A power flow analysis method for raft vibration isolation system based on multi-rigid body dynamics

Abstract

The invention discloses a power flow analysis method for a floating raft vibration isolation system based on multi-rigid body dynamics, comprising the following steps: S101, obtaining the equipment elements, raft frame elements, vibration isolator elements, and base elements of the system; S102, simplifying the mechanical model of the vibration isolation system based on the multi-rigid body dynamics, and constructing a six-degree-of-freedom matrix for each rigid body unit; S103, determining the external excitation signal input into the floating raft vibration isolation system, and inputting a random external excitation signal according to test requirements; S104, obtaining the system response value according to the algebraic operation of the differential equation of motion and the matrix; S105, providing the response signals and node forces at four tip points; S106, calculating the power flow signals of the selected floating raft vibration isolation system points, and analyzing the power flow vibration level difference; S107, calculating the power flow of the monitoring point of the finite element model according to the result of S103; S108, performing error analysis on the data obtained in S106 and S107, and providing the vibration isolation analysis and vibration prediction of the system.

Description

Technical Field

[0001] The present invention relates to a power flow analysis method for a floating raft vibration isolation system based on multi-rigid body dynamics, which belongs to the field of vibration prediction. Background Art

[0002] Extensive research and practical applications have demonstrated the widespread application of floating raft vibration isolation structures in marine, aviation, and mechanical equipment to reduce vibration transmission and noise interference, ensuring stable equipment operation and environmental comfort. Floating raft vibration isolation systems typically consist of multiple devices, raft frames, and isolators. Their dynamic behavior is complex, involving the coupling of multiple degrees of freedom.

[0003] Based on the system's equations of motion, the multi-body dynamics method comprehensively describes the dynamic interactions between components and is a valuable tool for analyzing floating raft vibration isolation systems. By incorporating the mass and stiffness matrices of the equipment and raft frame, as well as external excitation forces, the multi-body dynamics method accurately simulates the system's vibration response characteristics, providing theoretical support for the prediction and optimization of vibration isolation performance. Furthermore, multi-body dynamics can analyze the dynamic characteristics of isolators under complex connection conditions, such as stiffness nonlinearity and offset coupling effects, thereby better guiding the design and improvement of vibration isolation systems.

[0004] At present, there have been many studies on multi-rigid body dynamics. For example, see Wang Kun, Xing Haijun, Xu Mengchao, et al. Simplified modeling and simulation of multi-rigid body dynamics based on ADAMS [J]. Journal of Graphics, 2019, 40(04): 733-738. And Chen Ju, Huang Ziheng, Tian Qiang. Lie group variational integral algorithm and symmetry reduction method for multi-rigid body dynamics simulation [C] / / Dynamics and Control Professional Committee of the Chinese Society of Mechanics, Nonlinear Vibration Professional Committee of the Chinese Society of Vibration Engineering. Abstracts of the 18th National Nonlinear Vibration and the 15th National Nonlinear Dynamics and Motion Stability Academic Conference (NVND2021). School of Aeronautics and Astronautics, Beijing Institute of Technology; 2021: 1. DOI: 10.26914 / c.cnkihy.2021.055908. Most of these studies focus on the application of multi-rigid body dynamics in simulation to solve related mechanical problems.

[0005] When it comes to vibration, acceleration or velocity levels are often used as indicators to assess a system's isolation level and its impact on the system. In recent years, power flow, as a key indicator of vibration energy propagation, has evolved into a highly effective and reliable method for evaluating the performance of floating raft isolation systems.

[0006] Power flow analysis can determine the propagation path, distribution characteristics, and dissipation efficiency of vibration energy, providing a basis for optimizing key vibration transmission links in the system. In floating raft vibration isolation systems, power flow analysis can reveal the energy exchange patterns between the isolator and the raft frame, evaluate the isolator's energy isolation and vibration dissipation performance, and thus assist in designing system structures with improved vibration isolation. Unlike traditional transmissibility analysis, power flow analysis focuses more on the overall transfer of system energy and the quantitative characterization of local behavior, making it suitable for evaluating the vibration performance of complex multi-degree-of-freedom systems.

[0007] At present, the concept of power flow is also used in many studies on mechanical analysis. For example, the use of power flow to solve vibration problems in coupled structures is discussed in Zhang Yu, Li Jin, and Dong Junhong. Research on vibration power flow and acoustic radiation characteristics of plate-beam coupled structures [J]. Journal of China Engineering Machinery, 2024, 22(05): 620-625. DOI: 10.15999 / j.cnki.311926.2024.05.016. Wu Jianghai, Yin Zhiyong, Sun Yudong, et al. Research on vibration power flow and acoustic radiation characteristics of pipe-cylindrical shell coupled structures [J]. China Shipbuilding, 2021, 62(02): 145-153.

