic model using the Lagrange method to obtain the complete dynamic model of the ground simulation platform;

[0132] The Lagrange daily quantity is calculated as L = TU.

[0133] The formula for calculating the left-hand side of the Lagrange dynamics equations is as follows:

[0134]

[0135] For the calculation of the right-hand side of the Lagrange dynamics equations, the position vector of the force under the inner frame system is (x F ,y F ,z F ) N Then for the position vector of the inertial frame, it is

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142] The force in the inner frame system is of magnitude F. N =(F x ;F y ;F z ) N In an inertial frame of reference

[0143] The formula for calculating the right-hand side of the Lagrange dynamics equations is as follows:

[0144]

[0145] Step 5: Simplify the complete dynamic model of the ground simulation platform by making assumptions to obtain a simplified dynamic model;

[0146] Reasonable assumptions are made about the quantities involved in the above Lagrange dynamic equations.

[0147] 1. Small Angle Assumption. During the motion of this simulation platform, the rotation angles of each pivot are extremely small, satisfying the small angle assumption, i.e.

[0148] cosθ1=1, sinθ1=θ1, cosθ2=1, sinθ2=θ2, cosθ3=1, sinθ3=θ3, cosθ4=1, sinθ4=θ4, cosθ5=1, sinθ5=θ5

[0149] 2. Leveling Assumption Regarding Inner Frame Rotational Inertia. The inner frame of this simulation platform was leveled during the design and assembly process; therefore, its rotational inertia satisfies a certain relationship.

[0150] I 12,N =0, I 13,N =0, I 21,N =0, I 23,N =0, I 31,N =0, I 32,N =0

[0151] 3. Discard higher-order terms. The left-hand and right-hand terms of the derived Lagrange dynamics equations are all first-order terms.

[0152] The first-order terms involved are generalized coordinates, angular velocities of generalized coordinates, and angular accelerations of generalized coordinates. Their product or squared terms are higher-order small quantities.

[0153] Rewriting the dynamic equation based on the above four assumptions yields the left-hand side term as follows:

[0154]

[0155]

[0156]

[0157]

[0158]

[0159] Rewriting the dynamic equation based on the above four assumptions yields the right-hand side term as follows:

[0160]

[0161]

[0162]

[0163]

[0164]

[0165] Step 6: Perform mass balancing on the simplified dynamic model to obtain a near-zero stiffness spacecraft ground microgravity semi-physical simulation platform;

[0166] Based on the simplified left-hand side of the Lagrange dynamics equations, terms without pivot stiffness are eliminated by adjusting the position of the involved centroids. The conclusion is as follows:

[0167] x1=0,y1=0,z1=0,x2=0,y2=0,z2=0,x3=0,y3=0,x4=0,y4=0,z4=0

[0168] Based on the left-hand side of the obtained dynamic equations, terms containing pivot stiffness are processed and eliminated by adjusting the position of the involved center of mass. The conclusion is as follows:

[0169]

[0170] After elimination, the terms containing pivot stiffness are processed again. A second elimination is performed by adjusting the position of the involved center of mass, resulting in the mass-balanced Lagrange dynamic equations.

[0171]

[0172]

[0173]

[0174]

[0175]

[0176] The specific parameters for this simulation are as follows: To verify that this mass balancing method enables the platform to achieve approximately zero stiffness, the right-hand side (generalized force term) of the Lagrange dynamic equations is always set to 0. We take g = 9.8 m / s². 2 , l=1m, k1=9.8N·m / rad, I 11,M =I 11,N =I 22,M =I 22,N =I 22,O =I 33,N =20kg·m 2 ,k2=0.98N·m / rad,m=8kg,m N =4kg, z3=0.05m.

[0177] The initial values ​​for the angles of each generalized coordinate are θ1 = 0.1°, θ2 = 0.15°, θ3 = 0.2°, θ4 = 0.25°, and θ5 = 0.05°. The initial value for the angular velocity of each generalized coordinate is 0, and the initial value for the angular acceleration of each generalized coordinate is... The results were obtained from the dynamic equations. The results show that the generalized coordinates θ1, θ2, θ3, and θ4 remain constant with time, while the generalized coordinate θ5 oscillates with time, which is consistent with the phenomenon exhibited by the dynamic equations after mass balancing.

