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

Abstract

The invention discloses a floating raft vibration isolation system power flow analysis method based on multi-rigid-body dynamics. The floating raft vibration isolation system power flow analysis method comprises the steps that S101, equipment elements, raft frame elements, vibration isolator elements and base elements of a system are obtained; s102, performing mechanical model simplification on the vibration isolation system based on multi-rigid-body dynamics, and constructing a respective six-degree-of-freedom matrix of each rigid body unit; s103, determining an external excitation signal input into the buoyant raft vibration isolation system, and inputting a random external excitation signal according to a test requirement; s104, obtaining a system response value according to algebraic operation of the motion differential equation and the matrix; s105, giving response signals and node acting forces on four tip point locations; s106, calculating a power flow signal of the selected floating raft vibration isolation system point location, and analyzing a power flow vibration level fall; s107, calculating the monitoring point power flow of the finite element model according to the result of S103; and S108, carrying out error analysis on data obtained in S106 and S107, and giving vibration isolation analysis and vibration forecast of the system.

Description

Technical Field

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

[0002] A large number of studies and practices have shown that floating raft vibration isolation structures are widely used in ships, aviation and mechanical equipment to reduce vibration propagation and noise interference, and ensure stable operation of equipment and environmental comfort. The floating raft vibration isolation system is usually composed of multiple devices, raft frames and vibration isolators, and its dynamic behavior is complex, involving the coupling of multiple degrees of freedom.

[0003] The multi-rigid body dynamics method is based on the system's equation of motion and can fully describe the dynamic interactions between the components. It is an important tool for analyzing the floating raft vibration isolation system. By introducing the mass matrix, stiffness matrix and external excitation force of the equipment and raft, the multi-rigid body dynamics method can accurately simulate the vibration response characteristics of the system, thereby providing theoretical support for the prediction and optimization of vibration isolation performance. In addition, multi-rigid body dynamics can also analyze the dynamic characteristics of the vibration isolator under complex connection conditions, such as stiffness nonlinearity and offset coupling effects, so as to better guide the design and improvement of the vibration isolation system.

[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 Chinese Society of Mechanics, Nonlinear Vibration Professional Committee of 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 are aimed at the application of multi-rigid body dynamics in the direction of simulation to solve related mechanical problems.

[0005] In terms of vibration, people usually use acceleration level or velocity level as an indicator to judge the vibration isolation level of the system and the impact of vibration on the system. In recent years, power flow, as one of the important indicators to measure the vibration energy propagation characteristics, has gradually developed into an efficient and reliable method to evaluate the performance of floating raft vibration isolation systems.

[0006] Through power flow analysis, the propagation path, distribution characteristics and dissipation efficiency of vibration energy can be determined, providing a basis for optimizing the key vibration transmission links in the system. In the floating raft vibration isolation system, power flow analysis can reveal the energy exchange law between the vibration isolator and the raft frame, evaluate the energy isolation effect and vibration dissipation performance of the vibration isolator, and thus help design a system structure with better vibration isolation effect. Different from traditional transmissibility analysis, power flow analysis focuses more on the overall transmission of system energy and the quantitative characterization of local behavior, and is suitable for the vibration performance evaluation 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 the vibration problem in coupled structures, see Zhang Yu, Li Jin, Dong Junhong. Research on vibration power flow and acoustic radiation characteristics of plate-beam coupled structure [J]. Journal of China Engineering Machinery, 2024, 22(05): 620-625. DOI: 10.15999 / j.cnki.311926.2024.05.016. and Wu Jianghai, Yin Zhiyong, Sun Yudong, et al. Research on vibration power flow and acoustic radiation characteristics of pipeline-cylindrical shell coupled structure [J]. China Shipbuilding, 2021, 62(02): 145-153.

[0008] The application of multi-rigid body dynamics in rafts is not widespread, and most of the application environments are used to solve problems related to simulation. Only a small number of people use programming theory analysis based on multi-rigid body dynamics to simplify the calculation analysis of engineering problems. For example, see Li Xiaoming. Research on vibration isolation and impact resistance characteristics of ship raft system [D]. Dalian University of Technology, 2007. In this paper, the matrix of the multi-rigid body dynamics system is constructed, and the response value of the raft vibration isolation system is obtained by solving the differential equation of motion, and the response vibration level is solved to represent the vibration isolation capacity of the system. However, this method has certain limitations. Only the response value cannot describe the influence of force on the structure during the vibration process, nor can it describe in detail the transmission method and transmission ratio of the vibration energy in the system structure after it is transmitted into the system. 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, and an efficient and reliable structural vibration analysis method is provided. The concept of power flow is used to simultaneously express the distribution and changes of the response and force in the system, so that the vibration energy transfer of the floating raft vibration isolation system and the vibration isolation performance of the overall structure can be better predicted and analyzed.