[0008] The application of multi-body dynamics in rafts is not widespread, and most applications are focused on solving simulation-related problems. Only a small number of researchers use programming theory based on multi-body dynamics to simplify computational analysis of engineering problems. For example, see Li Xiaoming. Research on Vibration Isolation and Shock Resistance Characteristics of Ship Raft Systems [D]. Dalian University of Technology, 2007. This paper constructs a matrix of a multi-body dynamics system and solves the differential equations of motion to obtain the response values ​​of the raft vibration isolation system and calculate the response vibration level to represent the system's vibration isolation capability. However, this approach has certain limitations. The response value alone cannot describe the influence of forces on the structure during vibration, nor can it fully describe the transmission method and proportion of the vibration energy within the system structure after it is introduced. Summary of the Invention

[0009] Purpose of the invention: In order to overcome the deficiencies in the prior art, the present invention provides a power flow analysis method for a floating raft vibration isolation system based on multi-rigid body dynamics. Multi-rigid body dynamics is used to simplify the calculation process, providing an efficient and reliable structural vibration analysis method. By using the concept of power flow, the distribution and changes of the response and force in the system are simultaneously expressed, which can better predict and analyze the vibration energy transfer of the floating raft vibration isolation system and the vibration isolation performance of the overall structure.

[0010] Technical solution: To solve the above technical problems, the present invention provides a power flow analysis method for a floating raft vibration isolation system based on multi-rigid body dynamics, comprising the following steps:

[0011] S101. Obtain the system's equipment elements, raft elements, vibration isolator elements, and foundation elements;

[0012] S102. Simplify the mechanical model of the vibration isolation system based on multi-rigid body dynamics and construct a six-degree-of-freedom matrix for each rigid body unit;

[0013] S103 determines an external excitation signal input to the floating raft vibration isolation system, and inputs a random external excitation signal according to test requirements;

[0014] S104 obtains the system response value based on the algebraic operation of the differential equation of motion and the matrix;

[0015] S105 gives the displacement response signal, velocity response signal, acceleration response signal and node force at four tip points;

[0016] S106 calculates the power flow signal of the selected floating raft vibration isolation system points and analyzes the power flow level difference between different points;

[0017] S107 performs finite element modeling analysis on the floating raft vibration isolation system with given relevant data based on the results of S103, performs modal analysis on the model, inputs an excitation signal, and calculates the power flow at the monitoring point of the finite element model.

[0018] S108 performs error analysis on the data obtained in S106 and S107. If the error conditions are met, the obtained power flow level drop data of the floating raft vibration isolation system is fitted to provide the vibration isolation analysis and vibration prediction of the system. If the error conditions are not met, repeat steps S103-S108.

[0019] Preferably, the equipment elements in S101 include: the number of equipment, geometric structure data of each different equipment, the mass of each different equipment, the installation position coordinates of each different equipment with respect to the raft reference system and the base reference system, and the installation method of each different equipment; the raft elements include: the geometric dimensions of the raft, the mass of the raft, the type of the raft, and the specific structural data of the raft; the vibration isolator elements include: the type of vibration isolators used, the number of different vibration isolators, the installation positions of different vibration isolators, the installation methods of different vibration isolators, the stiffness values ​​of different vibration isolators, and the damping values ​​of different vibration isolators; the base elements include: the base type, base mass, and base impedance;

[0020] Preferably, the vibration isolation system in S102 includes: multiple devices, a raft, a base and multiple vibration isolators connecting them; the multi-rigid body dynamics simplification method refers to considering only the mass of the devices and the raft in the system, treating them as rigid body units, and establishing a body-dependent coordinate system of the raft and a fixed coordinate system of the base through the interconnection of vibration isolators to determine the changes in the generalized coordinates of each component in the system, so as to calculate the overall displacement response values ​​of the devices and the raft in the system; the mechanical model simplification refers to: based on the system elements input in S101, some elements are removed and simplified according to the actual conditions of the simplified algorithm, and only the physical elements required for the system of interaction of the described rigid body units are considered; the six-degree-of-freedom matrix includes: the mass six-degree-of-freedom matrix of the rigid body unit, which describes the inertial force influencing element of the rigid body unit; the stiffness six-degree-of-freedom matrix of the rigid body unit, which describes the elastic force influencing element of the rigid body unit; the damping six-degree-of-freedom matrix of the rigid body unit, which describes the damping force influencing element of the rigid body unit;

[0021] Preferably, the position where the external excitation signal acts in S103 is the center of gravity of all devices and rafts in the system, which is obtained by S101 and S102, and the external excitation signal is numbered and classified according to the device number and raft. If there is no corresponding external excitation on a certain device or raft, the value of the external excitation signal received by the rigid body unit is recorded as 0; the form of the external excitation signal is a simple harmonic force containing six degrees of freedom, that is, a periodic force formed by the combination of shear force in three directions of the corresponding coordinate system and torque in three directions;

[0022] Preferably, the motion differential equation in S104 is a system motion equilibrium equation that includes the mass matrix, stiffness matrix, damping matrix and current calculated frequency value of all rigid body units in the system. The construction of this multi-degree-of-freedom matrix motion differential equation and the acquisition of specific parameters of the internal matrix refer to the vibration isolation system elements mentioned in S101 and the mechanical model simplification mentioned in S102 in claim 1; the matrix algebraic operation method is the Gaussian elimination method based on the Fortran program; the system response value is the overall six-degree-of-freedom response of multiple devices and raft structures in the system, including translational displacements in three directions and rotational displacements in three directions in the base fixed coordinate system.