[0178] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for dynamic modeling and mass balancing of a spacecraft ground microgravity simulation platform, characterized in that, Includes the following steps: Based on the component assembly relationship of the spacecraft ground microgravity semi-physical simulation platform, distinguish individual components and component groups; Based on the individual components, component groups, and the overall situation, coordinate systems are established for each component and component group; dynamic derivation is performed based on the coordinate systems to obtain the dynamic model. The dynamic model was analyzed using the Lagrange method, resulting in a complete dynamic model of the ground simulation platform. By simplifying the complete dynamic model of the ground simulation platform through assumptions, a simplified dynamic model is obtained; Mass balancing of the simplified dynamic model yields a near-zero stiffness spacecraft ground microgravity semi-physical simulation platform; The process of establishing coordinate systems for each component and component group based on the individual components, component groups, and the overall situation includes the following steps: Establish an inertial coordinate system: the origin is located at the center of the bottom surface of the platform; the direction of the angle bisector of the telescope is... x The axial direction, the direction opposite to the local gravitational force is z Axial direction, y shaft and x shaft and z The relationship between the axes is determined by the right-hand coordinate system; Establish a platform coordinate system for the platform: the origin is located at the three-axis rotation center of the rotating part; the three coordinate axes point in the same direction as the three coordinate axes of the inertial coordinate system. Establish an outer frame coordinate system: the origin is located at the three-axis rotation center of the rotating part; it coincides with the platform system in the nominal state; the pivot connecting the outer frame and the platform plate is arranged along the y-axis of the outer frame coordinate system. Establish a coordinate system for the middle frame: the origin is located at the three-axis rotation center of the rotating part; under nominal conditions, it coincides with the platform system and rotates around the x-axis; the pivot connecting the middle frame and the outer frame is arranged along the x-axis direction of the middle frame coordinate system. Establish an inner frame coordinate system: the origin is located at the three-axis rotation center of the rotating part; under nominal conditions, it coincides with the platform system and rotates around the z-axis; the pivot connecting the inner frame and the middle frame is arranged along the z-axis direction of the inner frame coordinate system. The inertial coordinate system is denoted by I; the platform coordinate system is denoted by P; the outer frame coordinate system is denoted by O; the middle frame coordinate system is denoted by M; and the inner frame coordinate system is denoted by N. The dynamic derivation based on the coordinate system to obtain the dynamic model includes the following steps: Five generalized coordinates are selected; for four links of equal length, it is assumed that the first link is rotated around... Rotation of generalized coordinates in the negative direction of the axis , then around Rotation of generalized coordinates in the positive direction of the axis All angles here are based on the vertical direction; the rotation angle of the outer frame coordinate system around the platform coordinate system is a generalized coordinate. The rotation angle of the middle frame coordinate system around the outer frame coordinate system is a generalized coordinate. The rotation angle of the inner frame coordinate system around the middle frame coordinate system is a generalized coordinate. The coordinates of the center of the inertial frame are defined as follows: The platform's upper four pivot centers are , or expressed as The platform's center of gravity is The coordinates of the outer frame's centroid are The coordinates of the center of gravity of the middle frame are The coordinates of the inner frame's centroid are The masses of the platform top, outer frame, middle frame, and inner frame are respectively... , , and ; In this context, the superscript I represents coordinates in the I coordinate system; the superscript P represents coordinates in the P coordinate system; the superscript O represents coordinates in the O coordinate system; the superscript M represents coordinates in the M coordinate system; and the superscript N represents coordinates in the N coordinate system. The length of the connecting rod; This is the distance from the center of the four pivots on the upper platform to the center of rotation of the three axes of the rotating part; For the outer frame, assume the rotation of the outer frame about the y-axis is... Furthermore, the principal axes of inertia of the frame coincide with those of the outer frame system, and the inertia matrix at its centroid is... Its rotational angular velocity relative to the inertial frame is: For the middle frame, assume the rotation of the middle frame about the x-axis is... Furthermore, the principal axes of inertia of the frame coincide with those of the middle frame system, and its inertia matrix is... Its rotational angular velocity relative to the inertial frame is: For the inner frame, assume the outer frame rotates about the z-axis as follows: Its inertia matrix is: Its rotational angular velocity relative to the inertial frame is: The transition matrix mentioned above is: ， ， Unifying the parameters of the five selected generalized coordinate systems into the inertial coordinate system yields the following parameter coordinates: Platform upper plate four-pivot center Platform three-axis rotation center , center of gravity of upper plate on platform outer frame center of gravity Mid-frame center of gravity Inner frame center of gravity ; Kinetic energy is divided into rotational kinetic energy about the center of mass and translational kinetic energy about the center of mass: in, For the speed of the outer frame, For the speed of the middle frame, For the speed of the inner frame, The speed at which the platform is loaded; T Kinetic energy; Solve for potential energy: in, Let z be the z-component of the outer frame's centroid in the inertial coordinate system. Let z be the z-component of the center of gravity of the middle frame in the inertial coordinate system. Let z be the z-component of the inner frame's centroid in the inertial coordinate system. Let z be the component of the platform's center of gravity in the z-direction in the inertial coordinate system. U Potential energy; The process of analyzing the dynamic model using the Lagrange method to obtain the complete dynamic model of the ground simulation platform includes the following steps: Calculating Lagrange quantities ; The formula for calculating the left-hand side of the Lagrange dynamics equations is as follows: For the calculation of the right-hand side of the Lagrange equation, the position vector of the force under the inner frame system is: Then for the position vector of the inertial frame, it is The magnitude of the force under the inner frame system is In an inertial frame of reference ; The formula for calculating the right-hand side of the Lagrange dynamics equations is as follows:

2. The method for dynamic modeling and mass balancing of a spacecraft ground microgravity simulation platform according to claim 1, characterized in that, The process of distinguishing individual components and component groups based on the component assembly relationship of the spacecraft ground microgravity semi-physical simulation platform includes the following steps: The spacecraft ground microgravity simulation platform includes a base, a platform top plate, four equal-length connecting rods, two types of pivots, an outer frame, a middle frame, and an inner frame. The base is fixed to the ground. The platform top plate is connected to the base via the four equal-length connecting rods and pivots. The outer frame is connected to the platform top plate via pivots. The middle frame is connected to the outer frame via pivots. The inner frame is connected to the middle frame via pivots.

3. The method for dynamic modeling and mass balancing of a spacecraft ground microgravity simulation platform according to claim 1, characterized in that, The process of simplifying the complete dynamic model of the ground simulation platform by making assumptions to obtain the simplified dynamic model includes the following steps: Reasonable assumptions are made about the quantities involved in the Lagrange dynamic equations: The small-angle assumption applies; the rotation angles of each pivot axis of the spacecraft's ground microgravity simulation platform are extremely small during motion, satisfying the small-angle assumption, i.e. The inner frame rotational inertia is leveled as follows: The inner frame of the spacecraft's ground microgravity simulation platform is leveled during the design and assembly process, therefore its rotational inertia satisfies a certain relationship, namely... Discard higher-order terms; retain first-order terms in both the left-hand and right-hand sides of the derived Lagrange dynamics equations; the first-order terms involved are generalized coordinates, and the product of the angular velocity and angular acceleration of the generalized coordinates or the square of the product of the two terms is the higher-order small quantity. Rewriting the Lagrange dynamics equations based on the above assumptions yields the simplified left-hand side terms as follows: Rewriting the Lagrange dynamics equations based on the above assumptions yields the simplified right-hand side as follows:

4. The method for dynamic modeling and mass balancing of a spacecraft ground microgravity simulation platform according to claim 3, characterized in that, The process of mass balancing the simplified dynamic model to obtain a spacecraft ground-based microgravity semi-physical simulation platform with approximately zero stiffness includes the following steps: Based on the simplified left-hand side of the Lagrange dynamics equations, terms that do not contain pivot stiffness are processed and eliminated by adjusting the position of the centroid involved. After elimination, the terms containing pivot stiffness are processed again. By adjusting the position of the involved centroids, a second elimination is performed to obtain the mass-balanced Lagrange dynamic equations.

5. The method for dynamic modeling and mass balancing of a spacecraft ground microgravity simulation platform according to claim 4, characterized in that, The process of eliminating terms without pivot stiffness based on the simplified left-hand side of the Lagrange dynamics equations by adjusting the position of the centroid involved includes the following steps:

6. The method for dynamic modeling and mass balancing of a spacecraft ground microgravity simulation platform according to claim 5, characterized in that, The process of eliminating the pivot stiffness and then processing the terms containing pivot stiffness by adjusting the position of the centroid involved includes the following steps: The term containing pivot stiffness was processed by adjusting the position of the involved centroid for secondary elimination, and the conclusion is:

7. The method for dynamic modeling and mass balancing of a spacecraft ground microgravity simulation platform according to claim 6, characterized in that, The obtained mass-balanced Lagrange dynamic equations include the following steps: After balancing the mass, the Lagrange dynamic equations after mass balancing are as follows:

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