[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 equipment elements, raft elements, vibration isolator elements, and foundation elements of the system;

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

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

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

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

[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 according to the result of S103, performs modal analysis on the model, inputs excitation signals, and calculates the monitoring point power flow of the finite element model. The monitoring point power flow;

[0018] S108 performs error analysis on the data obtained in S106 and S107. If the error condition is met, the obtained power flow vibration 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 condition is 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 for 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 type of base, the base mass, and the 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 rafts in the system, treating them as rigid body units, and establishing the body coordinate system of the raft and the fixed coordinate system of the base to determine the changes in the generalized coordinates of each component in the system through the form of interconnection of vibration isolators, so as to calculate the overall displacement response values ​​of the devices and rafts 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 inertial force influencing elements of the rigid body unit; the stiffness six-degree-of-freedom matrix of the rigid body unit, which describes the elastic force influencing elements of the rigid body unit; the damping six-degree-of-freedom matrix of the rigid body unit, which describes the damping force influencing elements of the rigid body unit;

[0021] Preferably, the position where the external excitation signal acts in S103 is the center of gravity of all the equipment and the raft in the system, which is obtained by S101 and S102, and the external excitation signal is numbered and classified according to the equipment number and the raft. If there is no responsive 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 forces in three directions of the corresponding coordinate system and torques 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 algebraic operation method of the matrix 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 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 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 according to the equipment subsystem reference coordinate system in the multi-rigid body dynamics analysis, the corresponding node force is calculated.

[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 the transmission process 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 mentioned 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 make it meet 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 the excitation signal to solve the speed response signal and the force at the monitoring point. The speed response and force solving means that according to the result of the modal analysis in S201, the continuous external excitation signal input in S103 is also input into the finite element model, the effect of the external excitation signal on the model is considered at the natural frequency, and the monitoring point is set at the same position in the theoretical analysis through the relevant analysis module in the finite element analysis software to directly obtain the speed response signal and the force at the monitoring point;

[0028] S203 calculates the monitoring point power flow of the finite element model, wherein the monitoring point power flow refers to the average vibration power flow at the monitoring point calculated in the time history of the finite element analysis 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 S106 and S107, entering data less than an error threshold into a data statistics library, deleting data greater than the error threshold, and returning to S103 to re-input a random excitation signal, and obtaining a new set of power flow data through the same analysis steps;

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

[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 and simpler estimation analysis.

[0033] The vibration reference element of this invention is the power flow level drop, which adds the analysis of the force in the vibration process compared to the generalized response level drop commonly used in this academic field. In the actual floating raft vibration isolation system experiment, if you want to analyze the effect of force, you need to add a force measuring ring device at the corresponding monitoring point, and 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 system of the floating raft vibration isolation system, and provide 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] The present invention is only partially verified by finite element simulation relying on software, which can more conveniently change 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 It is a flow chart 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 from the input of device 1 to 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 in conjunction with 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 comprises the following steps:

[0041] S101 obtains the equipment elements, raft elements, vibration isolator elements, and foundation elements of the system.

[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 shape outline of the equipment represented as a rectangular block with fixed length, width and height, with the center of gravity of the equipment as the center point; 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 center of gravity of the raft on the upper surface of the raft is taken as the coordinate origin to determine the position of the center of gravity of each equipment in the coordinate system; for 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 more common flat raft 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 center coordinates of the holes, and the chamfer size of the holes, the number of openings along the width direction of the raft, the size of the rectangular openings, the center coordinates of the holes, and the chamfer size of the holes, and the coordinates here should each take the center point of the side surface where the hole is located as the coordinate origin.

[0044] The system vibration isolator elements include: the type of vibration isolators 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 models of vibration isolators 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 in a symmetrical manner relative to the projection center of the center of gravity of the device on the lower surface of the device, and the distance vector moduli of the four vibration isolators in a group from the center of gravity of the device in the device reference system are all equal; 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 a 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 in the vibration isolation system, including all equipment, rafts, bases, and all vibration isolators. The equipment and rafts are simplified into rigid units that only consider the mass, and the mass is concentrated at the center of mass; the base is simplified into a panel that only provides boundary conditions, and the rest of the parts are rigidly fixed, and the mass of the base is concentrated at the center of mass of the base; the vibration isolator is simplified into a one-dimensional linear spring unit, and its mass is no longer considered, and only its stiffness and damping properties are retained.