[0023] Preferably, the tip point described in S105 includes: the upper end points of all upper vibration isolators connected to the equipment, the lower end points of all upper vibration isolators connected to the raft, the upper end points of all lower vibration isolators connected to the raft, and the lower end points of all lower vibration isolators connected to the base; the displacement response signal refers to the six-degree-of-freedom response obtained in S104, and according to the particle offset matrix of multi-rigid body dynamics, the six-degree-of-freedom response of the particle is converted into the displacement response signal at the tip point, and by taking the derivative of the displacement response, the corresponding velocity response signal and acceleration response signal are obtained, and the corresponding node force is calculated according to the equipment subsystem reference coordinate system in the multi-rigid body dynamics analysis.

[0024] Preferably, the power flow signal described in S106 is an average power flow signal obtained by the response signal, which is obtained by the speed response signal and the node force obtained in S105; the power flow level difference is the logarithm of the quotient of the power flow signal between any two points in the floating raft vibration isolation system between the center of gravity of the equipment and the base panel, which is used to express the vibration isolation performance of the floating raft vibration isolation system and the proportion of energy loss during energy transfer in the system.

[0025] Preferably, the S107 comprises the following steps:

[0026] S201 performs finite element modeling analysis on the floating raft vibration isolation system with given relevant data, and performs modal analysis on the model. The relevant data mentioned are the system equipment elements, system raft elements, system isolator elements, and system base elements input in S101; the finite element modeling analysis is to complete the geometric model establishment and material property assignment of the floating raft vibration isolation system in commercial software (such as Abaqus) to ensure that it meets the various system elements described in S101; the modal analysis is to obtain the natural frequency of the finite element model and provide a frequency reference range for subsequent specific analysis;

[0027] S202 inputs an excitation signal to solve for the velocity response signal and the force at the monitoring point. The velocity response and force calculations involve inputting the continuous external excitation signal input in S103 into the finite element model based on the results of the modal analysis in S201, considering the effect of the external excitation signal on the model at that natural frequency, and using the relevant analysis module in the finite element analysis software to set monitoring points at the same locations as those used in the theoretical analysis to directly obtain the velocity response signal and force at the monitoring points.

[0028] S203 calculates the power flow at the monitoring point of the finite element model. The power flow at the monitoring point refers to the average vibration power flow at the monitoring point during the time history of the finite element analysis, calculated based on the monitoring point velocity and monitoring point force obtained in S202.

[0029] Preferably, the step S108 performs error analysis on the obtained data, wherein the error analysis includes: performing error analysis on the data obtained in steps S106 and S107, entering data smaller than an error threshold into a data statistics database, deleting data larger than the error threshold, and returning to step S103 to re-input a random excitation signal, and performing the same analysis steps to obtain a new set of power flow data;

[0030] S108 performs an error analysis on the obtained data. The error analysis further includes: calculating the median of the power flow level drop for the data group that meets the first error analysis, calculating the relative error between the data and the median, deleting the power flow level drop data that exceeds the relative error threshold, and returning to S103 to re-input the random excitation signal. Through the same analysis steps, a new set of power flow level drop data is obtained.

[0031] Beneficial effects: The power flow analysis method of the floating raft vibration isolation system based on multi-rigid body dynamics of the present invention has the following advantages:

[0032] Through this invention, the transmission mode and loss degree of vibration energy in the floating raft vibration isolation system can be analyzed more intuitively. Since this invention is a simple calculation method based on multi-rigid body dynamics, it increases the efficiency of vibration analysis and improves the calculation speed while ensuring that the error value meets general engineering conditions. It has higher accuracy than the general simpler estimation analysis.

[0033] The vibration reference factor of this invention is the power flow level drop, which adds an analysis of the force during the vibration process compared to the generalized response level drop commonly used in this academic field. In a real floating raft vibration isolation system experiment, in order to analyze the effect of force, it is necessary to add a force ring device to the corresponding monitoring point. This device will change the original floating raft vibration isolation system structure and increase the complexity of the experiment. Through the power flow level drop analysis, combined with the generalized response level drop analysis and the vibration force analysis, it is possible to more comprehensively characterize the proportion of concentration, transmission, loss, etc. of vibration energy in each sub-reference frame of the floating raft vibration isolation system, providing a more detailed engineering reference for the prediction of the vibration effect of the entire floating raft vibration isolation system and the analysis of the vibration isolation performance.

[0034] This invention is only partially verified by finite element simulation software, which can more conveniently change the various elements of the pre-analyzed floating raft vibration isolation system to suit different system structures and analysis conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Flowchart of the present invention.

[0036] Figure 2 This is a diagram of the finite element simulation of the floating raft vibration isolation system.

[0037] Figure 3 The power flow between the input of device 1 and the output of the base terminal.

[0038] Figure 4 is the power flow level difference of device 1. DETAILED DESCRIPTION

[0039] The present invention will be further described below with reference to the accompanying drawings.

[0040] like Figure 1 As shown, the present invention provides a power flow analysis method for a floating raft vibration isolation system based on multi-rigid body dynamics, which specifically includes the following steps:

[0041] S101 obtains the system's equipment elements, raft elements, vibration isolator elements, and base elements.

[0042] Among them, the system equipment elements include: the number of equipment; the geometric structure data of each different equipment, including the geometric simplified length, width and height values ​​of each equipment, the geometric simplified length, width and height refer to the equipment's center of gravity as the center point, representing the equipment's outline as a rectangular block with fixed length, width and height; the mass of each different equipment, it is assumed here that the mass of the equipment is evenly distributed in the rectangular block outline; the installation position coordinates of each different equipment with respect to the raft reference system and the base reference system, because the installation positions of the raft and the base are relatively fixed, only the installation coordinates of the equipment on the raft are considered here, and the projection point of the raft center of gravity on the upper surface of the raft is used as the coordinate origin to determine the position of the center of gravity of each equipment in the coordinate system; the installation method of each different equipment, the boundary conditions between the equipment and their respective upper vibration isolators are rigidly fixed, and the equipment will not have unnecessary displacement.

[0043] The system raft elements include: the geometric dimensions of the raft, similarly, with the center of gravity as the center point, the outer contour of the raft is geometrically simplified into a rectangular parallelepiped with fixed length, width and height; the mass of the raft, assuming that the mass of the raft is evenly distributed in the rectangular parallelepiped outline; the type of raft, selecting the flat-plate raft that is more common in engineering applications, and using a partially hollow elastic stiffened plate to represent the raft; the specific structural data of the raft, including the number of openings along the length direction of the raft, the size of the rectangular openings, the coordinates of the center of the holes, and the chamfer size around the holes, and the number of openings along the width direction of the raft, the size of the rectangular openings, the coordinates of the center of the holes, and the chamfer size around the holes, and the coordinates here should each take the center point of the side surface where the holes are located as the coordinate origin.

[0044] The system vibration isolator elements include: the type of vibration isolator used, all of which use metal-rubber vibration isolators with fixed stiffness and damping values; the number of different vibration isolators, here it is assumed that the vibration isolator models used on the same device are the same, and the models and numbers of vibration isolators installed between different devices may be different, and the number here refers to the number of vibration isolators installed on each device; the installation positions of different vibration isolators, which refers to the installation coordinates of the vibration isolators in the same device relative to the reference system with the center of gravity of the device as the origin; the installation methods of different vibration isolators, the vibration isolators of the same device are installed in a group of four symmetrically relative to the center of gravity of the device on the projection center of the lower surface of the device, and the four vibration isolators in a group have the same distance vector modulus from the center of gravity of the device in the device reference system; the stiffness values ​​of different vibration isolators, here it is assumed that the stiffness of the vibration isolator is evenly distributed in all directions and there is no torsional stiffness; the damping values ​​of different vibration isolators, here it is assumed that the damping coefficient of the vibration isolator is constant and evenly distributed in all directions.

[0045] The system base elements include: base type, which selects the more common flat base; base mass, which assumes that the mass of the base is evenly distributed and concentrated at the center of gravity; base impedance, which refers to the input impedance value at the surface of the base.

[0046] S102 simplifies the mechanical model of the vibration isolation system based on multi-rigid body dynamics and constructs a six-degree-of-freedom matrix for each rigid body unit.

[0047] The simplification steps include extracting the elements of the vibration isolation system, including all equipment, rafts, bases, and all isolators. The equipment and rafts are simplified into rigid units with only mass considered, with the mass concentrated at the center of mass. The base is simplified into a panel that only provides boundary conditions, with the rest of the components rigidly fixed, with the base's mass concentrated at the center of mass. The isolators are simplified into one-dimensional linear spring units, with their mass no longer considered, retaining only their stiffness and damping properties.

[0048] Among them, the six-degree-of-freedom matrix includes: mass matrix, stiffness matrix after coordinate transformation, damping matrix after coordinate transformation, response matrix, and excitation matrix.

[0049] Assume that the value of uniform mass is m i The geometrically simplified length, width, and height of the selected equipment or raft are a, b, and c respectively.

[0050] Mass matrix M i Should be of the following form:

[0051]

[0052] Since the physical geometry of the equipment or raft is set as a uniform cuboid, the non-diagonal elements can be simplified.

[0053] Since the stiffness matrix and damping matrix only consider the influence in the translation direction, it is necessary to apply a coordinate offset matrix to them through multi-rigid body dynamics to make them conform to the reference system in which the calculation is performed.

[0054] Assume that the offset of the isolator's installation position is determined by the center of gravity of the upper equipment / raft supported by the isolator. For example, if the coordinate position of the isolator's installation point relative to the equipment / raft subsystem reference system is (dx, dy, dz), then its offset matrix should be in the following form:

[0055]

[0056] Here, i represents the equipment number, j represents the isolator number on the equipment, and since there is only one raft, all isolators on the raft are numbered using k.

[0057] Then, the stiffness matrix and damping matrix of the isolator after offset are:

[0058]

[0059] where K j i and C j i Respectively represent the stiffness and damping matrices of the isolator itself, which should be third-order diagonal matrices. For example, for an isolator with a stiffness coefficient of k and a damping coefficient of c, its stiffness and damping matrices should be:

[0060]

[0061] The excitation matrix, as an input item, should be in the form of six rows and one column. The first three rows represent the shear force along the reference coordinate axis, and the last three rows represent the bending moment on the normal plane of the reference coordinate axis, as shown in the following figure:

[0062]

[0063] The response matrix, as the item to be solved, should be in the form of six rows and one column. The first three rows represent the translational response of each rigid body in the system along the coordinate axis, and the last three rows represent the rotational response of each rigid body on the normal plane of the coordinate axis, as shown in the following figure:

[0064]

[0065] S103 determines the external excitation signal input into the floating raft vibration isolation system, and inputs a random external excitation signal according to the test requirements.