[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] It is assumed that the offset of the installation position of the vibration isolator is determined according to the center of gravity of the upper equipment / raft supported by the vibration isolator. For example, the coordinate position of the installation point of a vibration isolator with respect to the reference system of the equipment / raft subsystem where it is located is (dx, dy, dz), then its offset matrix should be in the following form:

[0055]

[0056] Here, i represents the number of the equipment, and j represents the number of the vibration isolator on the equipment. Since there is only one raft, the vibration isolators on the raft are uniformly 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 They 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 system coordinate axis, and the last three rows represent the bending moment on the normal surface of the reference system coordinate axis, as follows:

[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 follows:

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

[0067] F(t)=Asin(ωt+φ)

[0068] The excitation force is converted through the Euler formula, and the complex expression of F is obtained as follows:

[0069] F(t)=Re{Ae i(ωt+φ)}=Re{F 0 e iωt}

[0070] Among them, F 0 =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 selected to meet the conditions of random response, while the circular vibration frequency ω and time t describe the frequency / time history conditions of the change of the excitation force in the system, which should vary with the specific analysis.

[0072] S104 obtains the system response value according to the algebraic operation of the motion differential equation 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 influence of all rigid body units in the system. The matrix is ​​constructed according to the interconnection relationship between them. For example, for a system in which a raft is installed on a base panel through a vibration isolator, and two other devices are installed on the raft through their own vibration isolators. In the matrix, since there is no connection between the devices and the mass between the device and the raft is an independent attribute, the expansion of its motion differential equation 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 ​​of the lower isolator and the base under the combined effect of the term need to be calculated taking into account the input impedance of the base panel. For the impedance, there is the following formula:

[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 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{X 0 e iωt}

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

[0088] (M(-ω 2 )+iωC+K)X 0 =F 0

[0089] According to 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 item of 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 gives the displacement response signal, velocity response signal, acceleration response signal and node force at four tip positions.

[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 end points 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 vibration 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 get the velocity response and force values ​​of these points, and solve the average power flow of the node based on these values:

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

[0106]

[0107] According to the velocity response in the frequency domain and the node force, 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 represents 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 The term ω represents reactive power, which describes the energy exchange between the energy storage elements (springs, dampers, masses) in the system and does not result in a net transfer of energy.

[0110] For example, the point where device 1 is connected to the upper end of upper vibration isolator 1 and the point where device 2 is connected to the upper end of upper vibration isolator 2 cannot be called tip points of different levels, because they describe the power flow characteristics of different components within the subsystem of device-upper vibration isolation. However, the point where device 1 is connected to the upper end of upper vibration isolator 1 and the point where lower vibration isolator 1 is connected to the base panel can be called tip points of different levels, because they are in different reference frames in the analysis of multi-rigid 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 drop 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, which is:

[0114] P1→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 to the raft by equipment 1 and equipment 2 through their respective upper vibration isolators, that is, the energy transmitted from the equipment subsystem to the raft subsystem.

[0116] That is, due to the action of device 1, the coupled vibration energy generated to 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 analysis on the floating raft vibration isolation system with given relevant data, and performs modal analysis on the model; S202 inputs the excitation signal to solve the velocity response signal and the force at the monitoring point; S203 calculates the power flow at the monitoring point of the finite element model. These three steps all use finite element simulation to perform error analysis on the data, and are explained here in a unified manner.

[0120] According to the data given in S101, point mass units are used to simulate the equipment, and the geometric simplified length, width and height of the equipment are simulated by setting the moment of inertia; elastic stiffened plates 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 and the lower surface of the bracket are rigidly fixed; 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 node forces of these points are obtained through finite element simulation analysis.

[0123] According to the obtained speed response signal and node force at the monitoring point, the power flow value of each point under the finite element simulation and the power flow level difference value between different points are calculated in the same way as in S106.

[0124] S108 performs error analysis on the obtained data. The error analysis requires analyzing the possible causes of the errors, and 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 shapes, 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 ​​Gaussian elimination, some high-order small quantities will be discarded during the programming and calculation process, resulting in slight error accumulation. With the increase in the number of equipment and the complexity of the floating raft vibration isolation system, 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 also requires fitting the obtained velocity response first. 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 some 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 of S1081 is to compare the power flow obtained by numerical analysis in S106 with the power flow obtained by finite element simulation in S203. For the same exciting force, the average power flow between all equipment and the upper vibration isolator nodes is analyzed, and the average power flow between all lower vibration isolators and the base panel is analyzed. The data obtained by numerical analysis is taken as the actual value, and the data obtained by finite element simulation is taken as the theoretical value. The relative error between them is calculated. If the relative error is less than the error threshold of 15%, it is determined that the error analysis conditions are met and enter S1082. Otherwise, S103-S108 are repeated.