[0066] For example, the excitation force with amplitude A, circular vibration frequency ω, and initial phase angle φ should be in the form of:

[0067] F(t)=Asin(ωt+φ)

[0068] Convert the excitation force through Euler's formula to obtain the complex number expression of F:

[0069] F(t)=Re{Ae i(ωt+φ)}=Re{F0e iωt}

[0070] Where F0 = Ae iφ , which is independent of time, represents the initial value of the excitation force F.

[0071] Here, the amplitude A and the initial phase angle φ can be arbitrarily set to meet the conditions of random response, while the circular vibration frequency ω and time t describe the frequency / time history conditions of the excitation force changing in the system, which should vary with the specific analysis.

[0072] S104 obtains the system response value according to the algebraic operation of the differential equation of motion and the matrix.

[0073] The differential equation of motion is:

[0074]

[0075] It is a differential equation used to describe the relationship between excitation and response in a vibration system. The M, C, K, X, and F matrices in the formula represent the total matrix that integrates the effects of all rigid body elements in the system. The matrix is ​​constructed based on the interconnected relationships between them. For example, for a system where a raft is mounted on a base panel via isolators, and two other devices are mounted on the raft via their own isolators. In the matrix, since there is no interconnection between the devices and the masses of the devices and the raft are independent properties, the expanded differential equation of motion should be:

[0076]

[0077] It is important to note that the K in the third row and third column of the stiffness matrix and the damping matrix k Item and C k The stiffness and damping values ​​represented by the term ∠ under the combined effect of the lower isolator and the base need to be calculated taking into account the input impedance of the base panel. For impedance, the following formula is used:

[0078] The complex impedance expression of the lower vibration isolator is:

[0079] Z 下层,k (ω)=k 下层,k +iωc 下层,k

[0080] In the lower vibration isolation subsystem, the lower vibration isolators are connected in parallel with each other and in series with the base, so the equivalent impedance of the lower vibration isolation system is:

[0081]

[0082] According to the equivalent impedance, the equivalent stiffness and equivalent damping of the lower layer can be obtained as follows:

[0083] k k =Re{Z 等效 (ω)}

[0084]

[0085] Since the input excitation force is converted into a complex form, the output response value also needs to be converted into a complex form, such as:

[0086] X(t)=Re{X0e iωt}

[0087] Then the complex differential equation of motion is expressed as:

[0088] (M(-ω 2 )+iωC+K)X0=F0

[0089] Depending on the number of devices in the system, we can obtain: For example, when the number of devices in the system is n, we can obtain a 6(n+1)-order dynamic stiffness matrix and a 6(n+1)-order response X matrix, where each entry in the X matrix represents the six-degree-of-freedom displacement response value of a certain device or raft.

[0090] Based on the Fortran programming method, the Gaussian elimination method is used to solve the differential equation of motion, and (n+1) groups of different six-degree-of-freedom response matrices are solved. These matrices represent the displacement response values ​​at the center of gravity of the equipment / raft.

[0091] S105 provides the displacement response signal, velocity response signal, acceleration response signal and node force at the four tip points.

[0092] The tip points include: the upper end points where all upper vibration isolators are connected to the equipment, the lower end points where all upper vibration isolators are connected to the raft frame, the upper end points where all lower vibration isolators are connected to the raft frame, and the lower end points where all lower vibration isolators are connected to the base.

[0093] For the upper endpoints where all upper isolators are connected to the equipment:

[0094] Displacement response signal: X i (t), speed response signal: Acceleration response signal: Nodal forces:

[0095] For the lower ends of all upper isolators connected to the raft:

[0096] Displacement response signal: Speed ​​response signal: Acceleration response signal: Nodal forces:

[0097] For the upper ends of all lower isolators connected to the raft:

[0098] Displacement response signal: Speed ​​response signal: Acceleration response signal: Nodal forces:

[0099] For the lower end points where all lower isolators are connected to the base:

[0100] Due to the boundary conditions between the base and the lower isolator, the actual displacement response of the lower endpoint is 0, and the node force is the reaction force of F3. Here, the displacement value at the base panel is obtained through the input impedance characteristics of the base.

[0101] k k，b =Re{Z 基座 (ω)}

[0102]

[0103] S106 calculates the power flow signal of the selected floating raft vibration isolation system points and analyzes the power flow level difference between different points.

[0104] In S105, we obtain the velocity response and force values ​​of these points, and use these values ​​to solve the average power flow of the node:

[0105] First, the power flow is analyzed in the frequency domain, so the velocity response signal and node force need to be converted from the time domain to the frequency domain:

[0106]

[0107] According to the velocity response and node force in the frequency domain, the average complex power flow at the analysis point is obtained as:

[0108]

[0109] The complex power flow represents the destination of all energy at the node in the system, where the real part P(ω)=Re{P c (ω)} represents the active power, which is the real part of energy transferred from the outside to the system or from the system to the outside; the complex part Q(ω)=Im{P c (ω)} represents reactive power, which describes the energy exchange between the energy storage elements (springs, dampers, and masses) in the system and does not result in a net transfer of energy.

[0110] For example, the point where device 1 connects to the upper endpoint of upper isolator 1 and the point where device 2 connects to the upper endpoint of upper isolator 2 cannot be called tip points at different levels because they describe the power flow characteristics of different components within the device-upper isolator subsystem. However, the point where device 1 connects to the upper endpoint of upper isolator 1 and the point where lower isolator 1 connects to the base panel can be called tip points at different levels because they are in different reference frames in the analysis of multi-body dynamics.

[0111] For points at different levels, such as the point where the device 1 is connected to the upper end of the upper vibration isolator 1 and the point where the lower vibration isolator 1 is connected to the base panel, since there is no direct coupling relationship between them, the power flow level difference formula between them should be:

[0112]

[0113] For points at the same level, for example, the point where device 1 is connected to the upper end point of upper vibration isolator 1 and the point where device 2 is connected to the upper end point of upper vibration isolator 2, the coupled power flow between them satisfies the energy conservation theorem, as follows:

[0114] P 1→2 (ω)=P 1→f (ω)+P f→2 (ω)=P 1→f (ω)-P 2→f (ω)

[0115] Among them, 1→f and 2→f refer to the vibration energy transmitted from device 1 and device 2 to the raft through their respective upper vibration isolators, that is, the energy transmitted from the device subsystem to the raft subsystem.

[0116] That is, due to the action of device 1, the coupled vibration energy generated on device 2 through the device-upper vibration isolation subsystem should be the energy transmitted from the subsystem of device 1 minus the energy transmitted from the subsystem of device 2.

[0117] Then, the formula for the coupling power flow level difference between them should be:

[0118]

[0119] S201 performs finite element modeling and modal analysis on the floating raft vibration isolation system, given relevant data. S202 inputs excitation signals to determine the velocity response signals and forces at the monitoring points. S203 calculates the power flow at the monitoring points within the finite element model. All three steps utilize finite element simulation to perform error analysis on the data, and are described here together.

[0120] According to the data given in S101, point mass units are used to simulate the equipment, and the simplified length, width and height of the equipment are simulated by setting the moment of inertia; elastic stiffeners with unit properties of shell units are used to simulate the raft part of the system; combine units are used to simulate massless spring units, and their stiffness and damping performance are simulated by inputting stiffness and damping in three directions; solid units are used to simulate a flat base, and all ribs of the base are rigidly fixed to the lower surface of the bracket; the isolator is bound to the installation points of the raft and the base through the constraint type, the node-surface discretization method is selected, and the rotational degrees of freedom are bound. The completed modeling is as follows Figure 2 shown.

[0121] After the modeling is completed, the model is meshed and its modal values ​​between 0-200 Hz are analyzed.

[0122] A force input point is set at the center of gravity of the equipment and the raft frame, and the excitation signal expected to be input to the floating raft vibration isolation system is set here. The four tip points mentioned in S105 are taken as monitoring points, and the velocity response values ​​and nodal forces of these points are obtained through finite element simulation analysis.

[0123] Based on the obtained speed response signal and the nodal force at the monitoring point, the power flow value at each point and the power flow level difference value between different points under the finite element simulation are calculated using the same method as S106.

[0124] S108 performs error analysis on the obtained data. The error analysis requires analyzing the possible causes of the errors. The main causes of the errors are composed of the following parts:

[0125] The first part is the possible error caused by the simplified algorithm of this patent in the process of simplifying the conditions. The reason for this part of the error is that the geometric shape, stiffness and damping characteristics of the raft and the base themselves affect the calculation results during the simplification.

[0126] In the second part, since the method used in this patent to solve the motion differential matrix is ​​the Gaussian elimination method, some high-order small quantities will be discarded during the programming and calculation process, resulting in slight error accumulation. As the number of devices increases and the floating raft vibration isolation system becomes more complex, the error gradually increases.

[0127] The third part is that when solving the power flow, this patent needs to perform Fourier transform on the node force and node velocity response to obtain the signal in the frequency domain. This requires fitting the obtained velocity response first, and insufficient fitting accuracy will also produce certain errors.

[0128] The fourth part is that when this patent uses multi-rigid body dynamics to calculate the response values ​​of each component in the system, the accuracy of the selected frequency step has an upper limit. If there are certain special points that are covered by the minimum frequency step, it will cause certain errors in the response analysis of the frequency point.

[0129] The specific process of error analysis for the above four parts should be divided into two steps:

[0130] The first step, S1081, involves comparing the power flow obtained through numerical analysis in S106 with the power flow obtained through finite element simulation in S203. For the same excitation force, the average power flow between all devices and the upper isolator nodes is analyzed, as well as the average power flow between all lower isolators and the base panel. The relative error between the numerical analysis data and the finite element simulation data is calculated, using the actual value and the theoretical value, respectively. If the relative error is less than the 15% error threshold, the error analysis criteria are met and the process proceeds to S1082. Otherwise, repeat S103-S108.