[0131] S1082 The second step requires the power flow level difference between the average power flow of all equipment and the upper vibration isolator nodes obtained in the first step and the average power flow between all lower vibration isolators and the base panel. For the same system, the power flow level difference represents the proportional relationship of vibration energy transfer, so for different exciting forces, the power flow level difference obtained should be the same. For multiple groups of power flow level differences generated by different excitation forces, their medians are taken as theoretical values, and the actual level differences are taken as actual values. The relative error between them is calculated. If the relative error is less than the error threshold of 15%, it is determined that the error analysis conditions are 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] Among them, the fitting processing of the system power flow level drop 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 +......+a 0

[0136] The resonance peak of L(ω) is fitted by the Lorentz function in the resonance frequency band, and the form should be:

[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, which is like Figure 2 In the floating raft vibration isolation system, the power flow at the device 1 and the base panel and the power flow vibration level difference curve between them.

[0140] Each set of different excitation forces F(t) can obtain such a set of L(ω), which includes the performance values ​​of power flow transfer and loss between any two points in the system. Then, this value can be used to perform vibration isolation analysis and vibration prediction on the raft vibration isolation system in the following ways.

[0141] Analyze the path 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, and you can get the proportion of the vibration energy input by device 1 in each path, and you can get the main path prediction of energy transmission. You can use the method of adding damping on the main transmission path to enhance the 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 from equipment 1 to base point 1, the sensitivity of the vibration energy transfer of a certain unit to different attributes 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 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 best 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 principle 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: Includes steps: S101. Obtain the equipment elements, raft elements, vibration isolator elements, and foundation elements of the system; S102, simplifying the mechanical model of the vibration isolation system based on multi-rigid body dynamics, and constructing a six-degree-of-freedom matrix for each rigid body unit; S103 determines an external excitation signal input into the floating raft vibration isolation system, and inputs a random external excitation signal according to the test requirements; S104 obtains the system response value according to the algebraic operation of the motion differential equation and the matrix; S105 gives the displacement response signal, velocity response signal, acceleration response signal and node force at four tip positions; 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; S107 performs finite element modeling analysis on the floating raft vibration isolation system with given relevant data according to the result of S103, performs modal analysis on the model, inputs an excitation signal, and calculates the power flow of the monitoring point of the finite element model; S108 performs error analysis on the data obtained in S106 and S107. If the error condition is met, the obtained power flow vibration 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 condition is not met, repeat steps S103-S108.

2. The power flow analysis method of 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 equipment, the 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 type of base, the base mass, and the base impedance.

3. The power flow analysis method of a floating raft vibration isolation system based on multi-rigid body dynamics according to claim 1 is characterized in that: 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 the raft in the system, treating them as rigid body units, and establishing the body coordinate system of the raft and the 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: 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 elements of the rigid body unit; the stiffness six-degree-of-freedom matrix of the rigid body unit, which describes the elastic force influencing elements of the rigid body unit; the damping six-degree-of-freedom matrix of the rigid body unit, which describes the damping force influencing elements of the rigid body unit.

4. The power flow analysis method of 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 the 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 the raft. If there is no responsive 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 external excitation signal is in the form of 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 of 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 of 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 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 according to the equipment subsystem reference coordinate system in the multi-rigid body dynamics analysis, the corresponding node force is calculated.

7. The power flow analysis method of a floating raft vibration isolation system based on multi-rigid body dynamics according to claim 1 is characterized by: 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 vibration level difference is the logarithmic value 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 the transmission process in the system.

8. The power flow analysis method of 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. 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 mentioned 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 make it meet 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; S202 inputs the excitation signal to solve the speed response signal and the force at the monitoring point. The speed response and force solving means that according to the result of the modal analysis in S201, the continuous external excitation signal input in S103 is also input into the finite element model, the effect of the external excitation signal on the model is considered at the natural frequency, and the monitoring point is set at the same position in the theoretical analysis through the relevant analysis module in the finite element analysis software to directly obtain the speed response signal and the force at the monitoring point; S203 calculates the monitoring point power flow of the finite element model, wherein the monitoring point power flow refers to the average vibration power flow at the monitoring point calculated in the time history of the finite element analysis based on the monitoring point velocity and monitoring point force obtained in S202.

9. The power flow analysis method of 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. For data less than the error threshold, the data is entered into the data statistics library. For data greater than the error threshold, the data is deleted and the process returns to S103 to re-input the random excitation signal and go through the same analysis steps.

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