[0131] The second step, S1082, involves calculating the power flow level difference between the average power flow between all devices and the upper isolator nodes, obtained in the first step, and the average power flow between all lower isolators and the base panel. For the same system, the power flow level difference represents the proportional relationship of vibration energy transfer, so the power flow level difference obtained for different excitation forces should be the same. For multiple sets of power flow level differences generated by different excitation forces, their medians are used as the theoretical values, and the actual level differences are used as the actual values. The relative error between them is calculated. If the relative error is less than the 15% error threshold, the error analysis criteria are determined to be met. Otherwise, repeat S103-S108.

[0132] S109 performs fitting processing on the obtained power flow vibration level drop data of the floating raft vibration isolation system, and provides the vibration isolation analysis and vibration prediction of the system.

[0133] The fitting process of the system power flow level difference data includes:

[0134] Perform polynomial fitting on L(ω) in the general frequency band. At this time, L(ω) has no obvious peak and the form should be:

[0135] L(ω)=a n ω n +a n-1 ω n-1 +......+a0

[0136] Fitting the resonance peak of the Lorentz function to L(ω) in the resonance frequency band should be in the form of:

[0137]

[0138] Where a and c are function fitting coefficients, which are used to adjust the amplitude and offset of the function; ω r is the resonance frequency; γ is the resonance width, which is used to reflect the damping effect.

[0139] Combining the two frequency bands yields a general power flow curve, for example: Figure 3 It describes the unit force under the shape of Figure 2 The power flow at device 1 and the base panel and the power flow level difference curve between them in the floating raft vibration isolation system.

[0140] Each set of different excitation forces F(t) yields a set of L(ω) values, which contain performance values ​​for power flow and loss between any two points in the system. These values ​​can then be used to perform vibration isolation analysis and vibration prediction on the raft isolation system in the following ways.

[0141] Analyze the paths of vibration energy transmission. For example, select any unit in the system, such as device 1. Calculate the power flow level difference between device 1 and other units to determine the proportion of vibration energy input from device 1 in each path. This also predicts the main energy transmission path. Adding damping to the main transmission path can be used to enhance vibration isolation performance.

[0142] Identify the concentration point of vibration energy. For example, select multiple monitoring points on the raft and calculate the power flow level difference between them. If the power flow level difference calculated at a certain point is mostly positive, it means that most of the energy is transferred to this point from the outside and other positions on the raft, so this point can be judged as the concentration point of vibration energy.

[0143] Analyze the significance of the excitation force. For example, for a certain power flow level drop curve, such as the vibration energy transfer curve between equipment 1 and base point 1, the sensitivity of the vibration energy transfer of a certain unit to different properties of the excitation force can be examined by changing the amplitude, frequency, phase angle, action position, etc. of the input excitation. This can be used as an engineering reference for raft design.

[0144] Optimize the design of each component of the floating raft. For example, if the vibration isolation focus of a certain floating raft vibration isolation system is device 1, then the various elements of the floating raft vibration isolation system mentioned in S101 can be adjusted, and the L(ω) curve of device 1 under different excitation forces can be observed to find the optimal floating raft design for device 1.

[0145] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A power flow analysis method for a floating raft vibration isolation system based on multi-rigid body dynamics, characterized in that: Including steps: S101. Obtain the system's equipment elements, raft elements, vibration isolator elements, and foundation elements; S102. Simplify the mechanical model of the vibration isolation system based on multi-rigid body dynamics and construct a six-degree-of-freedom matrix for each rigid body unit; S103 determines an external excitation signal input to the floating raft vibration isolation system, and inputs a random external excitation signal according to test requirements; S104 obtains the system response value based on the algebraic operation of the differential equation of motion and the matrix; S105 gives the displacement response signal, velocity response signal, acceleration response signal and node force at four tip points; S106 calculates the power flow signal of the selected floating raft vibration isolation system points and analyzes the power flow level difference between different points. The power flow signal in S106 is an average power flow signal obtained by the response signal, which is obtained by the velocity response signal and the node force obtained in S105. The power flow level difference is the logarithm of the quotient of the power flow signal between any two points in the floating raft vibration isolation system between the center of gravity of the equipment and the base panel, which is used to express the vibration isolation performance of the floating raft vibration isolation system and the proportion of energy loss during energy transfer in the system. S107 performs finite element modeling analysis on the floating raft vibration isolation system with given relevant data based on the results of S103, performs modal analysis on the model, inputs an excitation signal, and calculates the power flow at the monitoring point of the finite element model; S108 performs error analysis on the data obtained in S106 and S107. If the error conditions are met, the obtained power flow level drop data of the floating raft vibration isolation system is fitted to provide the vibration isolation analysis and vibration prediction of the system. If the error conditions are not met, repeat steps S103-S108.

2. The power flow analysis method for a floating raft vibration isolation system based on multi-rigid body dynamics according to claim 1 is characterized by: The equipment elements in S101 include: the number of devices, the geometric structure data of each different device, the mass of each different device, the installation position coordinates of each different device with respect to the raft reference system and the base reference system, and the installation method of each different device; the raft elements include: the geometric dimensions of the raft, the mass of the raft, the type of the raft, and the specific structural data of the raft; the vibration isolator elements include: the type of vibration isolators used, the number of different vibration isolators, the installation positions of different vibration isolators, the installation methods of different vibration isolators, the stiffness values ​​of different vibration isolators, and the damping values ​​of different vibration isolators; the base elements include: the type of base, the base mass, and the base impedance.

3. The power flow analysis method for a floating raft vibration isolation system based on multi-rigid body dynamics according to claim 1 is characterized by: The vibration isolation system described in S102 includes: multiple devices, a raft, a base and multiple vibration isolators connecting them; the multi-rigid body dynamics simplification method refers to considering only the mass of the devices and raft in the system, treating them as rigid body units, and establishing the body-attached coordinate system of the raft and the fixed coordinate system of the base through the mutual connection of the vibration isolators to determine the changes in the generalized coordinates of each component in the system, so as to calculate the overall displacement response values ​​of the devices and raft in the system; the mechanical model simplification refers to: according to the system elements input in S101, some elements are removed and simplified according to the actual conditions of the simplified algorithm, and only the physical elements required for the system of interaction of the described rigid body units are considered; the six-degree-of-freedom matrix includes: the mass six-degree-of-freedom matrix of the rigid body unit, which describes the inertia force influencing factors of the rigid body unit; the stiffness six-degree-of-freedom matrix of the rigid body unit, which describes the elastic force influencing factors of the rigid body unit; the damping six-degree-of-freedom matrix of the rigid body unit, which describes the damping force influencing factors of the rigid body unit.

4. The power flow analysis method for a floating raft vibration isolation system based on multi-rigid body dynamics according to claim 1 is characterized by: The position where the external excitation signal in S103 acts is the center of gravity of all the equipment and raft in the system. The center of gravity is obtained by S101 and S102, and the external excitation signal is numbered and classified according to the equipment number and raft. If there is no corresponding external excitation on a certain equipment or raft, the value of the external excitation signal received by the rigid body unit is recorded as 0; the form of the external excitation signal is a simple harmonic force containing six degrees of freedom, that is, a periodic force formed by the combination of shear force in three directions of the corresponding coordinate system and torque in three directions.

5. The power flow analysis method for a floating raft vibration isolation system based on multi-rigid body dynamics according to claim 1 is characterized by: The motion differential equation in S104 is a system motion equilibrium equation that includes the mass matrix, stiffness matrix, damping matrix and current calculated frequency value of all rigid body units in the system. The construction of this multi-degree-of-freedom matrix motion differential equation and the acquisition of specific parameters of the internal matrix refer to the vibration isolation system elements mentioned in S101 and the mechanical model simplification mentioned in S102 in claim 1; the matrix algebraic operation method is the Gaussian elimination method based on the Fortran program; the system response value is the overall six-degree-of-freedom response of multiple devices and raft structures in the system, including translational displacements in three directions and rotational displacements in three directions in the base fixed coordinate system.

6. The power flow analysis method for a floating raft vibration isolation system based on multi-rigid body dynamics according to claim 1 is characterized by: The tip point described in S105 includes: the upper end points where all upper vibration isolators are connected to the equipment, the lower end points where all upper vibration isolators are connected to the raft, the upper end points where all lower vibration isolators are connected to the raft, and the lower end points where all lower vibration isolators are connected to the base; the displacement response signal refers to the six-degree-of-freedom response obtained in S104, and according to the particle offset matrix of multi-rigid body dynamics, the six-degree-of-freedom response of the particle is converted into a displacement response signal at the tip point, and by taking the derivative of the displacement response, the corresponding velocity response signal and acceleration response signal are obtained, and the corresponding node force is calculated according to the equipment subsystem reference coordinate system in the multi-rigid body dynamics analysis.

7. The power flow analysis method for a floating raft vibration isolation system based on multi-rigid body dynamics according to claim 1 is characterized by: The S107 comprises the following steps: S201 performs finite element modeling analysis on the floating raft vibration isolation system with given relevant data, and performs modal analysis on the model, wherein the relevant data are the system equipment elements, system raft elements, system isolator elements, and system base elements input in S101; the finite element modeling analysis is to complete the geometric model establishment and material property assignment of the floating raft vibration isolation system in commercial software so that it meets the various system elements described in S101; the modal analysis is to obtain the natural frequency of the finite element model to provide a frequency reference range for subsequent specific analysis; S202 inputs an excitation signal to solve for a velocity response signal and a force at the monitoring point, wherein solving for the velocity response and the force refers to inputting the continuous external excitation signal input in S103 into the finite element model based on the results of the modal analysis in S201, considering the effect of the external excitation signal on the model at the natural frequency, and setting a monitoring point at the same position as in the theoretical analysis through a related analysis module in the finite element analysis software to directly obtain the velocity response signal and the force at the monitoring point; S203 calculates the power flow of the monitoring point of the finite element model, wherein the power flow of the monitoring point refers to the monitoring point velocity and the monitoring point force obtained by S202, and calculates the average vibration power flow at the monitoring point during the time history of the finite element analysis.

8. The power flow analysis method for a floating raft vibration isolation system based on multi-rigid body dynamics according to claim 1 is characterized by: The step S108 performs error analysis on the obtained data. Data with a value less than the error threshold is entered into the data statistics library. Data with a value greater than the error threshold is deleted. The process then returns to step S103 to re-input the random excitation signal and perform the same analysis steps.

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